1999 Mts [aerospatiale Aeronautique - Composite Stress Manual Mts00

Technical Manual MTS 006 Iss. B Outhouse distribution authorised

Composite stress manual 1 4

5 4

2 1 2

5

Structural Design Manual

Purpose

Scope

To list and homogenise the calculation methods and the allowable values for the composite materials used at the Aerospatiale Design Office. To be used as reference document for all Aerospatiale and subcontractors' stressmen.

Data processing tool supporting this Manual

Summary

Document responsibility

See detailed summary

Dept. code : BTE/CC/SC

Validation

Name : P. CIAVALDINI

Name : JF. IMBERT Function: Deputy Department Group Manager Dept. code : BTE/CC/A Date : 06/05/99 Signature

This document belongs to AEROSPATIALE and cannot be given to third parties and/or be copied without prior authorisation from AEROSPATIALE and its contents cannot be disclosed. © AEROSPATIALE - 1999

Composite stress manual

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© AEROSPATIALE - 1999

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Composite stress manual

Foreword

This issue is incomplete and existing chapters are liable to change. All allowable values and coefficients related to the various materials described in chapter Z are updated with each issue of the manual. This means that different values may be found in the stress dossiers prior to latest issue. The data processing tools are given for information purposes only.

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SUMMARY OF CHAPTERS Iss. DETAILED SUMMARY B INTRODUCTION - COMPOSITE MATERIAL PROPERTIES

A

Date

Editor

A

Jan 98 P. Ciavaldini

B

Apr 99 P. Ciavaldini

COMPOSITE PLATE THEORY

B

*

MONOLITHIC PLATE - MEMBRANE ANALYSIS

C

A

Jan 98 P. Ciavaldini

MONOLITHIC PLATE - BENDING ANALYSIS

D

A

Jan 98 P. Ciavaldini

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS

E

A

Jan 98 P. Ciavaldini

MONOLITHIC PLATE - TRANSVERSAL SHEAR ANALYSIS

F

B

Apr 99 P. Ciavaldini

MONOLITHIC PLATE - FAILURE CRITERIA

G

B

Apr 99 P. Ciavaldini

MONOLITHIC PLATE - FATIGUE ANALYSIS

H

*

MONOLITHIC PLATE - DAMAGE-TOLERANCE

I

**

B

Apr 99 P. Ciavaldini

MONOLITHIC PLATE - BUCKLING

J

*

MONOLITHIC PLATE - HOLE WITHOUT FASTENER ANALYSIS

K

B

Apr 99 P. Ciavaldini

MONOLITHIC PLATE - FASTENER HOLE

L

B

Apr 99 P. Ciavaldini

MONOLITHIC PLATE - SPECIAL ANALYSIS

M

B

Apr 99 P. Ciavaldini

B

B

B SANDWICHIC - MEMBRANE / BENDING / SHEAR ANALYSIS

*

N

SANDWICH - FATIGUE ANALYSIS

O

*

SANDWICH - DAMAGE-TOLERANCE APPROACH

P

*

SANDWICH - BUCKLING ANALYSIS

Q

*

SANDWICH - SPECIFIC DESIGNS

R

*

BONDED JOINTS

S

A

Jan 98 P. Ciavaldini

B BONDED REPAIRS

T

B

Apr 99 P. Ciavaldini

BOLTED REPAIRS

U

A

Jan 98 P. Ciavaldini

B THERMAL CALCULATIONS

V

B

Apr 99 P. Ciavaldini

ENVIRONMENTAL EFFECT

W

*

NEW TECHNOLOGIES

X

*

STATISTICS

Y

*

Z

**

B

Apr 99 P. Ciavaldini

B MATERIAL PROPERTIES

*: chapter not dealt with. **: chapter partially dealt with.

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MTS 006 Iss. B

Composite stress manual

HOW TO USE THE COMPOSITE MANUAL? reference of chapter

title(s) of subchapter(s)

reference(s) of subchapter(s)

title of chapter

N 4.2.1

SANDWICH Effect of normal load Ny

1/2

4.2.1 . Effect of normal load Ny Assuming that all layers are in a pure tension or compression condition, a normal load Ny applied at the neutral line results in a constant elongation over the whole cross-section. This elongation may be formulated as follows:

reference of relation

n3

ε =

Ny b (EMi ei + EMc ec + Ems es )

This elongation this unduces: - in the lower skin, a stress σi = Emi ε, - in the core, a stress σc = Emc ε, - in the upper skin, a stress σs = Ems ε. The equivalent membrane modulus of the sandwich beam may be determined by the relationship m14.

Remark: In the case of a sandwich beam in which Emc ec << Emi ei and Emc ec << Ems es, the relationship becomes:

n4

ε ≈

Ny b (EMi e i + Ems e s ) Z

σs Ems es

Ny

Y σc

Emc ec Emi ei b X

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σi

ε

page number

Composite stress manual

HOW TO USE THE COMPOSITE MANUAL? reference of chapter

title(s) of subchapter(s)

reference(s) of subchapter(s)

title of chapter

N5

SANDWICH Example

1/7

5 . EXAMPLE Let a 10 mm wide sandwich beam be defined by the following stacking sequence: - an upper skin (carbon layers) of thickness es = 1.04 mm and of longitudinal 2 elasticity Es = 6000 daN/mm , - a core (honeycomb) of thickness ec = 10 mm and of longitudinal elasticity 2 modulus Ec = 15 daN/mm , - a lower skin (carbon cloths) of thickness ei = 0.9 mm and of longitudinal 2 elasticity modulus Ei = 4500 daN/mm .

We shall assume that the beam is subjected to the following two loads and moment: - Ny = 800 daN, - Mx = 2000 daN mm,

Z Tz = 250 daN

- Tz = 250 daN.

Mx = 2000 daN mm

1,04

Y

10

Ny = 800 daN

0,9 X

reference of relation

10

1 step: to determine elongation ε induced by normal load Ny. st

{n3}

ε=

800 = 7612 µd 10 ( 4500 0.9 + 15 10 + 6000 1.04 ) Z

Y

ε = 7612 µd X

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DETAILED SUMMARY A . INTRODUCTION - COMPOSITE MATERIAL PROPERTIES 1 . Introduction - General 2 . Composition 2.1 . Fibres 2.2 . Matrices 3 . Processing methods 4 . Composite structure design 5 . Assembly 6 . Advantages - Disadvantages (environmental parameters) 7 . Similitudes with metals 7.1 . System equilibrium 7.2 . Load distribution 7.2.1 . Normal load N 7.2.2 . Bending moment M 7.2.3 . Shear load T 7.3 . Material strength laws - Behavior laws 7.4 . General instability 8 . Differences with metals

B . COMPOSITE PLATE THEORY 1 . Ply 1.1 . Tapes - Fabrics 1.2 . Ply behavior (unidirectional orthotropic) 1.3 . Definitions - Notations 2 . Laminate 2.1 . Principle 2.2 . Assembly 3 . Sandwich 3.1 . Principle 3.2 . Assembly

C . MONOLITHIC PLATE - MEMBRANE ANALYSIS 1 . Notations 2 . General definitions 2.1 . Homogeneity - Isotropy 2.2 . Coupling phenomena 2.2.1 . Plane coupling 2.2.2 . Mirror symmetry 3 . Analysis method 4 . Deformations and equivalent properties 5 . Graphs 5.1 . Failure envelopes 5.1.1 . Theoretical principle 5.1.2 . Margin search - Methodology 5.2 . Mechanical properties 6 . Example

D . MONOLITHIC PLATE - BENDING ANALYSIS 1 . Notations 2 . Introduction 3 . Analysis method © AEROSPATIALE - 1999

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4 . Deformations and equivalent properties 5 . Example

E . MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS 1 . Notations 2 . Introduction 3 . Analysis method 4 . Example

F . MONOLITHIC PLATE - TRANSVERSAL SHEAR ANALYSIS 1 . Notations 2 . Introduction 3 . Design method 4 . Example

G . MONOLITHIC PLATE - FAILURE CRITERIA 1 . Notations 2 . Inventory of static failure criteria 2.1 . Maximum stress criterion 2.2 . Maximum strain criterion 2.3 . Norris and Mac Kinnon's criterion 2.4 . Puck's criterion 2.5 . Hill's criterion 2.6 . Norris's criterion 2.7 . Fischer's criterion 2.8 . Hoffman's criterion 2.9 . Tsaï - Wu's criterion 3 . "Aerospatiale"'s criterion: Hill's criterion 4 . Example

H . MONOLITHIC PLATE - FATIGUE ANALYSIS

I . MONOLITHIC PLATE - DAMAGE TOLERANCE 1 . Notations 2 . Introduction 3 . Damage sources and classification 3.1 . Manufacturing damage or flaws 3.2 . In-service damage 3.2.1 . Fatigue damage 3.2.2 . Corrosion damage and environmental effects 3.2.3 . Accidental damage 4 . Inspection of damage 4.1 . Minimum damage detectable by a Special Detailed Inspection 4.2 . Minimum damage detectable by a Detailed Visual Inspection 4.3 . Minimum damage detectable by a General Visual Inspection 4.4 . Minimum damage detectable by a Walk Around Check 4.5 . Classification of accidental damage by detectability ranges 5 . Effects of flaws/damage on mechanical characteristics 5.1 . Health flaws 5.1.1 . Porosity 5.1.2 . Delaminations 5.1.2.1 . Delaminations outside stiffener © AEROSPATIALE - 1999

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5.1.2.2 . Delaminations in stiffener area of an integrally-stiffened panel 5.1.3 . Delamination in spar radii 5.1.4 . Delamination on spar flange edges 5.1.5 . Foreign bodies 5.1.6 . Translaminar cracks 5.1.7 . Delaminations consecutive to a shock 5.2 . Visual flaws 5.2.1 . Sharp scratches 5.2.2 . Indents 5.2.3 . Scaling 5.2.4 . Steps 6 . Justification of permissible manufacturing flaws 7 . Justification of in-service damage 7.1 . Justification philosophy 7.1.1 . Undetectable damage 7.1.2 . Readily and obvious detectable damage 7.1.3 . Damage susceptible to be detected during scheduled in-service inspections 7.1.3.1 . Aerospatiale semi-probabilistic method 7.1.3.1.1 . Process for determining inspection intervals 7.1.3.1.2 . Inspection interval calculation software 7.1.3.1.3 . Load level K to be demonstrated in the presence of large VID 7.1.3.2 . CEAT semi-probabilistic method 7.2 . Examples 7.2.1 . AS method applied to A340 ailerons 7.2.2 . CEAT method applied to A340 nacelles

J . MONOLITHIC PLATE - BUCKLING 1 . Local buckling 1.1 . Design conditions 1.1.1 . General 1.1.2 . Specific to composite materials 1.2 . Design rules 2 . General buckling 2.1 . Variable inertia 2.2 . Off-centering 2.3 . Post local buckling

K . MONOLITHIC PLATE - HOLE WITHOUT - FASTENER ANALYSIS 1 . Notations 2 . Introduction 3 . General theory st 3.1 . 1 method (Whitney and Nuismer) nd 3.2 . 2 method (NASA) rd 3.3 . 3 method (isotropic plate) th 3.4 . 4 method (empirical) 4 . Associated failure criteria 4.1 . Point stress 4.2 . Average stress 4.3 . Empirical 5 . Examples

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Composite stress manual

L . MONOLITHIC PLATE - FASTENER HOLE 1 . Notations 2 . General - Failure modes 2.1 . Bearing failure 2.2 . Net cross-section failure 2.3 . Plane shear failure 2.4 . Cleavage failure 2.5 . Cleavage and net cross-section failure 2.6 . Fastener shear failure 3 . Single hole with fastener 3.1 . Pitch p definition 3.2 . Membrane design - Short cut method 3.2.1 . Theory 3.2.2 . EDP computing program PSG33 3.3 . Bending design - Short cut method 3.4 . Justifications 3.5 . Nominal deviations on a single hole 3.5.1 . Changing to a larger diameter 3.5.2 . Pitch decrease 3.5.3 . Edge distance decrease 3.6 . "Point stress" finite element method 3.6.1 . Description of the method 3.6.2 . Justifications 4 . Multiple holes 4.1 . Independent holes 4.2 . Interfering holes 4.3 . Very close holes 5 . Examples

M . MONOLITHIC PLATE - SPECIAL ANALYSIS 1 . Stiffener run-out 2 . Bending on border 3 . Effect of "stepping" 4 . Edge effects

N . SANDWICH - MEMBRANE/BENDING/SHEAR/ANALYSIS 1 . Notations 2 . Specificity 3 . Construction principle 4 . Design principle 4.1 . Sandwich plate 4.2 . Sandwich beam 4.2.1 . Effect of a normal load Ny 4.2.2 . Effect of a shear load Tx 4.2.3 . Effect of a shear load Tz - Honeycomb shear 4.2.4 . Effect of a bending moment Mx 4.2.5 . Effect of a bending moment Mz 4.2.6 . Equivalent properties 5 . Example

O . SANDWICH - FATIGUE ANALYSIS

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Composite stress manual

P . SANDWICH - DAMAGE TOLERANCE APPROACH 1 . Impact damages 1.1 . Delamination 1.2 . Separation 1.3 . Design rules 2 . Manufacturing defects 2.1 . Porosity/bubbling 2.2 . Fissures/cracks

Q . SANDWICH - BUCKLING ANALYSIS 1 . Local buckling 1.1 . Dimpling 1.2 . Wrinkling 2 . General buckling 2.1 . Bending 2.2 . Shear load

R . SANDWICH - SPECIAL DESIGNS 1 . Densified zones 2 . Slopes/ramps

S . BONDED JOINTS 1 . Notations 2 . Bonded single lap joint 2.1 . Elastic behavior of materials and adhesive 2.1.1 . Highly flexible adhesive 2.1.2 . General case (without cleavage effect) 2.1.3 . General case (with cleavage effect) 2.1.4 . Scarf joint 2.2 . Elastic-plastic behavior of adhesive and elastic behavior of materials 3 . Bonded double lap joint 4 . Bonded stepped joint 5 . Software 6 . Examples

T . BONDED REPAIRS 1 . Notations 2 . Introduction 3 . Analysis method 3.1 . Analytical method 3.2 . Digital method 4 . Example

U . BOLTED REPAIRS 1 . Notations 2 . Stiffness of fasteners 2.1 . Fastener in single shear 2.2 . Fastener in double shear 3 . Assumptions 4 . Geometrical characteristics 5 . Mechanical properties © AEROSPATIALE - 1999

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Composite stress manual

6 . Assessment of mechanical distributed in-plane forces on the doubler 6.1 . Distribution of flow Nx 6.2 . Distribution of flow Ny 6.3 . Distribution of shear flow Nxy 7 . Assessment of thermal in-plane forces on the doubler ? 8 . Assessment of flows in the panel 9 . Assessment of loads per fastener 9.1 . Repair with 1 row of fasteners 9.2 . Repair with 2 rows of fasteners 9.3 . Repair with 3 rows of fasteners 9.4 . Repair with 4 rows of fasteners 9.5 . Repair with a number of rows of fasteners greater than 4 9.6 . General resolution method for direction x 10 . Assessment of loads per fastener due to the transfer of shear loads Nxy 11 . Justifications 12 . Summary flowchart 13 . Examples

V . THERMAL CALCULATIONS 1 . Notations 2 . Introduction 3 . Hooke - Duhamel law 4 . Behavior of unidirectional fibre 5 . Behavior of a free monolithic plate 5.1 . Calculation method 5.2 . Residual curing stresses 5.3 . Equivalent expansion coefficients 6 . Theory of the bimetallic strip 6.1 . Determining stresses of thermal origin 6.2 . Study of the link between two parts 6.2.1 . Bolted or riveted joints 6.2.1.1 . Force F taken by one fastener 6.2.1.2 . Force F taken by two fasteners 6.2.1.3 . Force F taken by three fasteners 6.2.1.4 . Force F taken by four or more fasteners 6.2.2 . Bonded joints 7 . Influence of temperature on aircraft structures 7.1 . General 7.2 . Temperature of ambient air 7.2.1 . Temperature envelope 7.2.2 . Variation of ambient air temperature 7.2.2.1 . Ambient temperature on ground 7.2.2.2 . Ambient temperature in flight 7.3 . Wall temperature 7.3.1 . Influence of solar radiation 7.3.1.1 . Maximum solar radiation 7.3.1.2 . Solar radiation during the day 7.3.2 . Influence of aircraft speed 7.3.3 . Temperature of structure 7.3.3.1 . Calculation method 7.3.3.2 . Thermal characteristics of the materials 7.3.3.3 . Temperatures of structure on ground 7.3.3.4 . Temperatures of structure in flight 7.4 . Recapitulative block diagram 8 . Computing softwares 9 . Examples © AEROSPATIALE - 1999

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Composite stress manual

W . ENVIRONMENTAL EFFECT 1 . Temperature 2 . Aging 3 . Humidity

X . NEW TECHNOLOGIES 1 . R.T.M. 2 . Thermoplastic 2.1 . Shoft fibres 2.2 . Long fibres 3 . Glare-Arall

Y . STATISTICS

Z . MATERIAL PROPERTIES 1 . Prepreg unidirectional tapes 1.1 . First generation epoxy high strength carbon 1.2 . Second generation epoxy intermediate modulus carbon 1.3 . Epoxy R glass 1.4 . Bismaleimide carbon 2 . Fabrics 2.1 . Epoxy resin prepreg 2.1.1 . Carbon 2.1.2 . Glass 2.1.3 . Kevlar 2.1.4 . Hybrid 2.1.5 . Quartz polyester hybrid 2.2 . Phenolic resin prepreg 2.2.1 . Carbon 2.2.2 . Glass 2.2.3 . Kevlar 2.2.4 . Fiberglass carbon hybrid 2.2.5 . Quartz polyester hybrid 2.3 . Bismaleimide resin prepreg 2.3.1 . Carbon 2.4 . Wet lay--up epoxy (for repair) 2.4.1 . Carbon 2.4.2 . Glass 2.4.3 . Kevlar 2.4.4 . Fiberglass carbon hybrid 2.4.5 . Quartz polyester hybrid 3 . R.T.M. 3.1 . Epoxy resin 3.1.1 . Carbon 3.2 . Bismaleimide resin 3.3 . Phenolic resin 4 . Injection moulded thermoplastics 4.1 . Carbon 4.1.1 . PEEK 4.1.2 . PEI 4.1.3 . Polyamide 4.1.4 . PPS 4.1.5 . Polyarylamide 4.2 . Glass © AEROSPATIALE - 1999

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4.2.1 . PEEK 4.2.2 . PEI 5 . Long fibre thermoplastics 5.1 . Carbon 5.1.1 . PEEK 5.1.2 . PEI 5.2 . Glass 6 . Arall-Glare 7 . Metallic matrix composite materials (CMM) 8 . Adhesives 8.1 . Epoxy 8.2 . Phenolic 8.3 . Bismaleimide 8.4 . Thermoplastic 9 . Honeycomb 9.1 . Nomex - Hexagonal cells - OX-Core - Flex-Core 9.2 . Fiberglass honeycomb - Hexagonal cells - OX-Core - Flex-Core 9.3 . Aluminium honeycomb 10 . Foams

© AEROSPATIALE - 1999

MTS 006 Iss. A

Composite stress manual

A INTRODUCTION - COMPOSITE MATERIAL PROPERTIES

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Composite stress manual

INTRODUCTION General

A

1

1 . INTRODUCTION - GENERAL The importance of using composite materials in aeronautical construction, and specifically within the Aerospatiale group, has initiated the need to prepare a document the interest of preparing a document gathering all the design methods and mechanical properties of the main composite materials used and/or developed by the composite material Design Office. Each one of these two subjects shall make up one volume of the composite material design manual. Composite materials result from the association of at least two chemically and geometrically different materials. "Composite material" commonly means arrangements of fibres - continuous or not - of a resistant material (reinforcing material) which are embedded in a material with a much lower strength (matrix), and stiffness. The bond between the reinforcing material and the matrix is created during the preparation phase of the composite material and this bond shall have a fundamental effect on the mechanical properties of the final material. Composite materials include: - wood, - reinforced concrete, - fibre-reinforced organic matrices (polymer resins), - particle or fibre-reinforced metal matrices, - ceramic fibre-reinforced ceramic matrices. In the aeronautical industry, the term "composite" is mainly associated with fibrereinforced polymer resins.

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Composite stress manual

INTRODUCTION Composition - Fibres

A

2.1

2 . COMPONENTS OF COMPOSITE MATERIALS 2.1 . Fibres Their purpose is to ensure the mechanical function of the composite material. Fibres can be of very different chemical and geometrical types, and the following properties shall be specifically searched for: - high mechanical properties. - physico-chemical compatibility with the matrix. - easy to use. - good repeatability of the properties. - low density. - low cost. They are made up of several thousand filaments (the number of filaments being indicated by 3K: 3000 filaments, 6K: 6000 filaments or 12K: 12000 filaments) with a diameter between 5 and 15 µm, and they are commercialised in two different forms: - short fibres (a few centimeters long): they are felt, pylons (fabrics in which fibres are laid out randomly) and injected short fibres, - long fibres: they are cut during manufacture of the composite material, used as such or woven, • high strength fibres: glass, carbon, boron, • synthetic fibres: aramid (kevlar), nylon, polyester, • ceramic fibres: silica, alumina.

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INTRODUCTION Composition - Matrices - Implementation

A

2.2 3

1/3

2.2 . Matrices Their function is: - to provide a bond between the reinforcing fibres (cohesion of all fibres) while maintaining a regular interval between them, - to protect fibres against their environment, - to allow stress transfer from one fibre to another, There are three categories of matrix: - resin matrices: • thermoplastics (polyethylene, polysulfone, polycarbonate and polyamide, ...), • thermosetting (phenolic, epoxy and polyester, ...), • elastomers (polychloroprene, ethylene, propylene, silicone, ...), - mineral matrices (silicon carbides, carbon), - metal matrices (aluminium, titanium and nickel alloys).

3 . PROCESSING METHOD The reinforcing fibre/resin mix becomes a genuinely resistant composite material only upon completion of the last manufacturing phase, i.e; curing of the matrix.

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Composite stress manual

INTRODUCTION Implementation

A

3 2/3

* Material curing cycle This cycle is achieved following the chemical reaction between the various components this is the crosslinking phase. The chemical reaction is initiated as soon as products are in contact, and it is often accelerated by heat: the higher the temperature, the quicker and more explosive is the reaction: There are two types of chemical reactions: - the polyaddition reaction for epoxy resins where the weight of reactants is equal to the weight of the compound, - the condensation reaction (polycondensation) for phenolic resins where two compounds are formed (a solid one and a gaseous one). The curing cycle consist of a number of temperature levels of variable duration: - a gel level which allows getting a consistent temperature gradient throughout the material before full gelation to limit internal stresses, - a curing level which allows hardening, - a post-curing level which allows internal stresses to be relieved, and additional curing for a better temperature resistance. Note: the glass transition point is the temperature value at which all material properties change. This important property must be measured, before and after wet aging.

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Composite stress manual

INTRODUCTION Implementation

A

3 3/3

There are several types of manufacturing facilities and processes: - Manufacturing facilities: • Autoclave: parts are produced under pressure and at high temperature. • Oven: parts are vacuum produced and at high temperature. • Hot press: pressure is applied by a mechanical device or by hydraulic jacks. - Manufacturing processes: • Multiple shots process: laminate are cured separately, then bonding of laminates to the substructure (ribs, honeycombs, etc.) is performed as a second operation. • Semi-cocuring process: the external skin is cured separately, the substructure (rib, or honeycomb + internal skin and stiffeners) is then cocured on the external skin with an adhesive film spread, if necessary. • Single phase process: or "cocuring", skins are cured and bonded to the substructure (ribs or honeycomb or stiffeners) in one single operation.

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Composite stress manual

INTRODUCTION Design

A

4

4 . COMPOSITE STRUCTURE DESIGN The choice of the design principle depends on the following criteria: - element geometry. - element type. - level of loads to be transmitted. - manufactured parts suitability for inspection. - industrialization suitability of the part. Composite structures use the same types of design principles as metal ones: - Solid part type structure : • Multiple rib box type structure

B

• Multiple spar type structure

• Stiffened or milled out panel type structure

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Composite stress manual

INTRODUCTION Assembly

A

5

- Sandwich type structure: • Sandwich face sheet box

• Through - the - thickness sandwiches

5 . ASSEMBLY After being manufactured, the different composite (and metal) elements must be connected to one another to allow load transfer. The two most commonly used techniques are bonding and bolting (or riveting). Bonding techniques are tricky to implement (preparation of surfaces to be bonded) because they are sensitive to environmental conditions: hygrometry, temperature, cure date of adhesives. They are also difficult to control because even a sound adhesive film is a barrier to ultrasounds. More repetitive and reliable bolting techniques may generate: - stress concentration at fastener holes, - delamination during drilling or assembly operations, - corrosion of fasteners or of metal parts assembled with composite parts.

© AEROSPATIALE - 1999

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Composite stress manual

INTRODUCTION Advantages - Disadvantages

A

6

6 . ADVANTAGES - DISADVANTAGES OF COMPOSITE MATERIALS The use of composite materials has four major advantages: - a weight gain which is reflected by fuel saving and, therefore, by a payload increase, - the capacity to control stiffness and strength according to the areas of the structure, thanks to the different types of layered materials. Composite materials naturally offer membrane-bending coupling or plane coupling possibilities, which can have important applications in the field of aero-elasticity, - a good fatigue strength, which increases the life of aircraft parts concerned and lightens the maintenance program considerably, - absence of corrosion, which also lightens the maintenance program. However, composite materials remain sensitive to environmental conditions. Their mechanical properties change, due to: - humidity, - temperature, - the various aeronautical fluids such as Skydrol (hydraulic fluid), oils or solvents (MEK) and fuels, - radiation (ultraviolet). On the other hand, the effects of lightning strikes (temperature rise, melting, impacts, electronic damages) and shocks (delamination, separation, punctures) must be taken into account in the design and justification of composite parts.

© AEROSPATIALE - 1999

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Composite stress manual

INTRODUCTION Metal/composite material similitudes - System equilibrium

7 . COMPARISON STRUCTURES

BETWEEN

COMPOSITE

A

STRUCTURES

7 7.1

AND

1/4 METAL

Composite material and metal material structures obey the same basic rules of structural mechanics. On the other hand, composite material behavior laws are slightly different from those for metals. The purpose of this sub-chapter is to specify the similitudes between metal materials and composite materials for the structural justification of structures. Composite parts and metal parts have the same behavior with respect to: - static equilibrium. - load distribution rules among several elements. - basic rules of structural mechanics. - general instability problems (buckling).

7.1 . System equilibrium Whatever the type of system or element under study (metal, composite or combined), it is subject to a set of external loads which may be of several types: - Solid loads: distributed in the volume of the solid and of gravity (selfweight), dynamic (inertial forces), electrical or magnetic origin. - Areal loads: distributed over the external surface of the solid, such as normal pressures due to a fluid or tangential loads due to friction phenomena.

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INTRODUCTION

A

System equilibrium

7.1 2/4

- Line loads: distributed over a line and which are, in fact, an idealized density of surface load with a much smaller application width than length. - Concentrated loads (P): acting in one point and which are, in fact, an idealized density of surface load acting on a surface with smaller dimensions with respect to the dimensions of the solid under study. - Concentrated moments (M): acting in one point and which are, in fact, an idealized concentrated moment.

M ds

dl P dv Z Y X

To reach the equilibrium of the solid, all these external loads (C) must be equilibrated by reactions at the bearing surfaces (R). Σ (C) = - Σ (R)

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Composite stress manual

INTRODUCTION

A

System equilibrium

7.1 3/4

Let the solid be defined by its external loads and bearing surfaces:

external loads + bearing surfaces

a

A

Z

B Y X

deformed system

external loads + reactions at bearing surfaces Z

ra Y

RA

X

RB The general equilibrium is summed up by a system of six equilibrium equations: three equilibrated forces (F) and three equilibrated moments (Mt). Σ (Fx) = Σ (Cx) + Σ (Rx) = 0 Σ (Fy) = Σ (Cy) + Σ (Ry) = 0 Σ (Fz) = Σ (Cz) + Σ (Rz) = 0

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INTRODUCTION System equilibrium

A

7.1 4/4

Σ (Mt/x) = 0 Σ (Mt/y) = 0 Σ (Mt/z) = 0 If the system is isostatic, the solving alone of these six equations allows all reactions at the bearing surfaces to be found. If the system is slightly hyperstatic and consisting of a simple geometry, it is necessary to introduce new equations (the number depends on the degree of redundancy) of the deformation compatibility type that take element stiffness into account. If the system is complex or if the degree of redundancy is high, only a point stress or a matrix analysis makes it possible to find reactions at the bearing surfaces and the internal loads they generate. Whatever the case and whatever the type of structure (composite or metal), the three following rules must always be applied before any stress and deformation calculation: 1) External loading must be accurately defined. 2) Reactions must be fully determined. 3) The system must always be equilibrated.

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Composite stress manual

INTRODUCTION

A

Load distribution - Normal load N

7.2.1

7.2 . Distribution of loads among several closely bound structural elements 7.2.1 . Normal load N If a system made up of several parts which are connected together, is subject to a normal load N, then, the load distribution within the different elements (whether metal or composite) is as follows:

σ1 σ2

N

1 2 3 σ3

ε A.N.

we have:

N1 N2 N3 ε= = = = E1 S1 E2 S 2 E3 S3

a1

hence

Ni =

å å

3

Nk

k = 1

3

E k = 1 k

Sk

N Ei Si

å

3

E k =1 k

Sk

å å 3

a2

we may deduce

Eeq. memb. (1 + 2 + 3) =

E k =1 k 3

Ei: layer (i) elasticity modulus Si: layer (i) section

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Sk

Sk

k =1

where Ni: load transferred by layer (i)

=

N

å

3

E k = 1 k

Sk

Composite stress manual

INTRODUCTION

A

Load distribution - Bending moment M

7.2.2

7.2.2 . Bending moment M A bending moment M applied to the neutral axis of the system is picked up in each layer in proportion to its bending stiffness. The moment M breaks down, in each layer (i), into a bending moment Mi and a normal load Ni, so that: σe

εe

v1

M

1 2 3 σi

εi

A.N.

Ni =

a3

Mi =

a4

M Ei Si v i

å

3

E l k =1 k k

M Ei

å

ιi

3

E l k =1 k k

å å 3

a5

we may deduce

where

E eq. flex. (1 + 2 + 3) =

E l k =1 k k 3 l k =1k

Ni: normal load applied to layer (i) Mi: moment applied to layer (i) li: layer (i) inertia with relation to the system neutral axis

ιi: layer inertia of layer (i)

Si: layer (i) section vi: distance between layer (i) neutral axis and system neutral axis Ei: layer (i) elasticity modulus æ b h3 ö + S d2 ÷ li: inertia + "Steiner" inertia ç è 12 ø

ιi

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æ b h3 ö : layer inertia ç ÷ è 12 ø

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INTRODUCTION

A

Load distribution - Shear load T

7.2.3

7.2.3 . Shear load T Assuming that layers 1, 2 and 3 are parallel and of the same height, a shear load T is applied to each layer in proportion to its shear stiffness.

3

T

2 1 γ

τm1

we have:

T3 T1 T2 γ= = = = G S G G1 S1 2 2 3 S3

a6

å å

3

T k = 1 k

3

k = 1

Ti =

hence

T

=

å

Gk Sk

we may deduce

where

å

Gk Sk

3

Gk Sk

k =1

G eq. (1 + 2 + 3) =

å å

Ti: shear load transferred by layer (i) Gi: layer (i) shear modulus Si: layer (i) section

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k =1

T Gi Si

3

a7

3

MTS 006 Iss. B

k =1 3

Gk Sk Sk

k =1

τm2

τm3

Composite stress manual

INTRODUCTION Material strength laws - Behavior laws

A

7.3

7.3 . Material strength laws - Behavior laws Composite materials obey the general rules of structural mechanics. Stress - deformation relationship for a two-dimensional analysis: Hooke's law applies (σ) = (Aij) (ε), the matrix (Aij) is more complex for composite materials as described in chapter C.

The equation of the elastic line of a bent metal beam ∂2y = ∂x 2

M

å

n

∂2y M = ∂x 2 EI

becomes

for a composite structure.

Ek lk

k =1

Normal stress - normal load relationship: for a stressed or compressed metal beam, the N N Ei expression σ = becomes σi = for each layer of a composite beam. n S Ek Sk

å

k =1

Normal stress - bending moment relationship: for a bent metal Mv M Ei v i σ= becomes σi = for each layer of the composite beam. n l Ek lk

å

k =1

Shear stress - shear load relationship: for a sheared metal beam, τ = τi =

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å

T Ei w i

n

beam,

for each layer of the composite beam.

Ek lk bk

k =1

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TW becomes lb

Composite stress manual

INTRODUCTION General instability

A

7.4

7.4 . General instability For a beam, Euler's law which associates the general instability critical compression load with the geometrical and mechanical properties of the beam remains valid, whatever the material used (metal/isotropic or composite/orthotropic). Indeed, the critical load is formulated as follows:

Fc =

π2 E l for metal beams, l2 π2

Fc =

å

n

E l k = 1 k k 2 l

for composite beams,

where l is the buckling length. Regarding plates, the approach is more complex for composite materials, although bases are identical. The differential equation which governs composite plate instability is formulated in its most general form:

C11

∂4 w ∂4 w ∂4 w ∂2 w ∂2 w ∂2w + 2 ( C + 2 C ) + C = N + N + 2 N 12 33 22 x y xy ∂x 4 ∂x 2 ∂y 2 ∂y 4 ∂x 2 ∂y 2 ∂x ∂y

where C11, C12, C33 and C22 are the temps of the matrix (Cij) binding the rotation tensor and the bending load tensor (see chapter D). For isotropic materials such as metals, the relationship is simplified: æ ∂4 w E e3 ∂4 w ∂4 w ö ∂2w ∂2 w ∂2w + + 2 N N N = + + ç ÷ x y xy 12 (1 − ν2 ) è ∂x 4 ∂x 2 ∂y 2 ∂y 4 ø ∂x 2 ∂y 2 ∂x ∂y

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INTRODUCTION

A

Metal/composite material differences

8 1/3

8 . DIFFERENCES BETWEEN METAL AND COMPOSITE MATERIALS These differences are actually covered by the composite material manual. A few examples are given below: - Metal material isotropic/composite material anisotropic duality If metal and composite materials are both macroscopically homogeneous, composite materials are generally anisotropic. This means that their properties depend on the direction (see drawing below) along which they are measured. y l

F/S Isotropic material

F

F

2

1, 2, 3

1 3

∆l/l

x 0

Properties are independent from the coordinate system direction y

l

F/S Anisotropic material

F

F

1

2

2

1 3

3 x

Properties depend on the coordinate system direction

0

∆l/l

This difference may be an advantage. Through an optimization of the orientation of fibres, it allows a greater freedom to choose element rigidity and, therefore, a more accurate control of load routing.

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INTRODUCTION Metal/composite material differences

A

8 2/3

- Failure criteria Because of their microscopic heterogeneity, composite materials do not obey covariant failure criteria (independent from the coordinate system direction) like metal materials. Generally, they must be applied to each layer and are applicable only in a preferential direction (the direction of the fibre to be justified).

- Effect of holes Sizing of holes in composite materials not only takes into account the net crosssection coefficient (as for metal materials) due to material removal, but also a decrease of the intrinsic material strength.

- Effect of bearing The presence of bearing due to load transfer at a fastener in a laminate causes membrane stresses to be artificially increased by part of the bearing stresses and, as a result, residual strength to be decreased.

- Damage tolerance The presence of impact or manufacturing damages causes a significant decrease to the laminate static strength.

- Effect of fatigue/damage tolerance Corrosion and fatigue are the overriding factors of the limited life of metal structures. Metal fatigue is controlled by the number of cycles required, on the one hand, to initiate a crack and, on the other hand, bring it to its critical length (growth phase). Influent factors of this phenomena are stress concentrations and tension loads.

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INTRODUCTION

A

Différences composite/métal

8 3/3

As a general rule, fatigue is not a design factor for composite elements of civil aircraft with thin thicknesses and no structural irregularities. More specifically, mechanical properties are such that static design requirements naturally "cover" fatigue design requirements. Wohler curves are relatively flat and damaging loads are of the compression type (R = - 1). (Impact or manufacturing) Damage growth under mechanical fatigue is not allowed because of the high rate of delamination growth. The current inability to control through analysis the damage growth rate in composite materials does not allow a damage tolerance justification based on slow growth. For this reason, allowable damage tolerance values are low; this makes it possible to avoid any explosive evolution during the aircraft life.

- Metal material plasticity/composite material "brittleness" duality Metal materials have an elastic range and a plastic range, in their behavior, which lead to breaking, breaking occurs in carbon composite materials without plasticizing.

l

F/S F

l

F/S F

F

F

breaking breaking plastic zone

elastic zone

elastic zone 0

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∆l/l Plastic material (metal)

MTS 006 Iss. B

0

∆l/l Brittle material (composite)

Composite stress manual

INTRODUCTION References

A

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials

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B COMPOSITE PLATE THEORY

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C MONOLITHIC PLATE - MEMBRANE ANALYSIS

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MONOLITHIC PLATE - MEMBRANE Notations

1 . NOTATIONS (o, x, y): reference coordinate system (o, l, t): coordinate system specific to the unidirectional ply k: fibre coordinate system θ: fibre orientation nθ: number of plies in direction θ eθ: overall thickness of plies in direction θ: eθ = nθ x ep e: overall thickness of laminate n: number of plies in laminate (N): flux tensor (σ): stress tensor (ε): elongation tensor (Q): stiffness matrix of unidirectional ply (R): stiffness matrix of laminate (A): stiffness matrix of laminate El: longitudinal young's modulus of unidirectional ply Et: transversal young's modulus of unidirectional ply νit: longitudinal/transversal Poisson coefficient νtl = νlt

Et : transversal/longitudinal Poisson coefficient El

Glt: shear modulus of unidirectional ply ep: ply thickness Rlt: allowable longitudinal tension stress Rlc: allowable longitudinal compression stress Rtt: allowable transversal tension stress Rtc: allowable transversal compression stress S: allowable shear stress

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C

1

Composite stress manual

MONOLITHIC PLATE - MEMBRANE Definitions - Homogeneity - Isotropy - Coupling

C

2.1 2.2.1 2.2.2

2 . GENERAL DEFINITIONS 2.1 . Homogeneity - Isotropy - A material is so-called homogeneous when its properties are independent from the point considered. - A material is isotropic if it has the same properties in all directions. - A material is anisotropic if there is no property symmetry, i.e. properties depend on the direction and on the point considered. - A material is orthotropic if its properties are symmetrical with relation to two perpendicular planes. Axes of symmetry are so-called axes of orthotropy.

2.2 . Coupling phenomenon 2.2.1 . Plane coupling In the case of an orthotropic material, there is a “plane coupling” if the loading axis is not coincident with one of its axes of orthotropy. In that case, normal loading (σ) generates shear (γ) and shear loading (τ) generates elongation (ε). y

N1

x

N1

2.2.2 . Mirror symmetry The laminate must be such that each layer has an identical symmetrical layer with relation to the neutral plane. This symmetry allows the membrane-bending coupling to be eliminated, i.e. the occurrence of plate bending, when a tension load is applied in its plane.

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MONOLITHIC PLATE - MEMBRANE Design method

C

3 1/8

3 . DESIGN METHOD The design method for a flat plate consists in assessing stresses in each ply and in determining the corresponding Hill’s criterion (see § G.3). Let’s assume that all plies are made up of the same material, and that the laminate is provided with the mirror symmetry property. That is to say the central plane of the laminate (for example: (0°/45°/135°/90°) s = (0°/45°/135°/90°/90°/135°/45°/0°). This property implies that there is no coupling between the membrane effects and the bending effects. Which means that the membrane flux tensor (Nx, Ny, Nxy) induces εx, εy, and γxy type elongations only and that, on the other hand, the moment flux tensor (Mx, My, Mxy) induces χx, χy and χxy type rotations only. In other words, in the case of a laminate with the mirror symmetry property, the relationship which binds loading and elongation may be formulated as follows: εx

Nx Aij

Ny

0

εy γxy

Nxy = Mx My

χx 0

Mxy

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Cij

χy χxy

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MONOLITHIC PLATE - MEMBRANE

C

Design method

3 2/8

A laminate (as well as the sign convention for membrane type load fluxes) may be represented as follows: z y

y Ny > 0 Nxy > 0 x

3

Nx > 0

θ2

θ1 x

1

θ3

2

With each fibre direction (θ = 1, 2 or 3) is associated the number of corresponding plies nθ. 1st step: Design of the stiffness matrix for the unidirectional layer in its own coordinate system (l, t). This matrix shall be called (Ql, t). c1

(σl, t) = (Ql, t) x (εl, t)

t

l

σl

σt τlt

© AEROSPATIALE - 1999

=

El 1 − νlt ν tl

ν tl E l 1 − ν lt ν tl

0

εl

ν lt E t 1 − ν lt ν tl

Et 1 − ν lt ν tl

0

εt

0

0

Glt

γlt

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MONOLITHIC PLATE - MEMBRANE

C

Design method

3 3/8

2nd step: Design of the stiffness matrix for the unidirectional layer in direction θ in the reference coordinate system (x, y). This matrix shall be called (Qx, y,θ). c2

(Qx, y,θ) = (Tθ) x (Ql, t) x (T'θ)-1

y l t θ x

with:

(Tθ) =

(T'θ) =

(cos θ) 2

(sin θ) 2

− 2 x sin θ x cos θ

(sin θ) 2

(cos θ) 2

2 x sin θ x cos θ

sin θ x cos θ

− sin θ x cos θ

(cos θ) 2 − (sin θ) 2

(cos θ) 2

(sin θ) 2

− sin θ x cos θ

(sin θ) 2

(cos θ) 2

sin θ x cos θ

2 x sin θ x cos θ

− 2 x sin θ x cos θ

(cos θ) 2 − (sin θ) 2

Matrix (Tθ) corresponding to the basic transformation matrix for stress condition. Matrix (T'θ) corresponding to the basic transformation matrix for elongation condition.

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MONOLITHIC PLATE - MEMBRANE

C

Design method

3 4/8

Note: Let material be defined by the two following drawings: y

t

ds

σt l

τxy

τtl

σx

θ x

τyx i

σy

σt τtl τlt

y

t

σl σy τyx

l

σl τlt

τxy

ds

τlt

τxy

σl

σx

τtl σx σt θ x

τyx i

σy

By obtaining their equilibrium, we get the three following expressions: σl ds - σx ds (cosθ)2 - σy ds (sinθ)2 + τxy ds sinθ cosθi - τxy ds sinθ cosθ = 0 τlt ds + σx ds sinθ cosθ - σy ds sinθ cosθ - τxy ds (sinθ)2 - τxy ds (cosθ)2 = 0 σt ds - σx ds (sinθ)2 - σy ds (cosθ)2 + τxy ds cosθ cosθ - τxy ds sinθ sinθ = 0 Expressions from which the matrix (Tθ) terms are easily taken.

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MONOLITHIC PLATE - MEMBRANE Design method

Remark: the stiffness matrix (Qx,

y, θ)

C

3 5/8

also allows determination of the mechanical

properties of the unidirectional layer in direction θ in the reference coordinate system (o, x, y). For the unidirectional layer, we have: (σx, y) = (Qx, y, θ) x (εx, y) 1 E x (θ)

εx

εy

−

=

−

ν xy (θ) E x (θ) η x (θ) E x (θ)

γxy

(εx, y) = (Qx, y, θ)-1 x (σx, y)

hence ν yx (θ)

ηyx (θ)

Ey (θ)

Gxy (θ) µ yx

1 Ey (θ)

G xy (θ)

µ y (θ)

1

E y (θ)

G xy (θ)

where: 1

Ex(θ) =

æ 1 ν ö c s + + c2 s2 ç − 2 tl ÷ El Et Et ø è Glt 4

4

1

Ey(θ) =

æ 1 ν ö s c + + c2 s2 ç − 2 tl ÷ El Et Et ø è Glt 4

Gxy(θ) =

4

1

ν yx (θ) E y (θ)

=

(

c 2 − s2 æ 1 ν tl ö 1 +2 4c s ç + ÷ + Et ø Glt è El E t 2

2

æ1 ν tl 4 1 1ö c + s4 − c 2 s 2 ç + − ÷ Et è El E t Glt ø

(

νxy(θ) = νyx(θ)

)

E x (θ) E y (θ)

with c ≡ cos(θ) and s ≡ sin(θ)

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)

2

σx

σy

τxy

Composite stress manual

MONOLITHIC PLATE - MEMBRANE

C

Design method

3 6/8

3rd step: Knowing the stiffness matrix of each layer (Qx, y, θ) with relation to the reference coordinate system (x, y), the laminate stiffness matrix can be calculated in this same coordinate system: (Rx, y). For this, the mixture law shall be applied.

å

n

c3

(Rx, y) =

k =1

(Q x, y, θk )

or

n

(Rx, y) =

å

n k =1

ep (Q x, y, θk ) e

4th step: Determination of the laminate elongation tensor in the reference coordinate system. c4

(εx, y) =

1 x (Rx, y)-1 x (Nx, y) e

εx εy

Nx

=

1 (Rx, y)-1 e

γ xy

εx

Nx

or

Ny

Ny

Nxy

Nxy

= (A)

εy γ xy

where (A) is the laminate membrane stiffness matrix: (A) = e x (Rx, y). Matrix (A) is the stiffness matrix which binds the stress flux tensor (N) with the elongation tensor (ε). c5

(N) = (A) x (ε)

© AEROSPATIALE - 1999

εx

Nx

A 11

A 12

A 13

Ny

= A 21

A 22

A 23

Nxy

A 31

A 32

A 33

x

εy γ xy

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MONOLITHIC PLATE - MEMBRANE Design method

C

3

where c6

Aij =

å

n k = 1

(Ε

k ij

(z k − z k

)

− 1)

z

ply No. k thickness

ply No. 1

with Ε11(θ) = c4 Εl + s4 Εt + 2 c2 s2 (νtl Εl + 2 Glt) Ε22(θ) = s4 Εl + c4 Εt + 2 c2 s2 (νtl Εl + 2 Glt) Ε33(θ) = c2 s2 (Εl + Εt - 2 νtl Εl) + (c2 - s2)2 Glt Ε12(θ) = Ε21(θ) = c2 s2 (Εl + Εt - 4 Glt) + (c4 + s4) νtl Εl Ε13(θ) = Ε31(θ) = c s {c2 Εl - s2 Εt - (c2 - s2) (νtl Εl + 2 Glt)} Ε23(θ) = Ε32(θ) = c s {s2 Εl - c2 Εt + (c2 - s2) (νtl Εl + 2 Glt)} c ≡ cos(θ) where θ is the fibre direction in the reference coordinate system (o, x, y) s ≡ sin(θ) where θ is the fibre direction in the reference coordinate system (o, x, y) Εl =

El 1 − ν tl νlt

Εt =

Et 1 − ν tl νlt

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE

C

Design method

3 8/8

5th step: Determination of elongations in each fibre direction c7

(εl, t, θ) = (T' - θ) x (εx, y) (cos θ) 2

(sin θ) 2

sin θ x cos θ

εx

(sin θ) 2

(cos θ) 2

− sin θ x cos θ

εy

− 2 x sin θ x cos θ

2 x sin θ x cos θ

(cos θ) 2 − (sin θ) 2

γ xy

ε lθ ε tθ

=

γ lt θ

6th step: Determination of stresses in each fibre direction c8

(σl, t, θ) = (Ql, t) x (εl, t, θ) σ lθ σ tθ

ε lθ

= (Ql, t)

τ lt θ

ε tθ γ lt θ

7th step: Assessment of Hill’s criterion in each fibre direction. Refer to chapter G (failure criteria).

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MONOLITHIC PLATE - MEMBRANE Equivalent properties

C

4

4 . DEFORMATIONS AND EQUIVALENT MECHANICAL PROPERTIES Monolithic plates are microscopically heterogeneous. It is sometimes necessary to find their equivalent membrane stiffness properties in order to determine the passing loads and resulting deformations. Equivalent membrane young's moduli are directly derived from the laminate stiffness matrix (A): 1

c9

(A)-1 =

1 e

E xxmemb. equi. ν xymemb . equi. − E xxmemb. equi. x

−

ν yxmemb. equi. E yy memb. equi. 1

E yymemb . equi. x

x x 1 Gxy memb. equi.

If reference axes (o, x, y) are coincident with the axes of orthotropy of the laminate, we obtain: E xxmemb. equi. =

A11 A 22 − (A 12 )2 e A 22

E yymemb. equi. =

A 11 A 22 − (A12 )2 e A11

Gxymemb . equi. =

A 66 e

ν xy memb. equi. =

A12 A 22

ν yxmemb . equi. =

A 21 A 11

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MONOLITHIC PLATE - MEMBRANE

C

Graphs - Failure envelopes - Theoretical principle

5.1.1 1/3

5 . GRAPHS 5.1 . Failure envelopes 5.1.1 . Theoretical principle Let a laminate be made up of plies in the same material and described as follows: - overall thickness e, - percentage of plies at 0°, - percentage of plies at 45°, - percentage of plies at 135°, - percentage of plies at 90°. If membrane fluxes Nx, Ny and Nxy, are applied to the laminate, so that Nx2 + Ny2 + Nxy2 = 1, the design method outlined above allows loads inside each layer to be determined and the overall plate margin (m) to be found (see § G "Failure criteria").

Ny

Nx', Ny', Nxy' (zero margin)

Nx, Ny, Nxy (margin m) o

Nxy

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Nx

Composite stress manual

MONOLITHIC PLATE - MEMBRANE Graphs - Failure envelopes - Theoretical principle

Let's assume that the three fluxes are multiplied by the coefficient

C

5.1.1 2/3

m + 1. 100

In this case, the laminate subject to this new loading (Nx', Ny', Nxy') shall have a zero margin. Therefore, it is possible to associate each triplet (Nx, Ny, Nxy) with a flux triplet (Nx', Ny', Nxy') so that the margin associated with it is zero. If this operation is repeated for the set of points so that Nx2 + Ny2 + Nxy2 = 1 (sphere S with radius 1), then, surface S' is obtained, corresponding to the set of points with a zero margin. This is the material failure envelope.

Ny

S' S

o

Nx

Nxy

This three-dimensional representation of zero margin points is not easy to use.

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MONOLITHIC PLATE - MEMBRANE Graphs - Failure envelopes - Theoretical principle

C

5.1.1 3/3

It can be represented in a two-dimensional space (Nx, Ny) in the form of graphs (each curve corresponding to the intersection S' with an equation plane Nxy = Nxyi). Ny plane Nxy = 0

plane Nxyi plane Nxyn

Nx

Nxy

If this set of curves is projected onto the plane (o, Nx, Ny), a network of curves is obtained which constitutes the breaking graph of the laminate. Ny

Nxyi = 0

Nxyi Nxyn

o

Nx

This graph (corresponding to a given material and a specific lay-up) allows the laminate margin (Hill's criterion) to be determined graphically.

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MONOLITHIC PLATE - MEMBRANE

C

Graphs - Failure envelopes - Margin

5.1.2

5.1.2 . Margin search - Methodology Let a laminate be subject to fluxes Nxo, Nyo and Nxyo and the breaking graph associated with it. - Plot the straight line D crossing point o and point A of coordinates Nxo and Nyo. - Perpendicular to this straight line, plot the value Nxyi segment corresponding to the graph curve Nxyi. Repeat this operation for each graph curve. - Plot curve C. - From point A, plot point B so that AB = Nxyo and AB ⊥ D. - Determine point C, intersection of the straight line (o, B) and curve C. æo C ö - The composite plate margin is equal to 100 ç − 1÷ . èoB ø Ny

D

N

xy i

Nyo

A

N

xy

o

B o

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Nxo

C

c Nx

Composite stress manual

MONOLITHIC PLATE - MEMBRANE Graphs - Mechanical properties

C

5.2

In practice, curves are represented in stress and not in flux values. This makes it possible to group together some laminates per lay-up class (for example: 3/2/2/1 ≡ 6/4/4/2 ≡ 9/6/6/3). A number of orthotropic laminate failure envelopes in carbon T300/914 layers shall be found in chapter Z “material properties”.

5.2 . Mechanical properties For a given material, a set of graphs may be created giving the mechanical properties (strength and elasticity moduli) of an orthotropic laminate described by its percentages of plies in each direction (see drawing below). Gxy

% to 90°

Gxy

%

% to 45°

A number of those graphs associated with carbon T300/914 layer shall be found in chapter Z “material properties”.

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MONOLITHIC PLATE - MEMBRANE Example

C

6 1/8

6 . EXAMPLE Given a laminate made of T300/BSL914 (new) with the following lay-up: 0°: 6 plies 45°: 4 plies 135°: 4 plies 90°: 6 plies Mechanical properties of the unidirectional ply are the following: El = 13000 hb (130000 MPa) Et = 465 hb (4650 MPa) νlt = 0.35 νtl = 0.0125 Glt = 465 hb (4650 MPa) ep = 0.13 mm e = 2.6 mm Rlt = 120 hb (1200 MPa) Rlc = - 100 hb (1000 MPa) Rtt = 5 hb (50 MPa) Rtc = - 12 hb (120 MPa) S = 7.5 hb (75 MPa) The purpose of this example is to search for stresses applied to each ply (0°, 45°, 135°, 90°) knowing that the laminate is globally subject to the three following load fluxes in the reference coordinate system (x, y): Nx = 30.83 daN/mm Ny = - 2.22 daN/mm Nxy = 44.92 daN/mm These load fluxes being the continuation of the example covered in chapter K (Fastener hole).

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MONOLITHIC PLATE - MEMBRANE

C

Example

6 2/8

1st step: Design of stiffness matrix (Ml, t) for the unidirectional ply with relation to its own coordinate system (l, t). {c1}

(Ql, t) =

(Ql, t) =

13000 1 − 0.35 0.0125

13000 0.0125 1 − 0.35 0.0125

0

465 0.35 1 − 0.35 0.0125

465 1 − 0.35 0.0125

0

0

0

465

13057

163

0

163

467

0

0

0

465

All values being expressed in daN/mm2.

2nd step: Assessment of stiffness matrix for each unidirectional ply with relation to the reference coordinate system (x, y). {c2} 1

0

0

13057

163

0

1

0

0

(Qx, y, 0°) = 0

1

0

163

467

0

0

1

0

0

0

1

0

0

465

0

0

1

© AEROSPATIALE - 1999

MTS 006 Iss. A

−1

Composite stress manual

MONOLITHIC PLATE - MEMBRANE

C

Example

(Qx, y, 45°) =

− 1

13057

163

0

0.5

0.5

0.5

0.5

1

163

467

0

0.5

0.5

0.5

0.5

− 0.5

0

0

0

465

1

−1

0

0.5

0.5

1

13057

163

0

0.5

0.5

0.5

0.5

0.5

− 1

163

467

0

0.5

0.5

− 0.5

− 0.5

0.5

0

0

0

465

− 1

1

0

0

1

0

13057

163

0

0

1

0 −1

1

0

0

163

467

0

1

0

0

0

0

−1

0

0

465

0

0

−1

13057

163

0

163

467

0

0

0

465

3928

2998

3148

(Qx, y, 45°) = 2998

3928

3148

3148

3148

3299

(Qx, y, 135°) =

© AEROSPATIALE - 1999

− 0.5 − 1

0.5

Thus, we find:

(Qx, y, 0°) =

3/8

0.5

(Qx, y, 135°) =

(Qx, y, 90°) =

6

3928

2998

− 3148

2998

3928

− 3148

− 3148

− 3148

3299

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE Example

467

(Qx, y, 90°) = 163

163

0

13057

0

0

465

0

C

6 4/8

All values being expressed in daN/mm2.

3rd step: By applying the mixture law, the overall laminate stiffness matrix (Rx, y) is formulated as follows. {c3}

(Rx, y) =

6 x 13057 + 8 x 3928 + 6 x 467

12 x 163 + 8 x 2998

4 x 3148 − 4 x 3148

12 x 163 + 8 x 2998

6 x 467 + 8 x 3928 + 6 x 13057

4 x 3148 − 4 x 3148

4 x 3148 − 4 x 3148

4 x 3148 − 4 x 3148

12 x 465 + 8 x 3299

1 20

(Rx, y) =

(Rx, y)-1 =

5628

1297

0

1297

5628

0

0

0

1598

188 . xE − 4

− 4.32 x E − 5

− 6.11 x E − 20

− 4.32 x E − 5

188 . xE − 4

4.02 x E − 20

− 6.11 x E − 20

4.02 x E − 20

6.25 x E − 4

All values being expressed in daN/mm2 and mm²/daN.

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MONOLITHIC PLATE - MEMBRANE

C

Example

6 5/8

4th step: Determination of the laminate strain tensor in the reference coordinate system (x, y). {c4} εx εy

=

188 . xE − 4

− 4.32 xE − 5

− 611 . xE − 20

3083 .

− 4.32 xE − 5

188 . xE − 4

402 . xE − 20

− 2.22

− 611 . xE − 20

402 . xE − 20

6.25 x .E − 4

44.92

1 2.6

γ xy

All values being expressed in mm/mm.

5th step: Determination of the strain tensor in each fibre direction. {c7} 1

0

0

2262 x E − 6

(εl, t, 0°) = 0

1

0

− 673 x E − 6

0

0

1

10807 x E − 6

(εl, t, 45°) =

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2262 x E − 6

=

− 673 x E − 6 10807 x E − 6

0. .5

0.5

0.5

2262 x E − 6

0.5

0.5

− 0.5

− 673 x E − 6

− 1

1

0

10807 x E − 6

MTS 006 Iss. A

6198 x E − 6

=

− 4609 x E − 6 − 2935 x E − 6

2262 x E − 6

=

− 673 x E − 6 10807 x E − 6

Composite stress manual

MONOLITHIC PLATE - MEMBRANE

C

Example

(εl, t, 135°) =

(εl, t, 90°) =

0.5

0.5

− 0.5

2262 x E − 6

0.5

0.5

0.5

− 673 x E − 6

1

− 1

0

10807 x E − 6

0

1

0

2262 x E − 6

1

0

0

− 673 x E − 6

0

0

−1

10807 x E − 6

− 4609 x E − 6 6198 x E − 6

=

2935 x E − 6

− 673 x E − 6 2262 x E − 6

=

− 10807 x E − 6

All values being expressed in mm/mm.

6th step: With the previous results, stresses in each ply are determined. {c8}

(σl, t, 0°) =

(σl, t, 45°) =

© AEROSPATIALE - 1999

13057

163

0

2262 x E − 6

163

467

0

− 673 x E − 6

0

0

465

10807 x E − 6

13057

163

0

6198 x E − 6

163

467

0

− 4609 x E − 6

0

0

465

− 2935 x E − 6

MTS 006 Iss. A

29.42

=

0.06 5.03 80.17

=

− 114 . − 136 .

6 6/8

Composite stress manual

MONOLITHIC PLATE - MEMBRANE

C

Example

(εl, t, 135°) =

(εl, t, 90°) =

13057

163

0

− 4609 x E − 6

163

467

0

6198 x E − 6

0

0

465

2935 x E − 6

136 .

− 8.42

13057

163

0

− 673 x E − 6

163

467

0

2262 x E − 6

0

0

465

− 10807 x E − 6

6 7/8

− 59.17

=

=

2.14

0.95

− 5.03

All values being expressed in hb.

7th step: In each direction, the corresponding Hill’s criterion is calculated (see chapter G), which gives the following margins for each ply: 0° → 40 %

45° → 42 %

135° → 31 %

90° → 42 %

The ply at 135° is, therefore, the most brittle ply in this loading case.

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MONOLITHIC PLATE - MEMBRANE Example

C

6 8/8

8th step: The laminate margin may be found with the breaking graph corresponding to this material (see chapter Z). We have: Nx = 30.83 daN/mm Ny = - 2.22 daN/mm Nxy = 44.92 daN/mm Giving, for an overall thickness of 2.6 mm, the following stresses: σx = 11.86 hb σy = - 0.85 hb ≈ 0 h τxy = 17.28 hb

+

T = 22 HB

x

T = 21 HB

Y

T = 18 HB

+

T = 15 HB

x

T = 12 HB

Y

T = 9 HB T = 6 HB T = 3 HB T = 0 HB

Scale: 1 cm ↔ 3.33 hb æo C ö æ 72 ö Marge = 100 ç − 1÷ = 100 ç − 1÷ ≈ 41 % è 51 ø èoB ø

There is a 10 % error with respect to the analytical method (31 %).

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MTS 006 Iss. A

Composite stress manual

MONOLITHIC PLATE - MEMBRANE References

C

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials M. THOMAS, Analysis of a laminate plate subject to membrane and bending loads, 440.227/79 J.C. SOURISSEAU, 40430.030 J. CHAIX, 436.127/91

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D MONOLITHIC PLATE - BENDING ANALYSIS

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MONOLITHIC PLATE - BENDING Notations

1 . NOTATIONS (o, x, y): reference coordinate system (o, l, t): coordinate system specific to the unidirectional fibre u, v, w: displacement from any point on the beam uo, vo, wo: displacement from the beam neutral plane β: beam curvature at a given point R: beam radius of curvature at a given point εx, εy, γxy: strains at any point εox, εoy, γoxy: strains neutral plane (M): bending moment tensor (χ): rotation tensor (α): tensor of angles formed by the deformation diagram (C): inertia matrix of laminate k: fibre coordinate system

θ: fibre orientation El: longitudinal young's modulus of unidirectional ply Et: transversal young's modulus of unidirectional ply νlt: longitudinal/transversal poisson coefficient νtl = νlt

Et : transversal/longitudinal poisson coefficient El

Glt: shear modulus of unidirectional ply ep: ply thickness

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D

1

Composite stress manual

MONOLITHIC PLATE - BENDING

D

Introduction - Design method

2 3

1/4

2 . INTRODUCTION In chapter C, we examined the case of a laminate provided with mirror symmetry subject to membrane type loading. In the paragraph below, we shall examine the case of a laminate with the same properties but, this time, subject to pure bending type loads. By convention, we shall consider that any positive moment compresses the laminate upper fibre. Let’s assume that bending moment flows Mx, My and Mxy generate εx, εy and γxy type strains. Let’s assume also (Kirchoff) that the neutral plane is coincident with the neutral line.

3 . DESIGN METHOD Let a bent plate be represented as follows: z y My > 0

x

z R=

1 2 ∂ w 2 ∂x

Mx > 0 Mxy > 0

tg(β) =

∂w ∂x

w x, y

z

u, v

z

uo, vo

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w

wo x, y

Composite stress manual

MONOLITHIC PLATE - BENDING

D

Design method

3 2/4

If the displacements from a point at position Z are defined as u, v and w in the coordinate system (x, y, z), then we may write: u = uo - z

∂w o ∂x

v = vo - z

∂w o ∂y

w = wo where uo, vo et wo represent displacements from the neutral plane in the coordinate system (x, y, z). We deduce (by deriving with respect to coordinates) the corresponding non-zero strains:

d1

εx = εox - z

εy = εoy - z

∂2 w o ∂x 2

∂2 w o ∂y 2

γxy = γoxy - 2 z

∂2wo ∂x ∂y z

εx

z εox

neutral plan

o

tg(α) =

2 ∂ w 2 ∂x

x

where εox, εoy and γoxy rerepresent strains at a point located on the neutral plane and εx, εy and γxy represent strains at any point at position z.

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Composite stress manual

MONOLITHIC PLATE - BENDING

D

Design method

From the general expression for the bending moment: M =

h 2 h − 2

ò

3

σ z dz , we obtain the

relationship between the bending load tensor (M) and the rotation tensor (χ): d2

(M) = (C) x (χ)

Mx

C11

C12

C13

My

= C 21

C22

C 23

M xy

C 31

C32

C 33

∂2wO ∂x 2 ∂2wO ∂y 2 ∂2 w O 2 ∂x ∂y

where

d3

Cij =

å

n k = 1

æ k zk3 − zk3 − 1 ö çç Ε ij ÷÷ 3 è ø

with d4

Ε11(θ) = c4 Εl + s4 Εt + 2 c2 s2 (νtl Εl + 2 Glt) Ε22(θ) = s4 Εl + c4 Εt + 2 c2 s2 (νtl Εl + 2 Glt) Ε33(θ) = c2 s2 (Εl + Εt - 2 νtl Εl) + (c2 - s2)2 Glt Ε12(θ) = Ε21(θ) = c2 s2 (Εl + Εt - 4 Glt) + (c4 + s4) νtl Εl Ε13(θ) = Ε31(θ) = c s {c2 Εl - s2 Εt - (c2 - s2) (νtl Εl + 2 Glt)} Ε23(θ) = Ε32(θ) = c s {s2 Εl - c2 Εt + (c2 - s2) (νtl Εl + 2 Glt)}

c ≡ cos(θ) where θ is the ply direction in the reference coordinate system (o, x, y) s ≡ sin(θ) where θ is the ply direction in the reference coordinate system (o, x, y)

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3/4

Composite stress manual

MONOLITHIC PLATE - BENDING

D

Design method

3 4/4

with d5

Εl =

El 1 − ν tl νlt

Εt =

Et 1 − ν tl νlt

If the tensor of angles formed by the strain diagram in each direction is defined by (α): (αx, αy, αxy) we may write in a simplified form the relationship: d6

(χ) = tg (α) By convention, we shall assume that (α) is negative when the upper fibre is in tension. We have:

d7

(ε)z = - (χ) x z z

z

ply No. k

α

zk zk - 1 h

neutral plan

σ

ε

ply No. 1

This relationship makes it possible to determine each ply strain and, therefore, to find (using chapter C) stresses applied to it.

Remark: The terms Cij must be determined with relation to the laminate neutral line (Kirchoff’s assumption). In this case, the neutral plane shall also be used as a reference for the overall load pattern.

© AEROSPATIALE - 1999

MTS 006 Iss. A

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MONOLITHIC PLATE - BENDING

D

Equivalent mechanical properties

4

4 . DEFORMATIONS AND EQUIVALENT MECHANICAL PROPERTIES Monolithic plates are microscopically heterogeneous. It is sometimes necessary to find their equivalent bending stiffness properties in order to determine the passing loads and resulting deformations. Equivalent bending elasticity moduli are directly derived from the laminate stiffness matrix (C): 1 E xx bending equi.

d8

(C)-1 =

12 e3

x 1

x

E yy bending equi.

x

x

x x 1 Gxy bending equi.

If reference axes (o, x, y) are coincident with the axes of orthotropy of the laminate, we obtain:

Exxbending equi. = 12

Eyybending equi. = 12

Gxybending equi. = 12

© AEROSPATIALE - 1999

C11 C 22 − (C12 )2 e3 C 22 C 11 C 22 − (C 12 ) 2 e 3 C 11 C 66 e3

MTS 006 Iss. A

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MONOLITHIC PLATE - BENDING

D

Example

5 1/7

5 . EXAMPLE Let a T300/BSL914 laminate (new) be laid up as follows: 0°: 2 plies 45°: 2 plies 135°: 2 plies 90°: 2 plies Stacking from the external surface being as follows: 0°/45°/135°/90°/90°/135°/ 45°/0°.

k = 8 (0°) k = 7 (45°) k = 6 (135°) k = 5 (90°) k = 4 (90°) k = 3 (135°) k = 2 (45°)

z8 = 0.52 z7 = 0.39 z6 = 0.26 z5 = 0.13 z4 = 0

k = 1 (0°)

Mechanical properties of the unidirectional ply are the following: El = 13000 hb Et = 465 hb νlt = 0.35 νtl = 0.0125 Glt = 465 hb ep = 0.13 mm The purpose of this example is to search for elongations at the laminate external surface, knowing that the laminate is globally subject to the three following moment fluxes in the reference coordinate system (x, y):

© AEROSPATIALE - 1999

MTS 006 Iss. A

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MONOLITHIC PLATE - BENDING Exemple

D

5 2/7

Mx = 10 daN My = 0 daN/mm Mxy = - 5 daN/mm z

y

x

Mx = 10 daN

Mxy = - 5 daN

1st step: calculation of stiffness coefficients for the unidirectional ply: {d5} Εl =

13000 = 13057 daN/mm2 1 − 0.35 0.0125

Εt =

465 = 467 daN/mm2 1 − 0.35 0.0125

2nd step: For each ply, stiffness coefficients Εij expressed in daN/mm2 are calculated. {d4} ply at 0° Ε11(0°) = 13057 Ε22(0°) = 467 Ε33(0°) = 465 Ε12(0°) = Ε21(0°) = 0.0125 x 13000 = 163 Ε13(0°) = Ε31(0°) = 0 Ε23(0°) = Ε32(0°) = 0

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MONOLITHIC PLATE - BENDING Example

D

5 3/7

ply at 45° Ε11(45°) = 0.7074 13057 + 0.7074 467 + 2 x 0.7072 0.7072 (0.0125 x 13057 + 2 x 465) = 3925 Ε22(45°) = 0.7074 13057 + 0.7074 467 + 2 x 0.7072 0.7072 (0.0125 x 13057 + 2 x 465) = 3925 Ε33(45°) = 0.7072 0.7072 (13057 + 467 - 2 x 0.0125 x 13057) = 3297 Ε12(45°) = Ε21(45°) = 0.7072 0.7072 (13057 + 467 - 4 x 465) + (0.7074 + 0.7074) x 0.0125 x 13057 = 2995 Ε13(45°) = Ε31(45°) = 0.707 x 0.707 {0.7072 13057 - 0.7072 467} = 3146 Ε23(45°) = Ε32(45°) = 0.707 x 0.707 {0.7072 13057 - 0.7072 467} = 3146 ply at 135° Ε11(135°) = 3925 Ε22(135°) = 3925 Ε33(135°) = 3297 Ε12(135°) = Ε21(135°) = 2995 Ε13(135°) = Ε31(135°) = - 3146 Ε23(135°) = Ε32(135°) = - 3146 ply at 90° Ε11(90°) = 467 Ε22(90°) = 13057 Ε33(90°) = 465 Ε12(90°) = Ε21(90°) = 163 Ε13(90°) = Ε31(90°) = 0 Ε23(90°) = Ε32(90°) = 0

© AEROSPATIALE - 1999

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MONOLITHIC PLATE - BENDING

D

Example

5 4/7

3rd step: Calculation of laminate inertia matrix (C) coefficients Cij expressed in daN mm. The laminate being provided with the mirror symmetry property, coefficients Cij shall be calculated for the laminate upper half, then they shall be multiplied by 2. {d3} 90° æ . − 0 013 C11 = 2 ç 467 3 è 3

135° 3

+ 3925

0.26

3

− 013 . 3

45° 3

+ 3925

0.39

3

0° − 0.26 3

3

+ 13057

0.52 3 − 0.39 3 ö 3

÷ ø

æ . 3 − 03 . 3 013 0.26 3 − 013 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö + 2995 + 2995 + 163 C12 = 2 ç163 ÷ 3 3 3 3 ø è æ 0.13 3 − 0 3 0.26 3 − 0.13 3 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö − 3146 + 3146 + 0 C13 = 2 ç 0 ÷ 3 3 3 3 ø è æ . 3 − 03 013 0.26 3 − 0.13 3 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö + 2995 + 2995 + 163 C21 = 2 ç163 ÷ 3 3 3 3 ø è æ . 3 − 03 . 3 013 0.26 3 − 013 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö + 3925 + 3925 + 467 C22 = 2 ç13057 ÷ 3 3 3 3 ø è æ 0.13 3 − 0 3 0.26 3 − 0.13 3 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö − 3146 + 3146 + 0 C23 = 2 ç 0 ÷ 3 3 3 3 ø è æ 0.13 3 − 0 3 0.26 3 − 0.13 3 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö − 3146 + 3146 + 0 C31 = 2 ç 0 ÷ 3 3 3 3 ø è æ 0.13 3 − 0 3 0.26 3 − 0.13 3 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö − 3146 + 3146 + 0 C32 = 2 ç 0 ÷ 3 3 3 3 ø è æ . 3 − 03 . 3 013 0.26 3 − 013 0.39 3 − 0.26 3 0.52 3 − 0.39 3 ö + 3297 + 3297 + 465 C33 = 2 ç 465 ÷ 3 3 3 3 ø è

C11 = 858 C12 = 123 C13 = 55 C21 = 123 C22 = 194 C23 = 55 C31 = 55 C32 = 55 C33 = 151

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MTS 006 Iss. A

Composite stress manual

MONOLITHIC PLATE - BENDING Example

D

Thus, the following matrix is obtained: 858

123

55

(C) = 123

194

55

55

55

151

4th step: Search for the rotation tensor {d2}

Mx

858

123

My

= 123

194

Mxy

55

55

∂ 2 wo ∂x 2 ∂ 2 wo 55 = ∂y 2 ∂2 wo 2 151 ∂x ∂y 55

hence

∂ 2 wo ∂x 2 ∂ 2 wo ∂y 2 ∂2 wo 2 ∂x ∂y

© AEROSPATIALE - 1999

=

1287 . E−3

− 7.617 E − 4

− 1913 . E−4

− 7.617 E − 4

6.199 E − 3

− 198 . E−3

− 1913 . E−4

− 198 . E−3

7.414 E − 3

MTS 006 Iss. A

Mx

=

My Mxy

5 5/7

Composite stress manual

MONOLITHIC PLATE - BENDING Example

∂2wo ∂x 2 ∂2wo

=

∂y 2 ∂2 w o 2 ∂x ∂y

1287 . E−3

− 7.617 E − 4

− 1913 . E−4

− 7.617 E − 4

6.199 E − 3

− 198 . E−3

− 1913 . E−4

− 198 . E−3

7.414 E − 3

D

5 6/7

10

=

0

−5

Thus, we find: ∂2wo

13.82 E − 3

∂x 2 ∂2wo

=

∂y 2 ∂2 w o 2 ∂x ∂y

2.283 E − 3

− 38.98 E − 3

which is the rotation tensor (χ).

5th step: We now propose to calculate strains ε (0°) for the ply at 0° (at the external line of the layer). {d7} εx(0°) = -

∂2 w o h x 2 2 ∂x

εy(0°) = -

∂2 w o h x 2 2 ∂y

γxy(0°) = - 2

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∂2w o h x 2 ∂x ∂y

MTS 006 Iss. A

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MONOLITHIC PLATE - BENDING Example

D

5 7/7

hence: εx(0°) = - 1 x 13.82 E-3 x 0.52 = - 7186 µd εy(0°) = - 1 x 2.283 E-3 x 0.52 = - 1187 µd γxy(0°) = - 1 x - 38.98 E-3 x 0.52 = 20270 µd Stresses in the layer may be determined afterwards. To do this, refer to chapter C.

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MONOLITHIC PLATE - BENDING References

D

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials M. THOMAS, Analysis of a laminate plate subject to membrane and bending loads, 440.227/79 J.C. SOURISSEAU, 40430.030 J. CHAIX, 436.127/91

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MTS 006 Iss. A

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E MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Notations

1 . NOTATIONS (o, x, y): reference coordinate system (o, l, t): coordinate system specific to the unidirectional fibre εx, εy, γxy: material strains at any point wo: displacement from plate neutral plane (N): normal flux tensor (M): bending moment tensor (ε): membrane type strain tensor (χ): curvature tensor (A): laminate stiffness matrix (membrane) (B): laminate stiffness matrix (membrane/bending coupling) (C): laminate stiffness matrix (bending) θ: fibre orientation k: fibre coordinate system El: longitudinal elasticity modulus of unidirectional fibre Et: transversal elasticity modulus of unidirectional fibre νlt: longitudinal/transversal poisson coefficient νtl: transversal/longitudinal poisson coefficient Glt: shear modulus of unidirectional fibre ep: ply thickness

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Introduction

E

2

2 . INTRODUCTION We have seen in chapter C that there is a relationship which binds membrane strains and loading of the same type. This relationship may be formulated as follows: (N) = (A) x (ε).

We also saw in chapter D that there is a relationship which binds the curvature tensor and the moment tensor. This relationship may be formulated as follows: (M) = (C) x (χ).

If lay-up has the mirror symmetry property, then both phenomena are dissociated and independent. In other words, the overall relationship which binds the set of strains and the set of loadings may be formulated as follows: Nx

A11

A12

A13

0

0

0

εx

Ny

A 21

A 22

A 23

0

0

0

εy

Nxy

A 31

A 32

A 33

0

0

0

γ xy

= Mx

0

0

0

C11

C12

C13

My

0

0

0

C21

C 22

C23

Mxy

0

0

0

C31

C 32

C33

∂2wo ∂x 2 ∂2wo ∂y 2 ∂2 wo 2 ∂x ∂y

where coefficients Aij and Cij are defined in chapters C and D.

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Analysis method

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3 1/2

3 . ANALYSIS METHOD If lay-up is non-symmetrical, then all zero terms of the previous matrix become non-zero and there is a membrane/bending coupling. Both phenomena become dependent. The relationship between loadings and strains is thus: Nx

A11

A12

A13

B11

B12

B13

εx

Ny

A 21

A 22

A 23

B21

B22

B23

εy

Nxy

A 31

A 32

A 33

B31

B32

B33

γ xy

e1

= Mx

B11

B12

B13

C11

C12

C13

My

B21

B22

B23

C21

C 22

C23

Mxy

B31

B32

B33

C31

C 32

C33

where

e2

Bij = -

å

n k = 1

æ k zk2 − zk2 − 1 ö çç Eij ÷÷ 2 è ø

ply No. k zk zk - 1 neutral plane

ply No. 1

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∂2wo ∂x 2 ∂2wo ∂y 2 ∂2 wo 2 ∂x ∂y

Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Analysis method

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3 2/2

with e3

Ε11(θ) = c4 Εl + s4 Εt + 2 c2 s2 (νtl Εl + 2 Glt) Ε22(θ) = s4 Εl + c4 Εt + 2 c2 s2 (νtl Εl + 2 Glt) Ε33(θ) = c2 s2 (Εl + Εt - 2 νtl Εl) + (c2 - s2)2 Glt Ε12(θ) = Ε21(θ) = c2 s2 (Εl + Εt - 4 Glt) + (c4 + s4) νtl Εl Ε13(θ) = Ε31(θ) = c s {c2 Εl - s2 Εt - (c2 - s2) (νtl Εl + 2 Glt)} Ε23(θ) = Ε32(θ) = c s {s2 Εl - c2 Εt + (c2 - s2) (νtl Εl + 2 Glt)} where c ≡ cos(θ) where θ is the fibre direction in the reference coordinate system (o, x, y). s ≡ sin(θ) where θ is the fibre direction in the reference coordinate system (o, x, y). with

e4

Εl =

El 1 − ν tl νlt

Εt =

Et 1 − ν tl νlt

Remark: The terms Bij and Cij must be determined with relation to the laminate neutral line (Kirchoff’s assumption). In this case, the neutral plane shall also be used as a reference for the overall load pattern.

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

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4

4 . EXAMPLE Let a T300/BSL914 laminate (new) be laid up as follows: 0°: 1 ply 45°: 1 ply 135°: 1 ply 90°: 1 ply Stacking from the external surface being as follows: 0°/45°/135°/90°.

k = 4 (0°)

z4 = 0.26 z3 = 0.13

k = 3 (45°) k = 2 (135°)

z2 = 0 z1 = - 0.13

k = 1 (90°) z0 = - 0.26

Mechanical properties of the unidirectional fibre are the following: El = 13000 hb Et = 465 hb νlt = 0.35 νtl = 0.0125 Glt = 465 hb ep = 0.13 mm

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

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4 2/9

The purpose of this example is to search for strains at the laminate internal and external surfaces, knowing that the laminate is globally subject to the following fluxes in the reference coordinate system (x, y): Nx = 5 daN/mm Ny = 0 daN/mm Nxy = 0 daN/mm Mx = 0 daN æ mm daN ö My = - 0.15 daN ç ÷ è mm ø Mxy = 0 daN

z

y

My = - 0.15 daN

x

Nx = 5 daN/mm

1st step: calculation of stiffness coefficients for the unidirectional fibre: {e4} Εl =

13000 = 13057 daN/mm2 1 − 0.35 0.0125

Εt =

465 = 467 daN/mm2 1 − 0.35 0.0125

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MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

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4 3/9

2nd step: For each fibre direction, stiffness coefficients Εij expressed in daN/mm2, are calculated. {e3} fibre at 0° Ε11(0°) = 13057 Ε22(0°) = 467 Ε33(0°) = 465 Ε12(0°) = Ε21(0°) = 0.0125 x 13000 = 163 Ε13(0°) = Ε31(0°) = 0 Ε23(0°) = Ε32(0°) = 0 fibre at 45° Ε11(45°) = 0.7074 13057 + 0.7074 467 + 2 x 0.7072 0.7072 (0.0125 x 13057 + 2 x 465) = 3925 Ε22(45°) = 0.7074 13057 + 0.7074 467 + 2 x 0.7072 0.7072 (0.0125 x 13057 + 2 x 465) = 3925 Ε33(45°) = 0.7072 0.7072 (13057 + 467 - 2 x 0.0125 x 13057) = 3297 Ε12(45°) = Ε21(45°) = 0.7072 0.7072 (13057 + 467 - 4 x 465) (0.7074 + 0.7074) x 0.0125 x 13057 = 2995 Ε13(45°) = Ε31(45°) = 0.707 x 0.707 {0.7072 13057 - 0.7072 467} = 3146 Ε23(45°) = Ε32(45°) = 0.707 x 0.707 {0.7072 13057 - 0.7072 467} = 3146 fibre at 135° Ε11(135°) = 3925 Ε22(135°) = 3925 Ε33(135°) = 3297 Ε12(135°) = Ε21(135°) = 2995 Ε13(135°) = Ε31(135°) = - 3146 Ε23(135°) = Ε32(135°) = - 3146

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

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4 4/9

fibre at 90° Ε11(90°) = 467 Ε22(90°) = 13057 Ε33(90°) = 465 Ε12(90°) = Ε21(90°) = 163 Ε13(90°) = Ε31(90°) = 0 Ε23(90°) = Ε32(90°) = 0

3rd step: Calculation of laminate (membrane) stiffness matrix (A) coefficients Aij expressed in daN/mm. {c6} 90°

135°

45°

0°

A11 = (467 x 0.13 + 3925 x 0.13 + 3925 x 0.13 + 13057 x 0.13) A12 = (163 x 0.13 + 2995 x 0.13 + 2995 x 0.13 + 163 x 0.13) A13 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13) A21 = (163 x 0.13 + 2995 x 0.13 + 2995 x 0.13 + 163 x 0.13) A22 = (13057 x 0.13 + 3925 x 0.13 + 3925 x 0.13 + 467 x 0.13) A23 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13) A31 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13) A32 = (0 x 0.13 - 3146 x 0.13 + 3146 x 0.13 + 0 x 0.13) A33 = (465 x 0.13 + 3297 x 0.13 + 3297 x 0.13 + 465 x 0.13) hence A11 = 2779 A12 = 821 A13 = 0 A21 = 821 A22 = 2779 A23 = 0 A31 = 0 A32 = 0 A33 = 978

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

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4 5/9

4th step: Calculation of laminate (bending) inertia matrix (C) coefficients Cij expressed in daN mm. {d3} 90° 135° 45° 0° 3 3 3 3 3 3 3 3 æ ö 0 − (− 013 013 0.26 − 013 (− 013 . ) − (− 0.26) . ) . − 0 . + 3925 + 3925 + 13057 C11 = ç 467 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 3 3 æ 0 − (− 0.13) 013 0.26 − 0.13 ö (− 013 . ) − (− 0.26) . − 0 + 2995 + 2995 + 163 C12 = ç163 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 æ ( − 0.13) 3 − (− 0.26) 3 0 − (− 0.13) 0.13 − 0 0.26 − 0.13 ö − 3146 + 3146 + 0 C13 = ç 0 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 3 3 æ 0 − (− 013 013 0.26 − 0.13 ö (− 013 . ) − (− 0.26) . ) . − 0 + 2995 + 2995 + 163 C21 = ç163 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 3 3 æ ö 0 − (− 013 013 0.26 − 013 (− 013 . ) − (− 0.26) . ) . − 0 . + 3925 + 3925 + 467 C22 = ç13057 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 æ (− 0.13) 3 − (− 0.26) 3 0 − (− 0.13) 0.13 − 0 0.26 − 0.13 ö − 3146 + 3146 + 0 C23 = ç 0 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 æ ( − 0.13) 3 − (− 0.26) 3 0 − (− 0.13) 0.13 − 0 0.26 − 0.13 ö − 3146 + 3146 + 0 C31 = ç 0 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 æ ( − 0.13) 3 − (− 0.26) 3 0 − ( − 0.13) 0.13 − 0 0.26 − 0.13 ö − 3146 + 3146 + 0 C32 = ç 0 ÷ 3 3 3 3 è ø 3 3 3 3 3 3 3 3 æ ö 0 − (− 013 0.13 − 0 0.26 − 013 (− 013 . ) − (− 0.26) . ) . + 3297 + 3297 + 465 C33 = ç 465 ÷ 3 3 3 3 è ø

hence C11 = 75.1 C12 = 6.06 C13 = 0 C21 = 6.06 C22 = 75.1 C23 = 0 C31 = 0 C32 = 0 C33 = 9.59

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MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

4 6/9

5th step: Calculation of membrane - bending coupling coefficients Bij expressed in daN. {e2} 90° æ B11 = - ç 467 è æ B12 = - ç 163 è æ B13 = - ç 0 è

( − 0.13 )

( − 0.13)

æ B32 = - ç 0 è

− ( − 0.26 )

+ 3925

0

2

2

2

− ( − 0.26 )

2 + 2995

0

2

− 3146

0

2

( − 0.13 )

( − 0.13 )

2

( − 0.13 )

2

− ( − 0.26 )

2

+ 2995

0

2

− ( − 0.26)

2 + 3925

0

− 3146

0

2

2 + 3146

− ( − 0.13)

2

− ( − 0.26 )

− 3146

0

2

2 + 2995

− ( − 0.26 )

− 3146

0

2

− ( − 0.13)

2 + 3925

− ( − 0.26 )

2

+ 3297

0

0.26

2

− 0.13

+ 0

0.26

2

− 0.13

+ 3146

0.13

2

− 0

0.13

+ 3146

0.13

2

2 + 3146

0.13

2

2 + 163

− 0

− 0

2

− 0

2

0.26

2

− ( − 0.13)

2

B11 = - 319 B12 = 0 B13 = - 53.2 B21 = 0 B22 = 319 B23 = - 53.2 B31 = - 53.2 B32 = - 53.2 B33 = 0

MTS 006 Iss. A

+ 3297

0.13

− 0

2

2 + 467

0,26

2

2

ö ÷ ø

− 0.13

+ 0

+ 0

0.26

− 0.13

0.26

2

− 0.13

+ 0

0.26

2

− 0.13

2 − 0

2

2 2

2

ö ÷ ø

2

ö ÷ ø

2

ö ÷ ø

2

2

ö ÷ ø

2 + 465

0.26

2

− 0.13

2

ö ÷ ø

ö ÷ ø

− 0.13

2

2

2

2

2

2

2 2

2

2

2

2

− 0.13

2 2

2

− ( − 0.13 )

2

2

2 2

2 2

+ 163

2

− ( − 0.13 )

2

0.26

2

− 0

0.13

2 2

− 0

2

+ 13057

2

hence

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0.13

2

2 2

− 0

2

− ( − 0.13 )

2

( − 0.13 )

0.13

2 2

2

æ B33 = - ç 465 è

+ 2995

2

2

− ( − 0.26 )

2

2

2 2

0° 2

2

− ( − 0.13 )

2 2

0.13

2 2

2 ( − 0.13)

+ 3925

2 2

− ( − 0.13)

2 ( − 0.13)

2

2

− ( − 0.26 )

2

45°

− ( − 0.13 )

2

æ B22 = - ç 13057 è

æ B31 = - ç 0 è

135° 2

2

( − 0.13 )

æ B21 = - ç 163 è

æ B23 = - ç 0 è

2

2

ö ÷ ø

ö ÷ ø

Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

E

6th step: Expression of stiffness overall matrix {e1} Nx

A 11

A 12

A 13

B 11

B 12

B 13

εx

Ny

A 21

A 22

A 23

B 21

B 22

B 23

εy

Nxy

A 31

A 32

A 33

B 31

B 32

B 33

γ xy

= Mx

B 11

B 12

B 13

C 11

C 12

C 13

My

B 21

B 22

B 23

C 21

C 22

C 23

Mxy

B 31

B 32

B 33

C 31

C 32

C 33

∂2wo ∂x 2 ∂2wo ∂y 2 ∂2 wo 2 ∂x ∂y

then Nx

2779

821

0

− 319

0

53.2

εx

Ny

821

2779

0

0

319

53.2

εy

Nxy

0

0

978

53.2

53.2

0

γ xy

= Mx

− 319

0

53.2

75.1

6.06

0

My

0

319

53.2

6.06

75.1

0

Mxy

53.2

53.2

0

0

0

9.59

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∂2wo ∂x 2 ∂2wo ∂y 2 ∂2 wo 2 ∂x ∂y

4 7/9

Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

E

4 8/9

By reversing the relationship, we find: ε ε γ

x y

xy

∂2w

o

∂x 2 2 ∂ w o

=

1.15 x E − 3

− 5.0 x E − 4

3.80 x E − 4

5.00 x E − 3

1.99 x E − 3

3.61 x E − 3

N

− 5.0 x E − 4

1.15 x E − 3

− 3.8 x E − 4

− 2.0 x E − 3

− 5.0 x E − 3

3.61 x E − 3

N

3.80 x E − 4

− 3.8 x E − 4

1.28 x E − 3

2.33 x E − 3

2.33 x E − 3

0

N

5.00 x E − 3

− 2.0 x E − 3

2.33 x E − 3

3.57 x E − 2

7.23 x E − 3

1.67 x E − 2

M

2.00 x E − 3

− 5.0 x E − 3

2.33 x E − 3

7.23 x E − 3

3.57 x E − 2

− 1.67 x E − 2

M

3.61 x E − 3

3.61 x E − 3

0

1.67 x E − 2

− 1.67 x E − 2

1.44 x E − 1

M

∂y 2 ∂2w

2

o

∂x ∂y

x y

xy

x

y

xy

7th step: Search for the strain tensor By replacing loading by values quoted at the beginning of the example in the previous relationship, we find: εx

5.44 E − 3 mm / mm

(5440 µd)

εy

− 174 . E − 3 mm / mm

(− 1740 µd)

γ xy

154 . E − 3 mm / mm

(1540 µd)

∂2wo ∂x 2 ∂2wo ∂y 2 ∂2 wo 2 ∂x ∂y

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= 2.38 E − 2 mm −1 4.57 E − 3 mm −1 2.05 E − 2 mm −1

MTS 006 Iss. A

Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS Example

E

4 9/9

8th step: Search for strains in the upper fibre at ε (0°) To do this, membrane strains (εx, εy, γxy) are added to strains resulting from the bending 2 æ ∂2wo ∂2wo h ∂ wo h hö x x 2 x ÷ , , effect ç 2 2 2 ∂y 2 ∂x ∂y 2 ø è ∂x {d7} εx(0°) = εx -

∂2 w o h x 2 2 ∂x

εy(0°) = εy -

∂2 w o h x 2 2 ∂y

γxy(0°) = γxy - 2

∂2wo h x 2 ∂x ∂y

hence: εx (0°) = 5.44 E-3 + (-1) x 2.38 E-2 x 0.26 = - 748 µd εy (0°) = - 1.74 E-3 + (-1) x 4.57 E-3 x 0.26 = - 2928 µd γxy (0°) = - 1.54 E-3 + (-1) x 2.05 E-2 x 0.26 = - 3790 µd For the lower fibre, we would find: εx (90°) = 5.44 E-3 + 2.38 E-2 x 0.26 = 11628 µd εy (90°) = - 1.74 E-3 + 4.57 E-3 x 0.26 = - 552 µd γxy (90°) = + 1.54 E-3 + 2.05 E-2 x 0.26 = 6870 µd

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Composite stress manual

MONOLITHIC PLATE - MEMBRANE + BENDING ANALYSIS References

E

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials M. THOMAS, Analysis of a laminate plate subjected to membrane and bending loads, 440.227/79 J.C. SOURISSEAU, 40430.030 J. CHAIX, 436.127/91

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Composite stress manual

F MONOLITHIC PLATE - TRANSVERSAL SHEAR ANALYSIS

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Composite stress manual

MONOLITHIC PLATE - TRANSVERSAL SHEAR Notations

F

1

1 . NOTATIONS (o, x, y): reference coordinate system (o, l, t): coordinate system specific to the unidirectional fibre El: longitudinal elasticity modulus of unidirectional fibre Et: transversal elasticity modulus of unidirectional fibre νlt: longitudinal/transversal Poisson coefficient νtl: transversal/longitudinal Poisson coefficient Glt: shear modulus of unidirectional fibre ep: ply thickness Ek: longitudinal elasticity modulus with relation to x-axis of ply No. k n: total number of laminate layers θ: fibre orientation El: laminate overall inertia with relation to the (moduli weighted) neutral axis E Wk: static moment with relation to the (moduli weighted) neutral axis of the set of plies k to n τ: shear stress Txy, Tyz, T(β): shear load flux

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Composite stress manual

MONOLITHIC PLATE - TRANSVERSAL SHEAR

F

Introduction

2

2 . INTRODUCTION The purpose of this chapter is to determine interlaminar shear stresses in a monolithic plate subject to a shear load flux. For simplification purposes, we shall assume that the laminate is made up of n identical fibres but with different directions.

z Tyz > 0 y z

Txz > 0 x

y θ k=n ep

k=1 x

Layer No. k in direction θ has the following longitudinal elasticity modulus with relation to the reference coordinate system (o, x, y): f1

Ek =

1 æ 1 ν ö c s + + c 2 s2 ç − 2 tl ÷ El Et Et ø è Glt 4

4

see chapter C3.

with c ≡ cos(θ) s ≡ sin(θ)

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Composite stress manual

MONOLITHIC PLATE - TRANSVERSAL SHEAR Introduction - Analysis method

F

2 3

1/5

We shall assume that shear load Txz (direction z load shearing a plane perpendicular to xaxis) creates stress τxz and, based on the reciprocity principle, stress τzx. Similarly, we shall assume that shear load Tyz (direction z load shearing a plane perpendicular to y-axis) creates stress τyz and, based on the reciprocity principle, stress τzy. These shear stresses are called interlaminar stresses.

z

τzy τzx

τyz

τxz

y Tyz

Txz

x

3 . ANALYSIS METHOD To calculate interlaminar stresses τxz (τzx) generated by shear load Txz (Tyz), use the following methodology. We shall only consider the case of a laminate subject to shear load Txz. The analysis principle is the same for Tyz. In this case, inertias (El) and static moments (E W k) are measured with relation to y-axis. Elasticity moduli (Ek) are measured with relation to x-axis.

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Composite stress manual

MONOLITHIC PLATE - TRANSVERSAL SHEAR Analysis method

F

3 2/5

1st step: The position of the laminate neutral axis is determined. If the laminate lower fibre is used as a reference, then the neutral axis is defined by dimension zg, so that:

å 2å n

f2

zg =

(

E k z k2 − z k2 − 1

k =1 n

(

)

Ek z k − zk − 1

k =1

) z

ply No. n ply No. k zg

zk zk - 1 z1

ply No. 1

y

z0 = 0

2nd step: The (moduli weighted) bending stiffness of laminate El is determined with relation to the lay-up neutral axis

f3

El =

å

n

Ek

k =1

(z

k

− zk − 1 12

)

3

+

å

n

(

Ek z k − z k − 1

k =1

)

æ zk + zk − 1 ö − zg ÷ ç 2 è ø

2

z

ply No. k

zk

zk - 1

zg

y

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Composite stress manual

MONOLITHIC PLATE - TRANSVERSAL SHEAR Analysis method

F

3 3/5

3rd step: Then the (elasticity moduli weighted) static moment E W k (of the material surface located above the line where interlaminar stress is to be calculated), is determined. This static moment shall be calculated with relation to the plate neutral axis. If the line is a fibre interface surface (z = zk - 1), then we have the following relationship: f4

E Wk =

ö æ zi + z i − 1 Ei z i − z i − 1 ç − zg ÷ i=k 2 ø è

å

n

(

)

z

ply No. k

zk

zk - 1

zg

y

If the line is situated at the centre of a fibre at z =

f5

E Wk =

å

n i = k

(

Ei zi − zi

æ zk + z k Ek ç 2 è

− 1

− 1

) æçè

− zk

z i + zi 2 ö ø

− 1÷

− 1

zk + zk

− 1

2

, the relationship becomes:

ö − zg ÷ − ø

æ zk + z k ç 4 è

− 1

+

zk

− 1

2

ö − zg ÷ ø z

z +z

ply No. k

k

k − 1

2

zk

zg

zk - 1

y

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Composite stress manual

MONOLITHIC PLATE - TRANSVERSAL SHEAR Analysis method

F

3 4/5

4th step: Shear stress τxzk is determined, so that: f6

τxzk =

Txz . E Wk El

where Txz is the shear load applied to the laminate. By using this analysis method for each ply interface (or at the center of each ply for greater accuracy), it is possible to plot the interlaminar shear stress diagram over the entire plate width. The previous relationship shows that the shear stress is maximum when the static moment is maximum as well, i.e. at the neutral axis (z = zg). z

z

τxzk ply No. k τzxk zg

τxz

y

Remark: The previous analysis is based on a shear load flux Txz applied to a section perpendicular to x-axis. In the case of any section forming an angle β in the coordinate system (o, x, y), the shear load flux in this new section may be expressed as a function of Txz and Tyz.

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MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - TRANSVERSAL SHEAR Analysis method

F

3 5/5

y

T(β + π/2)

T(β)

ds

-Txz β x -Tyz

As shown in the drawing above, the z equilibrium of the hatched material element leads to the following relationship: T(β) ds - Txz ds cos(β) - Tyz ds sin(β) = 0 hence: T(β) = cos(β) Txz + sin(β) Tyz æ Tyz ö It is easy to show that for β = Arctg ç ÷ , a modulus extremum T(β) (called main shear è Txz ø load flux) is reached that is equal to:

f7

l T(β) l =

Txz 2 + Tyz 2

Example: if shear load fluxes Txz and Tyz are equal, then the maximum shear load flux is located in the plane with a direction β = 45°. Its modulus equals

© AEROSPATIALE - 1999

MTS 006 Iss. B

2 Txy (or

2 Tyz).

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B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 1/9

4 . EXAMPLE Let a T300/BSL914 laminate (new) be laid up as follows: 0°: 1 ply 45°: 1 ply 135°: 1 ply 90°: 1 ply Stacking from the external surface being as follows: 0°/45°/135°/90°. 0° 45° 135° 90°

Mechanical properties of the unidirectional fibre are the following: El = 13000 hb (130000 MPa) Et = 465 hb (4650 MPa) νlt = 0.35 νtl = 0.0125 Glt = 465 hb (4650 MPa) ep = 0.13 mm e = 0.52 mm The purpose of this example is to search for interlaminar shear stresses in the laminate, knowing that it is subject to the following shear load flux: Txz = 0.7 daN/mm

z

y

Txz = 0.7 daN/mm x

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MTS 006 Iss. B

Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 2/9

Knowing the mechanical properties of the unidirectional fibre, elasticity moduli of each fibre should be calculated in direction x. {f1} For the fibre at 90°: k = 1. E1 = Et = 465 hb (4650 MPa) For the fibre at 135: k = 2 E2 =

1 4

0.707 0.707 + 13000 465

4

0.0125 ö æ 1 + 0.707 2 0.707 2 ç − 2 ÷ è 465 13000 ø

E2 = 925 hb (9250 MPa) For the fibre at 45°: k = 3 E3 = 925 hb (9250 MPa) For the fibre at 0°: k = 4 E4 = El = 13000 hb (130000 MPa)

1st step: Analysis of the position of neutral axis zg {f2}

zg =

465 (0.13 2 − 0 2 ) + 925 (0.26 2 − 0.13 2 ) + 925 (0.39 2 − 0.26 2 ) + 13000 (0.522 − 0.39 2 ) 2 ( 465 (0.13 − 0) + 925 (0.26 − 0.13) + 925 (0.39 − 0.26 ) + 13000 (0.52 − 0.39 ))

zg = 0.42 mm

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Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 3/9

z

z4 = 0.52 z3 = 0.39 z2 = 0.26

zg = 0.42

z1 = 0.13 z0 = 0

2nd step: Analysis of the laminate bending stiffness El with relation to the neutral axis {f3}

El = 465

925

(0.26 − 0.13 ) 3 (0.13 − 0) 3 + 925 + 12 12 (0.52 − 0.39 ) 3 (0.39 − 0.26 ) 3 + 13000 + 12 12 2

ö æ 0.13 + 0 − 0.42 ÷ + 465 (0.13 − 0) ç 2 ø è 2

ö æ 0.26 + 0.13 − 0.42 ÷ + 925 (0.26 − 0.13) ç 2 ø è 2

ö æ 0.39 + 0.26 − 0.42 ÷ + 925 (0.39 − 0.26) ç 2 ø è ö æ 0.52 + 0.39 − 0.42 ÷ 13000 (0.52 − 0.39) ç 2 ø è

2

El = 0.085134 + 0.169352 + 0.169352 + 2.380083 + 7.618211 + 6.087656 + 1.085256 + 2.07025 El = 19.67 daN.mm

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Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 4/9

3rd step: Analysis of static moments E W k (with relation to the neutral line) at the base and center of each ply. At the top of ply at 0° {f4} E W 4 = 0 daN z

0° 45° 135° 90°

y

At the center of ply at 0° {f5} ö æ 0.52 + 0.39 − 0.42 ÷ − E W 4 = 13000 (0.52 − 0.39 ) ç 2 ø è ö æ 0.52 + 0.39 0.39 ö æ 0.52 + 0.39 − 0.39 ÷ ç + − 0.42 ÷ 13000 ç 4 2 2 øè ø è

E W 4 = 59.15 - 2.11 E W 4 = 57.04 daN z

0°

y

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Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 5/9

At the base of ply at 0° {f4} ö æ 0.52 + 0.39 − 0.42 ÷ E W 4 = 13000 (0.52 − 0.39 ) ç 2 ø è

E W 4 = 59.15 daN z

0°

y

At the center of ply at 45° {f5} ö ö æ 0.52 + 0.39 æ 0.39 + 0.26 − 0.42 ÷ + 925 (0.39 − 0.26 ) ç − 0.42 ÷ E W 3 = 13000 (0.52 − 0.39) ç 2 2 ø ø è è ö æ 0.39 + 0.26 0.26 ö æ 0.39 + 0.26 − 925 ç − 0.26 ÷ ç + − 0.42 ÷ 2 2 2 øè ø è

E W 3 = 59.15 - 11.42 + 7.67 E W 3 = 55.4 daNp z

45° y

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Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 6/9

At the base of ply at 45° {f4} æ 0.52 + 0.39 ö æ 0.39 + 0.26 ö − 0.42 ÷ + 925 (0.39 − 0.26 ) ç − 0.42 ÷ E W 3 = 13000 (0.52 − 0.39) ç 2 2 è ø è ø

E W 3 = 59.15 - 11.42 E W 3 = 47.73 daN z

45° y

At the center of ply at 135° {f5} æ 0.52 + 0.39 ö æ 0.39 + 0.26 ö − 0.42 ÷ + 925 (0.39 − 0.26 ) ç − 0.42 ÷ + E W 2 = 13000 (0.52 − 0.39) ç 2 2 è ø è ø ö æ 0.26 + 0.13 − 0.42 ÷ − 925 (0.26 − 0.13) ç 2 ø è ö æ 0.26 + 0.13 0.13 ö æ 0.26 + 0.13 − 0.13 ÷ ç + − 0.42 ÷ 925 ç 4 2 2 øè ø è

E W 2 = 59.15 - 11.42 - 27.06 + 15.48 E W 2 = 35.35 daN z

135° y

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MTS 006 Iss. B

Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 7/9

At the base of ply at 135° {f4} æ 0.52 + 0.39 ö æ 0.39 + 0.26 ö − 0.42 ÷ + 925 (0.39 − 0.26 ) ç − 0.42 ÷ + E W 2 = 13000 (0.52 − 0.39) ç 2 2 è ø è ø æ 0.26 + 0.13 ö − 0.42 ÷ 925 (0.26 − 0.13 ) ç 2 è ø

E W 2 = 59.15 - 11.42 - 27.06 E W 2 = 19.87 daN z

135° y

At the center of ply at 90° {f5} æ 0.52 + 0.39 ö æ 0.39 + 0.26 ö − 0.42 ÷ + 925 (0.39 − 0.26 ) ç − 0.42 ÷ + E W 1 = 13000 (0.52 − 0.39 ) ç 2 2 è ø è ø ö ö æ 0.26 + 0.13 æ 0.13 + 0 − 0.42 ÷ + 465 (0.13 − 0) ç − 0.42 ÷ − 925 (0.26 − 0.13) ç 2 2 ø ø è è ö æ 0.13 + 0 0 ö æ 0.13 + 0 − 0÷ ç + − 0.42 ÷ 465 ç 4 2 2 øè ø è

E W 1 = 59.15 - 11.42 - 27.86 - 21.46 + 11.71 z

E W 1 = 10.12 daN

90°

© AEROSPATIALE - 1999

MTS 006 Iss. B

y

Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

At the base of ply at 90° {f4} E W 1 = 0 daN z

90°

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MTS 006 Iss. B

y

F

4 8/9

Composite stress manual

B

MONOLITHIC PLATE - TRANSVERSAL SHEAR Example

F

4 9/9

4th step: calculation of maximum interlaminar shear stress In the example given, it is located at the point where the static moment is maximum, i.e. at the base of the ply at 0°. Its value equals at E W 0 = 59.15 daN, which gives stress τxz0: {f6} τxz0 =

0.7 x 59.15 = 2.1 hb (21 MPa) 19.67

If these interlaminar shear stresses are analysed for each fibre, stresses are distributed along the laminate thickness as follows: τxzk =

0.7 E Wk 19.67 0.52

0.455

0.39

0.325

z (mm)

0.26

0.195

0.13

0.065

0 0

0.5

1

1.5

τ (hb)

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2

2.5

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MONOLITHIC PLATE - TRANSVERSAL SHEAR References

F

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials

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Composite stress manual

G MONOLITHIC PLATE - FAILURE CRITERIA

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Composite stress manual

FAILURE CRITERIA Notations

1 . NOTATIONS σl (σl): longitudinal stress in unidirectional fibre σt (σ2): transversal stress in unidirectional fibre τlt (σ6): shear stress in unidirectional fibre εl (εl): longitudinal strain in unidirectional fibre εt (ε2): transversal strain in unidirectional fibre γlt (ε6): shear strain in unidirectional fibre Rl: allowable longitudinal stress Rlt: allowable longitudinal tension stress Rlc: allowable longitudinal compression stress Rt: allowable transversal stress Rtt: allowable transversal tension stress Rtc: allowable transversal compression stress S: allowable shear stress

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G

1

Composite stress manual

FAILURE CRITERIA Inventory

G

2

2 . INVENTORY OF STATIC FAILURE CRITERIA The purpose of this chapter is to describe various failure criteria of the unidirectional fibre within a laminate. The following criteria shall be presented in chronological order (this is not an exhaustive list): - maximum stress criterion - maximum strain criterion - Norris and Mac Kinnon's criterion - Puck's criterion - Hill's criterion - Norris's criterion - Fischer's criterion - Hoffman's criterion - Tsaï - Wu's criterion For three-dimensional criteria, we shall assume that the composite material is subjected to the following stress tensor and strain tensor: (σ) = (σ1, σ2, σ3, σ4, σ5, σ6) (ε) = (ε1, ε2, ε3, ε4, ε5, ε6)

For two-dimensional criteria, we shall assume that the unidirectional fibre is subjected to the following stress tensor and strain tensor: (σlt) = (σl, σt, τlt) (εlt) = (εl, εt, γlt)

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Composite stress manual

FAILURE CRITERIA Maximum stress criterion

G

2.1

2.1 . Maximum stress criterion This criterion is applicable for orthotropic materials only. The criterion anticipates failure of the material if: for 1 ≤ i ≤ 6 g1

σi = Xi

for tension stresses

or σi = - X'i

for compression stresses

For the two-dimensional case, the failure envelope may be represented as follows:

σt

σl

τlt

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Composite stress manual

FAILURE CRITERIA Maximum strain criterion

G

2.2

2.2 . Maximum strain criterion This criterion is applicable for orthotropic materials only. The criterion anticipates failure of the material if: for 1 ≤ i ≤ 6 g2

εi = Yi

for tension strains

or εi = - Y'i

for compression strains

For the two-dimensional case, the failure envelope may be represented as follows:

εt

εl

γlt

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Composite stress manual

FAILURE CRITERIA Norris and Mac Kinnon's criterion

G

2.3

2.3 . Norris and Mac Kinnon's criterion This criterion is valid for any material. The criterion anticipates failure of the material if:

å

6

1

C i (σ i ) 2 = 1

Coefficients Ci depend on the material used. For the two-dimensional case, the expression becomes: g3

C1 (σl)2 + C2 (σt)2 + C6 (τlt)2 = 1 The failure envelope may be represented as follows: σt

σl

τlt

This is the first criterion which calls for stress dependency.

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MTS 006 Iss. B

Composite stress manual

FAILURE CRITERIA Puck's criterion

G

2.4

2.4 . Puck's criterion This two-dimensional criterion is valid for orthotropic materials only. The criterion anticipates failure of the material if: σ1 = X1

for tension stresses

or σ1 = - X'1

for compression stresses

and 2

g4

2

2

æτ ö æ σ1 ö æσ ö ç ÷ + ç 2 ÷ + ç 12 ÷ = 1 è X1 ø è X2 ø è X6 ø

Coefficients X1, X2 and X6 depend on the material used. σt

σl

τlt

Accuracy close to that of Norris and Mac Kinnon's criterion.

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MTS 006 Iss. B

Composite stress manual

FAILURE CRITERIA Hill's criterion

G

2.5

2.5 . Hill's criterion This criterion is valid for orthotropic materials or for slightly anisotropic materials only. The criterion anticipates failure of the material if: F (σ2 - σ3)2 + G (σ3 - σ1)2 + H (σ1 - σ2)2 + L (σ4)2 + M (σ5)2 + N (σ6)2 = 1 Coefficients F, G, H, L, M and N depend on the material used. For a two-dimensional analysis, the expression becomes: g5

F (σt)2 + G (σl)2 + H (σl - σt)2 + N (τlt)2 = 1

σt

σl

τlt

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Composite stress manual

FAILURE CRITERIA Norris's criterion

G

2.6

2.6 . Norris's criterion This two-dimensional criterion is valid for orthotropic materials only. The criterion anticipates failure of the material if: F (σ2 - σ3)2 + G (σ3 - σ1)2 + H (σ1 - σ2)2 + L (σ4)2 + M (σ5)2 + N (σ6)2 = 1 and for 1 ≤ i ≤ 6 σi = Xi

for tension stresses

or σi = - X'i

for compression stresses

Coefficients F, G, H, L, M and N depend on the material used. For a two-dimensional analysis, the expression becomes: g6

F (σt)2 + G (σl)2 + H (σl - σt)2 + N (τlt)2 = 1 - X'1 ≤ σl ≤ X1 and - X'2 ≤ σt ≤ X2 and - X'6 ≤ τlt ≤ X6

σt

σl

τlt

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MTS 006 Iss. B

Composite stress manual

FAILURE CRITERIA Fischer's criterion

G

2.7

2.7 . Fischer's criterion This two-dimensional criterion is valid for orthotropic materials only. The criterion anticipates failure of the material if: 2

g7

2

2

æτ ö æ σl ö æσ ö σ σ ç ÷ + ç t ÷ − K l t + ç lt ÷ = 1 X1 X 2 è X 6 ø è X1 ø è X2 ø

Coefficients X1, X2 and X6 depend on the material used. σt

σl

τlt

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Composite stress manual

FAILURE CRITERIA Hoffman's criterion FAILURE CRITERIA

G

2.8

2.8 . Hoffman's criterion This criterion is valid for orthotropic materials only. The criterion anticipates failure of the material if: C1 (σ2 - σ3)2 + C2 (σ3 - σ1)2 + C3 (σ1 - σ2)2 + C4 (σ4)2 + C6 (σ6)2 + C5 (σ5)2 + C'1 σ1 + C'2 σ2 + C'3 σ3 = 1 Coefficients C1, C2, C3, C4, C5, C6, C'1, C'2 and C'3 depend on the material used. For a two-dimensional analysis, the expression becomes: g8

C1 (σt)2 + C2 (σl)2 + C3 (σl - σt)2 + C6 (τlt)2 + C'1 σl + C'2 σt = 1 σt

σl

τlt

Very good tension accuracy, but very bad compression results.

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Composite stress manual

FAILURE CRITERIA Tsaï - Wu's criterion

G

2.9

2.9 . Tsaï - Wu's criterion This criterion intends to be as general as possible and then, there is, a priori, no particular hypothesis. This criterion anticipates failure of the material if: For 1 ≤ i ≤ 6 Σ Fi σi + Σ Fij σi σj + Σ Fijk σi σj σk + … = 1 For a two-dimensional analysis, there is: g9

F1 σl + F2 σt + F6 τlt + F11 (σl)2 + F22 (σt)2 + F66 (τlt)2 + 2 F12 σl σt + 2 F26 σt τlt + 2 F16 σl τlt = 1 Coefficient F1, F2, F6, F11, F22, F66, F12, F26 and F16 depend on the material used.

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Composite stress manual

FAILURE CRITERIA

G

Aerospatiale's criterion

3 1/2

3 . Failure criterion used at Aerospatiale: Hill's criterion As seen previously, Hill's criterion is, in its general form, formulated as follows: F (σt)2 + G (σl)2 + H (σl - σt)2 + N (τlt)2 = 1 This non-interactive criterion is applicable at the elementary ply only. There is a laminate failure when the most highly loaded layer is broken. If the expression is developed, we obtain: (G + H) (σt)2 + (F + H) (σl)2 - 2 H σl σt + N (τlt)2 = 1 By definition, we shall assume that: (G + H) = (1/Rl)2 where Rl is the longitudinal strength of the unidirectional fibre. (F + H) = (1/Rt)2 where Rt is the transversal strength of the unidirectional fibre. 2 H = (1/Rl)2 N = (1/S)2 where S is the shear strength of the unidirectional fibre.

g10

æσ ö There is a failure if h = ç l ÷ è Rl ø

© AEROSPATIALE - 1999

2

2

æσ ö + ç t÷ è Rt ø

2

æτ ö + ç lt ÷ è Sø

MTS 006 Iss. B

2

æσ σ ö − ç l 2 t÷ = 1 è Rl ø

Composite stress manual

FAILURE CRITERIA Aerospatiale's criterion

G

3 2/2

Thus, the following Reserve Factor is deduced: g11

RF =

1 = h

1 2

2

2 æ σl σ t ö æ σt ö æ σl ö æ τ lt ö + + ÷ ç ÷ ç ÷ ç ÷ +ç 2 è Sø è Rl ø è Rt ø è Rl ø

This criterion is the one used by Aerospatiale. In order to avoid having a premature theoretical failure in the resin, the transversal modulus Et was considerably reduced (by a coefficient 2 approximately) with relation to the average values measured. This "design" value is determined so that the transversal strain is greater than the longitudinal one.

B

The allowable plane shear value S of the unidirectional fibre was determined for having, a good test/calculation correlation and significant tension and compression failures of notched or unnotched laminates.

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FAILURE CRITERIA Example

G

4 1/4

4 . EXAMPLE Hill's criterion shall be applied to the example considered in the chapter "plain plate membrane". Stresses applied to fibres are calculated and presented in the corresponding chapter (C.6) and quoted in the following pages. Let a T300/BSL914 laminate (new) be laid up as follows: 0°: 6 plies 45°: 4 plies 135°: 4 plies 90°: 6 plies Mechanical properties of the unidirectional fibre are the following: El = 13000 hb (130000 MPa) Et = 465 hb (4650 MPa) νlt = 0.35 Glt = 465 hb (4650 MPa) Rlt = 120 hb (1200 MPa) Rlc = 100 hb (1000 MPa) Rtt = 5 hb (50 MPa) Rtc = 12 hb (120 MPa) S = 7.5 hb (75 MPa) The laminate is globally subjected to the three following load fluxes in the reference coordinate system (x, y) (see chapter C.6) : Nx = 30.83 daN/mm Ny = - 2.22 daN/mm Nxy = 44.92 daN/mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

FAILURE CRITERIA Example

Reminder of stresses applied to the fibre with a 0° direction σl = 29.42 hb σt = 0.06 hb τlt = 5.03 hb {g10} 2

2

2

æ 29.42 ö æ 0.06 ö æ 5.03 ö æ 29.42 x 0.06 ö h = ç ÷ +ç ÷ +ç ÷ −ç ÷ =1 120 2 è 120 ø è 5 ø è 7 .5 ø è ø 2

h2 = 0.06 + 1.44 E-4 + 0.45 - 1.23 E-4 = 0.51

{g11} Reserve Factor: R.F. =

1 h2

=

1 0.51

= 14 .

Margin = 100 (R.F. - 1) ≈ 40 %

Reminder of stresses applied to the fibre with a 45° direction σl = 80.17 hb σt = - 1.14 hb τlt = - 1.36 hb {f10} æ 80.17 ö h2 = ç ÷ è 120 ø

2

. ö æ − 114 + ç ÷ è 12 ø

2

. ö æ − 136 + ç ÷ è 7.5 ø

2

. )ö æ 80.17 x (− 114 − ç ÷ 2 è ø 120

h2 = 0.45 + 0.009 + 0.033 + 0.006 = 0.498

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MTS 006 Iss. B

G

4 2/4

Composite stress manual

FAILURE CRITERIA Example

{g11}

Reserve Factor: R.F. =

1 0.498

= 142 .

Margin ≈ 42 %

Reminder of stresses applied to the fibre with a 135° direction σl = - 59.17 hb σt = 2.14 hb τlt = 1.36 hb {g10} æ − 59.17 ö h2 = ç ÷ è 100 ø

2

æ 2.14 ö + ç ÷ è 5 ø

2

. ö æ 136 + ç ÷ è 7.5 ø

2

æ − 59.17 x 2.14 ö − ç ÷ è ø 100 2

h2 = 0.35 + 0.183 + 0.033 + 0.0126 = 0.579

{g11} Reserve Factor: R.F. =

1 0.579

= 131 .

Margin ≈ 31 %

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4 3/4

Composite stress manual

FAILURE CRITERIA Example

Reminder of stresses applied to the fibre with a 90° direction σl = - 8.42 hb σt = 0.95 hb τlt = - 5.03 hb {g10} æ − 8.42 ö h = ç ÷ è 100 ø

2

2

æ 0.95 ö + ç ÷ è 5 ø

2

æ − 5.03 ö + ç ÷ è 7.5 ø

2

æ − 8.42 x 0.95 ö − ç ÷ è ø 100 2

h2 = 0.007 + 0.036 + 0.45 + 8 E-4 = 0.494

{g11} Reserve Factor: R.F. =

1 0.494

= 142 .

Margin ≈ 42 %

Conclusion: the laminate overall margin is therefore 31 %

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4 4/4

Composite stress manual

MONOLITHIC PLATE - FAILURE CRITERIA References

G

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials Comparative analysis of composite material damaging criteria BOUNIE, Failure criteria of mechanical bonds in composite materials, 1991, 440.180/91

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H MONOLITHIC PLATE - FATIGUE ANALYSIS

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I MONOLITHIC PLATE - DAMAGE TOLERANCE

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MONOLITHIC PLATE - DAMAGE TOLERANCE Notations

1 . NOTATIONS (o, x, y): panel reference frame Nx: x-direction normal flow Ny: y-direction normal flow Nxy: shear flow α i: orientation of fibre “i” εli: longitudinal strain of fibre “i” εti: transverse strain fibre “i” γlti: angular slip of fibre “i” εadm: permissible longitudinal strain of unidirectional fibre γadm: permissible slip of unidirectional fibre σli: longitudinal stress of fibre “i” σti: transverse stress of fibre “i” τlti: shear stress of fibre “i” Rl: permissible longitudinal stress of unidirectional fibre Rt: permissible transverse stress of unidirectional fibre S: permissible shear stress of unidirectional stress κR: reduction coefficient for permissible longitudinal stress κS: reduction coefficient for permissible shear stress

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I

1

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Introduction

I

2

2 . INTRODUCTION The regulatory requirements in terms of structural justification concern, on the one hand, the static strength JAR § 25.305 and, on the other hand, fatigue + damage tolerance JAR § 25.571. For the latter, three cases are to be considered: - § 25.571 (b) Damage tolerance - § 25.571 (c) Safe-life evaluation * § 25.571 (d) Discrete Source For the static strength evaluation, Acceptable Means of Compliance ACJ 25.603 § 5.8 requests resistance to ultimate loads with "realistic" impact damage susceptible to be produced in production and in service. This damage must be at the limit of the detectability threshold defined by the selected inspection procedure. Also, static strength must be demonstrated after application of mechanical fatigue (§ 5.2) and test specimens must have minimum quality level, that is, containing the permissible manufacturing flaws (§ 5.5) and "realistic" impact damage. The static strength range is defined therefore for a detection threshold and by a "realistic" cut-off energy leading to "realistic" impacts. The damage tolerance range is outside the static range. Detection threshold (impact depth in mm) Damage at detectability threshold limit

Damage Tolerance Range

Low thickness

Static strength range

High thickness Impact energy

Static cut-off energy

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MONOLITHIC PLATE - DAMAGE TOLERANCE Introduction

I

2 3 3.1

Distinction is made between the range above the detectability threshold where all damage will be detectable and the range above the static cut-off energy and below the detectability threshold where the damage will never be detected. In this "Damage tolerance" section, we shall discuss both manufacturing defects and impact damage for the static justification and the fatigue-damage tolerance justification. The basic assumption to be retained is the fatigue damage no-growth concept.

3 . DAMAGE SOURCES AND CLASSIFICATION Distinction is made between damage which may occur during manufacture and that which occurs in service.

3.1 . Manufacturing damage of flaws Manufacturing damage or flaws include porosities, microcracks and delaminations resulting from anomalies, during the manufacturing process and also edge cuts, unwanted routing, surface scratches, surface folds, damage attachment holes and impact damage (see § 3.2.3). Damage, outside of the curing process, can occur a detail part or component level during the assembly phases or during transport or on flight line before delivery to the customer. If manufacturing damage/flaws are beyond permissible limits, they must be detected by routine quality inspections. For all composite parts, the acceptance/scrapping criteria must be defined by the Design Office. Acceptable damage/flaws are incorporated into the ultimate load justification by analysis and into the test specimens to demonstrate the tolerance of the structure to this damage throughout the life of the aircraft.

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Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Fatigue damage

I

3.2 3.2.1

3.2 . In-service damage This damage occurs in service in a random manner. Distinction is made between three types of damage: - fatigue, - corrosion and environmental effects, - accidental.

3.2.1 . Fatigue damage Composite materials are said to be insensitive to fatigue; more exactly, their mechanical properties are such that the static dimensioning requirements naturally cover the fatigue dimensioning requirements. This is valid for a laminate submitted to plane loads, less than 60 % of ultimate load. However, complex areas or areas with a sudden variation in rigidity may favour the appearance of delaminations under triaxial loads. Today, it is very difficult to (analytically or numerically) model the growth rate of a possible flaw. This is why a "safe-life" justification philosophy has been adopted. It is based on two principles which must be underpinned by experimental results: - non-creation of fatigue damage (endurance), - no-growth of damage of tolerable size. On account of the dispersion proper to composites and the form of the "Wohler" curves associated with them (relatively flat curve with low gradient), the factor 5 normally used on metallic structures for the number of lives to be simulated during a fatigue test, was replaced by a load factor. All these points will be discussed in detail in section O (MONOLITHIC PLATE FATIGUE).

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MONOLITHIC PLATE - DAMAGE TOLERANCE Corrosion damage - Environmental effects

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3.2.2

3.2.2 . Corrosion damage and environmental effects a) Corrosion Composites are insensitive to corrosion. Nevertheless, their association with certain metallic materials can cause galvanic coupling liable to damage certain metal alloys. For information purposes, the table below shows various carbon/metal pairs over a scale ranging from A to E. We consider that type A and B couplings are correct and that those of types C, D and E

Coupling with carbon to be avoided

Coupling with carbon correct

are not.

A

Anodised titanium, protected titanium fasteners

A

Titanium and gold, platinium and rhodium alloys

B

Chromiums, chrome-plated parts

B

Passivated austenitic stainless steels

B

Monel, inconel

B

Martensitic stainless steels

C

Ordinary steels, low alloys steels, cast irons

D

Anodic or chemically oxidised aluminium and light alloys

D

Cadmium and cadmium-plated parts

D

Aluminium and aluminium-magnesium alloys

D

Aluminium-copper and aluminium-zinc alloys

b) Environmental effects At high temperatures, aggressions by hydraulic fluids may cause damage such as separation, delamination, translaminar cracks, etc. Rain can cause damage by erosion, etc. All these points will be discussed in detail in section W (INFLUENCE OF THE ENVIRONMENT).

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MONOLITHIC PLATE - DAMAGE TOLERANCE Accidental damage - Inspection of damage

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3.2.3 4

3.2.3 . Accidental damage This is the most important type of damage and the damage most liable to call into question the structural strength of the part. It can occur during the manufacture of the item (drilling delamination) or in service (drop of a maintenance tool, hail or bird strikes).

4 . INSPECTION OF DAMAGE One of the main preoccupations concerning the damage tolerance of composites is damage detection. This is true both during manufacture and in service. In service, the detectability threshold depends on the type of scheduled in-service inspection. There are four types of inspections: Inspection - Special detailed (ref: Maintenance Program Development: MPD): An intensive examination of a specific location similar to the detailed inspection except for the following differences. The examination requires some special technique such as non-destructive test techniques, dye penetrant, high-powered magnification, etc., and may required disassembly procedures. This type of inspection is mainly conducted during production but can be used exceptionally in service. Inspection - Visual Detailed (ref: Maintenance Program Development: MPD): An intensive visual examination of a specified detail, assembly, or installation. It searches for evidence of irregularity using adequate lighting and, where necessary, inspection aids such as mirrors, hand lens, etc. Surface cleaning and elaborate access procedures may be required. This type of inspection enables BVID (Barely Visible Impact Damage) to be detected.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Inspection of damage

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4 4.1 4.2

Inspection - General Visual (ref: Maintenance Program Development: MPD): A visual examination that will detect obvious unsatisfactory conditions/discrepancies. This type of inspection may require removal of fillets, fairings, access panels/doors, etc. Workstands, ladders, etc. may be required to gain access. Inspection - Walk Around Check (ref: Maintenance Review Board Document: MRB): A visual check conducted from ground level to detect obvious discrepancies.

In general, the Walk Around check is considered as a general daily visual inspection.

4.1. Minimum damage detectable by a Special Detailed Inspection These inspections are conducted with bulky facilities: ultrasonic, thermographic, X-rays, etc. Minimum detectable sizes are related to the size of the U.S. probes and the accuracy of the tools used, etc.

4.2 . Minimum damage detectable by a Detailed Visual Inspection This type of damage is called BVID (Barely Visible Impact Damage). The geometrical detectability criteria are as follows (cf. ref. 22S 002 10504):

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Depth of flaw "δ δ"

Inside box structure (broken fibres)

Outside box structure

Mean

0.1 mm

0.3 mm

"A" value

0.2 mm

0.5 mm

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MONOLITHIC PLATE - DAMAGE TOLERANCE Inspection of damage

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4.3 4.4

4.3 . Minimum damage detectable by a General Visual Inspection This type of damage is called Minor VID (Minor Visible Impact Damage). The geometrical detectability criteria are as follows (cf. ref. 22S 002 10504):

Depth of flaw "δ δ"

Size of perforation

2 mm or thickness of structure if < 2 mm

20 mm ∅

4.4 . Minimum damage detectable by a Walk Around Check This type of damage is called Large VID (Large Visible Impact Damage). The geometrical detectability criteria are not explicitly defined but the damage must be detectable without ambiguities during a Walk Around Check. We generally use a 50/60 mm ∅ perforation as criterion. The diagram below summarises these four detectability levels according the size of the damage. Special detailed inspection

Detailed visual inspection

General visual inspection

BVID

Depth of indent

δ = 0.3 mm

Minor VID

Large VID

δ = 2 mm 20 mm ∅

diameter

Walk around

50/60 mm ∅

In the remainder of this document, we will consider only visual inspections.

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Size of damage

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Classification of damage

I

4.5

4.5 . Classification of accidental damage by detectability ranges Depending on the type of visual inspection considered during the maintenance phases (general or detailed), we will define three clearly separate detectability ranges: a) Damage undetectable by visual means used in service. b) Damage susceptible to be detected during in-service inspections. c) Damage "inevitably" detectable that can be placed into two categories: - Readily detectable damage. - Obvious detectable damage. These ranges are positioned as follows on the previously defined detectability scale: → For Detailed Visual Inspection: Damage susceptible to be detected

Undetectable damage DVI

Inevitably detectable damage WA

BVID

Minor VID

Large VID

→ For General Visual Inspection: Damage susceptible to be detected

Undetectable damage

BVID

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GVI

WA

Minor VID

Large VID

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MONOLITHIC PLATE - DAMAGE TOLERANCE Influence of damage - Porosity

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4.5 5 5.1 5.1.1

Remark: Note that certain authors define the BVID notion according to the type of inspection selected. In this case, for a general inspection: MINOR VID ≡ BVID In our document, we will conserve the initial definition related to the visual detailed inspection.

5 . EFFECT OF FLAWS/DAMAGE ON MECHANICAL CHARACTERISTICS 5.1 . Health flaws 5.1.1 . Porosity → Description

By "porosity", we mean a heterogeneity of the matrix leading, more often than not, to lack of inter- or intra-layer cohesion, generally small in size, but distributed uniformly or almost throughout the complete thickness of the laminate. Note that for unidirectional tapes the porosities have a tendency to be located between the layers whereas, for fabrics, they are more generally located where the weft and warp threads cross. The porosity ratio given is a surface porosity ratio measured by the ultrasonic attenuation method. The permissible absorption level is fixed at 12 dB irrespective of the thickness inspected (cf. note 440.241/90 issue 2 - SIAM curve). All absorption areas above this limit will be considered as a delamination and meet therefore the same criteria as a delamination. However, only T300/N5208, more fluid than T300/BSL914 has a higher tendency to be porous.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Porosity

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5.1.1

→ Loss of mechanical characteristics due to porosity The test results were interpolated, for the V10F wing, on T300/N5208 with various porosity ratios distributed in all interply areas to determine the influence on the mechanical characteristics for a 3 % ratio considered as the acceptable limit. This ratio combined with the fatigue, ageing and residual test effects at 80° C, led to the following losses in mechanical characteristics:

T300/N5208

3 % porosity Loss of characteristics after F + VC1 + 80° C

Loss of characteristics after F + VC1 + 80° C

BENDING

- 15 %

- 19 %

INTERLAMINAR SHEAR

- 47 %

- 33.5 %

COMPRESSION

- 20 %

- 19 %

TENSILE (high bearing stress) joint not supported

- 20 %

- 19 %

→ Example of porosity acceptance criteria The 3 % acceptance criterion appears therefore as being non-conservative for interlaminar shear. However, let us recall: - that the spar boxes of the wings, movable surfaces or fin are subjected to very low interlaminar stresses, - only T300/N5208 had porosities, - that the 3 % porosity criterion distributed at all interply areas is today no longer applied to primary structures. The permissible porosity ratio depends on the thickness of the laminate.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations outside stiffener

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5.1.2 5.1.2.1 1/5

5.1.2 . Delaminations

A delamination is a lack of cohesion between the layers caused by a shear or transverse tensile failure of the resin or, more simply, by forgetting a foreign body.

5 1.2.1 . Delaminations outside stiffener Þ Skin bottom areas → Description A skin bottom delamination is a lack of cohesion between two well-defined plies. Natural delaminations appear during manufacture (surface contamination). A foreign body left in the laminate (separator) will be considered as a delamination.

→ Loss of characteristics due to a delamination For the V10F wing, a lack of interlayer cohesion up to 400 mm2 leads to a loss of compression strength of around 10 % for the two materials (T300/N5208 and T300/BSL914) tested in new condition at θ = 80° C. In aged/fatigue condition the drop in strength is 20 % for T300/N5208 and 13 % for T300/BSL914 in relation to the new state/80° C reference. Fatigue leads to no growth of the flaw.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations outside stiffener

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5.1.2.1 2/5

Þ Fastener areas → Description As for the skin bottom delaminations, the lack of cohesion in these areas occurs between two well-defined plies, sometimes at several levels but generally adjacent. These flaws come through to the bore. They are created during the drilling operations. The ultrasonic inspections conducted after each test case showed no evolution of existing flaws. The parameter representing the size of the damage is the number given by: φ =

damage ∅ fastener ∅

damage Ø fastener Ø

Vb Vc where Vb represents the "B value" (see section Y) relevant to all tests characterising the material and where Vc is the calculation value used. Provided that the calculation value is lower than the "B value", the integrity of the item is ensured. For safety reasons, we will impose a minimum margin of 10 % between the calculated value and the "b value".

The parameter representing the drop in characteristics is the number given by: ν =

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5.1.2.1 3/5

Two cases can occur: - if ν ≥ 1.1: no reduction will be made on the initial reserve factor RF, - if ν < 1.1: after reduction, the new reserve factor is equal to RF’ = RF

ν 1.1

The values of ν are given by the graphs in section Z for the prepreg epoxy carbon fibre T300/914. Generally speaking, the graphs gives the values of ν for the flaw (delamination) but also for repairs which may be made on it (injection of resin, NAS cup). They enable you to find therefore: - whether the flaw is acceptable as such, - what type of repair is to be chosen.

→ Examples of acceptance and concession criteria - in standard area, the delamination must be covered by a concession if its surface area is greater than: S mm2

75

120

160

285

440

440

Ø

3.2

4.1

4.8

6.35

7.92

9.52

These permissible delamination values are valid only for isolated delaminations. For delaminated hole concentrations and irrespective of the size of the delaminations, the flaw must be covered by a concession if: - for aligned fasteners, more than 20 % of the holes are delaminated and/or two flaws are less than 5 fastener pitches apart, - for a delamination at a fastener or of another skin bottom area, they are less than 120 mm apart. - in designated area, permissible delamination is defined as follows: S mm2

50

80

110

200

400

400

Ø

3.2

4.1

4.8

6.35

7.92

9.52

These permissible delamination values are valid only for isolated delaminations.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations outside stiffener

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5.1.2.1 4/5

For delaminated hole concentrations and irrespective of the size of the delaminations, the flaw must be covered by a concession if: - for aligned fastener, more than 10 % of the holes are delaminated and/or two flaws are less than 5 fastener pitches apart, - for a delamination at a fastener or of another skin bottom area, they are less than 120 mm apart. - for areas with several fastener rows: • if the fasteners are on same row: same as above, • if the flaws are located on several rows, they must be covered by a concession if they are less than 175 mm apart.

→ Examples of repairs to be made The table below summarises the repair solutions to be applied when delaminations are detected at fastener holes in materials T300/914, G803/914 and HTA/EH25 depending on the loads and the damage ∅ ratio. fastener ∅

The choice of the solution is governed by the following rules: - for a pure load, the repair or untreated delamination must resist ultimate loads under the most severe environmental conditions, - for a pure bearing stress test, the calculation value Vc is taken as reference. The Vb repair will not be acceptable if is lower than 1. Vc The validation range of the acceptable solutions given in the table below is damage ∅ ≤ 6. fastener ∅

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations outside stiffener

Load

Condition

Untreaded Injection via delamination vent hole

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5.1.2.1 5/5

Normal injection

NAS cup

New

Acceptable

Unacceptable

-

-

Aged-wet

Acceptable

Unacceptable

-

Acceptable

Acceptable

-

Acceptable

-

Acceptable

Pure tensile Acceptable New

damage ∅

< 4

fastener ∅

Bearing Tensile

Acceptable Aged-wet

damage ∅

< 4.5

fastener ∅

Acceptable damage ∅

< 4.5

fastener ∅

Acceptable New

Unacceptable Unacceptable Unacceptable

damage ∅

< 5

fastener ∅

Pure compression

Acceptable Aged-wet

Unacceptable Acceptable

New

damage ∅

< 4.75

fastener ∅

Bearing compression

damage ∅

< 2.5

fastener ∅

Acceptable

damage ∅

< 5.25

fastener ∅

Acceptable damage ∅

Acceptable

< 2

fastener ∅

Acceptable damage ∅

< 5.25

fastener ∅

Acceptable damage ∅

< 5.25

fastener ∅

Acceptable damage ∅

Unacceptable Unacceptable

Acceptable

Acceptable

Unacceptable

-

Acceptable

Acceptable

Unacceptable

-

Acceptable in "hollow"

Acceptable

Unacceptable

-

Unacceptable

Without bending

Unacceptable Unacceptable

-

Acceptable

Bending 1000 µd

Unacceptable Unacceptable

-

Acceptable in "hollow"

Bending 2500 µd

Unacceptable

-

Acceptable

Aged-wet

< 4

fastener ∅

Without bending JOINT tensile

JOINT compression

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Bending 1000 µd Bending 2500 µd

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Acceptable

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MONOLITHIC PLATE - DAMAGE TOLERANCE

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Delaminations in stiffener area

5.1.2.2 1/5

5.1.2.2 . Delaminations in stiffener area of an integrally-stiffened panel ❏ Stiffener runouts Stiffener runouts represent a critical point for dimensioning. When these stiffener runouts are made during moulding without later machining operations, these fairly tortured areas may include lacks of cohesion either in the base, or in the stiffener itself.

U-section

Half core Baseplate

U-section

Wedge

Þ Crater → Description This flaw is consecutive to too short a wedge which gives, after machining of the stiffener runout, a crater at the end of the stiffener.

L e

l

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations in stiffener area

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5.1.2.2 2/5

→ Loss of characteristics due to crater

Size of flaw

ATR 72 T300/914 L = 10 mm l = 4 mm e = 1 mm

ATR 72 HTA/EH25

Test conducted

Conditions

Loss of characteristics due to flaw

Tensile Compression (stiffener runouts not protected)

New θ = 20° C

- 28 %

Tensile Compression (stiffener runouts protected)

New θ = 20° C

0%

Compression (with reinforcement) Compression (without reinforcement)

-4% Aged θ = 70° C

- 12 %

For unprotected stiffener runouts (that is, when it was impossible to thicken the skin to make structure relatively simple to manufacture), this flaw must be covered by a concession. When it is located at protected stiffener runouts (that is with a significant skin overthickness at stiffener runout), this flaw will be covered by a concession only if its size is greater than the following values: L = 10 mm

l = 2 mm

e = 0.5 mm

Þ Punching → Description This flaw is due to an imperfect Mosite cut leading to flaws at stiffener ends.

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MONOLITHIC PLATE - DAMAGE TOLERANCE

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Delaminations in stiffener area

5.1.2.2 3/5

L e

l

e

→ Loss of characteristics due to punching

Size of flaw

Test conducted

Conditions

Loss of characteristics due to flaw

ATR 72 T300/914

Tensile Compression (stiffener runouts not protected)

New θ = 20° C

- 20 %

Tensile Compression (stiffener runouts protected)

New θ = 20° C

0%

L = 10 mm e = 1 mm

Must be covered by a concession when located at unprotected stiffener runouts. When located at protected stiffener runouts, it will be covered by a concession only if it size is greater than the following values: L = 10 mm

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l = 2 mm

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e = 0.5 mm

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations in stiffener area

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5.1.2.2 4/5

Þ Flaws "E", "B", "AB" and "BC" → Description These flaws are located at various levels: FLAW E

FLAW B

FLAW AB

Delamination in radius between U-sections and base

Delamination under wedge

Delamination at skin midthickness

Flaws BC correspond to one or more lacks of cohesion of stiffener wedge as shown on diagram below: Flaw BC A B

C Wedge

U-section Half core

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations in stiffener area

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5.1.2.2 5/5

Þ Loss of characteristics due to flaw

Type of flaw

Test conducted

Conditions

Loss of characteristics due to flaw

V10F T300/N5208 200 mm2 (flaw B)

Tensile (between wedge and base skin)

New θ = 20° C

- 17 %

ATR 72 T300/914 (flaw BC)

Tensile (unprotected stiffener runouts)

Wet ageing θ = 50° C

- 20 %

ATR 72 T300/914 (flaw BC)

Compression (unprotected stiffener runouts)

Wet ageing θ = 50° C

0%

❏ Stiffener top Lack of interlayer cohesion at top of stiffener between the U-section and the wedge does not seem to modify the mechanical characteristics.

❏ Stiffener base Lack of interlayer cohesion in stiffener base hardly modifies the mechanical characteristics. Within the scope of the V10F programme, the greatest drop is less than 10 % in standard stiffener compression case with a type BC flaw.

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Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Delamination in spar radii Delamination on edge of spar flanges

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5.1.3 5.1.4

5.1.3 . Delamination in spar radii This flaw correspond to lack of cohesion between two well-defined plies in the web/flange blend-in radius.

The maximum permissible surface area for a flaw is 100 mm2. Þ In standard areas: maximum local surface area between 2 ribs for a radius is 250 mm2, including delaminations and foreign bodies. Þ

In designated areas: maximum local surface area between 2 ribs for a radius is

150 mm2, including delaminations and foreign bodies.

5.1.4 . Delamination on spar flange edges l

L

Delamination

Delamination acceptable after repair is defined as follows : - 1 delaminated interface only, - l ≤ 5 mm, - L ≤ 25 mm. An acceptable flaw will however require a Hysol 9321 sealing operation on edge. Any other flaws shall be covered by a concession.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Foreign bodies - Translaminar cracks

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5.1.5 5.1.6

5.1.5 . Foreign bodies Same criteria as given for delaminations (cf. § 5.1.2.1).

5.1.6 . Translaminar cracks Translaminar cracks have been detected on the ATR 72 outer wing spar box, the A340 aileron, the 2000 fin, the A300/A310 (cf. note 494.048/91); however there are none on the flight V10F (cf. note 494.007/91). These are elongated flaws due to the use of a corrosive stripper (MEK, Methyl Ethyl Ketone). Currently, baltane is used. T300/914 and G803/914 have these flaws; the tests conducted on IM7/977-2 and HTA/EH25 showed no translaminar cracks (cf. note 494.056/91). These cracks are detected by ultrasonic inspection in the fastener areas (the back surface echo totally disappears). They concern all ply directions but do not touch between two plies with different orientations. It is in the high crack density area that the ultrasonic signal is totally damped. There a transition zone between this area and the healthy part of the laminate where crack density decreases and the ultrasonic back surface echo reappears. These cracks are parallel to the fibres leaving the holes. They first affect the plies at 0°, then the plies at ± 45°. Some cracks are observed in the central plies at 90°. The axes of these crack networks correspond approximately to the hole diameters. They do not lead to a drop in the mechanical characteristics (cf. note 437.115/91). The existence of flaws at fasteners can be masked by high density translaminar cracks. Therefore, the threshold of the surface areas of the translaminar cracks which must be plotted is coherent with the size of acceptable delaminations.

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MONOLITHIC PLATE - DAMAGE TOLERANCE

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Delaminations consecutive to a shock

5.1.7 1/4

5.1.7 . Delaminations consecutive to a shock (during production and in service) → Description An impact causes lack of interlayer cohesion at several levels depending on the energy of the impact. Damaged area

Delaminated area Impactor indent

→ Loss of characteristics due to a delamination Generally speaking, a composite material with a non-through delamination is much more sensitive from a structural strength viewpoint to compression or shear loads (resin) than to tensile loads (fibre). The drops in characteristics within the scope of the V10F programme are: - 18 % in tensile strength for a maximum invisible impact, - 36 % in compression strength for a maximum invisible impact. All points of the tests conducted on the V10F test specimens were plotted on the graph below (the points of the static and fatigue test specimens are combined on this curve as it has been demonstrated that the ageing effect is not significant for damage tolerance). The curve used at Aerospatiale for the new states/residual test at ambient temperature and aged/fatigue states/residual test at ambient temperature is shown on the curve below by comparison at static test specimen and fatigue test specimen points.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations consecutive to a shock

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5.1.7 2/4

Behaviour to impact damage V10F Static test specimen (CES) Fatigue test specimen (CEF) 0

500

1000

1500

2000

2500

- 1000

- 1500

Allongement de compression (µd)

- 2000

- 2500

i32 - (- 2800 µd) Arrêt CEF

- 3000

i22 - (- 3108 µd) Rupture CES

- 3500

- 4000

COURBE ACTUELLE VALEURS DE CALCUL Etat neuf/température ambiante ou Etat vieilli/fatigue à 20° C/température ambiante

- 4500

CES CEF

- 5000

Delaminated surface area (mm2) → Ultimate strength of a delaminated laminate The problem is generally posed as follows: we take a laminate consisting of a set of tapes (or fabrics) that we will assume to be made of the same material, each one of them having a specific orientation in relation to the reference frame (o, x, y). The laminate is submitted to shear forces (of membrane type) Nx, Ny and Nxy. In the presence of a delamination (without ply failure) in surface area Sd, what is the strength of the plain composite plate? Today, there are three methods for evaluating the residual strength in the presence of a delamination (established from experimental results) which call on the stresses and/or strains of the unidirectional fibre and not those of the laminate considered as a homogeneous plate. Each fibre direction must therefore be justified.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations consecutive to a shock

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5.1.7 3/4

We will describe here these three methods in chronological order. 1st method: This first method consists in calculating a failure criterion determined from the strains of each fibre in relation to their intrinsic frame (o, l, t). By referring to the "plain plate - calculation method" section, it is possible to calculate the strains in the various layers of the composite from the global flows Nx, Ny and Nxy applied to the laminate and from the characteristics of the material used. For layer "i" defined by its orientation α i, the strains of the fibre "i" in its own frame are defined by the following strain tensor: (εli, εti, γlti). We can define the following failure criterion C1 for each layer "i": 2

i1

C1 =

æ γ ö æ εl i ö ÷ + ç lt i ÷ ç ÷ çε çγ ÷ è adm ø è adm ø

2

where εadm and γadm are the permissible strains (longitudinal and shear) of the unidirectional fibre (equivalent). These values (obtained from the test results) depend on the material and the surface area Sd of the delamination considered and the types of loads. They are given in section Z (sheets giving calculation values and coefficients used). This criterion was used for the dimensioning of the ATR 72 wing panels (dossier 22S00210460). 2nd method: This second method consists in calculating a failure criterion C2 (Hill type criterion in which the permissible stresses are reduced by coefficients κR and κS) calculated from the stresses in each fibre in relation to their intrinsic frames (o, l, t).

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations consecutive to a shock

I

5.1.7 4/4

By referring to the "plain plate - calculation method" section, it is possible to calculate the strains in the various layers of the composite from the global flows Nx, Ny and Nxy applied to the laminate and from the characteristics of the material used. For layer "i" defined by its orientation α1, the stresses of the fibre "i" in its own frame are defined by the following stress tensor: (σli, σti, τlti). We can define the following failure criterion C2 for each layer "i":

i2

C2 =

æ σ li ç çκ R è R l

2

2

2

σ li σ t i æ τ ö æσ ö ö ÷ + ç t i ÷ + ç lt i ÷ − ç κ S÷ çR ÷ ÷ (κ R R l )2 è s ø è tø ø

where Rl, Rt and S are the permissible longitudinal, transverse and shear stresses of the unidirectional fibre respectively (equivalent) and where κR and κs are the reduction coefficients for these permissible stresses. These coefficients depend on the material used and the surface area of the delamination considered and are determined from the test results. They are given in section V (sheets giving calculation values and coefficients used). This criterion was used for the sizing of the A330/340 inboard and outboard aileron panels. 3rd method: This method consists in calculating a failure criterion C3 (similar to the one of method 1) calculated from the strains of each fibre in relation to their intrinsic farmes (o, l, t). For layer "i" defined by its orientation αi, the strains of the fibre "i" in its own frame are defined by the following strain tensor: (εli, εti, γlti). We can define the following failure criterion C3 for each layer "i" :

i3

C3 =

æ ε li ç çε è a

2

æ γ ö ÷ + ç lt i çγ ÷ è adm ø

2

ε ε ö ÷ + li t i ÷ (ε ab )2 ø

where: if 2 ôεadmô ≤ ôγadmô

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MONOLITHIC PLATE - DAMAGE TOLERANCE Delaminations consecutive to a shock Visual flaws - Sharp scratches

i4

1

εa =

3

−

2 (ε adm )

2

i5

I

5.1.7 5.2 5.2.1

2

(γ adm )2

1

εab =

3

2 (ε adm )

2

−

6

(γ adm )2

else εa = εadm εab = + ∞ The particularity of this method is that it takes into account (in a significant manner) the load transverse to the fibre. Tests have shown that presence of a tensile force perpendicular to the fibre direction compression increases the ultimate strength of the laminate. Criterion C3 takes this phenomenon into account. Indeed, if εti is of tensile type and εli of compression type, the third term of the criterion C3 becomes negative and tends to increase the reserve factor and therefore the margin (RF = 1/C3). Today, it is recommended to use this third finer method based on a high number of experimental results.

5.2 . Visual flaws

5.2.1. Sharp scratches → Description Sharp scratches are made by scalpels or cutting tools. Sharp scratches lead to drops in tensile characteristics of around 15 %; for compression, we assume that there is no drop in characteristics.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Sharp scratches

I

5.2.1

→ Examples of acceptance criteria for sharp scratches A long anomaly is acceptable without concession within following limits: Þ On the ATR 72 outer wing carbon box structure, → In standard areas: permissible scratches are defined as follows: - maximum length: 100 mm, - maximum depth: 1 ply irrespective of the thickness. → in designated areas: the acceptance criteria are as follows: - maximum length: 100 mm, - maximum depth: 1 ply irrespective of the thickness, - all scratches though to a hole, an hedge or stopping less than 5 mm away must be covered by a concession. Any scratch concentrations must be covered by a concessions if the flaws are less than 20 mm apart. Þ On A330/A340 inboard and outboard ailerons, if length of scratch is less than 100 mm and if its depth is less than 0.15 mm for tapes and 0.3 mm for fabrics, sealing with Hysol 9321 will be performed. Þ On A330/A340, A320, A319, A321 nose landing gear doors (carbon fabrics G803/914), → at fittings, the permissible scratches are defined as follows: - maximum length: 10 mm, - maximum depth: 1 ply irrespective of the thickness. → outside fittings: the acceptance criteria are as follows : - maximum length: 250 mm, - maximum depth: 1 ply irrespective of the thickness.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Indents - Scaling

I

5.2.1 5.2.2 5.2.3

1/3

Þ On A330/A340, A320, A319, A321 main landing gear doors (carbon fabrics G803/914), → at fittings, the acceptance criteria as follows: - maximum length: 10 mm, - maximum depth: 1 ply irrespective of the thickness. → outside fittings: the acceptance criteria area as follows : - maximum length: 100 mm, - maximum depth: 1 ply irrespective of the thickness.

5.2.2 . Indents "Indent" type flaws due, for instance, to abrasion of skin by a rototest are permissible if: - surface area of indent is ≤ 20 mm2 (∅ 5), - only the 1st ply is totally damaged, that is 2nd ply visible. Any flaw concentrations must be covered by a concession if two indents are less than 100 mm apart.

5.2.3 . Scaling → Description By "scaling", we mean separation or removal of several fibres (locally) altering only the first surface ply on monolith edge or on outgoing side of drilled holes. → Examples of scaling acceptance criteria Þ On ATR 72 outer wing carbon box structure, → in standard areas: the permissible scaling flaws are defined as follows: Maximum surface area = 30 mm2 Maximum depth: 1 ply for th < 20 plies 2 plies for th ≥ 20 plies

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I

5.2.3 2/3

For scaled hole concentrations, this flaw must be covered by a concession if, for aligned fasteners, more than 20 % of the holes are scaled and/or two flaws are less than 5 fastener pitches apart.

Flaw 1

Flaw 2

→ in designated area: permissible scaling flaws are defined as follows: Maximum surface area = 20 mm2, Maximum depth: 1 ply irrespective of the thickness. For scaled hole concentrations, this flaw must be covered by a concession if: - for aligned fasteners, more than 10 % of the holes are scaled and/or two flaws are less than 5 fastener pitches apart,

Flaw 1

Flaw 2

- for areas with several fasteners rows (e.g. piano area)

175 mm Flaw 1

For flaws 1 and 3: to be covered by a concession Flaw 2 For flaws 1 and 2: if S1 and S2 ≤ permissible surface area permissible

Flaw 3

• for fasteners on same row: same as above, • for flaws on several rows; must be covered by a concession if they are less than 175 mm apart.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Scaling

I

5.2.3 3/3

All scaled areas will be sealed with Hysol 9321 to restore flat surface and avoid scaling developing during later operations. Þ On A330/A340 inboard and outboard ailerons, scaling on 1 ply of skin will be sealed with Hysol 9321. Permissible scaling flaws are defined as follows: → panels (delaminations at fasteners) Maximum surface area = 30 mm2 For flaw concentrations at fasteners, two flaws on same row must be separated by 9 fasteners. Areas with several fastener rows: - on same row: see above, - between different fastener rows minimum distance = 175 mm → panels (leading edge joints), ribs, spar Maximum surface area = 30 mm2 Maximum depth: 0.2 mm For flaw concentrations, 5 flaws maximum on 10 consecutive fasteners. → panels (other areas) (scaling at fasteners) Maximum surface area = 30 mm2 Maximum depth: 0.2 mm For flaw concentrations, two flaws on a given row must be separated by 9 fasteners.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Steps

I

5.2.4 1/2

5.2.4 . Steps → Description This is a fold of one or more skin plies which may occur between two (spar support) blocks or on a sandwich skin during co-curing or in spar webs.

50 mm

Filleralu

→ Examples of acceptance criteria Þ On ATR 72 outer wing carbon box structure → On bearing surfaces (spar, rib passage) - Standard areas: steps on spar and rib passage areas are acceptable within a limit of 0.3 mm. This type of flaw will be compensated for by Filleralu over a width of 50 mm on either side of the step. - Designated areas: this flaw must be covered by a concession irrespective of its geometry. → On stiffeners - standard areas: steps on stiffener flanges are acceptable within a height limit of 0.3 mm provided that: • there are no flaws in stiffener radius, • two flaws are at least 400 mm apart in Y-direction (wing frame), • two adjacent stiffeners are not affected in the same section, • an ultrasonic inspection demonstrates absence of "delamination" type flaws. - designated areas: steps on stiffener flanges must be covered by a concession.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Steps - Justification of permissible manufacturing flaws

I

5.2.4 2/2

Þ On A330/A340 inboard and outboard ailerons under spar and rib bearing surfaces, steps lower than or equal to 0.2 mm and with a width lower than or equal to 3 mm will be accepted, but: - they must never be trimmed, - they will be compensated for by Filleralu, - in other areas, acceptable height is 0.4 mm. Þ On A330 Pratt et Whitney thrust reverser sandwich skins mainly in areas with high curvatures, steps with a height less than 0.5 mm are accepted in production. Steps greater than 0.5 mm will be examined case by case.

6 . JUSTIFICATION OF PERMISSIBLE MANUFACTURING FLAWS

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MONOLITHIC PLATE - DAMAGE TOLERANCE Justification of in-service damage

I

7 7.1 7.1.1

7 . JUSTIFICATION OF IN-SERVICE DAMAGE 7.1. Justification philosophy A justification philosophy in agreement with European regulations (JAR) is associated with each damage detectability range § 4.5 (undetectable damage; damage susceptible to be detected [during inspection]; readily and obvious detectable damage).

7.1.1. Justification philosophy for undetectable damage ACJ 25.603 § 5.1 : The static strength of the composite design should be demonstrated through a programme of component ultimate load tests in the appropriate environment, unless experience with similar design, material systems and loadings is available to demonstrate the adequacy of the analysis supported by subcomponent tests, or component tests to agreed lower levels. ACJ 25.603 § 5.2 : The effect of repeated loading and environmental exposure which may result in material property degradation should be addressed in the static strength evaluation… ACJ 25.603 § 5.5 : The static test articles should be fabricated and assembled in accordance with production specifications and processes so that the test articles are representative of production structure. ACJ 25.603 § 5.8 : It should be shown that impact damage that can be realistically expected from manufacturing and service, but not more than established threshold of detectability for the selected inspection procedure, will not reduce the structural strength below ultimate load capability. This can be shown by analysis supported by test evidence, or by test at the coupon, element or subcomponent level.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Justification of in-service damage

I

7.1.2 7.1.3 1/3

Undetectable damage, whether due to accidental impacts (in-service damage undetectable by a detailed visual inspection and therefore corresponding to BVID) or manufacturing flaws must be covered by a static justification at ultimate load under the most severe environmental conditions (humidity and temperature) and at end of aircraft life. During the certification tests, this damage will be introduced into minimum margin areas

7.1.2 . Justification philosophy for readily and obvious detectable damage As laid down in the regulations, any damage which cannot withstand the limit loads must be readily detectable during any general visual inspection (50 flights) or obvious. Þ Damage readily detectable within an interval of 50 flights must withstand 0.85 LL. Þ Obvious damage (engine burst) which occurs in flight with crew being aware of it must withstand 0.7 LL (get-home loads capability).

7.1.3 . Justification philosophy for damage susceptible to be detected during scheduled in-service inspections Þ Regulatory aspects ACJ 25.603 § 6.2.1 : Structural details, elements, and subcomponents of critical structural areas should be tested under repeated loads to define the sensitivity of the structure to damage growth. This testing can form the basis for validating a no-growth approach to the damage tolerance requirements… ACJ 25.603 § 6.2.3 : ...The evaluation should demonstrate that the residual strength of the structure is equal to or greater than the strength required for the design loads (considered as ultimate)... ACJ 25.603 § 6.2.4 : ...For the case of no-growth design concept, inspection intervals should be established as part of the maintenance programme. In selecting such intervals the residual strength level associated with the assumed damage should be considered.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Justification of in-service damage

I

7.1.3 2/3

Þ General For metallic structures, the two fundamental damage tolerance parameters are the initiation of the damage and its growth before detection. Many tests have been conducted therefore to evaluate the growth speed of the damage and the time required to reach its critical size and therefore its residual strength (limit load). The critical loading mode is mainly tensile loading. εresidual

Repair

εU.L. εL.L. METALLIC Growth Initiation threshold

Time

Inspection intervals

In contrast, impact damage to the composite structure of perforation/delamination type cause, when it occurs, a very substantial drop in the mechanical strength but it does not grow under the fatigue load levels on civil aircraft. The critical loading mode is mainly compression (and shear) loading εresidual

εU.L. εL.L. COMPOSITE Time At time of impact

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MONOLITHIC PLATE - DAMAGE TOLERANCE Justification of in-service damage

I

7.1.3 3/3

Several methods are used for demonstrating conformity with regulations: a) Semi-probabilistic methods If the no-growth concept of the flaw is demonstrated (by fatigue test), the size of the damage no longer depends on an evolving phenomenon but on a random event (accidental). For the damage range between BVID and VID, the aim of the (analytical) justification will be to determine an inspection interval so that the probability (Re) of simultaneously having a flaw and a load greater than its residual load will be a highly improbable event (probability per flight hour less than 10-9). This probabilistic damage occurrence versus time aspect therefore replaces the deterministic concept for metallic materials where the occurrence of a flaw depends either on fatigue initiation, or, for certain areas, on an accidental impact; the effect of the latter being a modification in the threshold. The complete philosophy can be summarised by the curve below. It expresses the load level to be demonstrated and the type of justification versus the damage range considered. The portion of the curve between the BVID and the VID depends on the results of the probabilistic analysis.

Probabilistic analysis TOLDOM

εresidual

≥ L.L.

Re = E - 9

≥ U.L.

εBVID εU.L. εVID

εL.L.

0.85 εL.L. 0.7 εL.L. ULTIMATE LOADS BVID

These methods are used by AS and CEAT.

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VID OBVIOUS READILY DETECTABLE

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Aerospatiale semi-probabilistic method Determining inspection intervals

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7.1.3 7.1.3.1 7.1.3.1.1

1/6

b) deterministic method (Boeing) This method is based on two analysis and test configurations: - demonstrating positive margins at ultimate load with BVID, - demonstrating positive margins at limit load with extensive damage. The non-growth aspect of the fatigue damage must be demonstrated.

7.1.3.1 . AEROSPATIALE semi-probabilistic method (cf. note 432.0162/96) 7.1.3.1.1 . Process for determining inspection intervals As stated above and in § 4.5, certain damage is susceptible to be detected during inspections which implies that the aircraft may possibly fly between two inspections with damage in a structure the residual strength of which may be lower than the ultimate loads. In order not to design composite structures less reliable than metallic ones, an inspection programme has been defined so that the probability of simultaneously having a flaw and a load greater than its residual strength will be a highly improbable event (probability per flight hour less than 10-9). In mathematical form, this requirement can be written: probability of occurrence of an impact with given energy (Pat) x probability of not detecting the resulting flaw (1- Pdat) x probability of occurrence of loads greater than the residual strength of the damage (Prat) ≤ 10-9/fh or again: i6

Pat x (1 - Pdat) x Prat ≤ 10-9/fh This condition involves several notions that we will specify in the following sections.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Determining inspection intervals

I

7.1.3.1.1 2/6

❑ Pdat: probability of detecting the damage. We defined, in § 4.2 to 4.4, the visual detection criteria for "A" value and "B" value damage and the mean value for various types of in-service inspections. Knowing that the "A" values correspond to a detection probability of 99 %, the "B" values to a probability of 90 % and the mean values to a probability of 50 %, we can deduce the curve below which shows the probability of detection versus the depth of the indent and the type of inspection. Depth of indent (mm) General visual inspection: * Detailed visual inspection: ** 5 * 2 0,5 **

0,3

0

0.5

0.99 1

Pdat Detection probability

❑ Pat: probability of occurrence of an impact with given energy. Several sources of impacts can be considered (this list is not restrictive): - projection of gravel, - removal of the item, - dropping of tools or removable items, - shock with maintenance vehicle. Each impact source will be defined by its incident energy. As for detection, we will define an impact source by a statistical distribution (in this case, the Log-normal distribution). We will therefore speak of the impact probability (or, more precisely, the impact energy range) that we will call (Pat) and which will be characterised by mean energy Em and a standard deviation (according to Sikorsky, the standard deviation σ has a constant value equal to 0.217). The probability of having an impact energy between E et E+2 Joules is equal to E+2

Pat =

ò

f (E) x dE

E

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MONOLITHIC PLATE - DAMAGE TOLERANCE

I

Determining inspection intervals

7.1.3.1.1 3/6

∞

We also obtain

ò

f (E) x dE = 1

0

f(E)

Pat

Em

E 2J

The impact energy will generally be limited to 50 J (cut-off energy), except for THS root: 140 J corresponding to the energy of a tool box failing from the top of the fin. Now that the impact has been defined, we must find the relation between the incident energy (E), the size of the damage (Sd) and its indentation (f). Generally, we have : Sd = Ksd æEö f = Kf ç ÷ èeø

E e 3.3

Test campaigns are however necessary to determine the coefficients Ksd and Kf which depends on the types of materials, their thickness and the item bearing conditions. ❑ Prat: probability of having a loading case greater than the residual strength of the impacted laminate. As we saw in paragraph § 5.1.7, the residual strength of a laminate with a delamination defined by its surface area Sd can be determined by the numbers C1, C2 and C3 that we will call more generally C in the remainder of this section. The need to have three variables to characterise the number C (εl, εt, γlt ou σl, σt, τlt) makes all theoretical exploitations of the item loads (or deformations) difficult.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Determining inspection intervals

I

7.1.3.1.1 4/6

ε admissible which represents the permissible C strain of damage of size Sd under a single compression load.

We will therefore define a number εresidual =

This residual deformation depends of course on the size of the damage Sd. The general form of this relation can be represented by the following curve: Sd

εnominal

εresidual

It is therefore possible to determine, for each point on the item studied, the probability of occurrence of the load leading to the failure of the laminate with a delamination of size Sd Knowing that the following gust occurrence probabilities are generally admitted: - 2 x 10-5 for limit loads, - 1 x 10-9 for ultimate loads, We can plot the curve below associating a probability of occurrence Prat with all residual strength levels (εresidual = k x εL.L.) such that: i7

Prat = 10- 8.6 k + 3.9 Prat

2 x 10

-5

10

-9

εL.L.

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εU.L.

εresidual

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Determining inspection intervals

I

7.1.3.1.1 5/6

This curve will in fact be compared to a log-normal type occurrence law (or a first approximation linear law) for a larger deformation range. PROBABILITY DETERMINATION LOGIC DIAGRAM - to have an impact in a given energy range, - to detect damage, - to encounter a load greater than the residual strength of the laminate.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Determining inspection intervals f(E)

I

7.1.3.1.1 6/6

Known impact source

Impact energy range

Pat

Energy

Em mean

Detection probability f

f Depth of indent

General visual inspection: * Detailed visual inspection: **

*

æEö Kf ç ÷ èeø

3.3

** Energy

Pdat Pdat

1

Sd

Sd Delaminated surface

Ksd

εresidual

Prat

2 x 10

-5

Prat

10

-9

εL.L.

εU.L.

εresidual

The inspection interval must be such that risk of failure in the interval: Pat x (1 - Pdat) x Prat ≤ 10-9/flight hours

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E e

Energy

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Determining and calculating inspection intervals

I

7.1.3.1.1 7.1.3.1.2 1/4

Prat Linear law 1

Log-normal law 0.5 2 x 10

-5

10

-9

εmean

εL.L.

εU.L.

εresidual

This curve, like all statistical distribution curves, is characterised by a mean value and a standard deviation. A simple calculation enables us to obtain the following expressions: εmean = 10(Log (εU.L.) - 0.5554) σ = 0.0928 To sum up, it is clear that by choosing a given impact energy range, the values of Pat, f, Pdat, Sd, εresidual and Prat are implicitly determined. The drawing above shows the links between these various quantities.

7.1.3.1.2 . Inspection interval calculation software The calculation tool is based on the fundamental principle described above: all damage susceptible to be detected during an inspection must have a probability of encountering a load greater than its residual strength lower than 10-9 per flight hour (maximum value at end of aircraft life or before last inspection). This principle involves three probabilities: ❑ Pat: probability of occurrence of an impact with a given energy. ❑ Pdat: probability of detecting the damage. ❑ Prat: probability of occurrence of a loading case greater than the residual strength of the impacted laminate.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Calculating inspection intervals

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7.1.3.1.2 2/4

This principle can be stated in a more useable form: The probability of having damage susceptible to encounter a load greater than its residual strength is equivalent to the sum of the probabilities of having: - damage relevant to an incident energy between 0 and 2 J susceptible to encounter a load greater than its residual strength and - damage relevant to an incident energy between 2 and 4 J susceptible to encounter a load greater than its residual strength and - damage relevant to an incident energy between 48 and 50 J susceptible to encounter a load greater than its residual strength. By discretizing the incident energy and therefore the type of the damage, each flaw range can be dealt with independently of the others. f(E)

E

We can therefore apply the fundamental principle to each energy interval then add the results. First of all we will consider an incident energy range between E and E+2 Joules. The trickiest bit is to determine the probability of existence of damage of a well-defined size versus time knowing that its probability of occurrence is equal to Pat (per flight hour) and its probability of non-detection during inspections is equal to (1 - Pdat).

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MONOLITHIC PLATE - DAMAGE TOLERANCE Calculating inspection intervals

I

7.1.3.1.2 3/4

If Pat is the probability of occurrence of the flaw per flight hour at time t1 (before first inspection for instance) the probability of existence of the flaw is equal to: 1 - (1 - Pat)t1. After the first inspection, the probability of occurrence of the flaw is therefore reduced to: [1 - (1 - Pat)t1] (1 - Pdat) then increases according to same curve as before but with a time shift as initial probability is no longer zero. We repeat this operation up until the last inspection. The form of the function makes the calculations difficult; it is for this reason that we compare the curve to its tangent: 1 - (1 - Pat)t ≈ t x Pat. This approximation remains valid as long as the term t x Pat is small in comparison with 1. This therefore gives the following configuration: Probability of occurrence of a flaw

1 1 - (1 - Pat) ^ t1 [1 - (1 - Pat) ^ t1] (1 - Pdat)

IT1

IT2

t1

t2

IT3

t3

IT4

t4

t

The curve [1 - (1 - Pat) ^ t] will be compared to its limited development: t x Pat Probability of occurrence of a flaw

1

IT x Pat x (1 - Pdat)

IT

IT x Pat x (1 - Pdat) ^ 2

IT x Pat x (1 - Pdat) ^ 3

IT

IT ERL = n x IT

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IT x Pat

IT x Pat

IT x Pat

MTS 006 Iss. B

IT x Pat

IT

t

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Calculating inspection intervals

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7.1.3.1.2 4/4

For constant inspection intervals, the mean probability of occurrence of the flaw is equal to: IT x Pat n − 1 n − i x IT x Pat x (1 − Pdat )i + 2 n i =1

å

The maximum probability of occurrence of the flaw (Rd) is equal to: n −1

i8

Rd = IT x Pat +

å IT x Pat x (1 − Pdat )

i

i=1

The mean probability of failure (Rr) of the flaw is therefore equal to: ìïIT x Pat n − 1 n − i üï Prat x í x IT x Pat x (1 − Pdat) i ý + 2 n ï ï i =1 î þ

å

The maximum probability of failure (Rr) of the flaw is therefore equal to: n −1 ìï üï Rr = Prat x íIT x Pat + IT x Pat x (1 − Pdat) i ý ï ï i =1 î þ

å

i9

To find the mean overall risk per flight hour, all we need to do is to integrate this result into all possible incident energy ranges. ìïIT x Pat n − 1 n − i üï Prat x í + x IT x Pat x (1 − Pdat) i ý 2 n ï ï E=0J i=1 î þ

E = 50 J

å

å

The overall maximum risk per flight hour (Re) is equal to: Re =

i10

ìï Prat x íIT x Pat + ï E=0J î

E = 50 J

å

ü

n −1

iï

i =1

þ

å IT x Pat x (1 − Pdat) ýï

This risk must be lower than 10 E-9. The table below summarises (by giving the mathematical links between the various variables) the method used to determine Re.

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MONOLITHIC PLATE - DAMAGE TOLERANCE Load level K

I

7.1.3.1.2 7.1.3.1.3 1/5

IT & ERL

E

f

Sd

εresidual

Prat

Pdat

Pat

Rd

0-2J 2-4J 4-6J . . . . . . . . . . 44 - 46 J 46 - 48 J 48 - 50 J

Rr

i8

i9

i10 Re 7.1.3.1.3 . Load level K to be demonstrated in the presence of Large VID The previous analysis can be substantiated by a static test with VID and a load level k.CL (1 ≤ k ≤ 1.5). ❑ First method: This method consists in initially evaluating the reduction coefficient α on the permissible strengths of the material so that the final calculated risk Re is equal to 10-9 per flight hour (this determination can only be done by successive approximations). This means that we can suppose that the damage tolerance behaviour of the material is degraded in relation to that really used, that is a material whose strength (under compression loading after impact) will be equal to a certain percentage, called α, of that of the real material.

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Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Load level K

I

7.1.3.1.3 2/5

In this case, the (εresidual; Sd) is submitted to a homothety in relation to the x-axis.

Sd Basic curve → Re Reduced curve -9 → Re = 10 /fh

xα εresidual

The number

1 can therefore legitimately be compared to a reserve factor. α

We will thus define a static test with VID (Visible Impact Damage) such that the margin in relation to the residual strain ε (VID) of the flaw is the one defined above. We obtain: 1 ε ( VID) = α K x εL.L.

hence: K=α

i11

ε ( VID) = α x k ( VID) ε L.L.

value representing the load level K to be demonstrated with VID. ❑ Second method: Another method would consist in directly considering the probability and load notions.

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Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Load level K

I

7.1.3.1.3 3/5

It is clear that for a static test, we can consider that the probabilities of occurrence of the flaw (Pat) and the probabilities of detecting (Pat) and not detecting (1 - Pdat) the flaw are equal to 1 as we are sure that it is present in the item. If we write the equivalence between the test and the maximum risk per flight hour from a probabilistic viewpoint, we obtain: Re = Prat x PatVID x (1 - PdatVID) = Prat. The method consists therefore in determining a fictive ultimate load level such that the probability of the flaw residual load level is equal to Re. The drawing below shows that we must randomly subject the curve (strain level ε; Prat) to 1 a homothety with a factor so as to move point A to point B level. In this case, it appears η that the permissible load level of the VID has a probability of occurrence Re. We see that this transformation also moves point A' to point B' which corresponds to the fictive ultimate load level that must be applied to the structure. Prat

1

Permissible deformation of VID /η

2 x 10

-5

10

-9

A'

B'

A

B

Re εU.L. fictive εL.L.

εU.L.

εresidual

ε VID

By zooming in onto the part of the graph which concerns us and imposing a logarithmic scale on the y-axis, we obtain the following representation:

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MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE

I

Load level K

7.1.3.1.3 4/5

- Log(Prat)

B

- Log(Re)

B'

9

/η

8.6 x K - 3.9 A

A'

4.7

1 K(VID)

k =

1.5

12.9 x K ( VID )

− Log(Re ) + 3.9

− Log(Re ) + 3.9

8 .6

ε residual ε L.L.

We obtain: η=

axis( A ) − Log(Re) + 3.9 = axis(B ) 8.6 x k( VID)

We can deduce the fictive ultimate load level to be demonstrated in the presence of VID K =

i12

12 .9 x k ( VID ) − Log(Re ) + 3.9

Load level K must always be between 1 and 1.5. The graph below represents the previous relation (the maximum risk Re per flight hour on the x-axis and the load level K to be demonstrated on the y-axis). Each curve is relevant to a residual load level of the flaw K.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - DAMAGE TOLERANCE Load level K

I

7.1.3.1.3 5/5

K Safety factor to be applied to limit loads

ULTIMATE LOAD 1.5

1.4 K = 1.17

1.3

K = 1.7

k = 20 k = 1.9

Re = E-15

k = 1.8

k = damage residual load level

k = 1.7

1.2 k = 1.6 k = 1.5 k = 1.4

1.1

k = 1.3 k = 1.2 k = 1.1

LIMIT LOAD 1

Risk of failure per flight hour in Log Log(Re)

0.9 9

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11

12

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14

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J MONOLITHIC PLATE - BUCKLING

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Composite stress manual

K MONOLITHIC PLATE - HOLE WITHOUT FASTENER ANALYSIS

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Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Notations

K

1

1 . NOTATIONS (o, x, y): reference coordinate system of panel (o, 1, 2): orthotropic axis of laminate φ: angle formed by loading with the orthotropic axis α: angular position of point to be calculated with the orthotropic coordinate system Ex: longitudinal modulus of laminate in the reference coordinate system Ey: transversal modulus of laminate in the reference coordinate system Gxy: shear modulus of laminate in the reference coordinate system νxy: Poisson coefficient of laminate in the reference coordinate system E1: longitudinal modulus of laminate in the orthotropic coordinate system E2: transversal modulus of laminate in the orthotropic coordinate system G12: shear modulus of laminate in the orthotropic coordinate system ν12: Poisson's ratio of the laminate in the orthotropic coordinate system σ ∞x : stress to infinity σx (y): stress along y-axis σt (α): tangential stress around circular hole K ∞T : hole coefficient for an infinite plate width K LT : hole coefficient for a finite plate width β: "finite plate width" coefficient L: plate width ∅: hole diameter R: hole radius

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MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Introduction - Theory - First method

K

2 3.1 1/3

2 . INTRODUCTION The purpose of this chapter is to assess stresses at the edge of a hole without fastener on an axially loaded composite plate and to anticipate failure of a notched laminate.

3 . GENERAL THEORY 3.1 . First method (Withney and Nuismer) From a theoretical point of view, the problem is formulated as follows: let an infinite plate be subjected to stress flux σ ∞x and with the diameter hole: ∅. The method is valid only if the x-axis is the laminate orthotropic axis. What is the stress σx (y) distribution along the y-axis?

y

σx (y) σ∞ x σx (y = R) x ∅ = 2R

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Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - First method

K

3.1 2/3

First, the following number needs to be considered: k1

K ∞T =

σ x ( y = R) σ ∞x

=

hole edge stress inf inite stress

This coefficient expresses hole edge stress concentration for the case of an infinitely large plate. This is the hole coefficient. For a composite plate, this term may be formulated as a function of the mechanical properties of the laminate as follows:

k2

æ E ö E x K ∞T = 1 + 2 ç − ν xy ÷ + x ç E ÷ G y xy è ø

Stress σx (y) evolution along the y-axis may be expressed as follows:

k3

σx (y) =

σ ∞x 2

2 4 æ æ ç 2 + æç R ö÷ + 3 æç R ö÷ − K ∞ − 3 ç 5 T ç ç è yø è yø è è

(

)

æ Rö ç ÷ è yø

6

If y = R, then this function is reduced to expression k1. If the material is near-isotropic, then:

k4

σx (R + do) ≈ σ ∞x

k5

with: ξ =

© AEROSPATIALE - 1999

2 + ξ2 + 3 ξ4 2

R R + do

MTS 006 Iss. B

æ Rö −7ç ÷ è yø

8

öö ÷÷ ÷÷ øø

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - First method

K

3.1

If the plate is not infinitely large and has a length L, then:

k6

σ∞ σx (y) = β x 2

2 4 6 8 ö æ æ ö ç 2 + æç R ö÷ + 3 æç R ö÷ − K ∞ − 3 ç 5 æç R ö÷ − 7 æç R ö÷ ÷ ÷ T ç è yø ç è yø è yø è y ø ÷ø ÷ø è è

(

)

with: 3

k7

∅ö æ 2 + ç1 − ÷ è Lø β= as a first approximation ∅ö æ 3 ç1 − ÷ è Lø or ∅ö æ 3 ç1 − ÷ 6 æ è 1 1 æ ∅ Mö Lø ∞ = + ç ÷ K T − 3 çç 1 − 3 2è L ø β ∅ö è æ 2 + ç1 − ÷ è ø L

(

in which: M2 =

)

æ ∅ Mö ç ÷ è L ø

2

ö ÷÷ as a second approximation ø

æ ö ∅ ç 3 æç 1 − ö÷ ÷ è Lø ÷ −1 1− 8 ç 1 − 3 ç ÷ ∅ ç 2 + æç 1 − ö÷ ÷ è è ø Lø æ ∅ö 2ç ÷ èLø

2

y

σx (y) σ∞ x σx (y = R) L

x ∅ = 2R

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3/3

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - Second method

K

3.2 1/3

3.2 . Second method (NASA) This method is based on a NASA study. For an infinite plate, it expresses the ratio K ∞T between the loading stress to infinity σ ∞x and the tangential normal stress at the edge σt (α) around the hole. The position of the point is defined by the angle α with relation to the orthotropic It shall be assumed that loading is uniaxial.

y

2

σ∞ x

σt (α) α ∅ = 2R

x φ

1

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Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - Second method

K

3.2 2/3

The first step consists in searching for the orthotropic axes (o, 1, 2) of the material. Angles φ and α are thus determined (α being the angular coordinate of the point to be considered with relation to the orthotropic coordinate system). The hole coefficient expression is the following: k8

K ∞T =

{

σt(α ) Eα = (− cos 2 φ + (k + n) sin 2 φ) k cos 2 α + (1 + n) cos 2 φ − k sin 2 φ sin 2 α − ∞ E σx 1

[

]

n (1 + k + n) sin φ cos φ sin α cos α}

with

k9

k=

k10

Eα = E1

K11

n=

E1 E2

1 sin 4 α +

ö E1 1æ E cos 4 α + ç 1 − 2 ν12 ÷ sin 2 2α E2 4 è G12 ø

ö æE E 2 çç 1 − ν 12 ÷÷ + 1 ø G12 è E2

where E1, E2, G12 and ν12 are the mechanical properties of the laminate in the orthotropic coordinate system (o, 1, 2).

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Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - Second method

K

3.2 3/3

If the laminate lay-up is equilibrated, the expression is simplified and becomes: K ∞T =

σ t (α ) σ ∞x

=

Eα − k cos 2 α + (1 + n) sin 2 α E1

{

}

If the laminate lay-up is nearly-isotropic, the expression is reduced to: K ∞T =

σ t (α ) σ ∞x

= − cos 2 α + 3 sin 2 α

For a nearly-isotropic lay-up and uniaxial loading, hole coefficients for 0°, 45°, 135° and 90° fibre directions are thus: 3, 1, 1 and - 1.

y

1 1 1 1

3

K∞ T

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MTS 006 Iss. B

σ∞ x

1 -1

x

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - Third method

K

3.3

3.3 . Third method (isotropic plate theory) If the material is isotropic (or nearly-isotropic) and if the plate is infinitely large, then the stress tensor may be formulated for any point P (identified by its coordinates r and α) on the plate as follows:

k12

σr =

σ ∞x 2

σt =

σ ∞x æ 3 R4 ö R2 ö σ ∞ æ ç 1 + 2 ÷ − x ç 1 + 4 ÷ cos 2α 2 è 2 è r ø r ø

τrt = −

æ 3 R4 R 2 ö σ ∞x æ R2 ö 1 1 4 − + + − ÷ cos 2α ç ÷ ç 2 è r2 ø r4 r2 ø è

σ ∞x æ 3 R4 2 R2 ö ç 1 − 4 + 2 ÷ sin 2α 2 è r r ø

y

t r P

r

σ∞ x

α x ∅ = 2R

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MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - Fourth method

K

3.4 1/2

3.4 . Fourth method (empirical) This method is simple, fast but conservative. For more details, refer to chapter L (MONOLITHIC PLATE - FASTENER HOLE) by considering the bearing load as zero. Let a plate of length L be subjected to stress triplet σ ∞x , σ ∞y , and τ ∞xy . σ∞ y

y τ∞ xy

L

x

σ∞ x

∅

The first step consists in calculating the principal stresses σ p∞ and σ p'∞ and in weighting them with the net cross-section coefficient

L . L−∅

Thus, the main net stresses σ Np and σ Np' are obtained. Both stresses are then divided by coefficients Kt (K ct or K tt for direction p) and K't (K' ct or K' tt for direction p').

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Theory - Fourth method

K

3.4 2/2

These coefficients (smaller than 1) are a function of the material, the elasticity moduli in the direction considered (p or p'), the hole diameter (∅) and the type of load (tension "t" or compression "c"). They are found in the form of graphs (for carbon T300/914 layer in particular) in chapter Z (sheets 3 and 4 T300/914). The two following final stresses are obtained : σ Fp =

σ Fp' =

σ Np Kt σ Np' K t'

Both stresses are expressed in the main coordinate system (o, p, p').

σN p'

p'

y σN /Kt p σN /K't p'

L

p ∅ x

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Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER "Point stress" - Failure criterion

K

4.1 1/2

4 . ASSOCIATED FAILURE CRITERIA 4.1 . Failure criterion associated with the "point stress" method (Whitney and Nuismer) To determine the failure of a notched laminate, it is generally allowed (for composite materials) to search for edge stresses at a certain distance do from the hole edge. Indeed, edge distance stress release through microdamages causes them to be analyzed at the edge distance do in practice. This distance depends on the type of load of the fibre considered (compression or tension), on the hole diameter and on the material (see chapter Z sheets 9 and 10 for T300/914). At the composite material stress office of the Aerospatiale Design Office, one considers ("point stress" method) that there is a failure in the laminate when the longitudinal stress of the most highly loaded fibre (located at the edge distance do) tangent to the hole is greater than the longitudinal stress allowable for the fibre. k13

There is a failure if: σl (y = R + do) > Rl σl: longitudinal stress of the fibre tangent to the hole

fibre at 0°

fibre at 90° fi b

re

at

45

°

Rl: longitudinal stress allowable for the fibre

fib re at 13 5°

do

σl

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MTS 006 Iss. B

σl

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER "Point stress" - Failure criterion

K

4.1 2/2

For complex loads, there is a software (PSH2 on mx4) which automatically models a finite element mesh and finds loads in fibres that are tangent to the hole. Longitudinal stress analysis is performed in a circle of elements, its center of gravity being located at the hole edge distance do.

2 do

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MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER "Average stress" - Failure criterion

K

4.2

4.2 . Failure criterion associated with the "average stress" method (Whitney and Nuismer) This method consists in determining the average stress average σx average (ao) between coordinate points (0, R) and (0, R + ao). It is assumed that the plate is infinitely large and the loading uniaxial. y σx average (ao)

(ao)

σ∞ x

x ∅ = 2R

Based on the previous theory (see K 3.1), the following may be formulated as: σx average (ao) =

1 ao

ò

R + ao

R

σ x (y) dy

After development, we obtain:

k14

σx average (ao) ≈ σ ∞x

k15

with: ξ =

© AEROSPATIALE - 1999

2 − ξ2 − ξ4 2 (1 − ξ)

R R + ao

MTS 006 Iss. B

Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER Empirical method - Failure criterion

K

4.3

It is possible to choose ao so that: σx average (ao) ≈ σx (R + do) This condition allows the "point stress" and the "average stress" method to become equivalent. The "average stress" method is rarely used at Aerospatiale, the same failure criterion as for the "point stress" method may be applied: one considers that there is a failure in the laminate when the longitudinal stress of the most highly loaded fibre tangent to the hole is greater than the longitudinal stress allowable for the fibre.

4.3 . Failure criterion associated with the empirical method After determining stresses σ Fp and σ Fp' , a smooth calculation must be performed (see chapter C) in order to assess longitudinal stresses in fibres tangent to the hole. B

The Hill's failure criterion shall be used to each single ply (see chapter G3). It may be noted that this method is relatively conservative because both coefficients Kt and K't are assessed for different points, each one being the most critical with relation to directions p and p'. On the other hand, coefficient Kt and K't values were determined only for diameters between ∅ 3.2 to ∅ 11.1. It is, therefore, necessary to use the theory for large diameters.

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MTS 006 Iss. B

Composite stress manual

HOLE WITHOUT FASTENER First example

K

5.1 1/4

5 . Example 5.1 . First example Let a T300/BSL914 (new) square laminate plate of width L = 120 mm be laid up as follows: 0°: 6 plies 45°: 4 plies 135°: 4 plies 90°: 2 plies In the coordinate system (o, x, y), it is subjected to the following loading: N ∞x = 10 daN/mm N ∞y = 0 daN/mm N ∞xy = 0 daN/mm The plate has a diameter hole ∅ = 40 mm. y

2 4 6 4

L = 120

x ∅ = 40

L = 120

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MTS 006 Iss. B

Nx = 10

Composite stress manual

HOLE WITHOUT FASTENER First example

K

5.1 2/4

Let's analyse, along the y-axis, the evolution of stress flux Nx (y). The mechanical properties of the laminate in the reference coordinate system are the following: Ex = E1 = 6256 daN/mm2 (62560 MPa) Ey = E2 = 3410 daN/mm2 (34100 MPa) Gxy= Gv12 = 1882 daN/mm2 (18820 MPa) νxy = ν12 = 0.4191 νyx = ν21 = 0.2285 The value of K ∞T is deduced as follows: {k2}

K ∞T = 1 +

æ 6256 ö 6256 − 0.4191÷ + 2ç = 3.28 ç 3410 ÷ 1882 è ø

This number represents the hole edge coefficient for the case of a plate of infinite width. Since the plate does not have an infinite width L = 120 mm, we are led to calculate the following number : {k3} 40 ö æ 2 + ç1 − ÷ 120 ø è β= 40 ö æ 3 ç1 − ÷ 120 ø è

© AEROSPATIALE - 1999

3

= 1.148

MTS 006 Iss. B

Composite stress manual

HOLE WITHOUT FASTENER

K

First example

5.1 3/4

We thus obtain the evolution of normal stress fluxes along the y-axis:

Nx (y) = 1.148

10 2

2 4 6 8 ö æ ö æ ç 2 + æç 20 ö÷ + 3 æç 20 ö÷ − (3.28 − 3) ç 5 æç 20 ö÷ − 7 æç 20 ö÷ ÷ ÷ ç ç ç ÷ ÷ ÷ ç ÷ ÷ ç ç è y ø è y ø è y ø è y ø ÷ø ø è è

2 4 8 æ æ æ 20 ö 6 æ 20 ö æ 20 ö æ 20 ö ö÷ ö÷ ç ç Nx (y) = 5.74 ç 2 + çç ÷÷ + 3 çç ÷÷ − 0.28 5 çç ÷÷ − 7 çç ÷÷ ÷ ç è y ø è y ø è y ø è y ø ÷ø ø è è

40 37.65 35

30

25

Nx (y)

20

15 12.32 10

10

5

0 0

10

20

30 y

40

50

60

And we obtain, at the plate edge (y = 60) a flux of 12.32 daN/mm and at the hole edge (y = 20) a flux of 37.65 daN/mm.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

HOLE WITHOUT FASTENER First example

K

5.1 4/4

If one determines the flux at a hole edge distance do = 1 mm (see do in tension for the T300/914), one gets: Nx (y = 20 + 1) = 32.47 daN/mm. A smooth plate calculation (chapter C) with this flux makes it possible to determine the longitudinal stress of the most highly loaded fibre (fibre at 0°): σl = 32.41 hb. On the other hand, as the allowable longitudinal tension stress of the same fibre is equal to Rl = 120 hb, based on the "point stress" failure criterion, we obtain: æ 120 ö − 1÷ 100 = 270 % Margin: ç è 32.41 ø

At a hole edge distance do = 1 mm (see tension do for fibre T300/914 in chapter Z), flux Nx is now only 32.47 daN/mm. A smooth plate calculation makes it possible to find that fibres with a 0° direction are subjected to a 32.41 hb longitudinal stress at this particular hole edge distance. The longitudinal tensile strength of fibre T300/914 being 120 hb, the targeted margin is thus: æ 120 ö Margin = 100 ç − 1÷ = 270 % 32 . 41 è ø

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

HOLE WITHOUT FASTENER

K

Second example

5.2 . Second example Let a T300/BSL914 (infinitely large) laminate plate be laid up as follows: 0°: 6 plies 45°: 4 plies 135°: 4 plies 90°: 2 plies In the coordinate system (o, x, y), it is subject to the following loading: N ∞x = 2.8 daN/mm N ∞y = - 7.8 daN/mm N ∞xy = 5.3 daN/mm The plate has a diameter hole ∅ = 40 mm.

Ny = - 7.8

y Nxy = 5.3

2 4 6 4 Nx = 2.8 x ∅ = 40

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MTS 006 Iss. B

5.2 1/5

Composite stress manual

HOLE WITHOUT FASTENER

K

Second example

5.2 2/5

Let's determine the normal stress fluxes of the hole edge at point P (fibre at 0° tangent to hole). To do this, we shall use the second method First of all, (in order to eliminate the shear flux), let's be positioned in the main coordinate system (o, p, p') which forms a 22.5° angle with the reference coordinate system (o, x, y). Stress fluxes then become N p∞ = 5 daN/mm, N p'∞ = - 10 daN/mm. Orthotropic axes (o, 1, 2) are coincident with the reference coordinate system (o, x, y). The plate and its loading may then be described as follows: Np' = - 10

p'

4

2 4 6

2

φ' = 112.5°

P

y

α = 90°

Np = 5 p

φ = 22.5° ∅ = 40 1 x

In the coordinate system (o, p, p'), the mechanical properties of the laminate are the following: Ep = 5800 daN/mm2 (58000 MPa) Ep' = 3749 daN/mm2 (37490 MPa) Gpp' = 1788 daN/mm2 (17880 MPa) νpp' = 0.3481 νp'p = 0.225

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

HOLE WITHOUT FASTENER Second example

K

5.2 3/5

In the reference coordinate system (o, x, y) and in the orthotropic coordinate system (o, 1, 2), the laminate properties are the following: Ex = E1 = 6256 daN/mm2 (62560 MPa) Ey = E2 = 3410 daN/mm2 (34100 MPa) Gxy= G12 = 1882 daN/mm2 (18820 MPa) νxy = ν12 = 0.4191 νyx = ν21 = 0.2285 A first step shall consist in calculating the effect of the main flux N p∞ at point P as follows: We have: {k9}

k=

6256 = 1.354 3410

{k10} E 90° = E1

1 6256 1 æ 6256 ö sin 4 90° + cos 4 90° + ç − 2 x 0.4191÷sin 2 2 x 90° 3410 4 è 1882 ø

E90° 1 = =1 E1 1

{k11}

n=

© AEROSPATIALE - 1999

æ 6256 ö 6256 − 0.4191÷ + 2ç = 2.48 ç 3410 ÷ 1882 è ø

MTS 006 Iss. B

Composite stress manual

HOLE WITHOUT FASTENER

K

Second example

5.2 4/5

{k1} K ∞T =

σ t ( α = 90°) σ p∞

=

{

6256 ( − cos 2 22.5° + (1.354 + 2.48 ) sin 2 45°) 1.354 cos 2 90° + 6256

((1 + 2.48 ) cos 2 22.5° − 1.354 sin 2 22.5°) sin 2 90° − 2.48 (1 + 1.354 + 2.48) sin 22.5° cos 22.5°

sin 90° cos 90°}

K ∞T =

σ t (α = 90°) σ p∞

= 2.773 p'

4

2

2

4 6

y

2.773 Np = 5

P p

1 x

A second step shall consist in calculating the effect of the main flux N p'∞ at point P. {k1} K' ∞T =

σ t ( α = 90°) σ p∞'

=

{

6256 ( − cos 2 112.5° + (1.354 + 2.48 ) sin 2 45°) 1.354 cos 2 90° + 6256

((1 + 2.48 ) cos 2 112.5° − 1.354 sin 2 112.5°) sin 2 90° − 2.48 (1 + 1.354 + 2.48 ) sin 112.5° cos 112.5°

sin 90° cos 90°}

K' ∞T =

© AEROSPATIALE - 1999

σ t (α = 90°) σ p∞'

= − 0.646

MTS 006 Iss. B

Composite stress manual

HOLE WITHOUT FASTENER

K

Second example

5.2 5/5

Np' = - 10

p'

4

2

2

4 6

y

- 0.646 P p

1 x

The deduction is that the normal stress flux tangent to the hole crossing point P is equal to: Nt (P) = 2.773 N p∞ + (- 0.646) N p'∞ = 2.773 x 5 + (- 0.646) x (- 10) = 20.31 daN/mm

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MTS 006 Iss. B

Composite stress manual

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Composite stress manual

MONOLITHIC PLATE - HOLE WITHOUT FASTENER References

K

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Résistance des matériaux S.C. TAN, Finite width correction factors for anisotropic plate containing a central opening, 1988

B

J. Rocker, Composite material parts: Design methods at fastener holes 3 ≤ φ ≤ 100 mm. Extrapolation to damage tolerance evaluation, 1998, 581.0162/98 W.L. KO, Stress concentration around a small circular hole in a composite plate, 1985, NSA TM 86038 WHITNEY - NUISMER, Uniaxial failure of composite laminates containing stress concentration, American Society for testing materials STP 593, 1975 ERICKSON - DURELLI, Stress distribution around a circular hole in square plate, loaded uniformly in the plane, on two opposite sides of the square, Journal of applied mechanics, vol. 48, 1981

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MONOLITHIC PLATE - FASTENER HOLE Notations

L

1

1 . NOTATIONS (o, x, y): initial coordinate system (o, M, M'): coordinate system specific to the bearing load (o, P, P'): stress main coordinate system F: bearing load ∅: fastener diameter Sf: countersink surface of fastener e: actual thickness of laminate e*: thickness taken into account in bearing calculations p: fastener pitch σ Nt : net cross-section stress at the hole σm: bearing stress σR: allowable stress of material (general designation) σxa: allowable normal stress of material in direction x σya: allowable normal stress of material in direction y τxya: allowable shear stress of material τvisa: allowable shear stress of screw N Bx N By N

gross fluxes in panel

B xy

N Nx N Ny N

net cross-section fluxes

N xy

N NM N NM'

net cross-section fluxes in the coordinate system specific to the bearing load

N NMM' Nm M

additional flux due to the bearing load

β: bearing load angle with relation to the initial coordinate system

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE Notations

L

NPN

net cross-section global fluxes in the main coordinate system NPN'

α: main coordinate system angle with relation to the bearing load N Fx N Fy N

corrected final fluxes

F xy

K mc : compression bearing coefficient K mt : tension bearing coefficient Km : bearing coefficient in the broad meaning of the term K ct : compression hole coefficient K tt : tension hole coefficient Kt: hole coefficient in the broad meaning of the term Kf: bending hole coefficient

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General - Failure modes

2.1 2.2

2 . GENERAL/FAILURE MODES The purpose of this chapter is to assess the structural strength of a notched and loaded laminate fitted with fastener. Depending on the loading level and the type of geometry, such a system may fail as per several failure modes.

2.1 . Bearing failure F ≥ σRm ∅e

e

∅

F

∅

F

2.2 . Net cross-section failure F ≥ σxa (b − ∅) e

b

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE

2.3 2.4 2.5

L

General - Failure modes

2.3 . Plane shear failure F ≥ τxya 2 (L − 0,35 ∅) e

e

L

45°

F

2.4 . Cleavage failure F ≥ σya ∅ö æ çL − ÷ e è 2ø

e

L

∅

∅

F

2.5 . Cleavage: net cross-section failure σxa (b - ∅) + τxya L ≤

2F e e

L

∅

b

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F

∅

Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE

L

Failure modes - Pitch definition

2.6 3.1

2.6 . Fastener shear failure 4F ≥ τvisa π ∅2 e

∅

F

∅

where: σxa is the allowable normal stress of the notched material in direction x σya is the allowable normal stress of the notched material in direction y τxya is the allowable shear stress of the notched material σRm is the allowable bearing stress of the material τvisa is the allowable shear stress of the screw

3 . SINGLE HOLE WITH FASTENER The purpose of this sub-chapter is to outline the justification method of a hole with a fastener to which is applied a bearing load in any direction, the laminate being subjected to membrane type surrounding load fluxes and/or bending moment fluxes. The failure mode associated with this method is a combined net cross-section failure mode in the presence of bearing (see 2.1 and 2.2).

3.1 . Pitch p definition If the main loading is in the F1 direction, the pitch taken into account in the calculations p1 + p2 . shall be equal to: p = 2

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MONOLITHIC PLATE - FASTENER HOLE Membrane analysis - Short cut method - Theory

L

3.2.1 1/8

If the main loading is direction F2, the pitch (which is more commonly called edge distance) taken into account in the designs shall be equal to: p = 2 p3. For complex loading (or for simplification purposes), the following pitch value may be used: p = mini (p1; p2; 2 p3). It should be noted that for membrane or membrane and bending loading, pitch p is limited to k ∅ where k depends on the material used. The value of k is generally between 4.5 and 5. For pure bending loading, this limitation does not apply.

F1

p1

p2

p3 F2

p=

p1 + p2 2

3.2 . Membrane analysis - Short cut method 3.2.1 . Theory Generally speaking, a failure is reached at a fastener hole when: l1

σ Nt + Km σm ≥ Kt σR In the case of a membrane loaded single hole with fastener, the various justification (broadly summed up by relationship I1) steps must be followed:

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MONOLITHIC PLATE - FASTENER HOLE

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Membrane analysis - Short cut method - Theory

3.2.1 2/8

1st step: For load introduction zones (fittings, splices), the membrane gross flux NB to be taken into account at fasteners is deduced from the constant flux to infinity N∞ by the following relationship: l2

NB =

p N∞ if p > 5 ∅ 5∅

NB = N∞ if p ≤ 5 ∅

If the zone to be justified is a typical zone (ribs, spars), then: NB = N∞

N∞ B

N

5Ø Flux

The drawing above shows the difference between the flux to infinity and the actual flux at fasteners for a load introduction zone and highlights the existence of a working strip at each fastener of a width equivalent to 5 Ø. This phenomenon is comparable to the one described in chapter M.1.

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MONOLITHIC PLATE - FASTENER HOLE Membrane analysis - Short cut method - Theory

L

3.2.1 3/8

2nd step: It consists in transforming pitch corrected gross fluxes (see previous step) into net cross-section flux in the initial coordinate system:

y F β<0 x ∅

l3

B

p

Nx

p

N Nx = N Bx

p−∅−

Sf e

p

N Ny = N By

p−∅−

N Nxy = N Bxy

Sf e

p p−∅−

Sf e

y N

Nx

F β<0 ∅

Thus, the equivalent diameter may be determined: ∅' = ∅ +

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x

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MONOLITHIC PLATE - FASTENER HOLE

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Membrane analysis - Short cut method - Theory

3.2.1 4/8

where the countersink surface is equal to: Sf = b h = h2 tgθ b h

θ

e

∅ ∅'

3rd step: It consists in transforming the previously designed fluxes in the coordinate system specific to the bearing load: NNM

l4

NNM' NNMM'

=

(cos β)2

(sin β)2

− 2 x sin β x cos β

NNx

(sin β)2

(cos β)2

2 x sin β x cos β

NNy

sin β x cos β

− sin β x cos β

(cos β)2 − (sin β)2

NNxy

N

NM

M'

M

y F

β<

0 x

Angle β is, in the trigonometric coordinate system, the angle leading from the M-axis (bearing coordinate system) to the x-axis (reference coordinate system).

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L

Membrane analysis - Short cut method - Theory

3.2.1 5/8

4th step: Once positioned in the bearing coordinate system, the flux due to the bearing load N NM (reduced by coefficient Km), is added to (or subtracted from) flux N m M . l5

Nm M =

Fe ∅ e*

e* = mini (e; 2.6 ∅) for double shear. e* = mini (e; 1.3 ∅) for single shear. The bearing height e* is voluntarily reduced for a large thickness to take into account stress concentration at the element surface.

SINGLE SHEAR DOUBLE SHEAR

The resulting fluxes are thus expressed by: NNM ± Nm M Km m

± Km N M

N

l6

NNM'

NM M'

M

NNMM' y F 0 < β x

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MONOLITHIC PLATE - FASTENER HOLE Membrane analysis - Short cut method - Theory

L

3.2.1 6/8

The values of Km depend on the type of loading, the bearing stress and the material used (see chapter Z). Three calculations shall be made with the following values: - Km; + Km; 0.

5th step: It consists in transferring fluxes so determined in their main coordinate system: NPN

l7

NPN'

=

0

(cos α ) 2

(sin α ) 2

2 x sin α x cos α

NNM ± Nm M Km

(sin α ) 2

(cos α ) 2

− 2 x sin α x cos α

NNM'

− sin α x cos α

sin α x cos α

(cos α ) 2 − (sin α ) 2

NNMM'

where: α=

æ ö 2 NNMM' 1 Arctg ç N ÷ m N 2 è NM ± NM K m − NM' ø P N

NP

M'

α>0

M

P'

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3.2.1 7/8

Angle α is, in the trigonometric coordinate system, the angle leading from the M-axis (bearing coordinate system) to the P-axis (main coordinate system).

6th step: Fluxes are maximized by coefficient

1 where Kt is the hole coefficient. Kt

Kt values depend on the type of loading (tension or compression), the fastener diameter, the mechanical properties and the material used (see chapter Z). It should be noted that to each of both main fluxes is associated a hole coefficient which may be different. This is why their notation differs from the sign*.

l8

NPN Kt NPN' K *t P

0 NPN Kt

M'

α>0

M

P'

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MONOLITHIC PLATE - FASTENER HOLE

L

Membrane analysis - Short cut method - Theory

3.2.1 8/8

7th step: Fluxes so maximized are recalculated in the initial coordinate system (o, x, y). P y

P' F F

Nx

α-β>0

NFx

l9

NFy NFxy

2

(sin(β − α ))

2

(cos(β − α ))

(cos(β − α ))

=

(sin(β − α ))

− sin(β − α ) x cos( β− α )

x

2

2 x sin(β − α ) x cos( β − α )

2

− 2 x sin(β − α ) x cos( β − α )

sin(β − α ) x cos( β − α )

(cos(β − α ))

2

− (sin(β − α ))

2

NPN Kt NPN' K *t 0

Angle (α - β) are, in the trigonometric coordinate system, the angle leading from the x-axis (reference coordinate system) to the p-axis (main coordinate system).

8th step: A smooth plate calculation is made with fluxes NF previously determined (see chapter C) to obtain the margin.

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MONOLITHIC PLATE - FASTENER HOLE

L

EDP computing program PSG33

3.2.2

3.2.2 . Computing program PSG33 B

This software, which can be used on mx4 or PC, is simply the digital application of the theory presented above, the eight steps being integrated into the calculation. Let input data relating to the example covered further in this chapter be as follows. CARACMF 1 2 *3 1 2 3 MAT03 1 *2 *

3 4 1 4.8 21.6 T300 neuf 0.78 0.52 0. 45. 3. 13000. 465. -12. 7.5

4PE

8.

-6.

4.91

-30.

0.52 -45.

0.78 90.

465. .13

.35

77.

40.

120.0

-100.

5.

20.

The software gives the design margin for each value of Km, as well as all intermediate results. To allow a quick check of loading, it represents the bearing load and main net fluxes in the reference coordinate system. ^90 I N2 = -20.19 I N1 = 22.19 * I * * I * * I * * I * / * I * / * I * / *I*/ FM = 77. --------------------------------------->0 I I I I I I I

Note the bearing load direction (β = - 30°).

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L

Bending analysis

3.3 1/5

3.3 . Bending analysis - Short cut method If the notched plate is subjected to bending moment fluxes Mx, My and Mxy, follow the additional steps described hereafter:

1st step: Determine stresses on the external and internal surfaces corresponding to bending loads only. As a first approximation, these stresses may be assessed by the general relationship Mv 6M ≈ 2 . In that case, the material shall be considered as homogeneous. σ≈ l e external surface

internal surface

σ Be

σB l

It is nevertheless recommended to determine these stresses with the computing software PSD48 (stacking homogenizing and analysis) which takes into account stiffness variations within the laminate or to refer to chapter D. external surface

internal surface

σ Be

σB l

Thus, for each design direction (x, y and xy), the following stresses are obtained: σe Bx , σe By , τe Bxy : gross stresses on external surface. σi Bx , σi By , τi Bxy : gross stresses on internal surface.

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MONOLITHIC PLATE - FASTENER HOLE Bending analysis

L

3.3 2/5

2nd step: From these stresses, "equivalent" membrane gross fluxes are evaluated. ∆neBx

σ eBx

∆neBy

σ eBy

∆neBxy

τ eBxy

l10

for external surface

=e ∆niBx

σiBx

∆niBy

σiBy

∆niBxy

τ iBxy

for int ernal surface

B

∆n e

external surface e

B

∆n i

internal surface

3rd step: On the contrary of membrane analysis, no majoration between fluxes to infinity N∞ and gross fluxes NB will be taken into account at load introduction areas. NB = N∞ 4th step: "Equivalent" membrane net fluxes are evaluated from "equivalent" membrane gross fluxes. l11

∆ne Nx = ∆ne Bx

∆ne Ny = ∆ne By

∆ne Nxy

© AEROSPATIALE - 1999

p p−∅−

Sf e

p

Sf p−∅− e p = ∆ne Bxy Sf p−∅− e

for external surface (with countersunk fastener head)

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MONOLITHIC PLATE - FASTENER HOLE Bending analysis

p p−∅ p ∆ni Ny = ∆ni By p−∅ p ∆ni Nxy = ∆ni Bxy p−∅

L

3.3 3/5

∆ni Nx = ∆ni Bx

for internal surface (no countersunk fastener head)

Confer to sub-chapter L.3.1 to determine fastener pitch. N

∆n e

external surface

N

internal surface

∆n i

5th step: "Equivalent" membrane net fluxes are divided by the coefficient Kf (bending hole coefficient) which depends on the material (in general Kf = 0.9). Hence, we get the (majorated) "equivalent" membrane net fluxes:

l12

∆ne Fx = ∆ne Fy

=

∆ne Fxy =

∆ni Fx = ∆ni Fy ∆ni Fxy

© AEROSPATIALE - 1999

= =

∆n e Nx Kf ∆n e Ny Kf

for external surface

∆n e Nxy Kf ∆ni Nx Kf ∆niNy Kf

for internal surface

∆n i Nxy Kf

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L

3.3 4/5

6th step: Final membrane fluxes from relation I9 are, then, added to fluxes calculated from relation I12. l13

N Fx + ∆ne Fx N Fy + ∆ne Fy

for external surface (without bearing)

N Fxy + ∆ne Fxy

N Fx + ∆ni Fx N Fy + ∆ni Fy

for internal surface (with bearing)

N Fxy + ∆ni Fxy

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MONOLITHIC PLATE - FASTENER HOLE

L

Membrane + bending analysis - Summary table

3.3 5/5

The overall method for the membrane and bending analysis is summarized in the figure here below. External surface Membrane Bending Data in the initial coordinate system

Nx

B

∆n x

B

∆n y

B

∆n yx

B

p

B

Nx =Nx

p−∅−

Net crosssection analysis

N

Ny =Ny

p−∅−

N

N

Sf

Sf

N xy = N xy p−∅−

p p−∅−

∆n y = ∆n y

p−∅−

N

N

Sf

Sf

p−∅−

e

p−∅−

Sf

Sf

N

p−∅−

p−∅−

e

N

N

N M'

Sf

α F

N

NP

p

−

N

∅

Hole coefficient maximizing

Kt N

NP'

Kt

Kt

α

∆n y

N

F

∆n xy =

∆n xy

↓

N

β N

m

N M ± Km N M N

↓

N M' N

N

NP

↓

N

N P'

N P'

α-β

α-β N

F

N

NP

NP

Kt

Kt

N

N

NP'

NP'

Kt

Kt

α-β

α-β

∆n x =

∆n x Kt

N

F

∆n y =

∆n y Kt

N

F

∆n xy =

∆n xy

Rotation in the initial coordinate system

Nx

Nx

↓

F

Ny

F

F

N xy

Nx

↓

F

Ny

F

F

N xy

F

F

N x + ∆n x

F

F

N y + ∆n y

F

N xy + ∆n xy

N y + ∆n y F

N xy + ∆n xy

© AEROSPATIALE - 1999

F

Ny

N xy N x + ∆n x

Addition of fluxes

Kt F

MTS 006 Iss. B

∅

p p

N MM'

Kt F

−

B

N

β

N

N

F

∆n y =

p

∅

p

∆n xy = ∆n xy

N M'

∆n x Kt

−

B

∆n y = ∆n y

N

∆n x =

p

e

β

N

N

∅

p

N MM'

NP

↓

p

N MM' N

N

−

p

B

∆n x = ∆n x

N

m

N

N P'

p

N

∅

NM

N M ± Km N M

NP

−

B

N

N

p p

N xy = N xy

β

Rotation in the main coordinate system

B

e

N

↓

∆n yx

B

B

N MM'

↓

B

Ny =Ny

N M'

N

Addition of bearing

∆n y

Sf

p

B

N xy = N xy

↓

B

B

NM

↓

B

Nx =Nx

N

Rotation in the load coordinate system

Ny

e

N

Ny =Ny

N

∆n x

p

B

e

p

B

∆n xy = ∆n xy

B

p

B

N

Nx

Ny

Nx =Nx

e

p

B

e

Sf

B

Ny

B

N

p

B

B

Ny

∆n x = ∆n x

e

p

B

B

B

Ny

Internal surface Membrane Bending

Nx

B

Ny

N

Neutral line Membrane

F

F

F

F

F

F

−

∅

Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE Justifications - Nominal deviations

L

3.4 3.5.1

3.4 . Justifications Whatever the type of load (membrane or membrane + bending), make sure that: - the plain monolithic plate subject to "equivalent" membrane load fluxes (NF + ∆neF) or (NF + ∆niF) is acceptable from a structural strength point of view (refer to chapter C), - the allowable bearing stress of material σm (which depends on the material, the fastener diameter and the thickness to be clamped - see chapter Z) is greater or equal to the bearing stress applied corresponding to a laminate thickness that is smaller or equal to 1.3 ∅ for single shear or 2.6 ∅ for double shear (see sub-chapter L.2.1 - 4th step):

3.5 . Nominal deviations on a single hole This sub-chapter is directly related to concession processing. Here, simple rules are outlined, that shall allow the stressman to assess the effect of a geometrical deviation, such as a fastener diameter, its pitch or edge distance, on an initial margin. The following paragraphs are valid only for a hole with fastener subject to membrane fluxes.

B

However, for greater accuracy, it is recommended to redo the calculation or use the software psg33.

3.5.1 . Changing to a larger diameter Following a drilling fault, it is sometimes necessary to change to a repair size or to oversize the fastener.

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L

Nominal deviations - Pitch decrease

3.5.2

Based on the theory we have just presented, any diameter change (∅ changes to ∅') shall have an effect on: - the net cross-section coefficient: the resulting reduction shall be equal to: Sf' e k= Sf p−∅− e p − ∅' −

l14

- the bearing stress: we shall assume that there is no effect on the bearing stress, even if it tends to decrease (this assumption is conservative), - the hole coefficient: if we assume that the hole coefficient value is in the most unfavorable case Kt = 0.003684 ∅2 - 0.08806 ∅ + 0.886 (see corresponding curve in chapter Z - material T300/914), the resulting reduction shall be equal to:

k' =

0.0037 ∅' 2 − 0.088 ∅' + 0.89 0.0037 ∅ − 0.088 ∅ + 0.89 2

≈

∅ ∅'

Thus, the general relationship may be given as follows:

l15

RF' ≈ RF k k' ≈ RF

Sf' p − ∅' − ∅ e ∅' p − ∅ − Sf e

3.5.2 . Pitch decrease If loads are parallel to the free edge, no reduction is necessary on the reserve factor: RF' ≈ RF F2

p' p © AEROSPATIALE - 1999

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MONOLITHIC PLATE - FASTENER HOLE Nominal deviations - Edge distance decrease

L

3.5.3 1/2

If loads are perpendicular to the free edge, the reduction on the reserve factor is equal to: Sf e RF' ≈ RF Sf p−∅− e p' − ∅ −

l16

F1

p' p

3.5.3 . Edge distance decrease If loads are parallel to the free edge, the reduction on the reserve factor is equal to: Sf e RF' ≈ RF Sf p−∅− e p' − ∅ −

p

p' F2

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MONOLITHIC PLATE - FASTENER HOLE Nominal deviations - Edge distance decrease

L

3.5.3 2/2

If loads are perpendicular to the free edge, the reduction on the reserve factor is equal to:

l17

æ p' ö RF' ≈ RF çç ÷÷ èpø

0.54

æ p' ö RF' ≈ RF çç ÷÷ èpø

0.73

æ p' ö RF' ≈ RF çç ÷÷ èpø

1.65

→ (100 % ± 45°)

→ (50 % 0; 50 % ± 45°)

→ isotrope

F1 p

p'

Important remarks: - These empirical relationships are valid only for low edge distance variations (2 ∅ ≤ p' ≤ 2.5 ∅). - For low edge distances, the fact that the failure mode described in sub-chapter L.2.3 is not critical shall have to be demonstrated.

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MONOLITHIC PLATE - FASTENER HOLE "Point stress" finite element method - Description

L

3.6.1

3.6 . "Point stress" finite element method (membrane analysis) 3.6.1 . Description of the method Procedure PSH2 allows the calculation of stresses in fibres around a circular hole with fastener in a multilayer composite plate subjected to membrane type surrounding fluxes. It is based on a finite element display of a drilled plate. Mapping calls for two separate parts: - the bolt (rivet/screw/bolt), - the drilled plate. The drilled hole is modeled by 8-junction quadrangular elements and 6-junction triangular elements. The area adjacent to the hole is modeled by two rings of elements. The ring nearest to the hole is thin and is not utilized directly on issued sheets. Issues are presented on the second ring, the center of gravity of elements being at a design distance from the hole corresponding to the point stress theory (do). 2 do

Contact elements between the plate and the bolt (which also simulate clearance between the fastener and the edge distance) are of the variable stiffness type. Their stiffness is very low when there is no contact with the plate, their stiffness is very high if there is a contact. Loading is achieved by (normal and shear) fluxes on plate edges.

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MONOLITHIC PLATE - FASTENER HOLE "Point stress" finite element method - Justifications

L

3.6.2

3.6.2 . Justifications Make sure that: - longitudinal stresses in fibres tangent to the hole edge distance (and located at a

Fibre at 0°

Fibre at 90° Fib re

at 45 °

distance do) are smaller than the longitudinal stress allowable for fibre Rl,

Fi br e

at 13 5°

do

σl

σl

- The allowable bearing stress of the material σm is greater or equal to the bearing stress applied corresponding to a laminate thickness that is smaller or equal to 1.3 ∅ for single shear or 2.6 ∅ for double shear (see sub-chapter L.2.1 - 3rd step).

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MONOLITHIC PLATE - FASTENER HOLE Multiple holes - Independent holes - Interfering holes

L

4.1 4.2

4 . MULTIPLE HOLES The previous study allowed us to find the structural effect of a single hole with fastener (or distant enough from others) on a monolithic plate subject to membrane or bending type loads. We shall now study the effect of several lined up holes. We shall assume that the plate is subjected to a membrane type uniaxial load flux that is perpendicular to the row of fasteners. If loading is parallel to the row of fasteners, refer to chapter L.3.4.2 calculation.

4.1 . Independent holes If each fastener pitch is greater of equal to 5 ∅, each fastener may be considered as a single hole. Refer to sub-chapter L.3.

5∅

pas = 5 ∅

5∅

5∅

4.2 . Interfering holes (0 < d < 3.5 ∅) If the distance between two holes is smaller than 5 ∅, the net cross-section coefficient to be used changes to: 5∅−d

l18

5∅−d−∅−

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Sf e

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE Multiple holes - Very close holes

L

4.3 1/2

On the other hand, the hole coefficient in tension must also be modified. It changes to:

l19 B

2 æ ö æ 5 ∅ − dö æ5 ∅ − dö η Kt ≈ ç 0.065 ç ÷ − 0.65 ç ÷ + 2.625 ÷ k t (see values of η on next page) ç ÷ è ∅ ø è ∅ ø è ø

The hole coefficient in compression is unchanged (cf. note 440.197/84), but the connection of the holes is ignored for the net section calculation. These new values are to be taken into account in relationships l3 and l8. pas = 5 ∅ - d

d

4.3 . Very close holes (d = 3.5 ∅ soit p = 1.5 ∅) When holes are very close to each other, the diameter ∅' envelope hole shall be considered. The net cross-section coefficient then changes to: pitch

l20

pitch − ∅' −

Sf e

The hole coefficient is not modified by the number η but applies to diameter ∅'. pitch = 4.25 ∅ ∅' 1.5 ∅ d

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MONOLITHIC PLATE - FASTENER HOLE

L

Multiple holes - Kt correction coefficient

4.3 2/2

Kt correction coefficient

E

2

P

P

1.9

O

1.8

L

1.7

V

E

1.6

1.5 N

η

E

1.4

U

1.3

R

O

1.2

T

1.1

1 1

1.5

2

2.5

3

3.5

4

4.5

5

5∅−d ∅ pitch = 5 ∅ - d

pitch ∅' 1.5 ∅

d

d

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pitch = 5∅

5∅

Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE

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First example

5.1 1/7

5.1 . First example Let a T300/BSL914 (new) laminate be laid up as follows: 0°: 6 plies 45°: 4 plies 135°: 4 plies 90°: 6 plies Total thickness: e = 20 x 0.13 = 2.6 mm It is subjected to the three following fluxes in the initial coordinate system (o; x; y): N Bx = 8 daN/mm N By = - 6 daN/mm N Bxy = 20 daN/mm and to the bearing load: F = 185 daN β = - 30° The fastener is a ∅ 4.8 mm countersunk head one (100° countersink angle, which corresponds to a 4.91 mm2). The fastener pitch is 21.6 mm. y 6 4

F = 185 daN 6 β = - 30°

4

x

The purpose of the example is to determine the three final fluxes that shall be used for the equivalent smooth plate design, which shall provide the hole margin looked for (this calculation shall be covered in chapter C).

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MONOLITHIC PLATE - FASTENER HOLE First example

L

5.1 2/7

Design of net cross-section fluxes in the initial coordinate system: {l3} NNx = 8 x

21.6 4.91 21.6 − 4.8 − 2.6

NNy = ( − 6) x

NNxy = 20 x

= 11.59 daN / mm

21.6 21.6 − 4.8 −

4.91 2.6

21.6 4.91 21.6 − 4.8 − 2.6

= − 8.69 daN / mm

= 28.97 daN / mm

Flux transfer in the bearing coordinate system (o, M, M'): {l4} N NM = 31.61 daN/mm N NM' = - 28.71 daN/mm N NMM' = 5.7 daN/mm β = - 30° Bearing flux addition: 3 cases shall be considered The bearing stress is equal to: σm =

185 = 14.82 hb 4. 8 x 2. 6

{l5} Nm M = 14.82 x 2.6 = 38.54 daN/mm The flux in the load direction being a tension flux (+ 31.61 daN/mm), the value of K mt is thus equal to 0.135 (see chapter Z - material T300/914 - Sheet 2).

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MONOLITHIC PLATE - FASTENER HOLE First example

L

5.1 3/7

If the bearing flux minimized by coefficient K mt , is added to previously determined fluxes, the three configurations K mt > 0; K mt < 0 and K mt = 0 are obtained: {l6} K mt = 0.135 N NM = 31.61 + 0.135 x 38.54 = 36.81 daN/mm N NM' = - 28.71 daN/mm N NMM' = 5.7 daN/mm β = - 30° {l6} K mt = - 0.135 N NM = 31.61 - 0.135 x 38.54 = 26.4 daN/mm N NM' = - 28.71 daN/mm N NMM' = 5.7 daN/mm β = - 30° {l6} K mt = 0 N NM = 31.61 + 0 = 31.61 daN/mm N NM' = - 28.71 daN/mm N NMM' = 5.7 daN/mm β = - 30°

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE

L

First example

5.1 4/7

Rotation in the main coordinate system (o ; P ; P'): {l7} N NP = 37.3 daN/mm N PN' = - 29.2 daN/mm α = 4.9° P

y

M α = 4.9°

β = - 30° x N

N P = 37.3 daN/mm N

N P' = - 29.2 daN/mm

{l7} N NP = 26.98 daN/mm N PN' = - 29.29 daN/mm α = 5.8° {l7} N NP = 32.14 daN/mm N PN' = - 29.24 daN/mm α = 5.4° Angle α is the angle formed by the main coordinate system and the bearing coordinate system.

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MONOLITHIC PLATE - FASTENER HOLE

L

First example

5.1 5/7

Application of hole coefficients: Monolithic lay-up under study gives the following elasticity and shear moduli in the main axes: α + β = - 34.9°

E = 4470

G = 2078

α + β = - 35.8°

E = 4455

G = 2092

α + β = - 35.4°

E = 4461

G = 2086

E = 2.151 G E = 2.13 G E = 2.139 G

K tt ≈ 0.6

K ct ≈ 0.87

K tt ≈ 0.6

K ct ≈ 0.87

K tt ≈ 0.6

K ct ≈ 0.87

The values are derived from chapter Z (T300/914 sheets 3 and 4). Which gives the following new values for corrected main fluxes : {l8} 37.3 = 62.17 daN/mm 0.6 − 29.2 N PN' = = - 33.56 daN/mm 0.87 α - β = 34.9°

N NP =

{l8} 26.98 = 44.97 daN/mm 0.6 − 29.29 N PN' = = - 33.67 daN/mm 0.87 α - β = 35.8°

N NP =

{l8} 32.14 = 53.57 daN/mm 0 .6 − 29.24 = - 33.61 daN/mm N PN' = 0.87 α - β = 35.4°

N NP =

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE First example

L

5.1 6/7

Rotation in the initial coordinate system (o; x; y): A rotation of angle (β - α) is achieved: {l9} N Fx = 30.83 daN/mm N Fy = - 2.22 daN/mm N Fxy = 44.92 daN/mm y

N Fxy = 44.92 daN/mm

N Fx = 30.83 daN/mm

x

N Fy = - 2.22 daN/mm

{l9} N Fx = 18.06 daN/mm N Fy = - 6.76 daN/mm N Fxy = 37.31 daN/mm {l9} N Fx = 24.32 daN/mm N Fy = - 4.36 daN/mm N Fxy = 41.17 daN/mm These fluxes are then used in a smooth plate design. Calculation shall be continued in chapter C.6. A 31 % (RF = 1.31) margin shall be found.

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MONOLITHIC PLATE - FASTENER HOLE First example

L

5.1 7/7

New, let's assume that, as a result of a defective drilling operation, the fastener diameter had to be changed to a ∅ 6.35 mm with a 8.62 mm2 countersunk surface. What would be the new margin? {l15}

RF' = 1.31 x

B

4.8 x 6.35

8.62 2.6 = 0.92 4.91 21.6 − 4.8 − 2.6

21.6 − 6.35 −

Which corresponds to a - 8 % margin, thus non allowable. However, a full manual analysis (or using software PSG33) would have made it possible to find a 0 % margin. If the calculation is conservative, it is due to the fact that the decrease of the bearing stress corresponding to fastener oversizing was not taken into account (see chapter L.3.5.1). The preceding example shall also be fully covered in the composite material manual part

B

"Calculation programs" (PSG33 instructions).

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE Second example

L

5.2 1/5

5.2 . Second example Let's assume that three moment fluxes are superposed on membrane fluxes: Mt Bx = - 4 daN mm/mm B y B Mt xy

Mt

= 3 daN mm/mm = 5 daN mm/mm z

y β = - 30°

F = 185 daN Mt By = 3 daN

x

Mt Bx = - 4 daN

Mt Bxy = 5 daN

If the material is considered (as a first approximation) as homogeneous, a strength l 2 .6 2 moment per unit of length equal to: = = 1.127 mm2 is found. v 6 Assuming that a positive moment flux creates compression stresses on the external surface, we obtain: for the external surface: σe Bx =

4 = 3.55 hb (35.5 MPa) 1.127

σe By =

−3 = - 2.66 hb (- 26.6 MPa) 1.127

τe Bxy =

−5 = - 4.44 hb (- 44.4 MPa) 1.127

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MONOLITHIC PLATE - FASTENER HOLE Second example

L

5.2 2/5

For the internal surface: σi Bx =

−4 = - 3.55 hb (- 35.5 MPa) 1.127

σi By =

3 = 2.66 hb (26.6 MPa) 1.127

τi Bxy =

4 = 4.44 hb (44.4 MPa) 1.127 EXTERNAL SURFACE - 4.44 hb 3.55 hb

y x

- 2.66 hb 4.44 hb - 3.55 hb

2.66 hb INTERNAL SURFACE

The purpose of this example is to determine which bending type fluxes must be added to membrane type fluxes for the fastener hole calculation. The "equivalent" gross bending type fluxes necessary for the calculations thus have the following value: {l10} for the external skin: ∆ne Bx = 3.55 x 2.6 = 9.23 daN/mm ∆ne By = - 2.66 x 2.6 = - 6.92 daN/mm ∆ne Bxy = - 4.44 x 2.6 = - 11.54 daN/mm

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MONOLITHIC PLATE - FASTENER HOLE Second example

L

for the internal skin: ∆ni Bx = - 3.55 x 2.6 = - 9.23 daN/mm ∆ni By = 2.66 x 2.6 = 6.92 daN/mm ∆ni Bxy = 4.44 x 2.6 = 11.54 daN/mm The "equivalent" net bending type fluxes thus have the following value: {l11} for the external skin: 21.6

∆ne Nx = 9.23

21.6 − 4.8 −

∆ne Ny = - 6.92

4.91 2.6

= 13.37 daN/mm

21.6 4.91 21.6 − 4.8 − 2.6

∆ne Nxy = - 11.54

= - 10.02 daN/mm

21.6 4.91 21.6 −4.8 − 2.6

= - 16.72 daN/mm

for the internal skin: ∆ni Nx = - 9.23

∆ni Ny = 6.92

21.6 = 8.9 daN/mm 21.6 − 4.8

∆ni Nxy = 11.54

© AEROSPATIALE - 1999

21.6 = - 11.87 daN/mm 21.6 − 4.8

21.6 = 14.84 daN/mm 21.6 − 4.8

MTS 006 Iss. B

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE Second example

L

5.2 4/5

Hole coefficient weighting {l12} for the external skin: ∆ne Fx =

13.37 = 14.86 daN/mm 0. 9

∆ne Fy =

− 10.02 = - 11.13 daN/mm 0 .9

∆ne Fxy =

− 16.72 = - 18.58 daN/mm 0 .9

for the internal skin: ∆ni Fx =

− 11.87 = - 13.19 daN/mm 0 .9

∆ni Fy =

8. 9 = 9.89 daN/mm 0. 9

∆ni Fxy =

14.84 = 16.49 daN/mm 0. 9

All prior calculations were made in the initial coordinate system (o; x; y). These "equivalent" bending type fluxes are thus to be added to the membrane type fluxes found in the first example (see summary table on next page).

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Composite stress manual

MONOLITHIC PLATE - FASTENER HOLE

L

Second example

5.2 5/5

This table summarizes the various steps of "equivalent" membrane flux calculation of the previous example. External surface Membrane Bending

Neutral line Membrane

Internal surface Membrane Bending

Data in the initial coordinate system

8 -6 20

9.23 - 6.92 - 11.54

8 -6 20

8 -6 20

- 9.23 6.92 11.54

Net crosssection design

11.59 - 8.69 28.97

13.37 - 10.02 - 16.72

11.59 - 8.69 28.97

10.29 - 7.71 25.71

- 11.87 8.9 14.84

↓

31.61 - 28.71 5.7 - 30°

28.06 - 25.48 5.06 - 30°

↓

Rotation in the bearing load coordinate system

↓

↓

+ Km 36.81 - 28.71 5.7 - 30°

- Km 26.4 - 28.71 5.7 - 30°

Km = 0 31.61 - 28.71 5.7 - 30°

+ Km 33.26 - 25.48 5.06 - 30°

- Km 22.86 - 25.48 5.06 - 30°

Km = 0 28.06 - 25.48 5.06 - 30°

↓

32.14 - 29.24 35.4°

↓

37.3 - 29.2 34.9°

26.98 - 29.29 35.8°

32.14 -29.24 35.4°

33.69 - 25.91 34.9°

22.59 - 26.01 36°

28.53 - 25.95 35.4°

↓

Hole coefficient maximizing

53.57 - 33.61 35.4°

14.86 - 11.13 - 18.58

62.17 - 33.56 34.9°

44.97 -33.67 35.8°

53.57 - 33.61 35.4°

56.15 - 29.78 34.9°

37.65 - 29.90 36°

47.55 -29.83 35.4°

- 13.19 9.89 16.49

Rotation in the initial coordinate system

24.32 - 4.36 41.17

↓

30.83 - 2.22 44.92

18.06 - 6.76 37.31

24.32 - 4.36 41.17

27.7 - 0.87 38.82

14.35 - 5.68 30.81

21.43 - 3.03 35.12

↓

Addition of final fluxes

39.18 - 15.49 22.59

161 % marging

14.51 9.02 55.31

1.16 4.21 47.3

8.24 6.86 51.61

8 % marging

Addition of bearing flux

↓

Rotation in the main coordinate system

31 % marging

The minimum margin is the only one considered, i.e.: 31 % for membrane design 8 % for membrane + bending design

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MONOLITHIC PLATE - FASTENER HOLE References

L

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials LAFON, Carbon fibre structures: simplified rules for sizing at fastener holes, 1983, PL No. 139/83 BOUNIE, Failure criteria of mechanical bonds in composite materials, 1991, 440.181/91 LAFON, Justification of design methods used for carbon fibre structures - thin sheet subject area, 1983, 440.156/83

B

J. ROCKER, Composite material parts: design methods at fastener holes, 3 ≤ ∅ ≤ 100 mm. Extrapolation to damage tolerance evaluation, 1998, 581.0162/98 LAFON, TROPIS, Structural strength of outer wing - justification of design values, 1989, 440.233/89

B

LAFON - LACOSTE, Synthesis of drilled carbon specimen tests, 1984, 440.197/84 issue 2.

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M MONOLITHIC PLATE - SPECIAL ANALYSIS

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N SANDWICH - MEMBRANE / BENDING / SHEAR ANALYSIS

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SANDWICH - MEMBRANE / BENDING / SHEAR Notations

1 . NOTATIONS Ny: normal load flux Mx: moment flux Mz: moment flux Tx: shear load flux Tz: shear load flux Emi: membrane elasticity modulus of lower skin Efi: bending elasticity modulus of lower skin Gi: shear modulus of lower skin ei: thickness of lower skin Emc: membrane elasticity modulus of core material Efc: bending elasticity modulus of core material Gc: shear modulus of core material ec: thickness of core material Ems: membrane elasticity modulus of upper skin Efs: bending elasticity modulus of upper skin Gs: shear modulus of upper skin es: thickness of upper skin zg: neutral axis position with respect to the lower skin Σ El: overall inertia of elasticity moduli weighted plate EW: elasticity moduli weighted static moment B

µd: microstrain (10-6 mm/mm)

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1

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Specificity - Construction principle - Design principle

N

2 3 4

2 . SPECIFICITY A sandwich is a three-phase structure consisting of a core generally made out of honeycomb or foam with a low elasticity modulus and two thin and stiff face sheets. Sandwich structures have a very high specific bending stiffness.

external face sheet adhesive bonding interface

core (honeycomb) internal face sheet

3 . CONSTRUCTION PRINCIPLE The face sheets and core are assembled by bonding with synthetic adhesives. There are several alternative manufacturing processes: - multiple phase process: face sheets are cured separately, then bonding of face sheets to the honeycomb is performed as a second operation, - semi-cocuring process: the external face sheet is cured separately, the honeycomb and the internal face sheet are then cocured on the external face sheet, - single phase or "cocuring" process: face sheets and the honeycomb are cured in one single operation.

4 . DESIGN PRINCIPLE The design rules that shall be developed are derived from the classical elasticity (refer to "distribution of load among several closely bound structural elements" in chapter A.7).

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SANDWICH - MEMBRANE / BENDING / SHEAR Sandwich plates - Sandwich beams

N

4.1 4.2 1/3

First of all, we shall consider that the three materials together are completely ordinary. Then, we shall simplify the relationships obtained by considering that face sheets are thin and stiff and that the sandwich core is thick and flexible.

4.1 . Sandwich plates Like monolithic metal or composite plates, sandwich plates are under the general plate equation (see § A.7.4). The determination of matrices (Aij), (Bij) and (Cij) which connect the strain tensor to the load tensor is described in chapters C, D and E.

4.2 . Short cut theory - "Sandwich" beams Here, we shall outline a short cut method applicable to sandwich beams. This method does not take into account transversal loading, transversal effects so-called "Poisson" effects and membrane-bending coupling. This simplification may lead to an error of approximately 10 % on results obtained in cases of complex loading. From the overall deformation point of view, sandwich plates obey the conventional equations of classical elasticity theory. Stiffness equivalences (with iso-cross-section) with homogeneous beams are described by relationships n14 to n18. Let a sandwich beam be made up of: - an upper skin of thickness es, of membrane elasticity modulus Ems and of equivalent bending elasticity modulus Efs, - a core thickness ec, of membrane elasticity modulus Emc and of equivalent bending elasticity modulus Efc, - a lower skin of thickness ei, of membrane elasticity modulus Emi and of equivalent bending elasticity modulus Efi.

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SANDWICH - MEMBRANE / BENDING / SHEAR

N

Sandwich beams

4.2 2/3

The bending modulus concept comes from the fact that lower and upper skins are generally (in the case of honeycomb sandwiches) laminates with different membrane and bending moduli (see chapters C and D). Its value depends on ply stacking. This concept was extended to all three materials. First of all, we shall develop the full sandwich beam theory while taking into account face sheet thickness and bending stiffnesses, then we shall outline at the end of each subchapter, the simplified relationships in which face sheets shall supposedly be thin and subject to membrane stress only. The neutral line of the sandwich beam is defined by dimension zg to that: Emi

n1

zg =

ei 2 e ö e ö æ æ + Emc ec ç ei + c ÷ + Ems e s ç ei + ec + s ÷ è è 2 2ø 2ø Emi ei + Emc ec + Ems es

Remark: In the case of a beam in which Emc ec << Emi ei and Emc ec << Ems es, the relationship becomes: Emi

n2

zg =

ei 2 e ö æ + Ems es ç ei + ec + s ÷ è 2 2ø Emi ei + Ems es

es ec ei Ems Efs Gs Emc Efc Gc Emi Efi Gi b zg

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SANDWICH - MEMBRANE / BENDING / SHEAR

N

Sandwich beams

4.2 3/3

We shall assume that the beam is subjected to the following overall load pattern at the neutral axis: - Ny: normal load in direction y - Tx: shear load in direction x - Tz: shear load in direction z - Mx: bending moment around x-axis - Mz: bending moment around z-axis Torsional moment My shall not be taken into account because it does not correspond to any realistic loading. The purpose of this chapter is to determine the stress and elongation diagram for each one of these five loads. We shall study the effects of Ny, Tx, Tz, Mx and Mz one by one.

z Tz Mx Mz

y Ny Tx x

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Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Effect of normal load Ny

N

4.2.1 1/2

4.2.1 . Effect of normal load Ny Assuming that all layers are in a pure tension or compression condition, a normal load Ny applied at the neutral line results in a constant elongation over the whole cross-section. This elongation may be formulated as follows: n3

ε=

Ny

b (Emi ei + Emc ec + Ems es )

This elongation thus induces: - in the lower skin, a stress σi = Emi ε, - in the core, a stress σc = Emc ε, - in the upper skin, a stress σs = Ems ε. The equivalent membrane modulus of the sandwich beam may be determined by the relationship n14. Remark: In the case of a sandwich beam in which Emc ec << Emi ei and Emc ec << Ems es, the relationship becomes: n4

ε=

Ny

b (Emi ei + Ems es ) z

σs Ny

y

Ems es

σc

Emc ec Emi ei

σi x

© AEROSPATIALE - 1999

b

MTS 006 Iss. B

ε

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Effect of normal load Ny

N

4.2.1 2/2

By taking into account the remark assumptions of the previous page (ei << ec, es << ec, Emc << Emi and Emc << Ems), it is possible to oversimplify load distribution in the different sandwich layers. We shall assume that load Ny applied at the beam neutral axis is fully picked up by two membrane type normal loads (Fs and Fi) in both face sheets. Both loads have the following value: n5

Fi ≈ Ny

Emi ei Emi ei + Ems es

Fs ≈ Ny

Ems e s Emi ei + Ems e s

z

Fs

Ny

y

Fi

x

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Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR

N

Effect of shear loads Tx

4.2.2

4.2.2 . Effect of shear load Tx Generally speaking, shear load Tx is distributed in each of the three materials in proportion with their shear stiffness. The maximum shear stress in each of the three layers may then be formulated as follows: n6

τs =

3 Tx Gs es 2 b es Gs es + Gc ec + Gi ei

τc =

3 Tx Gc e c 2 b e c Gs es + Gc ec + Gi ei

τi =

3 Tx Gi ei 2 b ei Gs es + Gc ec + Gi ei

The equivalent shear modulus with relation to the x-axis may be determined by the relationship n15. z

τs y

es Gs

τi

ei Gi b

x

© AEROSPATIALE - 1999

Tx

τc

ec Gc

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SANDWICH - MEMBRANE / BENDING / SHEAR

N

Effect of shear load Tz

4.2.3 1/3

4.2.3 . Effect of shear load Tz Generally speaking, shear stress τ in materials may be formulated by the relationship: T EW (Bredt generalized formula). τ= z b å El where 2

n7

b Efs es 3 e æ ö Σ El = + b Ems es ç ei + e c + s − z g ÷ + è ø 12 2 2

b Efc ec 3 e æ ö + b Emc e c ç ei + c − zg ÷ + è ø 12 2 b Efi ei3 æe ö + b Emi ei ç i − zg ÷ è2 ø 12

2

If we consider three critical points A, B and zg, moduli weighted static moments at these points are equal to: n8

e æ ö EW A = b Ems es ç e i + e c + s − z g ÷ è ø 2

zg ö æe e e ö æ EW zg = b Ems es ç e i + e c + s − z g ÷ + b Em c ç i + c + ÷ ø è 2 2 2ø è2

2

eö æ EW B = b Emi ei ç z g − i ÷ è 2ø

Shear stresses at these points are then equal to:

n9

τA =

Tz EWA b Σ El

τzg =

Tz EWz g b Σ El

τB =

Tz EWB b Σ El

Stress τzg corresponds to the maximum stress within the core. In the general case of a honeycomb sandwich material, this stress is the maximum shear stress of the honeycomb. Stresses τA and τB correspond to shear of (adhesive bonding) interface between the core and the skins (force sheets).

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SANDWICH - MEMBRANE / BENDING / SHEAR Effect of shear load Tz

N

4.2.3 2/3

The equivalent shear modulus with relation to the z-axis may be determined by the relationship n16. z τA τzg τB

Tz

y

es ec ei x

b

Remark 1: In the case of a sandwich beam in which Emc ec << Emi ei and Emc ec << Ems es, τA, τzg and τB take the following simplified from: n10

τA ≈ τzg ≈ τB ≈

Tz e e ö æ b ç i + ec + s ÷ è2 2ø z τA

Tz

τzg y

es

τB

ec ei x

b

Remark 2: It should be noted that the equivalent shear modulus of a thin face sheet sandwich beam is on the same order of magnitude as the core for the honeycomb it consists of, thus very low. For the assessment of a honeycomb sandwich beam (or plate) deflection, it is therefore important to take into account this significant effect with respect to the deformation due to the bending moment.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Effect of shear load Tz

N

4.2.3 3/3

For example, for a sandwich beam simply supposed, loaded in its center, the deflected shape due to the shear load may represent approximately 60 % of the overall deflection. Let an aluminium beam and a sandwich beam with equivalent bending stiffness be, giving:

1 daN

300 3 Aluminium

E = 7400 hb, G = 2840 hb 2 El = 1.85E6 daN mm ES = 2.22E5 daN GS = 8.52E4 daN

10 10

0.5 E = 8200 9G=2 0.5 E = 8200

Sandwich

El = 1.85E6 daN mm ES = 8.2E4 daN GS = 180 daN

f1

f2

Aluminium beam: f1 = 0.3041 mm (99.6 %); f2 = 0.0011 mm (0.4 %) Sandwich beam: f1 = 0.3041 mm (38 %); f2 = 0.5 mm (62 %) f1: deflection due to the bending moment f1 =

f2: deflection due to the shear load f 2 =

© AEROSPATIALE - 1999

P l3 48 E l

1.2 Pl 4GS

MTS 006 Iss. B

2

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Effect of bending moment Mx

N

4.2.4 1/2

4.2.4 . Effect of bending moment Mx A bending moment Mx applied at the neutral line results in the creation of a linear distribution of elongations along the cross-section. At the outer surfaces, we have: n11

εs =

Mx v s − Mx (ei + ec + es − z g ) = Σ El Σ El

εi =

Mx v i Mx z g = Σ El Σ El

with: 2

Σ El =

b Efs es 3 e æ ö + b Ems es ç ei + e c + s − z g ÷ + è ø 12 2 2

b Efc ec 3 e æ ö + b Emc e c ç ei + c − zg ÷ + è ø 12 2 b Efi ei3 æe ö + b Emi ei ç i − zg ÷ è2 ø 12

2

The equivalent bending modulus of the sandwich beam may be determined by the relationship n17. z

σs

Mx

εs

y

Ems Efs es Emc Efc ec Emi Efi ei

σi x

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b

MTS 006 Iss. B

εi

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Effect of bending moment Mx

N

4.2.4 2/2

Remark: In the case of a sandwich beam in which ei << ec, es << ec, Emc << Emi and Emc << Ems, self inertias of both face sheets and honeycomb stiffness may be disregarded: 2

e æ ö æe ö Σ El ≈ b Ems es ç ei + ec + s − zg ÷ + b Emi ei ç i − z g ÷ è ø è ø 2 2

2

We shall assume that moment Mx is fully picked up by two membrane type normal loads (F's and F'i) in both face sheets. Both loads have the same modulus but are opposite. Their value is equal to: n12

F'i ≈ - F's ≈

Mx es ö æ ei ç + ec + ÷ è2 2ø z F's Mx y

F'i

x

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MTS 006 Iss. B

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR

N

Effect of bending moment Mz

4.2.5

4.2.5 . Effect of bending moment Mz Generally speaking, bending moment Mz is distributed in each of the three materials in proportion to their natural bending stiffness (with relation to the z-axis). The maximum normal stress in each of the three materials may then be simply formulated as follows: n13

σs = ±

Ems e s 6 Mz 2 b es Ems e s + Emc e c + Emi ei

σc = ±

Emc e c 6 Mz 2 b ec Ems es + Emc e c + Emi ei

σi = ±

Emi ei 6 Mz 2 b ei Ems e s + Emc e c + Emi ei

The equivalent bending modulus with relation to the z-axis is identical to the equivalent membrane modulus with relation to the y-axis (see relationships n14 and n18). z σs

ε Mz

σc y

Ems es Emc ec Emi ei x

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- σi

b

MTS 006 Iss. B

-ε

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR

N

Equivalent mechanical properties

4.2.6

4.2.6 . Deformations and equivalent mechanical properties Sandwiches are microscopically heterogeneous. It is sometimes necessary to find their equivalent stiffness properties in order to determine the passing loads and resulting deformations. For a sandwich beam, equivalences (with iso-cross-section) with respect to typical loads are the following: e1

(3)

e2

(4)

e3

(5)

E1G1 (1)

E2G2 (2)

E3G3

å = å å = å 3

n14

(1) E equivalent normal load

k =1 3

k =1

3

n15

(2) G equivalent shear load

Ek ek

k =1 3

ek

Gk ek

e k =1 k

n16

(3)

1 G equivalent shear load

=

å

æ ek ö ç ÷ k =1 G è kø 3

å e å E l = å l å E e = å e 3

k=1 k 3

n17

(4) E equivalent bending moment

k =1 3

k k

k =1 k

n18

(5) E equivalent bending moment

3 k =1 k 3

k

k =1 k

æ e3 ö lk: self inertia + "Steiner" inertia ç + e d2 ÷ è 12 ø

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SANDWICH - MEMBRANE / BENDING / SHEAR

N

Example

5 1/7

5 . EXAMPLE Let a 10 mm wide sandwich beam be defined by the following stacking sequence: - an upper skin (carbon layers) of thickness es = 1.04 mm and of longitudinal elasticity modulus Es = 6000 daN/mm2 (the bending modulus being identical), - a core (honeycomb) of thickness ec = 10 mm and of longitudinal elasticity modulus Ec = 15 daN/mm2, - a lower skin (carbon cloths) of thickness ei = 0.9 mm and of longitudinal elasticity modulus Ei = 4500 daN/mm2 (the bending modulus being identical). We shall assume that the beam is subjected to the following two loads and moment: - Ny = 800 daN - Mx = 2000 daN mm - Tz = 250 daN

z

Tz = 250 daN Mx = 2000 daN mm y

1.04 10

Ny = 800 daN

0.9 10 x

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MTS 006 Iss. B

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR

N

Example

5 2/7

The purpose of the first part of the example is to determine inner and outer surface elongations of the beam subject to load Ny and moment Mx. 1st step: the neutral axis position has to be determined, this position being referenced with relation to the inner surface. {n1} 4500

Zg =

0. 9 2 10 ö 1.04 ö æ æ + 1510 ç 0.9 + ÷ + 6000 1.04 ç 0.9 + 10 + ÷ 2 2 ø 2 ø è è 4500 0.9 + 1510 + 6000 1.04

Zg = 7.09 mm z

zg = 7.09 y

x

2nd step: To determine elongation ε induced by normal load Ny. {n3} ε=

© AEROSPATIALE - 1999

800 = 7612 µd (microstrain) 10 ( 4500 0.9 + 1510 + 6000 1.04 )

MTS 006 Iss. B

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR

N

Example

5 3/7

Remark: If the simplified relationship is used, we obtain: {n4} ε=

800 = 7774 µd 10 ( 4500 0.9 + 6000 1.04 )

the error is 2 % z

Ny = 800 daN y

ε = 7612 µd x

3rd step: To determine maximum elongations εi and εs induced by moment flux Mx. {n11} −2000 (0.9 + 10 + 1.04 − 7.09 ) Σ El 2000 7.09 εi = Σ El

εs =

{n7} 2

Σ El =

10 6000 1.04 3 1.04 æ ö + 10 6000 1.04 ç 0.9 + 10 + − 7.09 ÷ + 12 2 è ø 2

10 15 10 3 10 æ ö + 10 15 10 ç 0.9 + − 7.09 ÷ + 12 2 è ø 10 4500 0.9 3 æ 0. 9 ö + 10 4500 0.9 ç − 7.09 ÷ 12 è 2 ø

2

Σ El = 5624 + 1169931 + 12500 + 2124 + 2733 + 1785629 = 2978541 daN mm2

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MTS 006 Iss. B

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Example

N

5 4/7

giving maximum elongations : εs = - 3256 µd εi = 4761 µd In fact, elongations (and stresses) are calculated at the center of each face sheet: 4.33 = - 2906 µd 4.85 6.64 εi = 4761 = 4459 µd 7.09

εs = - 3256

z εs = - 3256 µd Mx = 2000 daN mm y

- 2906 µd

4459 µd εi = 4761 µd x

Remark: If the simplified relationship is used, we obtain: {n12} F'i = - F's ≈

2000 = 182.3 daN 0.9 1.04 + 10 + 2 2

Which corresponds to average elongations in lower and upper face sheets equal to: − 182.3 ≈ - 2921 µd the error is 0.5 % 10 1.04 6000 182.3 ≈ 4501 µd the error is 0.9 % εi ≈ 10 0.9 4500

εs ≈

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MTS 006 Iss. B

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Example

N

5 5/7

4th step: Globally, we have: - at the lower fibre, an elongation of 7612 + 4761 = 12373 µd, - at the upper fibre, an elongation of 7612 - 3256 = 4356 µd. z εs = 4356 µd

Mx = 2000 daN mm

y Ny = 800 daN

εi = 12373 µd x

The second part of the example consists in calculating the evolution of shear stress due to shear load Tz, at the neutral axis in particular, at point A (upper face sheet - honeycomb interface) and at point B (lower face sheet - honeycomb interface). 1st step: To calculate the inertia of the elasticity moduli weighted beam. {n7} Σ El = 2978541 daN mm2 Remark: If the simplified relationship of a sandwich beam is used (see § M.3.2.4), we obtain the value: 2

1.04 æ ö æ 0 .9 ö Σ El ≈ 10 6000 1.04 ç 0.9 + 10 + − 7.09 ÷ + 10 4500 0.9 ç − 7.09 ÷ 2 è ø è 2 ø

Σ El ≈ 2955560 daN mm2 the error is 1 %

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2

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Example

N

5 6/7

2nd step: - To calculate the elasticity moduli weighted static moment EW zg (static moment with relation to the neutral axis of part of the material located above it). {n8} 1.04 æ ö æ 0.9 10 1.04 ö EW zg = 10 6000 1.04 ç 0.9 + 10 + − 7.09 ÷ + 10 15 ç + + ÷ 2 2 2 ø è ø è 2

2

EW zg = 275538 daN mm - To calculate the elasticity moduli weighted static moment EW A (static moment with relation to the neutral axis at the upper face sheet). 1.04 æ ö EW A = 10 6000 1.04 ç 0.9 + 10 + − 7.09 ÷ 2 è ø

EW A = 270192 daN mm - To calculate the elasticity moduli weighted static moment EW B (opposite of the static moment with relation to the neutral axis at the lower face sheet). æ 0.9 ö EW B = 10 4500 0.9 ç − + 7.09 ÷ è 2 ø

EW B = 268920 daN mm

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MTS 006 Iss. B

Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR Example

N

5 7/7

3rd step: to determine shear stresses at the neutral axis (shear stress in honeycomb), at point A and point B. {n9} τzg =

250 275538 = 2.31 hb (23.1 MPa) 10 2978541

τA =

250 270192 = 2.26 hb (22.6 MPa) 10 2978541

τB =

250 268920 = 2.25 hb (22.5 MPa) 10 2978541

It should be noted that, between point A and point B, the shear stress is practically constant. It would be totally constant if the honeycomb elasticity modulus were zero (which may be considered as such). z Tz = 250 daN -A

-B

y τA = 2.26 hb τzg = 2.31 hb τB = 2.25 hb

x

Remark: With the simplified formula, we find: {n10} τA ≈ τzg ≈ τB ≈

250 1.04 ö æ 0.9 10 ç + 10 + ÷ 2 ø è 2

= 2.28 hb (22.8 MPa)

The error is 2 %.

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Composite stress manual

SANDWICH - MEMBRANE / BENDING / SHEAR References

N

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials M. THOMAS, Analysis of a laminate plate subjected to membrane and bending loads, 440.227/79 J.C. SOURISSEAU, 40430.030 J. CHAIX, 436.127/91

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Composite stress manual

O SANDWICH - FATIGUE ANALYSIS

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Composite stress manual

P SANDWICH - DAMAGE TOLERANCE APPROACH

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Q SANDWICH - BUCKLING ANALYSIS

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R SANDWICH - SPECIAL DESIGNS

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Composite stress manual

S BONDED JOINTS

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Composite stress manual

BONDED JOINTS Notations

S

1 . NOTATIONS F: normal load transferred in bonded materials Fr: failure load of adhesively bonded joint tö æ M: cleavage moment ç M = F x ÷ 2ø è E1: longitudinal elasticity modulus of material 1 e1: thickness of material 1 E2: longitudinal elasticity modulus of material 2 e2: thickness of material 2 E: longitudinal elasticity modulus of materials 1 and 2, if they are similar e: thickness of materials 1 and 2, if they are similar Gc: shear modulus of adhesive Ec: longitudinal elasticity modulus of adhesive ec: thickness of adhesive h: width of adhesively bonded joint l: length of adhesively bonded joint lm: minimum length of adhesively bonded joint e e æ ö t: thickness of cleavage ç t = 1 + 2 + ec÷ è ø 2 2

λ: design constant k: design constant D: design constant τm: average shear stress in adhesively bonded joint τM: maximum shear stress in adhesively bonded joint τx: shear stress in adhesively bonded joint at dimension x τam: allowable average shear stress of adhesive τaM: allowable maximum shear stress of adhesive σm: average peel stress in adhesively bonded joint σM: maximum peel stress in adhesively bonded joint σa: allowable peel stress of adhesive

© AEROSPATIALE - 1999

MTS 006 Iss. A

1 1/2

Composite stress manual

BONDED JOINTS Notations

S

F1i: normal load passing through material 1 (at center of step No. i) F2i: normal load passing through material 2 (at center of step No. i) ∆Fi: normal load transferred by the adhesively bonded joint (in step No. i) E1i: longitudinal elasticity modulus of material 1 (in step No. i) e1i: thickness of material 1 (in step No. i) E2i: longitudinal elasticity modulus of material 2 (in step No. i) e2i: thickness of material 2 (in step No. i) li: length of adhesively bonded joint (in step No. i) τmi: average shear stress in adhesively bonded joint (in step No. i) τMi: maximum shear stress in adhesively bonded joint (in step No. i)

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1 2/2

Composite stress manual

BONDED JOINTS

S

Bonded single joint - Highly flexible adhesive

2.1.1

2 . BONDED SINGLE LAP JOINT This technique consists in assembling two (or several) elements by molecular adhesion. The adhesive must ensure load transmission. Bonding of two flat surfaces only shall be considered. Four cases shall be examined: - Single joints: • highly flexible adhesive with respect to bonded laminates, • general case (without cleavage effect), • general case (with cleavage effect). - Scarf joint.

2.1 . Elastic behavior of materials and adhesive 2.1.1 . Highly flexible adhesive

h

e1

E1

Gc ec

e2

E2

l

F

τ F

τ

τ

τm

- l/2

© AEROSPATIALE - 1999

MTS 006 Iss. A

l/2

x

if E1 and E2 >> Gc

Composite stress manual

BONDED JOINTS

S

General case - Without cleavage

2.1.2 1/3

In the case of an adhesive with a very low stiffness as opposed to the stiffness of the laminates to be assembled, shear stress may be considered as uniform and equal to: s1

τm =

F hxl

If τa is the allowable shear stress of the adhesive, the minimum length of the adhesively bonded joint shall be equal to: lm =

F h x τ am

The failure load is equal to: Fr = λ x τam x h In practice, check that the average stress (which, in this case, is equal to the maximum stress) is smaller or equal to τam.

2.1.2 . General case (without cleavage effect) F τ F

τ τ

- l/2

l/2 τ

- l/2

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MTS 006 Iss. A

τM

x

if E1 x e1 ≠ E2 x e2

x

if E1 x e1 = E2 x e2

τM

l/2

Composite stress manual

BONDED JOINTS General case - Without cleavage

S

2.1.2 2/3

In the case of any bonded assembly (E1 x e1 > E2 x e2) (see drawing on previous page) subjected to a normal load F, the shear stress in the adhesively bonded joint may be formulated as follows (VOLKERSEN) :

s2

τx = τm

E x e1 − E 2 x e 2 ö sinh (λ x x ) λ x l æ cosh ( λ x x ) ÷÷ x çç x 1 + 2 è sinh (λ x l / 2) cosh (λ x l / 2) E 1 x e1 + E 2 x e 2 ø

with:

s3

λ=

G c E 1 x e1 + E 2 x e 2 x e c E1 x e 1 x E 2 x e 2

and τm =

F hxl

Remark: If E1 x e1 = E2 x e2 = E x e the joint is so-called equilibrated If E1 = E2 = E and e1 = e2 = e the joint is so-called symmetrical In the case of an equilibrated joint, the maximum shear stress may be formulated as follows: s4

τM = τm x

λ xl æλ xlö x coth ç ÷ 2 è 2 ø

with

s5

λ=

2 x Gc E x e x ec

and τm =

F hxl

if λ x l << 0 then τM ≈ τm if λ x l >> 0 then τM ≈ τm x

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λ xl 2

MTS 006 Iss. A

Composite stress manual

BONDED JOINTS

S

General case - Without cleavage

2.1.2 3/3

In practice, check that τM ≤ τaM and that τm ≤ τam If τa is the allowable shear stress of the adhesive, the minimum length of the adhesively bonded joint shall be equal to: æ2 æ Fxλ lm = Max ç x Arcth ç ç 2 x τa x h çλ M è è

ö ö ÷; F ÷ ÷ τa x h ÷ m ø ø

The failure load is equal to: æ æ λ x l ö 2 x τ aM x h ö ; l x τ am x h ÷÷ Fr = Min çç th ç ÷x λ è è 2 ø ø

The latter relationship makes it possible to establish, for a bonded assembly, the concept of optimum bonding length. Indeed, the function "th ( )" is asymptotically directed towards 1 when "λ x l/2" increases; now, value 1 is practically reached for a value of "λ x l/2" equal to 2.7 (th (2.7) = 0.99). Thus, we have: λ x l = 2 x 2.7 hence:

l=

E x e x ec E x e x ec 5. 4 = 5 .4 x = 3.82 x λ 2 x Gc Gc

In practice, the following relationship shall be used:

s6

loptimal = 3.16 x

E x e x ec Gc F Fr ≈ 0.99.Fr

l loptimal

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Composite stress manual

BONDED JOINTS

S

General case - With cleavage

2.1.3

2.1.3 . General case (with cleavage effect) F F

F M t

F

M

In the case of a symmetrical assembly, the misalignment of neutral axes of parts to be Fxtö æ assembled causes secondary moments ç M = ÷ to appear in elements, which tends to 2 ø è create peeling stresses in the adhesive. Maximum shear and peeling stresses in the adhesive may, in that case, be formulated as follows (Bruyne and Houwnik) : s7

τM = τm x

λ xl ö æλ xl x 1 + 3 x k x coth ç x 1+ 3 x k ÷ 2 ø è 2

and

s8

σM = σ x

E k e F with σ = x 6x c x 2 E ec hxe

with s9

1

k= 1+

lxF l2 x F2 + 2 x D 24 x D 2

and

s10

D=

© AEROSPATIALE - 1999

E x t3

(

12 x 1 − n 2

)

MTS 006 Iss. A

Composite stress manual

BONDED JOINTS

S

Scarf joint 2

2.1.4 1/2

2

æτ ö æσ ö Check that τM ≤ τaM and that çç M ÷÷ + ç M ÷ ≤ 1. è σa ø è τaM ø

2.1.4 . Scarf joint

ec; Gc

e2

e1

F α

E1

E2

F

l

In the case of an angle α, scarf joint, the average shear stress is equal to: τm =

F x cos α lxh

The maximum shear stress τM may be assessed using graphs on next page: as abscissa: λ x l with λ2 =

as ordinate:

© AEROSPATIALE - 1999

ö Gc æ 1 1 ÷ + x çç e c è E1 x e1 E 2 x e 2 ÷ø

τm τM

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BONDED JOINTS

S

Scarf joint

Each curve is representative of a value of ratio

2.1.4 2/2

E1 x e1 E2 x e2 1

0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6

τm τM

0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1

0.5

1

10

20

30

λl

The peeling stress in the adhesively bonded joint shall be considered as constant. It shall be equal to the following value: σm =

F x sin α lxh

In practice, check that τM ≤ τaM and that τm ≤ τam.

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Composite stress manual

BONDED JOINTS

S

Elastic-plastic behavior

2.2 1/3

2.2 . Elastic-plastic behavior of adhesive and elastic behavior of laminates Case of an elastic-plastic behavior of adhesive (see drawing below).

ela sti c

τ

rupture

τr τp

Elastic

-plastic

γp

γt

γ

As long as maximum stresses at joint ends (τM) have not reached the critical value τp (plasticizing stress of adhesive), the bonded joint behaves like a flexible joint and stress evolution follows the rules defined in paragraph 1). If the load increases, a plasticizing zone (with stress τp) is formed at the most highly loaded end of the joint. If loading is yet increased, the shear stress of the adhesive in this plasticizing zone reaches the critical value τr (failure stress of adhesive), which causes the adhesively bonded joint failure.

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Composite stress manual

BONDED JOINTS

S

Elastic-plastic behavior

2.2 2/3

The drawing below illustrates, from a quality standpoint, the shear stress evolution in the adhesively bonded joint as the bonding force increases. τ

τr: failure τp: beginning of plasticizing

Load

τp

x l

Remark: There is no simple theory for the elastic-plastic behavior of a bonded joint. A finite element model only would allow justification of the structural strength of such a system in this case.

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BONDED JOINTS

S

Elastic-plastic behavior

2.2 3/3

However, in the case of an equilibrated joint and assuming that the adhesive has an elastic-plastic behavior such as described in the drawing below, it is possible to determine (M.J. DAVIS, The development of an engineering standard for composite repairs, AGARD SMP 1994) the length of plasticized adhesive and, of course, the length of adhesive in elastic behavior. ela sti c

τ

τp

elastic-plastic

γ

γp

In the case of such behavior, the shear stress diagram in the adhesive is the following: τ Lp

Le

Lp

τp

Lp ≈

F 4 x h x τp

Le ≈

E x e x ec 6 ≈6 2 x Gc λ

L

x

If the joint is equilibrated, the plasticized length is given by the following relationship: æ 1 æ ööö F æ L tanh ç Φ ç − + L p ÷ ÷ ÷ = τp ç L p − øøø 2 è 2 è Φ è

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with

Φ=

2 x Gc ec x E x e

Composite stress manual

BONDED JOINTS

S

Bonded double lap joint

3

3 . BONDED DOUBLE LAP JOINT

h

e1

E1

Gc ec

e1

x

E2

2 x e2

E1

l

For the case of a bonded double lap joint, shear stress distribution in the adhesive film is given by the following formula (in replacement of relationship s2) : ææ 1− β ö ö β ÷÷ cosh (λ x x ) − (1 − β) sinh (λ x x ) ÷ τx = τm x λ x l x çç çç + ÷ è è tanh (λ x l) sinh (λ x l) ø ø

æ E x e2 where β = çç1 + 2 E1 x e1 è

ö ÷÷ ø

−1

In the general case, the maximum shear stress at the joint ends is formulated as follows: τM = τm x λ x l x

(1 − β' ) + β' x cosh (λ x l) sinh (λ x l)

where β' = max (β; 1 - β)

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Composite stress manual

BONDED JOINTS

S

Bonded stepped joint

4 1/3

4 . ADHESIVELY BONDED STEPPED JOINT When the laminates to be bonded are too thick or when the loads to be transmitted are too high, the "stepping" or scarfing bonding technique is imperative. The drawing below shows the general geometry of such a joint (the drawing shows a three-stepped joint (n = 3), a higher number may be considered). The design method consists in determining, for each adhesively bonded joint portion, the load fraction crossing it, then, in considering each step "i" as elementary. This so-called "short cut" method is a strictly manual method which gives the order of magnitude of average shear stresses per step. For greater accuracy, it is recommended to use the computing software PSB2 (see § S4 and program PSB2 instructions). Assumptions: Let's assume that transversal effects are insignificant (εy = 0 or Fy = 0). Let's also assume that there is no secondary bending (off-centering from the neutral line shall not be taken into account): joints below are considered as equivalent.

EQUIVALENCE

h

F Material (2) F

Material (1)

l1

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Composite stress manual

BONDED JOINTS

S

Bonded stepped joint

4 2/3

1st step: Determination of loads (F1i et F2i) passing through both laminates (parent material "1" and repair material "2") at the center of each step. We shall assume that loads are distributed (at the center of each step) in proportion to the rigidity of each material:

s11

F1i = F x

E1i x e1i

F2i = F - F1i

E 1i x e1i + E 2i x e 2i

E2i, e2i

F

F2i F F1i

E1i, e1i

We shall assume that the load evolution in material 1 (and consequently in material 2) is linear by portions. Which leads to the following configuration: F21

F

F2i

F F11

F2n

F1i F1n

F2x

F F2n F2i

F2i x Evolution of the load transferred in the repair material

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BONDED JOINTS

S

Bonded stepped joint

4 3/3

2nd step: From the previously determined curve, the load (∆Fi) transferred by each step is calculated. s12

∆F1 =

∆Fi =

l 2 x F1 + l1 x F2 l1 + l 2 li + 1 x Fi + li x Fi + 1 li + li + 1

∆Fn = Fn −

−

li x Fi − 1 + li − 1 x Fi

2≤i≤n-1

li − + li

l n x Fn − 1 + ln − 1 x Fn ln − 1 + ln

We have also

å

n

(∆Fi ) = F

i=1

The diagram below presents the method used visually: ∆F1

F

∆Fi F

∆Fn

F2x

F ∆Fn ∆Fi ∆F1 x 0

3rd step: Then, the average stress τmi is assessed. We have: s13

τmi = 1.05 x

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∆Fi h x li

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BONDED JOINTS EDP software

S

5

where 1.05 is a fixed plus factor (according to the rule) allowing one to be conservative with respect to results established by EDP software. 4th step: Check for the following condition: For any step (i) τmi ≤ τam

5 . EDP SOFTWARE The EDP software PSB2 digitally processes problems with adhesively bonded stepped joints and, therefore, with adhesively bonded single joints as well. This computing program is based on a differential analysis of the adhesively bonded joint and not on the "short cut" method outlined in chapter § S3. The purpose of this software is to compute: - stresses in any point of a bonded stepped single or double joint (evolution of shear stress and average stress per step), - the evolution of normal stress in parent and repair laminates. For more information, refer to instructions for use or to the example in chapter § S6.2.

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BONDED JOINTS

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First example

6.1 1/2

6 . EXAMPLES 6.1 . First example: single joint Let the following symmetrical bonded joint be:

h = 100 mm Gc = 400 daN/mm e1 = 2 mm

E1 = 5000 daN/mm

2

2

ec = 0.1 mm

E2 = 5000 daN/mm

2

e2 = 2 mm

l = 50 mm

The allowable average shear value of the adhesive being: τam = 0.8 hb. Assuming that the joint is subjected to load F = 1000 daN and that there is no cleavage effect. 1000 1000 = 0.2 hb (2 MPa) = 100 x 50 5000

{s1}

τm =

{s5}

λ=

{s4}

τM = 0.2 x

2 x 400 = 0.9 5000 x 2 x 0.1 0.9 x 50 æ 0.9 x 50 ö x coth ç ÷ = 4.5 hb (45 MPa) 2 2 ø è

Check that the average stress τm is smaller than the allowable stress τam (0.8 hb; 8 MPa) and that the maximum stress τM is smaller than τaM (8 hb; 80 MPa). The margin thus obtained is equal to 77 % (RF = 1.77 = 8/4.5). Within the framework of the previous example, let's calculate the optimum bonding length from which any increase becomes useless over the decrease of maximum shear stress in the adhesive.

{s6}

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loptimale = 3.16 x

5000 x 2 x 0.1 = 5 mm 400

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BONDED JOINTS

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First example

6.1 2/2

This result proves that, concerning the maximum shear stress, a change in the bonding length from 50 mm to 5 mm increases (after calculations) this stress by only 1 %. The gain is thus insignificant. Concerning the average stress, the minimum length is equal to: lm =

1000 = 12.5 mm 0.8 x 100

The drawing below shows the evolution of the actual stress (smooth curve) and the value of the average stress (dotted curve) in the example quoted. 4.5

4

3.5

3

2.5 τ 2

1.5

1

0.5

0 - 25

- 20

- 15

- 10

-5

0 x

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BONDED JOINTS

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Second example

6.2 1/5

6.2 . Second example: three-stepped joint Let the following three-stepped joint be defined by its geometry and mechanical properties: h = 10 mm

F = 100 daN

F = 100 daN l1 = 15 mm

e21 = 0.26 mm 2 E21 = 5250 daN/mm

l2 = 10 mm

l3 = 15 mm

e22 = 0.52 mm 2 E22 = 5000 daN/mm

e23 = 0.78 mm 2 E23 = 7000 daN/mm

2 1

e11 = 0.78 mm 2 E11 = 7000 daN/mm

e12 = 0.52 mm 2 E12 = 5000 daN/mm

e13 = 0.26 mm 2 E13 = 5250 daN/mm

The allowable average shear value of the adhesive being: τam = 0.8 hb (8 MPa). The allowable maximum shear value of the adhesive being: τaM = 8 hb (80 MPa). We shall assume that the joint is subjected to load F = 100 daN and that there is no cleavage effect. The first stage consists in calculating, at the center of each step, loads passing through each material. Concerning the first step: {s11}

F21 = 100 x

0.26 x 5250 = 20 daN 0.26 x 5250 + 0.78 x 7000

F11 = 100 - 20 = 80 daN

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BONDED JOINTS

S

Second example

6.2 2/5

Concerning the second step : {s11}

F22 = 100 x

0.52 x 5000 = 50 daN 0.52 x 5000 + 0.52 x 5000

F12 = 100 - 50 = 50 daN Concerning the third step: {s11}

F23 = 100 x

0.78 x 7000 = 80 daN 0.26 x 5250 + 0.78 x 7000

F13 = 100 - 80 = 20 daN The determination of these values allows the load evolution curve passing through material 2, or repair material, to be plotted: F21

F

F22

F F11

F12

F23

F13

F2x

F = 100 daN F23 = 80 daN F22 = 50 daN F21 = 20 daN x

0

The second stage consists in calculating, from the previous curve, loads transferred by each step: {s12}

∆F1 =

15 x 50 + 10 x 20 - 0 = 38 daN 15 + 10

{s12}

∆F2 =

15 x 50 + 10 x 80 15 x 50 + 10 x 20 = 24 daN − 15 + 10 15 + 10

{s12}

∆F3 = 100 -

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15 x 50 + 10 x 80 = 38 daN 15 + 10

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BONDED JOINTS

S

Second example

6.2 3/5

The drawing below represents the different loads ∆Fi transferred by each step. ∆F1

F

∆F2 F

∆F3

∆F3 = 38 daN ∆F2 = 24 daN ∆F1 = 38 daN x

The third stage consists in determining for each step the average and maximum stresses in the adhesively bonded joint, based on ∆Fi calculated previously. steps 1 and 3 being equivalent for symmetry reasons, only the first two shall be justified. {s13} τm1 = 1.05 x

38 = 0.266 hb (2.66 MPa) 10 x 15

{s13} τm2 = 1.05 x

24 = 0.252 hb (2.52 MPa) 10 x 10

and τm3 = τm1 = 0.266 hb (2.66 MPa)

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BONDED JOINTS

S

Second example

6.2 4/5

The fourth stage consists in checking that average stresses are smaller than τam. 0.266 < 0.8 hb

F F

τ

τ = 0.266 hb

τ = 0.252 hb

τ = 0.266 hb x

Only a digital analysis (program PSB2) or a finite element analysis (program PSH14) shall be able to determine with accuracy the shear stress evolution along each step.

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BONDED JOINTS

S

Second example

6.2 5/5

For information purposes, we present below the output file of PSB2 corresponding to the previous example. Basic data: I 5) 3 3 10 1 F10) 10.0000000 10.0000000 A 8)BONDED STEPPED JOINT SAMPLE MAT1 MAT1 MAT1 MAT1 MAT1 MAT1

MF

4

1001) 2001) 3001) 4001)

4

2

5000.00000 3000.00000 0. 0.52000000

5250.00000 3000.00000 0. .260000000

← parent material

5000.00000 3000.00000 0. .520000000

7000.00000 3000.00000 0. .780000000

← repair material

3

5250.00000 3000.00000 0. .260000000

COLLE MF COLLE COLLE 1001) COLLE 2001)

3

.050000000 300.000000

VF

← loading

3

7000.00000 3000.00000 0. .780000000

MAT2P MF MAT2P MAT2P 1001) MAT2P 2001) MAT2P 3001) MAT2P 4001)

3

.050000000 300.000000

.050000000 ← adhesive 300.000000

25.0000000

40.0000000 ← step dimensions

3 1)

15.0000000

Output (average stresses in each step): AVERAGE STRESS IN THE ADHESIVE FOR EACH STEP STEPS UPPER STEPS HB 1 2 3

.229 .313 .229

← step No. 1 ← step No. 2 ← step No. 3

It may thus be observed that the short cut method provides (in this example), with respect to the PSB2 method, a difference of: + 16 % for external steps - 20 % for the central step Consequently, it is recommended to use as often as possible the software PSB2, its analytical model being "closer" to physical reality. The "short cut" method being mainly a manual method.

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BONDED JOINTS References

S

GAY, Composite materials, 1991 K. STELLBRINK, Preliminary Design of Composite Joints, DLR-Mitt.92-05 S. ANDRE, Structural strength of a bonded joint, AS 432.178/95 A. TROPIS, Study of the behavior of bonded junctions, AS 432.445/96 S. ANDRE, Elastic-plastic analysis of the behavior of a bonded junction with a bonding failure accounted for, AS 432.651/96 M.J. DAVIS, The development of an engineering standard for composite repairs, AGARD SMP 1994 NASA CR 112-235 NSA CR 112-236 D.A. BIGWOOD A.D. CROCOMBE, Elastic analysis and engineering design formulae for bonded joints L.J. HART SMITH, Adhesively bonded joints for fibrous composite structures, Mc Donnell Douglas Corporation L.J. HART SMITH, The design of repairable advanced composite structures, Mc Donnell Douglas Corporation 1985 L.J. HART SMITH, Adhesive bonded scraf and stepped lap joints, Mc Donnell Douglas Corporation J.W. VAN INGEN A. VLOT, Stress analysis of adhesively bonded single lap joint S. MALL N.K. KOCHHAR, Criterion for mixed mode fracture in composite bonded joints, University of Missourri-Rolla, 1986 S. MALL W.S. JONSHON, A fracture mechanic approach for designing adhesively bonded joints, University of Maine M. DE NEEF, Study of composite material bonding with edge effects accounted for, Alcatel Espace ; Août 1992 M. THOMAS, Stress distribution in bonded stepped joints, 440.128/77

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BONDED REPAIRS Notations

T

1 . GENERAL NOTATIONS (o, x, y): reference coordinate system of panel (o, p, p'): main coordinate system of stress fluxes Nx∝: normal flux in direction x Ny∝: normal flux in direction y Nxy∝: shear flux Np∝: principal flux in direction p Np'∝: principal flux in direction p' β: angle

In principal direction p τmi: average shear stress in adhesively bonded joint (in step No. i) τMi: maximum shear stress in adhesively bonded joint (in step No. i) Nsi: normal flux in parent material (in step No. i) Nri: normal flux in repair material (in step No. i)

In principal direction p' τ'mi: average shear stress in adhesively bonded joint (in step No. i) τ'Mi: maximum shear stress in adhesively bonded joint (in step No. i) N'si: normal flux in parent material (in step No. i) N'ri: normal flux in repair material (in step No. i) τam: allowable average shear stress of adhesive τaM: allowable maximum shear stress of adhesive

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BONDED REPAIRS

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Introduction

2

2 . INTRODUCTION When a panel undergoes a damage (hole, delamination, etc.), two types of repair may be considered: a bolted repair (see chapter U) or a bonded repair. Let the damaged (assuming that the damage is a hole) panel (monolithic skin) be subjected to stress fluxes Nx∝, Ny∝, Nxy∝. We shall assume that the repair is circular and of its stiffness close to that of the skin (no increase of parent skin fluxes due to load transfer in a repair that is too stiff).

Ny∝

Nxy∝

Nx∝

y

x

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BONDED REPAIRS Analytical method

T

3.1 1/6

3 . DESIGN METHOD 3.1 . Analytical method This is an extrapolation of the bonded joint method (see chapter S) and, therefore, it is not suited for shear flux transfer. Thus, it is necessary to work within the principal coordinate system in which stress fluxes are Np∝ and Np'∝ to return to the case of a single joint. This method is conservative.

1st step: Calculation of principal fluxes Np and Np' and of main angle β. t1

Np∝ =

t2

Np'∝ =

t3

β=

N x ∞ + Ny ∞ 2 N x ∞ + Ny ∞ 2

+

1 (Nx ∞ − Ny ∞ )2 + 4 Nxy ∞ 2 2

−

1 (N x ∞ − Ny ∞ )2 + 4 N xy ∞ 2 2

æ 2 N xy ∞ 1 Arctg çç 2 è Nx∞ − Ny∞

ö ÷ ÷ ø y

Np'∝

Np∝

β

x

p' p

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BONDED REPAIRS

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Analytical method

3.1 2/6

2nd step: For each calculation direction (p and p'), let's consider the repair as a 1 mm wide material strip. The drawing below shows that, based on a two-dimensional repair (R), two onedimensional bonded stepped joints (Jp) and (Jp') are determined (or isolated). Each one of these elementary bonded joints must transfer a normal load Fp = 1 Np∝ and Fp' = 1 Np'∝. For the determination of flux transfers from the parent material to the repair material, refer to the design method for bonded stepped joints (see chapter S) or to the computing software PSB2. y Np'∝

Np∝

J p' β

Jp

x

p'

m 1m

p

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T

Analytical method

3.1 3/6

3rd step: From this analysis, the following results are extracted for each step and each direction (p and p'): - for direction p: • average and maximum shear stresses in each step of the adhesively bonded joint: τmi (average stress in step i) and τMi (maximum stress in step i), • normal fluxes in the parent material for each step Nsi (step i), • normal fluxes in the repair material for each step Nri (step i).

Jp 4

1

i=

2

3

p τ Mi τ mi

τ

p

Nsi

N

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BONDED REPAIRS

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Analytical method

3.1 4/6

- for direction p': • average and maximum shear stresses in each step of the adhesively bonded joint: τ'mi (average stress in step i) and τ'Mi (maximum stress in step i), • normal fluxes in the parent material for each step N'si (step i), • normal fluxes in the repair material for each step N'ri (step i). p'

p'

N' r i

J p' N' s i

τ' m i

4 3

N p'

τ' M i

i=

2 N'

1

τ

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Analytical method

3.1 5/6

4th step: It consists of a combination of previously determined shear stresses and normal fluxes. - Average shear stresses in the adhesively bonded joint calculated for both directions p and p' are vertorially combined (although points are different) and the resulting stress for each step is compared with the allowable average shear value of the adhesive considered. t4

( τmi )2 + (τ'mi )2 ≤ τ a m

τmi (p)

τ'mi (p')

adhesively bonded joint step No. i

- Maximum shear stresses in the adhesively bonded joint calculated for both directions p and p' are vectorially combined (although points are different) and the value found for each step is compared with the allowable maximum shear value of the adhesive considered. t5

( τMi )2 + (τ'Mi )2 ≤ τ a M

τMi (p)

τ'Mi (p')

adhesively bonded joint step No. i

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Analytical method

3.1 6/6

- In a plain plate calculation (see chapter C), normal stress fluxes Nsi and N'si for the parent material are associated (although points are different). This calculation shall be performed where fluxes are maximum (at the beginning of each step).

N'si Nsi

es parent material step No. i

- In a plain plate calculation (see chapter C), normal stress fluxes Nri and N'ri for the repair material are associated (although points are different). This calculation shall be performed where fluxes are maximum (at the end of each step). N'ri Nri

er repair material step No. i

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Digital method

3.2

3.2 . Digital method In the case of a highly loaded bonded repair or with complex loading, the use of finite element modeling is preferable. The software PSH14 has been developed for this purpose. It allows automatic modeling of a circular bonded repair (see drawing below). This model is subjected to membrane stress only and does not take cleavage effects into account. The adhesively bonded joint is represented by type 29 volume elements (with elasticplastic behavior), the panel and repair by type 80 and 83 elements. Y-axis

507 407 same as st 1 quadrant

307

207 X-axis

same as st 1 quadrant

same as st 1 quadrant

details of step elements

107

36

The plotted results represent: - plane fluxes in the parent material, - plane fluxes in the repair material, - shear stresses in the adhesive. For more information, refer to program instructions.

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Example

4 1/8

4 . EXAMPLE Let the following repair be: Nxy∝ = 4 daN/mm

y

x

Parent material: G803/914 (new) Repair material: G803/914 (new) 0°/90° 45°/135° 0°/90° 45°/135° 0°/90° 45°/135° 0°/90° 45°/135°

0°/90° 45°/135° 0°/90° 45°/135° 0°/90° 45°/135°

i=1

i=2

12

20

Let's assume (with a view to simplification) that both materials are nearly-isotropic (their elasticity modulus being equal to 4417 daN/mm2 in all directions) for each step and that steps are 12 and 20 mm long. The parent panel is only subjected to shear flux Nxy∝ = 4 daN/mm.

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BONDED REPAIRS

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Example

4 2/8

We may deduce that the principal coordinate system has a 45° direction and that principal fluxes are equal to Np∝ = 4 daN/mm and Np'∝ = - 4 daN/mm. {t1} Np∝ = +

1 4 4 2 = 4 daN/mm 2

{t2} Np'∝ = -

1 4 4 2 = - 4 daN/mm 2

{t3} β=

1 1 æ2x 4ö 1 Arctg ç ÷ = Arctg (∞ ) = 90 = 45° 2 2 è 0 ø 2

y

Np∝ = 4 daN/mm

Np'∝ = - 4 daN/mm

J

Jp

p'

β = 45°

x

p'

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BONDED REPAIRS

T

Example

4 3/8

After running the software PSB2 (computation of a bonded stepped joint), the following results are found for direction p (results may be multiplied by - 1 for direction p'): - Shear stresses in the adhesive 3

2.2 hb 2

τ 1.35 hb 1.21 hb

1

0.207 hb 0.076 hb 0 0

5

10

15

20 p

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Example

4 4/8

- Stress fluxes in the parent material (direction p)

4

3.5

3

2.5

Nsi

2

1.512 daN/mm 1.5

1

0.5

0 0

5

10

15

20 p

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Example

4 5/8

- Stress fluxes in the repair material (direction p)

6

5

4

Nri

3 2.472 daN/mm

2

1

0 0

5

10

15

20 p

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T

4 6/8

• The first check consists of a vectorial combination of average shear stresses for each step. In this case, average shear stresses are the same (to the nearest sign) in both directions p and p'. The maximum value is equal to 0.207 daN/mm2 in each direction. We may deduce the vectorial resultant stress: {t4} (τm1 )2 + (τ'm1 )2 = 2 0.207 = 0.293 daN/mm2

This value is to be compared to the allowable average shear value of the adhesively bonded joint that is generally selected equal to 0.8 daN/mm2 (a 173 % margin is obtained).

• The second check consists of a vectorial combination of maximum shear stresses for each step. In this case, shear stresses are the same (to the nearest sign) in both directions p and p'. The maximum stress is reached at the beginning of the first step. The value reached is equal to 2.20 daN/mm2. We may deduce the vectorial resultant stress : {t5} (τM1 )2 + (τ'M1 )2 = 2 2.20 = 3.11 daN/mm2

This value is to be compared to the allowable maximum shear value of the adhesively bonded joint: 8 daN/mm2 (a 157 % margin is obtained).

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BONDED REPAIRS Example

T

4 7/8

• The third check consists of a plain plate calculation of the parent material for each step (where the flux is maximum: at the beginning of the step). At the beginning of the first step, the flux in direction p is Ns1 = 4 daN/mm and the flux in direction p' is N's1 = - 4 daN/mm, which corresponds to a shear flux Nxys1 equal to 4 daN/mm in the reference coordinate system. At this location, the parent material is made out of six fabrics (3 fabrics at 0°/90° + 3 fabrics at 45°/135°) G803/914 (supposed new). A running of the program PSB3 (plain plate computation) makes it possible to find a Hill's criterion margin equal to 966 %. At the beginning of the second step, the flux in direction p is Ns2 = 1.512 daN/mm and the flux in direction p' is N's2 = - 1.512 daN/mm, which corresponds to a shear flux Nxys2 equal to 1.512 daN/mm in the reference coordinate system. At this location, the parent material is made out of two fabrics (1 fabric at 0°/90° + 1 fabric at 45°/135°) G803/914 (supposed new). A running of program PSB3 (smooth plate computation) makes it possible to find a Hill's criterion margin equal to 843 %.

• The fourth check consists of a smooth plate calculation of the repair material for each step (where the flux is maximum: at the end of the step). At the end of the first step, the flux in direction p is Nr1 = 2.472 daN/mm and the flux in direction p' is N'r1 = - 2.472 daN/mm, which corresponds to a shear flux Nxyr1 equal to 2.472 daN/mm in the reference coordinate system. At this location, the repair material is made out of four fabrics (2 fabrics at 0°/90° + 2 fabrics at 45°/135°) G803/914 (supposed new). A running of the program PSB3 (plain plate computation) makes it possible to find a Hill's criterion margin above 1000 %.

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BONDED REPAIRS Example

T

4 8/8

At the end of the second step, the flux in direction p is Nr2 = 4 daN/mm and the flux in direction p' is N'r2 = - 4 daN/mm, which corresponds to a shear flux Nxyr2 equal to 4 daN/mm in the reference coordinate system. At this location, the repair material is made out of eight fabrics (4 fabrics at 0°/90° + 4 fabrics at 45°/135°) G803/914 (supposed new). A running of the program PSB3 (plain plate computation) makes it possible to find a Hill's criterion margin above 1000 %. B

In conclusion, the minimum safety margin is assessed at 157 % under maximum stress in the adhesively bonded joint.

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BONDED REPAIRS References

T

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials TRIQUENAUX, Investigation on the use of bonding and on dimensioning rules of bonded joints, 1995, DCR/M-62385/F-95 CUQUEL-LEONDUFOUR, Study of bonded repairs, 1995, 432.095/95 CIAVALDINI, Effect of stepped machining on the structural strength of a skin intended to receive a bonded repair, 1994, 440.133/94 STELLBRINK, Preliminary design of composite joints, 1992, DLR-Mitt.92-05 M. THOMAS, Stress distribution in bonded stepped joints, 440.128/77 M. MAHE - D. GRIMALD, Implementation of a digital model for the finite element design of bonded repairs on composite materials, 436.0086/95

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U BOLTED REPAIRS

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BOLTED REPAIRS Notations

U

1 . NOTATIONS ∅: diameter of damage Nx EF meca. : flux Nx derived from E.F.s not influenced by the repair Ny EF meca. : flux Ny derived from E.F.s not influenced by the repair Nxy EF meca. : flux Nxy derived from E.F.s not influenced by the repair ∞ Nx or Nx meca . : mechanical origin flux Nx upstream of the repair ∞ Ny or Ny meca . : mechanical origin flux Ny upstream of the repair ∞ Nxy or Nxy meca . : mechanical origin flux Nxy upstream of the repair

Nxr meca.: mechanical origin flux Nx crossing the doubler Nyr meca.: mechanical origin flux Ny crossing the doubler Nxyr meca.: mechanical origin flux Nxy crossing the doubler Nxr meca. + therm.: mechanical and thermal origin flux Nx crossing the doubler Nyr meca. + therm.: mechanical and thermal origin flux Ny crossing the doubler Nxr therm.: thermal origin flux Nx crossing the doubler Nyr therm.: thermal origin flux Ny crossing the doubler Nxs meca.: mechanical origin flux Nx in the panel below the doubler Nys meca.: mechanical origin flux Ny in the panel below the doubler Nxys meca.: mechanical origin flux Nxy in the panel below the doubler L sx and h sx : panel dimensions for calculation of direction x L sy and h sy : panel dimensions for calculation of direction y L rx and h rx : doubler dimensions for calculation of direction x L ry and h ry : doubler dimensions for calculation of direction y n: total number of load-carrying fasteners in the given direction r: elementary stiffness of fasteners. Exs: longitudinal elasticity modulus (direction x) of panel Eys: transversal elasticity modulus (direction y) of panel Gxys: shear modulus of panel es: panel thickness

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1 1/2

Composite stress manual

BOLTED REPAIRS Notations

U

1 2/2

αxs: coefficient of expansion of panel in direction x αys: coefficient of expansion of panel in direction y Exr: longitudinal elasticity modulus (direction x) of doubler Eyr: transversal elasticity modulus (direction y) of doubler Gxyr: shear modulus of doubler er: doubler thickness. αxr: coefficient of expansion of doubler in direction x αyr: coefficient of expansion of doubler in direction y R sx : stiffness of panel with respect to flux Nx R sy : stiffness of panel with respect to flux Ny R sxy : stiffness of panel with respect to flux Nxy R rx : stiffness of doubler with respect to flux Nx R ry : stiffness of doubler with respect to flux Ny R rxy : stiffness of doubler with respect to flux Nxy η: correcting factor of panel shear stiffness a and a*: fastener pitch ni: number of rows of fasteners on a "unit strip" ri: stiffness of all fasteners on row "i" A: distance between the last load-carrying row of fasteners and the axis of symmetry of the repair Fxi: overall load transferred by row of fasteners "i" in direction x Fyi: overall load transferred by row of fasteners "i" in direction y fx/xij: load on fastener identified by rows "i" and "j" due to flux Nx fy/yij: load on fastener identified by rows "i" and "j" due to flux Ny fx/xyij: direction x load on fastener identified by rows "i" and "j" due to flux Nxy fy/xyij: direction y load on fastener identified by rows "i" and "j" to flux Nxy lxi: position of row of fasteners "i" with relation to the axis of symmetry of the repair lyj: position of row of fasteners "j" with relation to the axis of symmetry of the repair Remark: Without an exponent, a notation looses its directional nature and thus becomes general and applicable to x and y-axes.

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BOLTED REPAIRS

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Stiffness of a fastener in single shear

2.1

2 . STIFFNESS OF FASTENERS One of the most important parameters for the justification of a bolted repair is the stiffness of fasteners which make it up. Their effect on load transfer is direct. The purpose of this sub-chapter is to make an analytical assessment of the stiffness of a fastener. Two cases are considered: single shear (the most common in our case) and double shear.

2.1 . Stiffness of a fastener in single shear Let a fastener of diameter D and longitudinal elasticity modulus E bind two parts of thickness er and es and of elasticity moduli Er and Es.

Er E er

Es es D

The stiffness of the fastener + parts system to be bound may be assessed by one of the three relationships quoted below. æ 1 1 5 1 = + 0.8 ç + ç r ED è Er er E s es

1 = r

0.85 er 2 D

er

æ 1 3 ö çç ÷÷ + + E 8 E è r ø

æ e + er ö 1 =ξç s ÷ r è 2D ø

2/ 3

ö ÷ ÷ ø

0.85 e s 2 D

es

→ Mac Donnel Douglas

æ 1 3 ö çç ÷÷ + E 8 E è s ø

æ 1 1 1 1 ö + + + ç ÷ → Huth è Er e r E s e s 2 er E 2 e s E ø

with ξ = 2.2 → rivet on metal joint ξ=3

→ screw on metal joint

ξ = 4.2 → carbon seal

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→ Boeing

MTS 006 Iss. A

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BOLTED REPAIRS

U

Stiffness of a fastener in double shear - Assumptions

2.2 3

1/2

In the software (Bolted Repairs), the stiffness of the fastener + parts system to be bound is calculated by the Huth method:

u1

æ e + er 1 = 4.2 çç s r è 2D

ö ÷÷ ø

2/3

æ 1 1 1 1 ö ÷÷ çç + + + è Er er E s e s 2 er E 2 e s E ø

2.2 . Stiffness of a fastener in double shear For the case of a load-carrying fastener in double shear, let's assume: rdouble shear ≈ 1.5 rsingle shear er 2

Er E Es es

D

3 . ASSUMPTIONS Let's have the five following assumptions: - a delamination type damage shall be considered as a hole if the load flux it is subjected to is a compression or shear flux. In tension, we shall consider that the panel retains its initial stiffness, - the panel is subjected to membrane stress. The bending effects cannot be taken into account in this method, - the panel and doubler have a constant thickness and all fasteners are similar, - the "Poisson" effect is ignored on the doubler,

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Assumptions

3 2/2

- no overload on panel due to the presence of the doubler: to take it into account, fluxes in the skin derived from finite element (N EF meca. ) should be increased in proportion to stiffnesses of the non-damaged skin alone and of the damaged skin with reinforcing piece. ∞ Nx meca .

∞ Ny meca .

=

Nx EF meca.

=

Ny EF meca.

EF ∞ Nxy meca . = Nxy meca.

Rrx + Rsx Rsx ∅ = 0 R ry + R sy R sy ∅ = 0 R rxy + R sxy R sxy∅ = 0

=

E x s e s hrx

with

R sx ∅ = 0

with

R sy ∅ = 0

with

R sxy∅ = 0 = Gxy s es

=

Lxs E y e s hry s

Lys

All type R βα stiffnesses are explained further. α: x; y; xy β: r; s Generally speaking, a bolted repair attached to a panel subjected to three load fluxes ∞ ∞ ∞ Nx meca . , Ny meca. , Nxy meca. may be represented as follows:

∞

Ny meca. ∞

Nxy meca.

∞

Nx meca.

∞

Nx meca.

y

∞

Nxy meca.

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x

∞

Ny meca.

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BOLTED REPAIRS

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Geometrical data - Mechanical properties

4 5

The justification method of such a repair shall first consist in calculating the three load fluxes crossing the doubler (Nxr meca., Nyr meca. and Nxyr meca.) then in assessing loads applied to the repair fasteners, based on these results. The set of fluxes at each fastener may be determined on a unique basis. Some geometrical and mechanical parameters of the structure shall be required for conducting this study.

4 . GEOMETRICAL CHARACTERISTICS Below are represented the general geometrical characteristics describing the repair. All other geometrical characteristics appearing further in the document may be formulated according to these characteristics. y

2 hr

a* x

2 hr

∅

y er es x

a

5 . MECHANICAL PROPERTIES The mechanical properties required are the following: For the panel: Longitudinal (direction x) and transversal (direction y) elasticity moduli, shear modulus and thickness: Exs; Eys; Gxys; es. For the doubler: Longitudinal (direction x) and transversal (direction y) elasticity moduli, shear moduli and thickness: Exr; Eyr; Gxyr; er.

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Distribution of flux Nx

6.1

For fasteners: Number of load-carrying fasteners (n) and elementary stiffness in shear (r) of each fastener.

6 . ASSESSMENT OF MECHANICAL ORIGIN FLUXES IN THE DOUBLER The assessment method of fluxes crossing the doubler (Nxr

meca.

, Nyr

meca.

and Nxyr

meca.

) is

∞ ∞ ∞ identical for all three fluxes Nx meca . , Ny meca. and Nxy meca. . It consists in calculating for each

one the equivalent stiffness of the panel (Rs) and the equivalent stiffness of the doubler (Rr) and in distributing the flux in proportion to those.

6.1 . Distribution of flux Nx ∞ If Nx meca . is the panel flux "far from the repair", the flux Nxr meca.crossing the doubler is equal

to:

u2

∞ Nxr meca. = Nx meca .

R rx R rx + R sx

with E xr e r hrx n r

u3

R rx =

E xr

4 Lxr e r hrx Lxr

+

nr 4

and

u4

R sx =

E x s es hsx Lxs

without chamfer

æ a* hx − a *ö R sx = Exs es ç x + s x ÷ with chamfer Ls ø è Ls − a

where 2 L rx is the distance between the centers of gravity of fasteners located on either side of the damage (see shaded fasteners on drawing below). The number of columns taken into account shall never exceed 3.

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BOLTED REPAIRS

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Distribution of flux Ny

hsx = hrx −

∅ 2

6.2

x

2 Ls

chamfer

∅ x

hs

y

x

Lr center of gravity of fasteners

x

6.2 . Distribution of flux Ny ∞ If Ny meca . is the panel flux "far from the repair", the flux Nyr meca. crossing the doubler is equal

to:

u5

∞ Nyr meca. = Ny meca .

R ry R ry + R sy

with E yr e r hry n r

u6

R ry =

E yr

4 Lyr e r hry Lyr

+

nr 4

and u7

R sy

=

Ey s es hsy Lys

without chamfer

æ a hy − a ö + s y ÷ with chamfer R sy = Eys es ç y Ls ø è Ls − a *

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Distribution of flux Nxy

6.3

where 2 L ry is the distance between the centers of gravity of fasteners located on either side of the damage (see shaded fasteners on drawing below). The number of columns taken into account shall never exceed 3. hys = hry −

∅ 2 center of gravity of fasteners

y

Lr

y

2 Ls

y

x

chamfer

y hs

6.3 . Distribution of flux Nxy ∞ If Nxy meca . is the panel flux "far from the repair", the flux Nxyr meca. crossing the doubler is

equal to:

u8

∞ Nxyr meca. = Nxy meca .

R rxy R rxy + R sxy

with Gxy r er n r

u9

R rxy =

8 Gxy r er +

nr 8

and u10

R sxy = η Gxys es Factor η makes it possible to take into account the effect of damage size ∅ on the panel shear stiffness below the doubler.

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Composite stress manual

BOLTED REPAIRS Thermal origin loads in doubler

u11

η=

V2 + W2

æ ç ç V − 1+ 1 1 ç 1− ç W è

U

7

0.5

2

ö æ ÷ ç ÷ + ç W − 1+ 1 1 ÷ ç 1− ÷ ç V ø è

ö ÷ ÷ ÷ ÷ ø

2

with V=

2 Lxs ∅

and W=

2 Lys ∅

7 . ASSESSMENT OF THERMAL LOADS IN THE DOUBLER In the case of two geometrically different plates (1) and (2) bound by a system with stiffness ℜ, the thermal loads applied to plate (1) are equal to: v9

F=

∆θ (α 2 L 2 − α1 L1) L1 L2 2 + + e1 b1 E1 e2 b 2 E2 ℜ

(cf. § V6.1)

(1)

ℜ

ℜ

(2)

L2 b1

L1

b2

By generalizing this relationship with the case of a bolted repair, we find thermal loads in directions x and y which apply to the doubler:

u12

Fxr therm. =

© AEROSPATIALE - 1999

(

2 ∆θ α x s Lxs − α xr Lxr Lxr e r hrx

E xr

+

Lxs e s h sx E x s

)

+

4 nr

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS Flux in panel - Loads per fastener due to Nx and Ny

Fyr therm. =

(

2 ∆θ α y s Lys − α yr Lyr Lyr er hry E yr

+

Lys e s h sy Ey s

U

8 9

)

+

4 nr

We may thus deduce the thermal gross fluxes in the doubler: Nxr therm. =

Nyr therm. =

Fx r

therm.

2 hrx Fyr

therm.

2 hry

8 . ASSESSMENT OF FLUXES IN THE PANEL Gross fluxes in the panel are deduced immediately form fluxes crossing the doubler: u13

∞ Nxs meca. = Nx meca . - Nxr meca. - Nxr therm. ∞ Nys meca. = Ny meca . - Nyr meca. - Nyr therm. ∞ Nxys meca. = Nxy meca . - Nxyr meca.

9 . ASSESSMENT OF LOAD S PER FASTENER DUE TO THE TRANSFER OF NORMAL LOADS Nx AND Ny Loads in fasteners are deduced from the geometry and from mechanical and thermal fluxes crossing the doubler and calculated previously. A half repair may be represented as follows. The analysis being similar for directions x and y, indexes x and y have been removed to make the diagram as general as possible. There are two possible cases (see drawings on next page): - straight edge, - edge with chamfer.

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BOLTED REPAIRS

U

Repair with 1 row of fasteners

i=6

i=5

i=4 i=3

i=2

9.1

i=1

r

∞ N meca. + therm.

2 hr er Er es Es

a

a

A Fr

F6

a

a

F5

a

F4

F3

F2

F1

F∞ Fs

r

2 hr

∞ N meca. + therm.

er Er es Es

A

a

a

a

a

a

9.1 . Repair with 1 row of fasteners If the number of rows of fasteners is equal to 1, the load transmitted in the doubler is equal to loads transmitted by all fasteners on the row (single). The load per fastener is then deduced immediately by the relationship:

f/fix. =

2 x Nr meca . + therm. x h r Fr = number of fasteners number of fasteners

F1 F1

F

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BOLTED REPAIRS

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Repair with 2 rows of fasteners

9.2

9.2 . Repair with 2 rows of fasteners

A

a

E2' S2'

E1' S1'

F1 + F2 r2

E2 S2

F2

r1

F1

E1 S1

F

The overall stiffness of row "i" fasteners is defined by (ri). ri = ni x r where ni is the number of fasteners on row "i". If F1 and F2 correspond to loads transmitted by the rows of fasteners, the system displacement resolution leads to the two following equations: æ A 1 A F2 çç + + è E 2 ' x S 2 ' r2 E 2 x S 2

ö æ A A ÷ + F1 ç çE x S + E x S ÷ 2' 2 2 è 2' ø

æ − 1ö æ Fxa a a 1ö F2 çç ÷÷ + F1 çç + + ÷÷ = è r2 ø è E1' x S1' E 1 x S 1 r1 ø E1 x S1

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ö FxA ÷÷ = ø E2 x S2

Composite stress manual

BOLTED REPAIRS

U

Repair with 3 rows of fasteners

9.3 . Repair with 3 rows of fasteners

A

E2' S2'

a

a

E2' S2'

E1' S1'

F1 + F2 - F3 r3

E2 S2

F3

r2

E2 S2

F2

r1

E1 S1

F1

F

æ æ ö A A 1ö A A ÷÷ + + + ÷÷ + F2 çç + F3 çç è E 2' x S 2' E 2 x S 2 ø è E 2' x S 2' E 2 x S 2 r3 ø æ ö FxA A A ÷÷ = + F1 çç è E 2' x S 2' E 2 x S 2 ø E 2 x S 2 æ − 1ö F3 çç ÷÷ + F2 è r3 ø

æ æ ö Fxa a a 1ö a a çç ÷÷ = + + ÷÷ + F1 çç + E x S E x S r E x S E x S E 2' 2 2 2 ø 2' 2 2 ø 2 x S2 è 2' è 2'

æ − 1ö æ Fxa a a 1ö F2 çç ÷÷ + F1 çç + + ÷÷ = è r2 ø è E1' x S1' E 1 x S 1 r1 ø E1 x S1

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Composite stress manual

BOLTED REPAIRS

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Repair with 4 rows of fasteners

9.4 . Repair with 4 rows of fasteners

A

E2' S2'

a

a

a

E2' S2'

E2' S2'

E1' S1'

F1 + F2 + F3 + F4 r4

E2 S2

F4

r3

E2 S2

F3

E2 S2

r2

F2

r1

E1 S1

F1

F

æ æ ö A A 1ö A A ÷÷ + + + ÷÷ + F3 çç + F4 çç è E 2' x S 2' E 2 x S 2 r4 ø è E 2' x S 2' E 2 x S 2 ø æ ö æ ö FxA A A A A ÷÷ + F1 çç ÷÷ = + + F2 çç è E 2' x S 2 ' E 2 x S 2 ø è E 2' x S 2' E 2 x S 2 ø E 2 x S 2 æ − 1ö F4 çç ÷÷ + F3 è r4 ø æ a F2 çç è E 2' x S 2 '

æ1 ö a a çç + ÷÷ + + è r3 E 2' x S 2' E 2 x S 2 ø ö æ ö Fxa a a a ÷÷ + F1 çç ÷÷ = + + E2 x S2 ø è E 2' x S 2' E 2 x S 2 ø E 2 x S 2

æ − 1ö F3 çç ÷÷ + F2 è r3 ø

æ æ a a 1ö a a çç + + ÷÷ + F1 çç + è E 2' x S 2' E 2 x S 2 r2 ø è E 2' x S 2' E 2 x S 2

æ − 1ö æ Fxa a a 1ö F2 çç ÷÷ + F1 çç + + ÷÷ = è r2 ø è E1' x S1' E 1 x S 1 r1 ø E1 x S1

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ö Fxa ÷÷ = ø E2 x S2

9.4

Composite stress manual

BOLTED REPAIRS

U

with a number of rows of fasteners greater than 4

9.5

9.5 . Repair with a number of rows of fasteners greater than 4 We may easily find the previous equation system type for a number of rows of fasteners greater than 4.

A

E2' S2'

a

a

a

E2' S2'

E2' S2'

E1' S1'

Σ Fi

rn

E2 S2

Fn

r(n-1)

F(n-1)

r2

E2 S2

F2

E2 S2

F1

r1

E1 S1

F

However, we shall consider that, for a number of rows of fasteners greater than 6, the rows greater or equal to 7 have an insignificant effect on load Fr transfer distribution (see diagram below).

Fr

F8 = 0

F7 = 0

F6

F5

F4

F3

F2

F1

F

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Composite stress manual

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General resolution method for direction x

9.6

9.6 . General resolution method for direction x (see drawing below) It consists in following the procedure indicated below: Matrixed resolution of the equation system by assuming F = 1. Assessment of unit loads Fi per row "i" of fasteners. ↓ Assessment of ratio k u14

k=

2 x N xr

meca . + therm .

x h rx

å

n

F i =1 i

Assessment of effective loads transferred by each row "i" of fasteners Fxi = k x Fi

u15

↓ Assessment of effective loads transferred by each fastener of row "i" u16

fxi =

1.15 x Fxi ni

where ni is the number of fasteners of row "i" ni =

2 x h rx (no chamfer) a*

or ni =

2 x h rx − 2 (with chamfer for the first row) a*

i=6 i=5

i=4

i=3

i=2

i=1

y x Fxi

fx/xi ∞ Nx meca. + therm.

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Composite stress manual

BOLTED REPAIRS

U

Assessment of loads per fastener due to Nxy

10

The fastener is identified by the letter "i" . "i" being the number of the row perpendicular to the load. By definition, only full lines shall be considered and it shall be assumed that row number 1 is located next to the free edge of the doubler.

10 . ASSESSMENT OF LOADS PER FASTENER DUE TO THE TRANSFER OF SHEAR LOADS Nxy Loads in the fasteners are deduced from the geometry and from the mechanical origin fluxes crossing the doubler. lx3 a

ly2

i=3 i=1

fy/xyij j=2

fx/xyij

a*

y

j=1

x

1≤j≤n=2 1≤i≤m=5

∞

Nxy meca.

Loads on fasteners due to the transfer of Nxyr meca. flux are equal to: u17

fx/xyij =

fy/xyij =

Nxyr

x a x ly j

meca .

å

n

Nxyr

j =1

ly j

x a * x lx i

meca .

å

m i =1

lx i

The fastener is identified by letters "i" and "j". "i" being the number of the row parallel to the y-axis and "j" being the number of the row parallel to the x-axis. By definition, only full lines shall be considered and it shall be assumed that row number 1 is located next to the free edge of the doubler.

© AEROSPATIALE - 1999

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BOLTED REPAIRS

U

Justifications

11 1/2

11 . JUSTIFICATIONS The repair justification consists of a notched and loaded plain plate calculation (for the parent skin and for the repair) and a check of the behavior of the existing damage. The most highly loaded fastener holes (of the four angles) must be justified by superposing loads due to fluxes Nx meca. (fx/x), Ny meca. (fy/y) and to flux Nxy meca. (fx/xy and fy/xy). This resulting load (f) must then be combined with fluxes N xs meca., Nys meca. and Nxys meca. (for the initial skin) or Nxr meca., Nyr meca. and Nxyr meca. (for the repair) at the fastener considered. REPAIR

PARENT SKIN

Nyr

Ny∝ Nxy∝ Nxyr

- fx/x

y

fy/y

- fx/xy

f

f

- fy/xy

Nxr

fy/xy

Nx∝ - fy/y

fx/xy

x

fx/x

On the other hand, the damage in the parent skin in the presence of fluxes Nxs meca., Nys meca. and Nxys meca. at the repair center shall be justified. General remark: It should be noted that there are two types of fastener arrangements: a so-called

"square"

arrangement

and

a

so-called

"staggered"

arrangement. The "square" arrangement is preferred because the hole coefficient is limited.

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BOLTED REPAIRS

U

Justifications

11 2/2

Both diagrams below show which value of "a" should be applied in the calculation of loads per fastener in each of these cases. a

a

"Square" arrangement

"Staggered" arrangement

This theory was implemented with the desktop computing program "REPBOUL" (refer to instructions).

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BOLTED REPAIRS

U

Summary flowchart

12

12 . SUMMARY FLOWCHART step No. 1 INITIAL LOADING Nx∝ Ny∝ Nxy∝

DOUBLER GEOMETRY

CALCULATE THE STIFFNESS OF FASTENERS r

step No. 2

step No. 3

ASSESS THE DOUBLER STIFFNESSES

ASSESS THE PANEL STIFFNESS

x

y

xy

x

y

xy

Rr Rr Rr

Rs Rs Rs

step No. 4

step No. 5

ASSESS FLUXES IN THE PANEL meca. + therm. Nxr Nyr Nxyr

ASSESS FLUXES IN THE PANEL meca. + therm. Nxs Nys Nxys

step No. 6 ASSESS THE RESULTING LOAD meca. + therm. fx/x fy/y fx/xy fy/xy

step No. 7 ASSESS THE RESULTING LOAD meca. + therm. f

© AEROSPATIALE - 1999

step No. 8

step No. 9

step No. 10

JUSTIFY THE FASTENER HOLES OF THE PARENT SKIN

JUSTIFY THE FASTENER HOLES OF THE DOUBLER

JUSTIFY THE DAMAGE

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BOLTED REPAIRS

U

Example 13 . Example Let the following repair be: Mechanical characteristics original panel Lay-up: 6/6/6/6 Exs = 4878 daN/mm2 Eys = 4878 daN/mm2 Gxys = 1882 daN/mm2 es = 3.12 mm Doubler Mechanical characteristics Lay-up: 2/4/4/2 Exr = 4008 daN/mm2 Eyr = 4008 daN/mm2 Gxyr = 2355 daN/mm2 er = 1.56 mm Fastener characteristics Total number n = 32 Stiffness r = 2000 daN/mm ∅ = 3.2 mm Fastener Elasticity modulus = 7400 daN/mm2

Ny∝ = - 32 daN/mm Nxy∝ = - 20 daN/mm a = 18

A x / xy

a* = 18

y

x y hs

= 35 mm x

2 L s = 72 mm y

2 h r = 90 mm

© AEROSPATIALE - 1999

A = 18

= 72 mm y r

∅ = 20 mm

y / xy

fA 1

2L

2L

y s

= 108 mm

fA 1 y/y fA 1

MTS 006 Iss. A

13 1/11

Composite stress manual

BOLTED REPAIRS Example

U

13 2/11

Assessment of fluxes in the doubler and the panel below the doubler This example does not include any thermal loads, we shall only cover mechanical fluxes. Therefore, notations shall not have any index. The first calculation step consists in determining both fluxes crossing the doubler (Nyr; Nxyr) which entails assessing panel and doubler stiffnesses with respect to both of these load types, first of all. The fact that flux Nx∝ is zero has the following consequence Nxr = Nxs = 0. Determination of doubler and panel stiffnesses {u6} 4008 x 1.56 x 45 30 x 2000 4 x 36 y Rr = = 5138 daN / mm 4008 x 1.56 x 45 30 x 2000 + 36 4

(30 is the total number of load-carrying fasteners in direction y). {u7} R sy =

4878 x 3.12 x 35 = 9864 daN / mm 54

{u9} 2355 x 1.56 x 32 x 2000 8 = 2518 daN / mm R rxy = 32 x 2000 2355 x 1.56 + 8

(32 is the total number of load-carrying fasteners in direction xy). We have: V=

72 = 3.6 20

W=

108 = 5.4 20

© AEROSPATIALE - 1999

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS

U

Example

{u11} η=

3. 6 2 + 5. 4 2

0.5

2

ö æ ö æ ÷ ç ÷ ç 1 1 ÷ ÷ + ç 5.4 − 1 + ç 3.6 − 1 + 1 ÷ 1 ÷ ç ç 1− 1− ÷ ç ÷ ç 3.6 ø 5.4 ø è è

2

= 0.94

{u10} R sxy = 0.94 x 1882 x 3.12 = 5494 daN/mm

Determination of fluxes crossing the doubler {u5} Nyr =

5138 Ny∝ = 0.34 Ny∝ = 0.34 (- 32) = - 10.96 daN/mm 5138 + 9864

{u8} Nxyr =

2518 Ny∝ = 0.31 Nxy∝ = 0.31 (- 20) = - 6.28 daN/mm 2518 + 5494

Determination of fluxes crossing the panel below the doubler {u13} Nys = - 32 - (- 10.96) = - 21.04 daN/mm Nxys = - 20 - (- 6.28) = - 13.72 daN/mm

© AEROSPATIALE - 1999

MTS 006 Iss. A

13 3/11

Composite stress manual

BOLTED REPAIRS Example

U

13 4/11

Assessment of loads on fastener A Load due to Ny Repair with 3 rows of fasteners: if F1, F2 and F3 corresponds to loads transmitted by the rows of fasteners, the system displacement resolution leads to the three following equations: æ ö 18 18 1 ÷÷ + F3 çç + + è 4008 x 1.56 x 90 4878 x 3.12 x 90 5 x 2000 ø æ ö 18 18 ÷÷ + + F2 çç è 4008 x 1.56 x 90 4878 x 3.12 x 90 ø æ ö F x 18 18 18 ÷÷ = F1 çç + è 4008 x 1.56 x 90 4878 x 3.12 x 90 ø 4878 x 3.12 x 90

æ −1 ö ÷÷ + F2 F3 çç è 5 x 2000 ø

æ ö 18 18 1 çç ÷÷ + + + è 4008 x 1.56 x 90 4878 x 3.12 x 90 5 x 2000 ø

æ ö F x 18 18 18 ÷÷ = F1 çç + 4008 x 1 . 56 x 90 4878 x 3 . 12 x 90 4878 x 3.12 x 90 è ø æ æ ö F x 18 −1 ö 18 18 1 ÷÷ + F1 çç ÷÷ = F2 çç + + è 5 x 2000 ø è 4008 x 1.56 x 90 4878 x 3.12 x 90 5 x 2000 ø 4878. x 3.12 x 90

by assuming F = 1, loads F1, F2 and F3 per row "i" of fasteners are deduced from the matrix resolution. F1 = 0.1366 daN F2 = 0.0669 daN F3 = 0.0273 daN

© AEROSPATIALE - 1999

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS

U

Example

13 5/11

{u14} Assessment of ratio k k=

2 x ( − ) 10.96 x 45 = − 4275 0.1366 + 0.0669 + 0.0273

{u15] Assessment of effective load transferred by row "i = 1" of fastener Fyi = - 4275 x 0.1366 = - 584 daN {u16} Assessment of effective loads transferred by each fastener of row "i = 1" fyi =

1.15 x − 584 = 1.15 x - 116.8 = - 134 daN 5

Load due to Nxy {u17} Loads on fasteners due to transfer of Nxyr flux are equal to: fx/xyij =

− 6.28 x 18.54 = - 56.56 daN 54 + 36 + 18

fy/xyij =

− 6.28 x 18 x 36 = - 113.13 daN 36

(

)

The resultant shall be equal to 56.56 2 + (113.13 + 134 ) = 254 daN and the slope angle of the load shall have the value Arctg (- 247.13/- 56.56) = 77° (- 180°) = - 103°.

© AEROSPATIALE - 1999

MTS 006 Iss. A

2 0.5

Composite stress manual

BOLTED REPAIRS

U

Example

At this fastener A, fluxes are: - on the panel Nxs = 0 daN/mm Nys = - 32 daN/mm Nxys = - 20 daN/mm - in the doubler Nxr = 0 daN/mm Nyr =

− 116.8 = - 6.49 daN/mm 18

Nxyr = - 6.28 daN/mm

fx/xy = - 57 daN

A fy/xy = - 113 daN - 103° fy = - 134 daN

254 daN y

x

© AEROSPATIALE - 1999

MTS 006 Iss. A

13 6/11

Composite stress manual

BOLTED REPAIRS Example

U

13 7/11

Now, let's assume that the carbon reinforcing plate is replaced by an Aluminium plate of thickness er = 0.84 mm (the thickness was selected so that the doubler stiffness may remain constant: 0.84 x 7400 = 1.56 x 4008 = 6252 daN/mm) and of coefficient expansion αr = 2.2 E-5/°C. The expansion factor of the parent skin (isotropic T300/314 laminate) is equal to: αs = 1.4 E-6/°C (refer to chapter § V 4.2 for the calculation of equivalent coefficient of expansion of a laminate). We shall look for thermal loads for an absolute temperature of + 74° C, which corresponds to a relative temperature with respect to the ambient temperature of ∆T = + 54° C (with a view to simplicity, mechanical loads shall be considered as zero). By applying the relationship {u12}, we find the thermal loads in the doubler in directions x and y. {u12} In direction x : Fxr therm. =

2 x 54 (1.4 E − 6 x 36 − 2.2 E − 5 x 27.69 ) 27.69 36 4 + + 0.84 x 63 x 7400 3.12 x 53 x 4878 26 x 2000

Fxr therm. = - 314 daN (26 is the total number of load-carrying fasteners in direction x) In direction y : Fyr therm. =

2 x 54 (1.4 E − 6 x 54 − 2.2 E − 5 x 36 ) 36 54 4 + + 0.84 x 45 x 7400 3.12 x 35 x 4878 30 x 2000

Fyr therm. = - 260 daN (30 is the total number of load-carrying fasteners in direction y)

© AEROSPATIALE - 1999

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS

U

Example

13 8/11

Thermal fluxes in the doubler are deduced by dividing the previous results by widths 2 h rx and 2 h ry : Nxr therm. =

− 314 = - 2.49 daN/mm 2 x 63

Nyr therm. =

− 260 = - 2.89 daN/mm 2 x 45

Initial material characteristics Lay-up: 6/6/6/6 Exs = 4878 daN/mm2 Eys = 4878 daN/mm2 Gxys = 1882 daN/mm2 es = 3.12 mm Doubler material characteristics Aluminium Exr = 7400 daN/mm2 Eyr = 7400 daN/mm2 h sy = 35 mm Gxyr = 2846 daN/mm2 er = 0.84 mm

= 108 mm

= 72 mm

y s

y r

2L

2L

∅ = 20 mm

Nxr therm. = - 2.49 daN/mm

h

x s

= 53 mm

= 126 mm x r

2h

Nyr therm. = - 2.89 daN/mm

y x

2 L r = 55.38 mm x

x

2 L s = 72 mm y

2 h r = 90 mm

© AEROSPATIALE - 1999

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS Example

U

13 9/11

Which allows calculation of thermal loads on the most highly loaded fasteners (those in angles). In direction x: Repair with two rows of fasteners: if F1 and F2 correspond to loads transmitted by the rows of fasteners, the system displacement resolution leads to the two following equations (see chapter § U 9.2) : æ ö 18 1 18 ÷÷ + F2 çç + + è 7400 x 126 x 0.84 6 x 2000 4878 x 126 x 3.12 ø æ ö F x 18 18 18 ÷÷ = + F1 çç è 7400 x 126 x 0.84 4878 x 126 x 3.12 ø 4878 x 126 x 3.12

æ −1 ö æ ö F x 18 18 18 1 ÷÷ + F1 çç ÷÷ = + + F2 çç è 6 x 2000 ø è 7400 x 126 x 0.84 4878 x 126 x 3.12 7 x 2000 ø 4878 x 126 x 3.12

By assuming that F = 1, loads F1 and F2 per row "i" of fasteners are deduced from the matrix resolution: F2 x 1.157 E-4 + F1 x 3.237 E-5 = 9.387 E-6 F2 x (- 8.333 E-5) + F1 x 1.038 E-4 = 9.387 E-6 We find: F1 = 0.1271 daN F2 = 0.0455 daN {u14} Assessment of ratio k k=

© AEROSPATIALE - 1999

2 x ( − 2.49 ) x 63 = − 1818 0.0455 + 0.1271

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS

U

Example

13 10/11

{u15} Assessment of effective load transferred by row "i = 1" of fasteners Fxi = - 1818 x 0.1271 = - 231 daN {u16} Assessment of effective loads transferred by each fastener of row "i = 1" fxi =

1.15 x − 231 = 1.15 x ( − 33 ) = − 37daN 7

In direction y: For calculation in direction y, just use results for the transfer of mechanical origin fluxes (distribution on rows of fasteners being independent from the load value - see § U 13 p. 5). We know that: mechanical loads: Nyr meca. = - 10.96 daN/mm

→ fyi = - 134 daN

therefore: thermal loads: Nyr therm. = - 2.89 daN/mm

→ fyi = − 134 x

− 2.89 = − 35 daN − 10.96

The resulting load on angle fasteners is equal to: Fresultant therm. =

© AEROSPATIALE - 1999

37 2 + 352 = 51 daN

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS

U

Example

13

At this fastener, the resulting load is equal to 51 daN. Thermal fluxes in the doubler have the following value:

Nxr therm. =

æ − 2.49 x F1 − 37 − 2.4 x 0.1271 ö ÷ = − 1.79 daN / mm çç = 18 x 1.15 0.1271 + 0.0455 ÷ø è F1 + F2

Nyr therm. =

æ − 2.89 x F1 ö − 35 − 2.89 x 0.1366 ÷÷ = − 1.69 daN / mm çç = 18 x 1.15 F + F + F 0 . 1366 + 0 . 0669 + 0 . 0273 2 3 è 1 ø

fx therm. = 37 daN

fy therm. = 35 daN Fresultant therm. = 51 daN y

x

© AEROSPATIALE - 1999

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© AEROSPATIALE - 1999

MTS 006 Iss. A

Composite stress manual

BOLTED REPAIRS References

U

BARRAU - LAROZE, Design of composite material structures, 1987 GAY, Composite materials, 1991 VALLAT, Strength of materials ESCANE - CIAVALDINI - TROPIS, Design of a bolted repair on a composite structure determination of mechanical loads in the reinforcing piece, 1992, 440.192/92 TROPIS - SAVOLDELLI, Repair of carbon self-stiffened panels - justification in compression, 1989, 420.535/90 TROPIS - SAVOLDELLI, Repair of carbon self-stiffened panels - justification in tension, 1990, 420.541/90 M. JANINI - P. CIAVALDINI, Design of a bolted repair on a composite structure determination of mechanical loads in the reinforcing piece, 440. 129/92

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© AEROSPATIALE - 1999

MTS 006 Iss. A

Composite stress manual

V THERMAL CALCULATIONS

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

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© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Notations

V

1

1 . NOTATIONS ∆T, ∆θ: relative temperature (difference between effective and ambient temperatures) Tather., θather.: athermane temperature Tamb., θamb.: ambient temperature Tstruc., θstruc.: structure temperature L: plates length r: attachment or link stiffness b1: plate width (1) e1: plate thickness (1) E1: plate modulus of elasticity (1) α1: plate thermal expansion coefficient (1) b2: plate width (2) e2: plate thickness (2) E2: plate modulus of elasticity (2) α2: plate thermal expansion coefficient (2) ∆L: thermal expansion ∆L': mechanical elongation F: global mechanical force of thermal origin f: force on fasteners τ: shear stress in adhesive Gc: adhesive shear modulus ec: adhesive thickness

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Introduction

V

2

2 . INTRODUCTION A homogeneous anisotropic solid subjected to a uniform variation of temperature expands differently in different directions. To characterize its behavior, several expansion coefficients must be defined. In addition, strains and (or) stresses will appear depending on the boundary conditions and the temperature range inside the solid. A free composite plate subjected to a uniform variation in temperature will be subjected to strains and stresses due to the different expansions of the fiber and the resin. As composite plates are generally manufactured by curing at a temperature greater than utilization θ, residual curing stresses appear in these plates. Although they can be high, they are generally not explicitly calculated but included implicitly into the calculation values determined on crosswise laminated plates (see § V 5.2). As well, a variation in temperature applied to an assembly (attached or bonded) of plates with different expansion coefficients leads to stresses and strains in these plates which are added to those induced by mechanical loading. The aim of this chapter is to study the stresses and strains of thermal origin for unidirectional fibers, composite plates, bimetallic strips and, lastly, aircraft structures, submitted to regulation environmental conditions.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Hooke - Duhamel law

V

3

3 . HOOKE - DUHAMEL LAW If a material is submitted to a mechanical load, the stress - strain relation can be written in its tensorial form: v1

εij = ηijkl x σkl ou

cf. § V 5

σij = λijkl x ε

kl

If a homogeneous, elastic and anisotropic solid which is free to deform is submitted to a change in temperature, the strain - temperature relation can be written in its tensorial form: v2

εij = αij (T - To) where To: original temperature (uniform) T: modified temperature (uniform) αij is the thermal expansion tensor which is a characteristic of the material. αij is symmetrical. For an orthotropic material in the orthotropy reference frame. éα l ê ê (α) = ê o ê ê ëo

o α ll o

où ú ú oú ú ú α lll û

If the material is submitted to a mechanical load, the stress - strain - temperature relation can be written: εtotal = εmechanical + εfree thermal v3

εij = ηijkl x σkl + αij (T - To) or σij = λijkl x εkl + βij (T - To)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Behavior of unidirectional fiber

4

where (η): flexibility tensor (λ): rigidity tensor (α): thermal expansion tensor (β): thermal modulus tensor T: absolute temperature applied To: reference temperature ∆T: relative temperature

4 . BEHAVIOR OF UNIDIRECTIONAL FIBER Let us take a unidirectional fiber defined by its longitudinal direction (l) and by its transverse direction (t), it is a transverse isotropic and orthotropic material. The unidirectional fiber will be characterized by two expansion coefficients in the orthotropic axis: t

l

t (3) t (y)

l (x)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Behavior of a monolith plate

5.1 1/3

The expansion coefficients are different in the two directions l and t: αl: longitudinal expansion coefficient of unidirectional fiber in x-axis. αt: transverse expansion coefficient of unidirectional fiber (resin) in y- and z-axes. o où éα l ú ê ú ê αt oú Generally αl << αt (α) = ê o ú ê ú ê o αt û ëo

5 . BEHAVIOR OF A FREE MONOLITHIC PLATE 5.1 . Calculation method As we saw in chapter E 3, the general relation between the strain sensor and the load sensor of a monolith plate can be written in its matrix form (relation to be compared with the relation v1): Nx

A11

A12

A13

B11

B12

B13

εx

Ny

A 21

A 22

A 23

B21

B22

B23

εy

Nxy

A 31

A 32

A 33

B31

B32

B33

γ xy

= Mx

B11

B12

B13

C11

C12

C13

My

B21

B22

B23

C21

C 22

C23

Mxy

B31

B32

B33

C31

C 32

C33

∂2wo ∂x 2 ∂2wo ∂y 2 ∂2 wo 2 ∂x ∂y

The sign conventions are as follows: z

z y

y

My > 0 Ny > 0 x

Mx > 0

Mxy > 0

x

SIGN CONVENTIONS FOR BENDING

© AEROSPATIALE - 1999

Nx > 0

Nxy > 0

SIGN CONVENTIONS FOR MEMBRANE

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Behavior of a monolith plate

V

5.1 2/3

If the plate is submitted to a relative uniform temperature ∆T = (T - To), the previous expression becomes (relation which is to be compared with relation v3): Nx Ny

A

B

Nxy

v4

= Mx My

B

C

Mxy

εx

αEh x

εy

αEh y

γ xy

αEh xy

∂2wo ∂x 2 ∂2wo ∂y 2 ∂2 wo 2 ∂x ∂y

- ∆t

αEh2 αEh2 αEh2

x

y

xy

where the thermoelastic behavior of the laminate is described by vector (αEh) which terms are equal to:

v5

æ c 2 El (α l + ν tl α t ) + s 2 E t ( νlt α l + α t ) ö ( z − z ) ç k ÷ k −1 k =1 1 − νlt ν tl è ø

αEh x =

å

αEh y =

å

n

αEh xy =

αEh

© AEROSPATIALE - 1999

2 x

æ s 2 El (α l + ν tl α t ) + c 2 E t ( νlt α l + α t ) ö (z k − z k − 1) ç ÷ k =1 1 − νlt ν tl è ø

n

å

=−

n k =1

å

æ c s E t ( ν lt α l + α t ) − c s E l (α l + ν tl α t ) ö ç ( zk − zk − 1 ) ÷ 1 − ν lt ν tl è ø

æ z k2 − z k2 − 1 c 2 El (α l + ν tl α t ) + s 2 E t ( νlt α l + α t ) ö ç ÷ ÷ k = 1ç 2 1 − νlt ν tl è ø

n

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Behavior of a monolith plate

αEh

2

αEh

2

y

xy

=−

å

=−

5.1 3/3

æ z k2 − z k2 − 1 s 2 E l (α l + ν tl α t ) + c 2 E t ( ν lt α l + α t ) ö ÷ ç ÷ k = 1ç 2 1 − ν lt ν tl ø è

n

æ z k2 − z 2 c s E ( ν + α + α ) − c s E (α + ν α ) ö k −1 t lt l t l l tl t ÷ ç k = 1ç ÷ ν ν 2 1 − lt tl è ø

å

n

y ply No. k

ek t

zk zk - 1

l

neutral plane θ ply No. 1

x

where: c ≡ cos(θ) where θ is the orientation of the fiber in the basic reference frame (o, x, y) s ≡ sin(θ) where θ is the orientation of the fiber in the basic reference frame (o, x, y) El: longitudinal modulus of elasticity of the unidirectional fiber Et: transverse modulus of elasticity of the unidirectional fiber νlt: longitudinal/transverse Poisson coefficient of the unidirectional fiber E νtl = νlt t : transverse/longitudinal Poisson coefficient of the unidirectional fiber El

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Curing stresses - expansion coefficients

V

5.2 5.3

5.2 . Residual curing stresses For thermosetting resin composites, the plates are made by juxtaposing different layers with different characteristics. These layers are manufactured simultaneously to the plate. We assume that when the resin cures, each layer is frozen in the state it is in at that time. Let Tp be the curing temperature; the stresses in the plate can be considered as zero at this temperature. To obtain the stresses at ambient temperature after cooling, apply relation v4. If the plate does not have mirror symmetry, the coupling terms, (B) and αEh2 of v4 are non zero; therefore, a uniform reduction in the temperature (from curing temperature to ambient temperature) will create a strain in the plane and a curvature of the neutral plane. In the same way, if there is in-plane coupling (terms A16, A26 non zero), that is if plies are not equal in + or - α, angular distortion will occur during cooling after curing, the plate will be "parallelogram" shaped.

5.3 . Equivalent expansion coefficients The equivalent expansion coefficient vector αequi. (αx equi., αy equi., αxy equi.) of an orthotropic composite plate, with mirror symmetry without in-plane coupling, can be determined by the following relation: v6

(αequi.) = (A)- 1 x (αEh) where terms Aij of the laminate rigidity matrix (A) can be determined by relation c6 of chapter C.3.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Bimetallic strip theory

V

6.1 1/4

6 . BEHAVIOR OF A SYSTEM CONSISTING OF TWO BEAMS WITH DIFFERENT EXPANSION COEFFICIENTS - BIMETALLIC STRIP THEORY 6.1 . Determining stresses of thermal origin The aim of this subchapter is to study the mechanical influence of the temperature on a system consisting of two beam elements with an infinitely rigid connection at their ends. The following analysis is unidirectional. Furthermore, we shall neglect the secondary bending effects and the Poisson effects. Let us take, therefore, two long plates (L >> b) with an infinitely rigid connection at their ends and with the following mechanical characteristics: Plate (1): - length: L - width: b - thickness: e1 - modulus of elasticity: E1 - expansion coefficient: α1

(§ V 5.3)

Plate (2) - length: L - width: b - thickness: e2 - modulus of elasticity: E2 - expansion coefficient: α2

© AEROSPATIALE - 1999

(§ V 5.3)

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Bimetallic strip theory

V

6.1 2/4

(1)

(2)

L

b

Initially, let us assume that the two plates are free at their ends. If we submit each one of them to a uniform relative temperature ∆T (in relation to the ambient temperature of the setup), they will expand by the following lengths: ∆L1 = ∆T α1 L where α1 ≠ α2 ∆L2 = ∆T α2 L

∆L2

(1)

(2)

∆L1

Now, as these two plates are rigidly attached at their ends, they will deform by the same length. Mechanical interaction forces of thermal origin (F1 and F2) are created: F1 : force of plate (2) on plate (1) F2 : force of plate (1) on plate (2)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Bimetallic strip theory

3/4

∆L'2

(1) F1

6.1

F1

F1 F2

- F1

- F1 ∆L'1

(2)

As the system is globally in equilibrium, the force applied to plate (1) is the same as the one applied to plate (2) except for the sign: F1 = - F2. The plate elongations due to these forces alone will be therefore: ∆L'1 =

F1 L E1 e1 b1

∆L'2 =

− F1 L F2 L = E2 e 2 L E2 e 2 b 2

The equal length principal implies the following relation: ∆L1 + ∆L'1 = ∆L2 +∆L'2 ∆L1 ∆L2

After development and simplification, we obtain: v7

F1 =

∆T (α 2 − α1) Γ

F2 =

∆T (α1 − α 2 ) Γ

where v8

Γ=

© AEROSPATIALE - 1999

1 1 + E1 e1 b1 E2 e2 b 2

MTS 006 Iss. B

∆L'2

∆L'1

Composite stress manual

THERMAL CALCULATIONS

V

Bimetallic strip theory

6.1 4/4

Remark: For two plates with totally different geometries attached at the ends by an element (one or several fasteners for example) of global rigidity ℜ, the previous relation is slightly modified. (1)

ℜ

ℜ

(2)

L2 b1

b2

L1

The equal length principle becomes: ∆L1 ∆L'1 ∆L 2 ∆L' 2 2F1 + = + + 2 2 2 2 ℜ ∆L1 2 ∆L'1 ∆L 2

∆L' 2

2

2

Force of thermal origin is then equal to:

v9

F1 =

© AEROSPATIALE - 1999

∆θ (α 2 L 2 − α1 L1) L1 L2 2 + + e1 b1 E1 e2 b 2 E2 ℜ

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2

Composite stress manual

THERMAL CALCULATIONS

V

Bolted system

6.2.1 6.2.1.1

1/2

6.2 . Study of the link between two parts In practice, the link between two parts is ensured either by fasteners or by bonding.

6.2.1 . Bolted or riveted joints We shall assume that the plates are sufficiently long so that the thermal expansion cannot be absorbed by the play (and the rigidity) of the fasteners (see previous remark). The thermal force, which will have been calculated previously by relation v4, will be expressed herein by letter F. Several hypotheses can be put forward concerning the number of fasteners (of rigidity r) likely to take force F.

6.2.1.1 . Force F taken by one fastener L

F -F

r f b

f=F For information purpose, the table on the next page shows the various forces applied to the structural elements for a splice and a doubler, these being submitted to tensile or compression loads and at a positive or negative relative temperature.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Bolted system

V

6.2.1.1 2/2

We will consider that the expansion coefficient of the upper material (aluminium for instance) is higher than that of the lower material (isotropic carbon laminate for instance). It is important to point out that the forces represented on the drawings are those applied to the structure by the fasteners. DOUBLER

COMPRESSION

TENSION

SPLICE

0°

∆T > 0

0°

upper α > lower α

upper α > lower α

0°

∆T < 0

0°

upper α > lower α

upper α > lower α

Table V6.2.1.1: Transfer of mechanical and thermal forces to the splices and doublers

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THERMAL CALCULATIONS

V

Bolted system

6.1.2.3 . Force F taken by two fasteners A

a

F -F

r f2

r f1 b

A+a Aar f1 = F 2A+a Γ+ Aar Γ+

v10

f2 = F - f1

6.2.1.3 . Force F taken by three fasteners A

a

a

F -F

r f3

r f2

r f1 b

v11

v12

ö 1 1 æA öæ + A Γ + ç − 1÷ ç ÷ 2 èa ø è3r + a Γ r ø r f1 = F 1 A æ1 ö + ç + a Γ÷ ø r a èr 1 f2 = F 3+aΓr

f3 = F - f1 - f2

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6.2.1.2 6.2.1.3

Composite stress manual

THERMAL CALCULATIONS

V

Bolted system

6.2.1.4

6.2.1.4 . Force F taken by four or more fasteners A

a

a

F -F

r f4

r f3

r f2

r f1 b

v13

ö 1 1 æA öæ + A Γ + ç − 1÷ ç 2÷ è ø a è3r + a Γ r ø F r f1 = 1 A æ1 δ ö + ç + a Γ÷ è ø r a r

where v14

δ=1+

n−3 10

where n equals number of fasteners. Remark: Relations v10 to v14 have been established analytically. It is however recommended for a large number of fasteners to solve the problem by a matrix calculation or a finite element model.

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THERMAL CALCULATIONS

V

Bonded joints

6.2.2 1/2

6.2.2 . Bonded joints For a bonded link, the (antisymmetrical) loading of the two plates is continuous from one end of the system to the other; the main part of the loading is however at the start of the bonded link. L

Doubler

τMax.

- τMax.

L 2

F -F

τMax.

The maximum shear stress at the interface of the two plates can be written as follows:

v15

τMax. =

Fλæ æ λ Lö æ λ L ö E1 e1 − E 2 e 2 ö ç coth ç ÷ ÷ + tanh ç ÷ è 2 ø è 2 ø E1 e1 + E 2 e 2 ø b è

where

v16

λ=

© AEROSPATIALE - 1999

Gc E1 e1 + E2 e2 e c E1 e1 E2 e2

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THERMAL CALCULATIONS

V

Bonded joints

6.2.2 2/2

where Gc is the shear modulus of the adhesive and ec its thickness. This relation has been established by analogy with the bonded joint theory (see chapter S) where the distribution of the shear stresses in the adhesive joint is of the symmetrical type and where the value of this stress, although negligible, is not zero in the center. Symmetrical distribution of shear stresses: Bonded splice

+

+ τ≈C

Antisymmetrical distribution of shear stresses: Bonded doubler

+ -

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Composite stress manual

THERMAL CALCULATIONS Influence of temperature

V

7.1 7.2 7.2.1

7 . INFLUENCE OF TEMPERATURE ON AIRCRAFT STRUCTURES 7.1 . General The influence of the temperature on the aircraft structures is twofold: - thermal stresses induced by the different expansion coefficients per unit length of the components of the composite and metallic structures (spars/skins/rib, etc.) and also between the fibers and the resin, - reduction of the mechanical properties especially the resin and the adhesives (certain fibers are also sensitive to the temperature). The demonstration of the resistance to the ultimate loads must be made in the most penalizing association case of the ultimate temperatures of the structure combined with selected design-critical mechanical loads. We shall first of all define the various types of temperatures involved in the procedure described in this chapter.

7.2 . Temperature of ambient air 7.2.1 . Temperature envelope The static air temperature envelope to be considered on the ground and in flight are given for each aircraft (DBD: Data Basis Design); they depend on changes in regulatory requirements and aircraft operational limits. For example, the maximum temperature to be considered on the ground was increased by 10° C between the A320 (45°) and the A340 (55°). The minimum temperature on the ground is - 54° C (see curves below).

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THERMAL CALCULATIONS

V

Influence of temperature

7.2.2 7.2.2.1

z (fts) 45000

41100 ft

40000 35000 30000

flight

25000 20000 15000 12500 ft 10000 ground 5000 - 80

- 60 - 54°C - 40

- 20

- 5000

0

20

40

60

OAT (° C)

We must therefore determine the ultimate temperatures of the structure for all aircraft flight phases (static and fatigue). This is dealt with in this subchapter.

7.2.2 . Variation of ambient air temperature 7.2.2.1 . Ambient temperature on ground The ambient temperature on the ground changes during the day. We will assume that its variation is homothetic to the quantity of heat Qϕ received by the ground (see chapter § V 7.3.1.2). It therefore depends on the time of the day and the geographical location on earth (latitude ζ/type of atmosphere). The table and curves below show change of ambient temperature on ground for a tropical atmosphere (55° C at 12 h ≡ ISA + 40° C) and for a polar atmosphere (regulatory lower limit of - 54° C).

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THERMAL CALCULATIONS

V

Influence of temperature

7.2.2.2

We consider however that heat builds up during the day which explains why the "night" temperature (32° C for the tropical atmosphere) starts at 20 h and not at 18 h. Time

6h

7h

8h

9h

10 h

11 h

12 h

13 h

Tamb. (° C)

32

38

43.5

48.3

51.9

54.2

55

54.5

Time

13 h

14 h

15 h

16 h

17 h

18 h

19 h

20 h

Tamb. (° C)

54.5

52.9

50.5

47.3

43.6

39.7

35.7

32

T amb. ground 55° C = ISA + 40° C STANDARD ATMOSPHERE

TROPICAL ATMOSPHERE Qϕ

32° C

15° C = ISA t

0 6h

12 h

18 h 20 h

24 h

- 54° C POLAR ATMOSPHERE

7.2.2.2 . Ambient temperature in flight The ambient temperature in flight depends on the ambient temperature on the ground (see previous chapter) and the altitude z. From 0 to 40000 fts (troposphere), we generally consider that the temperature decreases on average 0.5° C for every 328 fts increase in altitude with a lower limit of - 54° C. The diagram below gives the ambient temperature at a given altitude for all ambient temperatures on the ground. Tamb. z ≈ - 2 E-3 x z + Tamb. gnd where ∀ z Tamb. z ≥ - 54° C

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THERMAL CALCULATIONS

V

Wall temperature

7.3

60 ISA + 40°

40

20 ISA

0 Tamb. z (° C)

- 20

- 40

- 54 ° C - 60 -5

0

5

10

15

20

25

Altitude (x 1000 fts)

7.3 . Wall temperature The combined effects of the solar radiation in flight (optional effect) and the speed of the aircraft (Mach number M) lead to a significant increase in the wall temperatures when compared with the temperature of the ambient air in flight.

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THERMAL CALCULATIONS

V

Influence of solar radiation

7.3.1.1 7.3.1.2

1/3

7.3.1 . Influence of solar radiation 7.3.1.1 . Maximum solar radiation It is maximum outside the atmosphere (z ≥ 36000 fts) and is equal to 1360 w/m2. This radiation is lower on earth due to the influence of the ozone layer, humidity and other factors. At sea level (z = 0) and at 12-o-clock, Qs ≈ 1010 w/m2 in tropical areas. Between these two points, we assume that Qs varies in a linear manner as a function of the altitude: Qsz ≈ 9.72 E-3 x z + 1010 (see curve below).

1400 1360 1300

Qs z 1200 2 (w/m )

1100

1010 1000 0

5

10

15

20

25

30

35

Altitude (x 1000 fts)

Remark: These values are unchanged between ISA + 35° C and ISA + 40° C.

7.3.1.2 . Solar radiation during the day The quantity of heat Qϕ received by the ground depends on the quantity of heat Qs emitted by the sun and passing through the atmosphere (Qs = 1010 w/m2) and the angle of incidence ϕ between the light rays and the ground.

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THERMAL CALCULATIONS

V

Influence of solar radiation

ϕ

7.3.1.2 2/3

Qs Qs

Qϕ

ϕ

Qϕ

Ground

This angle of incidence ϕ itself depends on time t (represented by angle ω on the drawing) and on the latitude ζ of the point under study.

ϕ = 90°

ζ

ω

solar radiation

ϕ

ϕ = Arc (cos ζ x cos ω) = Arc (cos ζ x cos (15 t - 180)) for 18 h ≤ t ≤ 6 h In tropical atmosphere (ζ ≈ 0°), this expression is simplified and becomes: ϕ = Arc (cos 0° x cos ω) = 15 t - 180 for 18 h ≤ t ≤ 6 h The diagram below shows, between 6 h and 18 h the "theoretical" change in the quantity of heat Qϕ that the ground receives for different types of atmospheres.

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THERMAL CALCULATIONS

V

Influence of solar radiation

Qϕ

STANDARD ATMOSPHERE LATITUDE ζ ≈ 45°

1010 w/m 714 w/m

7.3.1.2 3/3

TROPICAL ATMOSPHERE LATITUDE ζ ≈ 0°

2

2

t

0

6h

12 h

18 h

24 h

POLAR ATMOSPHERE LATITUDE ζ ≈ 90°

Nevertheless, we will assume that during the night (from 18 h to 6 h), a certain quantity of heat (≈ 280 W/m2 for a tropical atmosphere) is exchanged between the outside medium and the structure ("night irradiation"). The table and curve below show the "regulatory" change in the quantity of heat Qϕ during the day in tropical atmosphere and at sea level. The curve Qϕ = Qs x cosϕ has therefore been (arbitrarily) offset at 280 w/m2 for 6 h and 18 h. Time

7h

8h

9h

10 h

11 h

12 h

Qϕ ϕ (w/m2)

636

838

929

980

1002

1010

Time

12 h

13 h

14 h

15 h

16 h

17 h

1010

1002

980

929

838

636

Qϕ ϕ (w/m ) 2

Qs

Q 1010 w/m

2

Qϕ 280 w/m

2

0

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Qs x cosϕ

t 6h

12 h

MTS 006 Iss. B

18 h

24 h

Composite stress manual

THERMAL CALCULATIONS Influence of speed - Temperature of structure

V

7.3.2 7.3.3

7.3.2 . Influence of aircraft speed The effect of the speed of the aircraft (friction of the air) increases the ambient temperature in flight to a level called the athermane temperature. The athermane temperature (or friction temperature) is the temperature at which the thermal flow exchange between the wall of the structure and the outside medium is zero. To find the athermane temperature at structure stagnation point, the ambient temperature at an altitude z must be multiplied by a coefficient which depends on the speed of the aircraft: æ ö γ −1 Tath. z = Tam. z x ç 1 + Mach2 ÷ γ è ø

where γ =

Cp = 1.4 γ: ratio between molar heat capacities (perfect gas constant). Cv

where Cp and Cv are the heat capacities of the gas (in this case, of the air at the altitude concerned) at constant pressure and volume.

7.3.3 . Temperature of the structure In the previous subchapters, we defined the various temperatures outside the structure (ambient temperature on ground, ambient temperature in flight, wall temperature and athermane temperature). The aim of the next chapter is to determine the temperature of the various structural elements.

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THERMAL CALCULATIONS Calculation method

V

7.3.3.1 1/2

7.3.3.1 . Calculation method The temperature of each structural element depends on: - the change of the athermane temperature which itself depends on the time, the altitude, the speed of the aircraft and the type of atmosphere, - the solar radiation at the altitude in question (generally not taken into account), - the geometrical and thermal characteristics of the various elements comprising the structure, - the color of the exterior paint. The calculation method consists in breaking down the structure into elements assumed to be at a uniform temperature at time t and in writing the thermal equilibrium of each of these elements assuming that at time t = 0 all the structure has a uniform temperature equal to the temperature of the ambient air. A finite difference calculation enables the problem to be solved including in transient phase. The quantity of heat required to vary the temperature of each element by ∆T in the time interval ∆t is: C x V x ∆T = Qa + Qc + Qi + (Qϕ - Qr) where: C = heat capacity of the material V = volume of the element Qc = quantity of heat exchanged with the boundary layer by convection Qa = quantity of heat exchanged by conduction with adjacent elements Qi = quantity of heat exchanged with the inside medium (kerosene) Qϕ = quantity of heat received by solar radiation Qr = quantity of heat lost by radiation

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THERMAL CALCULATIONS

V

Calculation method - Thermal characteristics

7.3.3.1 7.3.3.2

2/2

For "tank" structures, three kerosene levels can be studied: - all internal elements are in contact with the kerosene, - only the lower surface elements and a section of the spars are in contact with the kerosene, - only the upper surface elements are not in contact with the kerosene. This method enables us to find at time t the temperature of each element and therefore to deduce the forces and thermal stresses required for the fatigue and static justification. Remark: The effects of the radiation of a section of the structure to another section need not be taken into account in the calculations as this effect tends to make the temperatures uniform.

7.3.3.2 . Thermal characteristics of the materials - Conductivity Carbon fiber Nomex

Thermal conductivity (w/m/° C)

0.1

Light alloy

Titanium

143

Drawing

Transv.

6.7

25/25/25/25

50/20/20/10

10/20/20/50

4.5

5.2

3.8

3 440.092/92

22S.002.10502

B - Specific heat

Nomex

Specific heat (J/m3/° C)

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54 E3

Light alloy

Titanium

2.6 E6

2.4 E6

MTS 006 Iss. B

Carbon fiber Longi.

Transv.

2 E6

2 E6

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Composite stress manual

THERMAL CALCULATIONS

V

Temperatures of structure on ground

7.3.3.3

- Paints To calculate the temperatures on the ground (or optionally in flight), the absorptivity and emissivity coefficients of the paint must be defined. The emissivity coefficient ε is generally taken as equal to 0.85 or 0.9. The absoptivity coefficient α is related to the color of the paint.

Color

white

light gray

light yellow

dark gray

navy blue

α

0.2

0.5

0.5

0.65

0.8

7.3.3.3 . Temperatures of structure on ground The first step consists in determining, with software PST2, change in the temperature of the structure on the ground during the day in order to evaluate the most critical initial flight conditions. The study is generally conducted over a complete day from 0 h to 24 h but can be extended over two or three days in order to minimize the influence of the initil conditions (ambient temperature at 0 h: 32° C at ISA + 40° C). Several sections of the structure with different thermal and geometrical characteristics will be modeled. As the absoptivity coefficient corresponds to the color of the paint used and the ground ambient temperature and insolation curves, we calculate the maximum temperature on the ground for each structural item during a day (see drawing below).

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THERMAL CALCULATIONS

V

Temperatures of structure in flight

7.3.3.4 1/3

T struc. ground TEMPERATURE OF STRUCTURAL ELEMENT

ISA + 40° C

AMB. TEMPERATURE ON GROUND

t 0

12 h

24 h

7.3.3.4 . Temperatures of structure in flight As we saw previously, software PST2 enables us to define the changes in the temperatures of the structural elements on the ground. We shall apply the same method to find the changes of these elements in flight. For this, we must define the aircraft operating scenarios. These scenarios depend on: - typical aircraft mission (change of speed M and altitude z versus time), - distribution of the missions during the day (generally not taken into account for the static justification), - type of atmosphere, - initial conditions defined previously (see chapter V 7.3.3.3).

- Typical mission Several flight configurations or "missions" can be taken into account depending on the way in which the aircraft is used.

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THERMAL CALCULATIONS

V

Temperatures of structure in flight

7.3.3.4 2/3

TAXI-IN

12 DESCENT 210 KT

APPROACH 210 KT to 145 KT

LANDING

1500 fr

5

5

3.3 12.5

5000 fr

DECELERATION 240 KT to 210 KT

HOLD 5 mm - 240 kT

10000 fr

DECELERATION 250 KT to 240 KT

21.6

5

4.4 DECELERATION 335 KT to 250 KT

DESCENT 250 KT

42.8 DESCENT 0.82 M/335 KT

CRUISE 0.78 M

21.5

5.7

87.2 664.9

10.8

2.3 10.3

78.8 CLIMB 30 KT/0.78 M

ACCELERATION 250 KT to 330 KT

1.3 2.4

CLIMB 250 KT

31000 fr

T.O. + CLIMB

5 START UP AND TAXI-OUT

DIST. (nm)

TIME (min)

Generally, a typical "mission" can be described as follows (A300-600):

- Daily use of the aircraft A mean "typical" use is determined. For instance: for the A340, five 75' flights have been considered distributed over 1 day as shown below: 75'

75'

60' 0

75'

60'

75'

60'

400

75'

60' 1440

time (min)

Remark: For the static justification, we will not take into account the influence of the previous flight on the initial conditions of the mission under study. Each flight will be considered as isolated during the day. We shall therefore choose the most penalizing time for the start of the mission (generally 12 h for positive temperatures).

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THERMAL CALCULATIONS Temperatures of structure in flight

V

7.3.3.4 3/3

- Definitions of atmospheres Three types of atmospheres are to be considered in the analyses: - standard, - tropical, - polar. Remark: For the fatigue analysis, it is sometimes necessary (if we do not want to be too conservative) to use a random distribution of the type of atmosphere encountered during one year in service. The "standard" operating time can for instance be broken down as follows: - ¼ of operation in polar atmosphere, - ¼ of operation in standard atmosphere, - ½ of operation in tropical atmosphere. For the static justification, we shall choose the most penalizing atmosphere (tropical or polar).

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Qϕ Solar radiation on ground

12 h

t

Altitude z

Altitude z

Ambient temp. in flight

Speed M

x (1 + 0.18 Mach2)

Tamb. z 55° C - 54° C

t

Speed M

Altitude z

t

12 h

24 h

Qϕ z Radiation in flight

T athermane

Altitude z

T struc.

0h

Temperature of elements t

24 h

T wall

- Conduction - Convection - Radiation

V

Daily frequency

FATIGUE JUSTIFICATION

STATIC JUSTIFICATION

to be superimposed on the mechanical effects

7.4

: optional

Composite stress manual

MTS 006 Iss. B

Typical flight mission

0h

24 h

Block diagram

Ambient temp. on ground

THERMAL CALCULATIONS

Tamb. ground

- Standard - Tropical - Polar

7.4 . Recapitulative block diagram

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Typical atmosphere

Composite stress manual

THERMAL CALCULATIONS Computing softwares

V

8 1/2

8 . COMPUTING SOFTWARES For complex structures, there are three software programs to determine, on the one hand, the temperature ranges in the various structural elements and, on the other hand, the resulting thermal stresses and strains. Software PST2: It is used to determine the map of the temperatures of the structure over time versus changes in external conditions and the speed of the aircraft (during a mission for example). It is assumed that the temperature of the walls is equal to the athermane temperature, that æ ö γ −1 is the ambient temperature multiplied by the following factor: çç1 − x Mach 2 ÷÷ . γ è ø Knowledge of the thermal conductivity characteristics of the various materials (and the fluids contained in the structure: air, kerosene, etc.) is required together with the heat transfer coefficients between the various elements in order to evaluate the temperature map of the structure and its changes. Remark: We can, for simplification reasons, consider that the complete structure has a uniform temperature equal to the outside temperature or to the athermane temperature. Once the temperature range within the part has been determined, we must evaluate the stresses and strains of thermal origin. For this, in addition to the "manual" method previously described (§ V 6), this can be done by two computing software programs. Software PST1: It is used to determine for a long structure of the dissimilar beam type (several different metals) submitted to any temperature field (uniform or not) the stresses of thermal origin and the resulting longitudinal strains (x-direction).

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THERMAL CALCULATIONS Computing softwares

V

8 2/2

The part will be described by its current section which will be broken down into elementary parts defined by their positions (center of gravity) and their geometrical and mechanical characteristics (cross-section, inertia, modulus of elasticity, expansion coefficient, etc.).

cdg S l E α

x

BEAM TYPE PART

CURRENT SECTION

Software PST4: This calculation sequence is used to determine the thermoelastic stresses of a structure schematized by finite elements for any temperature range (a temperature is associated with each node of the structure).

θ

FINITE ELEMENT MODEL

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THERMAL CALCULATIONS

V

First example

9 . EXAMPLE

9.1 . First example: thermal stresses and forces in a bolted repair For the following bolted repair:

b = 15

b = 15

x

a = 15

fA

y

fA

A = 15

a = 15

fA

y

x

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A = 15

a = 15

9.1 1/4

Composite stress manual

THERMAL CALCULATIONS First example

V

9.1 2/4

Initial material: Material: T300/BSL914 Lay-up: 6/6/6/6 Exxs = 4878 daN/mm2 Eyys = 4878 daN/mm2 es = 3.12 mm αs = 3.5 E-6 mm/mm/° C Doubler material: Material: Aluminium Exxr = 7400 daN/mm2 Eyyr = 7400 daN/mm2 er = 2 mm αr = 24 E-6 mm/mm/° C Fasteners: D = 3.2 mm E = 10000 daN/mm2 Rigidity of fasteners: {u1} æ ö 1 5 1 1 ÷÷ = + 0.8 çç + r 10000 3.2 è 7400 x 2 4878 x 3.12 ø

r = 3800 daN/mm If there are no loads of mechanical origin, what are the forces on the fasteners and the flows at the center of the doubler and the panel if the panel and its repair are heated to an absolute temperature of 70° C (∆T = 50° C) ? The fasteners subjected to the highest loads are the ones located in the corners of the repair. We shall therefore study fastener A. As the thermal load (relevant to a strip of material of width b = 15 mm that we will consider as a bimetallic strip) is (in first approximation) independent of the length (relation v7), the components in the x- and y-directions are equal.

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THERMAL CALCULATIONS

V

First example

9.1 3/4

{v8} Γ=

1 1 + = 8.88 E − 6 daN −1 4878 x 3.12 x 5 7400 x 2 x 5

{v7} F=

50 (3.5 E − 6 − 24 E − 6) = − 115 daN 8.8 E − 6

→ compression force applied to the doubler

F = 115 daN

F = 115 daN

F = 115 daN

F = 115 daN

A

y

F = 115 daN

x

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THERMAL CALCULATIONS First example

V

9.1 4/4

We can deduce the force on the fastener A in x-direction: {v10} 15 + 15 15 x 15 x 3800 f Ax = 115 = 115 x 0.71 = 82 daN 2 15 + 15 8.88 E − 6 + 15 x 15 x 3800 8.88 E − 6 +

and the force on fastener A in the y-direction: {v11} 1 1 æ 15 ö æç + 15 x 8.88 E − 6 + ç − 1÷ ç 2 3800 15 è ø è 3 3800 + 15 x 15 x 3800 y f A = 115 1 15 æ 1 ö + + 15 x 8.88 E − 6 ÷ ç 3800 15 è 3800 ø

ö ÷ ÷ ø

= 115 x 0.6 = 69 daN

The global force on fastener A is therefore: fA =

692 + 82 2 = 107 daN

We can deduce the flows Nxr and Nyr of thermal origin in the center of the doubler: Nxr =

− 115 = − 7.67 daN / mm 15

Nyr =

− 115 = − 7.67 daN / mm 15

We can deduce the flows Nxs and Nys of thermal origin in the parent skin: Nxs =

115 = 7.67 daN / mm 15

Nys =

115 = 7.67 daN / mm 15

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Composite stress manual

THERMAL CALCULATIONS Second example

V

9.2 1/2

9.2 . Second example: thermal stresses in a bonded joint Let us suppose that the doubler is bonded and not bolted with an adhesive with the following mechanical characteristics: Gc: 300 daN/mm2 ec: 0.05 mm {v16} λ=

300 7400 x 2 + 4878 x 3.12 x = 894 E − 3 0.05 7400 x 2 x 4878 x 3.12

We can deduce the maximum shear stress at point A in x-direction: {v15} x τ Max =

x τ Max

805 x 894 E − 3 æ 105

æ 894 E − 3 x 75 ö æ 894 E − 3 x 75 ö 7400 x 2 − 4878 x 3.12 ö çç coth ç ÷÷ ÷ + tanh ç ÷x 2 2 è ø è ø 7400 x 2 + 4878 x 3.12 ø è

= 6.75 hb

where 805 (daN) is the global thermal load on the plate (115 x 7) and 105 (mm) is the total height of the plate. The maximum shear stress in y-direction is equal to: {v15} y = τ Max

575 x 894 E − 3 æ 75

æ 894 E − 3 x 105 ö æ 894 E − 3 x 105 ö 7400 x 2 − 4878 x 3.12 ö çç coth ç ÷÷ ÷ + tanh ç ÷x 2 2 è ø è ø 7400 x 2 + 4878 x 3.12 ø è

y τ Max = 6.75 hb

where 575 (daN) is the global thermal load on the plate (115 x 5) and 75 (mm) is the total width of the plate.

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Composite stress manual

THERMAL CALCULATIONS Second example

V

9.2 2/2

We can therefore deduce the global shear stress at point A: τMax. =

6.75 2 + 6.75 2 = 9.54 hb

This value is to be compared with the permissible value for the adhesive which generally is equal to 8 hb. If the plastic adaptation of the adhesive is not taken into account, the repair will unstick.

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MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Third example

9.3 1/7

9.3 . Third example: internal curing stresses in a laminated plate Let us consider a laminate consisting of four carbon tapes (T300/BSL914) with following lay-up: 0°/45°/135°/90°/90°/135°/45°/0°. For simplification reasons, we will determine the internal stresses in the fiber at 0° due to the increase in temperature on curing then to cooling: ∆T = Tambient - Tcuring = 20 - 180 = - 160° C

The mechanical characteristics of the unidirectional fiber are: El = 13000 hb (130000 MPa) Et = 465 hb (4650 MPa) νlt = 0.35 νtl = 0.0125 Glt = 465 hb (4650 MPa) ply thickness = 0.13 mm total thickness = 2.6 mm αl = - 1 E-6 mm/mm/° C αt = 40 E-6 mm/mm/° C z = 0.52 z = 0.39 z = 0.26 z = 0.13 z=0 z = - 0.13 z = - 0.26 z = - 0.39 z = - 0.52

t l z

0° 45° 135° 90° 90° 135° 45° 0°

© AEROSPATIALE - 1999

y

k=8 k=7 k=6 k=5 k=4 k=3 k=2 k=1

MTS 006 Iss. B

x

Composite stress manual

THERMAL CALCULATIONS

V

Third example

9.3 2/7

Let us calculate the membrane thermoelastic behavior coefficients of the laminate: {v5}

αEh

x

æ ç è

= 2 ç 0.13

0

2

(

)

(

2 x 13000 ( − 1 E − 6 ) + 0.0125 x 40 E − 6 + 1 x 465 0.35 x ( − 1 E − 6 ) + 40 E − 6 1 − 0.35 x 0.0125

) ö÷ ÷ ø

2 2 æ 0.707 x 13000 (( − 1 E − 6 ) + 0.0125 x 40 E − 6 ) + (− 0.707 ) x 465 (0.35 x ( − 1 E − 6 ) + 40 E − 6 ) ö÷ ç + 2 0.13 ÷ ç 1 − 0.35 x 0.0125 ø è

2 2 æ 0.707 x 13000 (( − 1 E − 6 ) + 0.0125 x 40 E − 6 ) + 0.707 x 465 (0.35 x ( − 1 E − 6 ) + 40 E − 6 ) ö ÷ ç ÷ 1 0 . 35 x 0 . 0125 − è ø 2 2 æ 1 x 13000 (( − 1 E − 6 ) + 0.0125 x 40 E − 6 ) +0 x 465 (0.35 x ( − 1 E − 6 ) + 40 E − 6 ) ö ÷ + 2 ç 0.13 ç ÷ 1 − 0.35 x 0.0125 è ø

+ 2 ç 0.13

-1

= 2 (0.002407375 + 0.000779095 + 0.000779095 - 0.000848713) = 6.232 E-3 daN mm ° C

αEh

y

æ ç è

= 2 ç 0.13

æ

+ 2 ç 0.13

ç è

(

)

-1

(

2 2 1 x 13000 ( − 1 E − 6 ) + 0.0125 x 40 E − 6 + 0 x 465 0.35 x ( − 1 E − 6 ) + 40 E − 6 1 − 0.35 x 0.0125

) ö÷ ÷ ø

(− 0.707 )2 x 13000 (( − 1 E − 6) + 0.0125 x 40 E − 6 ) + 0.707 2 x 465 (0.35 x ( − 1 E − 6) + 40 E − 6 ) ö÷ ÷ ø

1 − 0.35 x 0.0125

2 2 æ 0.707 x 13000 (( − 1 E − 6 ) + 0.0125 x 40 E − 6 ) + 0.707 x 465 (0.35 x ( − 1 E − 6 ) + 40 E − 6 ) ö ÷ ç ÷ 1 − 0.35 x 0.0125 è ø 2 2 æ 0 x 13000 (( − 1 E − 6 ) + 0.0125 x 40 E − 6 ) + 1 x 465 (0.35 x ( − 1 E − 6 ) + 40 E − 6 ) ö ÷ + 2 ç 0.13 ç ÷ 1 − 0 . 35 x 0 . 0125 è ø + 2 ç 0.13

-1

= 6.232 E-3 daN mm ° C

αEh

xy

-1

(

)

0 x 1 x 465 0.35 ( − 1E − 6 ) + 40E − 6 − 0 x 1 x 13000 ( − 1E − 6 ) + 0.0125 x 40E − 6

è

1 − 0.35 x 0.0125

(

)

(

)

(

)

(

) ö÷ ÷ ø

æ

0.707 x − 0.707 x 465 0.35 x ( − 1 E − 6 ) + 40 E − 6 − 0.707 x − 0.707 x 13000 ( − 1 E − 6 ) + 0.0125 x 40 E − 6

è

1 − 0.35 x 0.0125

+2ç ç 0.13

(

)

(

) ö÷ ÷ ø

æ

0.707 x 0.707 x 465 0.35 x ( − 1 E − 6 ) + 40 E − 6 − 0.707 x 0.707 x 13000 ( − 1 E − 6 ) + 0.0125 x 40 E − 6

è

1 − 0.35 x 0.0125

+ 2 çç 0.13

(

)

(

æ

1 x 0 x 465 0.35 x ( − 1 E − 6 ) + 40 E − 6 − 1 x 0 x 13000 ( − 1 E − 6 ) + 0.0125 x 40 E − 6

è

1 − 0.35 x 0.0125

+ 2 çç 0.13

= 2 (- 0.001627552 + 0.001627552) = 0 © AEROSPATIALE - 1999

(

æ

= 2 çç 0.13

MTS 006 Iss. B

) ö÷ ÷ ø

) ö÷ ÷ ø

Composite stress manual

THERMAL CALCULATIONS Third example

V

9.3 3/7

The terms Aij of the rigidity matrix of the laminate (in daN/mm) were calculated in chapter E 4: A11 = 2779 x 2 = 5558 A12 = 821 x 2 = 1642 A13 = 0 A21 = 821 x 2 = 1642 A22 = 2779 x 2 = 5558 A23 = A31 = A32 = 0 A33 = 978 x 2 = 1956

As external loads are zero, the relation v1 can be written as follows: {v4} 5558

1642

0

εx

6.232 E − 3

1642

5558

0

εy

= -160 6.232 E − 3

0

0

1956

γ xy

0

We can deduce the thermal expansions (in mm/mm) of the laminate in the reference frame (x, y): − 13.85 E − 5

εx εy γ xy

=

− 13.85 E − 5 0

The results above are the apparent thermal expansions of the plate in the reference frame (x, y) and the expansions of the fiber at 0° in its own reference frame (l, t):

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Third example

9.3 4/7

− 13.85 E − 5

(εl, t, 0°) = − 13.85 E − 5 0

To determine the internal stresses applied to the fiber at 0°, we must find what the expansions of this fiber would be if it was isolated and free from all strains: The thermoelastic coefficients of the unidirectional fiber at 0° in its reference frame (l, t) are equal to: {v5}

(

αEh = 0.26 − 0.13 l

2

)1

(

t

)0

(

)

(

)

x 465 0.35 x ( − 1 E − 6 ) + 40 E − 6

-1

= - 8.487 E-4 daN mm ° C

(

2

1 − 0.35 x 0.0125 -1

αEh = 0.26 − 0.13

)

x 13000 ( − 1 E − 6 ) + 0.0125 x 40 E − 6 + 0

2

(

)

2 x 13000 ( − 1 E − 6 ) + 0.0125 x 40 E − 6 + 1 x 465 0.35 x ( − 1 E − 6 ) + 40 E − 6 1 − 0.35 x 0.0125

= 2.407 E-3 daN mm-1 ° C-1 αEh

lt

(

= 0.26 − 0.13

) 1 x 0 x 465 (0.35 x ( − 1 E − 6) + 40 E − 6 ) − 1 x 0 x 13000 (( − 1 E − 6) + 0.0125 x 40 E − 6 ) 1 − 0.35 x 0.0125

=0 The coefficients Aij of the rigidity matrix of the unidirectional fiber at 0° are: A11 = 13057 x 0.13 = 1697 A12 = 163 x 0.13 = 21.19 A13 = 0 A21 = 21.19 A22 = 60.71 A23 = 0 A31 = 0 A32 = 0 A33 = 60.45

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Third example

9.3 5/7

Under the influence of a ∆T = - 160° C, the thermal expansions (in mm/mm) of an isolated fiber would satisfy the following relation: 1697

21.19

0

εl

8.487 E − 4

21.19

60.71

0

εt

= -160 2.407 E − 3

0

0

60.45

γ lt

0

We therefore obtain: 16 E − 5

εl εt

=

− 6.4 E − 3

γ lt

0

It is important to specify that in this case, the fiber is submitted to no internal thermal stresses as free from all strains. By simply calculating the difference, we find the "expansions" (in mm/mm) of the fiber at 0° if it was submitted to the stresses of thermal origin alone: ε'fiber thermal stresses 0° = εthermal of plate - εthermal of 0° fiber alone These three types of expansions must be determined in the same reference frame. For the fiber at 0°, no change of reference frame is required. If we had wanted to study for instance the internal stresses in the fiber at 45°, we would have had to determine the expansions of the plate in a frame oriented at 45° in relation to the reference frame (relation c7). We therefore obtain the expansions (in mm/mm) of the fiber at 0° due only to the thermal stresses which are applied to it:

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Third example

ε' l ε' t

13.85 E − 5

=

16 E − 5

− 13.85 E − 5

γ ' lt

-

6/7

29.85 E − 5

− 6.4 E − 3

0

9.3

=

6.259 E − 3

0

0

We can determine, by relation c8, the stresses (in hb) of thermal origin applied to the fiber at 0° (and therefore to all fibers as all directions are equivalent): {c8} σ'l σ' t

13057

163

0

− 29.85 E − 5

163

467

0

6.259 E − 3

0

0

465

0

=

τ'lt

− 2.88

=

2.88 0

In fact, these stresses are not to be taken into account in the justification of the laminate as they are indirectly taken into account when determining the permissible values for the unidirectional fiber of the material. It is also possible, by relation v6, to determine the equivalent membrane expansion coefficients of the laminate (in mm/mm/° C): {v6} α x equi. α y equi. α xyequi.

© AEROSPATIALE - 1999

=

−1

6.232 E − 3

5558

1642

0

1642

5558

0

6.232 E − 3

0

0

1956

0

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Third example

α x equi.

9.3

1.972 E − 4

− 0.583 E − 4

0

3.116 E − 3

0.583 E − 4

1.972 E − 4

0

3.116 E − 3

α xyequi.

0

0

0.511 E − 3

0

α x équi .

8.658 E − 7

α y equi.

α y équi .

=

=

α xy équi .

8.658 E − 7 0

This result can easily be checked: εx = ∆T αx equi. - 1.385 E-4 = - 160 8.658 E-7

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7/7

Composite stress manual

THERMAL CALCULATIONS

V

Fourth example

9.4 1/8

9.4 . Fourth example Calculation of the temperatures associated with a typical A340 mission on a section of an A340 aileron at bearing 1 (see note 440.092/92). In agreement with ACJ 25.603, we must, for the structural justification, associate the most penalizing environmental conditions (temperature and humidity) with the calculation cases. Here, we shall deal only with the temperature case. The atmosphere chosen will be tropical. The Loop 1A calculation cases corresponding to the various aircraft configurations is given in the table below:

Cas Conf. 0 1 2 10 11 12 13 14 15 16 17 18 19

C L L C C C C C C C C C C

Speed

Z (ft)

Mn

Pdyn (daN/m2)

nz (/q)

/ VFE VFE VC VC VC VC VC VC VD VD VD VD

35000 0 0 0 0 0 29900 29900 29900 0 0 29250 29250

0.82 0.28 0.28 0.499 0.499 0.499 0.86 0.86 0.86 0.552 0.552 0.93 0.93

1122.2 556.1 556.1 1766 1766 1766 1565 1565 1565 2161 2161 1885 1885

1 0.133 2 2.5 2 1 2.5 2 1 2.5 2 2.5 2

m (kg)

Cl max

CLwf (p)

AOA (°)

206911 / 0.512 186000 2.7 1.283 186000 2.7 1.846 250000 1.225 0.942 250000 1.225 0.758 250000 1.225 0.392 250000 1 1.067 250000 1 0.859 250000 1 0.444 250000 1.18 0.77 250000 1.18 0.621 250000 1 0.9 250000 1 0.725

3.12 3.46 9.86 10.03 7.9 3.64 8.33 6.59 3.1 8.07 6.36 9.04 7.19

We shall choose to study case Vc/Vd for an altitude z ≈ 29500 fts (cases 13, 14, 15, 18, and 19) the typical mission of which can be represented by the following diagram (time, speed, altitude):

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Composite stress manual

THERMAL CALCULATIONS

V

Fourth example

Speed (Mach)

9.4 2/8

z (fts)

Altitude

32000 fts 30000

1

20000 0.72 30

ts 0k

Speed 0.5

k 250

0

ts

10000

3

t (mm)

3540

60

First step: Consists in determining, from the meteorological data, the change in ambient temperature on the ground for a tropical atmosphere. This temperature depends on the quantity of heat due to the solar radiation Qϕ. By considering the change in the angle of incidence of the rays during the day, we find a variation of Qϕ versus the angle of incidence ϕ and therefore versus the time (Qϕ being taken as equal to 280 between 18 h and 6 h) t

6h

6 h 45

7h

7 h 20

8h

9h

10 h 10 h 20 11 h 11 h 30 12 h

Qϕ ϕ

280

545

636

727

838

929

980

12 h 12 h 30 13 h 13 h 40 14 h

15 h

16 h 16 h 40 17 h 17 h 15 18 h

1010

929

838

t Qϕ ϕ

© AEROSPATIALE - 1999

1008

1002

989

980

MTS 006 Iss. B

989

727

1002

636

1008

545

1010

280

Composite stress manual

THERMAL CALCULATIONS

V

Fourth example

9.4 3/8

1200

1000

800

Qϕ 2 (W/m )

600

400

200

0 0

3

6

9

12

15

18

21

24

t (time)

Second step: We will deduce the maximum ambient temperatures on the ground (z = 0) throughout the day (ISA + 40° C) which corresponds to a maximum temperature at 55° C at midday in a tropical atmosphere (the non-symmetry of the curve in relation to 12 h is explained by taking into account the buildup of heat during the day): t

6h

6 h 45

7h

7 h 20

8h

9h

10 h 10 h 20 11 h 11 h 30 12 h

Tamb.

32

36.6

38

39.9

43.5

48.3

51.9

t Tamb.

© AEROSPATIALE - 1999

54.8

55

12 h 30 13 h 13 h 40 14 h 15 h 16 h 16 h 40 17 h 17 h 15 18 h 19 h

20h

54.9

54.5

53.6

52.9 50.5 47.3

MTS 006 Iss. B

44.9

43.6

52.8

42.7

54.2

39.7 35.7

32

Composite stress manual

THERMAL CALCULATIONS

V

Fourth example

9.4 4/8

60

50

40

T amb. (° C)

30

20

10

0 0

3

6

9

12

15

18

21

24

t (time)

Third step: Consists in evaluating the temperature on the ground of the various structural items during a day in order to determine the most penalizing departure time. This calculation was done with software PST2 over three days so as to eliminate the effects of the initial conditions. The calculation method consists in dividing the structure into elementary sections (upper surface panel, lower surface panel, spar, leading edge, fittings) which initially have a uniform temperature (temperature of the ambient air) and in determining their changes before takeoff according to the three following phenomena: - conduction with adjacent elements, - convection with surrounding media (turbulences, kerosene), - solar radiation (α = 0.5; ε = 0.85)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Fourth example

9.4 5/8

By integrating all these data, we obtain the curve below which represents, over a period of 24 hours, the change in the temperature of the various structural elements. 11

1

56

52

Alu.

Tit.

ambient air (ISA + 40)

15

39 32

44 49

100 11

15

52/56

32/39/44

49 T struc. (° C) 55° C

1

20 0

12 t

© AEROSPATIALE - 1999

MTS 006 Iss. B

24

Composite stress manual

THERMAL CALCULATIONS Fourth example

V

9.4 6/8

We find (as was predictable) that the most unfavorable time for high temperatures is 12 h. We will therefore consider that the aircraft's mission starts at this time. Fourth step: consists, again with software PST2, in determining the change in temperature of each part during the mission itself by putting forward the (conservative) hypothesis that the ambient temperature on the ground is constant and equal to 55° C throughout the mission (ISA + 40° C) and by taking as initial values for the structural elements the previously defined temperatures at 12 o'clock. The curves below represent the change in temperature of each element of the part during the mission considered.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS

V

Fourth example

9.4 7/8

1

2

100 upper surface panel

spar

T struc. 55 (° C)

athermane temperature lower surface panel 0

Descent

t (s)

ACC

Climb 0.72M

Climb 0.72M

Climb 300 kts

Climb 300 kts

ACC

Climb 250 kts

Taxi TO Climb

3540

We can see that all the temperatures of the structural elements tend asymptotically to the athermane temperature (skin temperature) which depends on: - the ambient temperature on the ground (considered as being independent of time): 55° C, - the speed of the aircraft expressed in Mach number: M, - the altitude z.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

THERMAL CALCULATIONS Fourth example

V

9.4 8/8

Tather. ≈ Tamb. x (- 1.88 E-3 x z + 55) x (1 + 0.18 M2) Fifth step: Consists in combining throughout the mission, the loads of mechanical origin (aerodynamic) and the loads of thermal origin. This analysis (not covered by this chapter) gave two design-critical cases (see previous curve): - point Q: VC M = 0.86 t = 3426 s - point R: VD M = 0.92 t = 3510 s Remark: We could have also conducted a study on the negative temperature range were lower limit imposed by regulations is - 54° C. We however observed that the effect of the speed of the aircraft on the athermane temperature (1 + 0.18 M2) implied high temperatures in flight. We therefore limited the justification to - 54° C.

© AEROSPATIALE - 1999

MTS 006 Iss. B

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© AEROSPATIALE - 1999

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Composite stress manual

THERMAL CALCULATIONS References

V

GAY, Composite materials, 1991 J. HOEB, No. 22/S002.10502, Environment: justification of the count and of test PV No. 46534 - DCR/L, Thermal characterization of composite T300/914 PV No. 31/807/69, Study of thermo-optical factors PV No. 50879/88, Determination of "absortance" and "emittance" factors of ATR 72 finition paint A. TROPIS, A340 ailerons - Substantiation of tests and calculation environmental conditions, AS 440.092/92 P. MEUNIER, Aircraft S1 and S2 surface definition report A300-600, 26 X 002 10558/032

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W ENVIRONMENTAL EFFECT

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X NEW TECHNOLOGIES

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Y STATISTICS

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Z MATERIAL PROPERTIES

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© AEROSPATIALE - 1999

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Composite stress manual

SUMMARY Z . MATERIAL PROPERTIES 1 . Prepreg unidirectional tapes 1.1 . First generation Epoxy high strength carbon 1.2 . Second generation Epoxy intermediate modulus carbon 1.3 . Epoxy R glass 1.4 . Bismaleimide carbon 2 . Fabrics 2.1 . Epoxy resin prepreg 2.1.1 . Carbon 2.1.2 . Glass 2.1.3 . Kevlar 2.1.4 . Hybrid 2.1.5 . Quartz polyester hybrid 2.2 . Phenolic resin prepreg 2.2.1 . Carbon 2.2.2 . Glass 2.2.3 . Kevlar 2.2.4 . Fiberglass carbon hybrid 2.2.5 . Quartz polyester hybrid 2.3 . Bismaleimide resin prepreg 2.3.1 . Carbon 2.4 . Wet Lay-Up Epoxy (for repair) 2.4.1 . Carbon 2.4.2 . Glass 2.4.3 . Kevlar 2.4.4 . Fiberglass carbon hybrid 2.4.5 . Quartz polyester hybrid 3 . R.T.M. 3.1 . Epoxy resin 3.1.1 . Carbon 3.2 . Bismaléimide resin 3.3 . Phenolic resin 4 . Injection moulded thermoplastics 4.1 . Carbon 4.1.1 . PEEK 4.1.2 . PEI 4.1.3 . Polyamide 4.1.4 . PPS 4.1.5 . Polyarylamide 4.2 . Glass 4.2.1 . PEEK 4.2.2 . PEI 5 . Long fibre thermoplastics 5.1 . Carbon 5.1.1 . PEEK 5.1.2 . PEI 5.2 . Glass

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual 6 . Arall-Glare 7 . Metallic matrix composite materials (CMM) 8 . Adhesives 8.1 . Epoxy 8.2 . Phenolic 8.3 . Bismaleimide 8.4 . Thermoplastic 9 . Honeycomb 9.1 . Nomex - Hexagonal cells - OX-Core - Flex-Core 9.2 . Fiberglass honeycomb - Hexagonal cells - OX-Core - Flex-Core 9.3 . Aluminium honeycomb 10 . Foams

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

CLASSIFICATION OF FIBROUS MATERIALS/RESIN MATRICES IN ALPHABETICAL ORDER Chapters 1 to 5

TRADENAME OF MATERIAL 1581/501 181 + EPOXY resin 240/38/644 250/44/769 7781/V913 7788/54/M14 796/95/M14 APC2 (AS4/PEEK) CD282/PEI DE TENCATE E4049/RTM6 EHA 250-33-50 EHA 250-33-60 ES03/3752 ES36D/90120 ES36D/90285 ES36D/91581 F155/T120 G1151/RTM6 G803/145-4 G803/40/V200 G803/501 G803/914 G806 + T120/5052-9390-9396-501 G806/501 G806/5052 G806/9396 G814/501 G814/V913

© AEROSPATIALE - 1999

CHAPTER Z 2.4.2.1 Z 2.4.3.1 Z 2.2.2.1 Z 2.2.2.2 Z 2.1.2.1 Z 2.1.3.1 Z 2.1.3.2 Z 5.1.1.1 Z 5.1.2.1 Z 3.1.3 Z 2.2.3.3 Z 2.2.3.3 Z 2.1.4.2 Z 2.1.3.4 Z 2.1.3.3 Z 2.1.3.5 Z 2.1.2.2 Z 3.1.1 Z 2.1.1.3 Z 2.2.1.1 Z 2.4.1.1 Z 2.1.1.1 Z 2.2.4.1 Z 2.4.1.2 Z 2.4.1.3 Z 2.4.1.4 Z 2.4.1.5 Z 2.1.1.5

TRADENAME OF MATERIAL G815/V913 G874/V250 G973/913 G986/RTM6 GB305/DA3200 (*) GB305/XB5142 (*) GF520/LY564-1 + HY2954 (*) GF630/RTM6 HF360/LY564-1 + HY2954 (*) HTA7 (6K) EH25 (46280/25/42 %) HTA7 EH25 IM7/977-2 IXEF 1022 IXEF C36 KEVLAR economic 285 + GENIN 90285/ES36D EPOXY resin KEVLAR economic 285 + BROCHIER 1454/914 resin M14/1237 RYTON R04 T300/914 T300/N5208 T800H DA508T ULTEM 2310 VICOTEX 108/788 VICOTEX 145.2/788 VICOTEX 145.4/796 VOCPTEX 145.4/914 VICOTEX 250/788 VICOTEX 250/796

MTS 006 Iss. B

CHAPTER Z 2.1.1.4 Z 2.2.4.2 Z 2.1.4.1 Z 3.1.2 Z 3.1.4 Z 3.1.6 Z 3.1.8 Z 3.1.5 Z 3.1.7 Z 2.1.1.2 Z 1.1.3 Z 1.2.2 Z 4.1.5.1 Z 4.1.5.2 Z 2.1.3.10 Z 2.1.3.11 Z 2.1.5.1 Z 4.1.4.1 Z 1.1.1 Z 1.1.2 Z 1.2.1 Z 4.1.1.1 Z 2.1.3.6 Z 2.1.3.7 Z 2.1.3.8 Z 2.1.3.9 Z 2.2.3.1 Z 2.2.3.2

Composite stress manual

CLASSIFICATION BY TYPE OF FIBROUS MATERIALS/RESIN MATRICES

RESIN

TYPE OF MATERIAL

Prepreg carbon unidirectional tapes st

CURING TEMPERATURE

TRADENAME OF MATERIAL

PQ

CHAPTER

PAGES

180° C

T300/914

10139-261-01

Z 1.1.1

1-10

180° C

T300/N5208

10139-250-01

Z 1.1.2

1

180° C

HTA7 EH25

10139-501-01

Z 1.1.3

1

180° C

T800 H DA508T

Z 1.2.1

1

190° C

IM7/977-2

Z 1.2.2

1-3

180° C

G803/914

10139-353-01

Z 2.1.1.1

1-5

180° C

HTA7 (6K) EH25 (46280/25/42 %)

10139-353-02

Z 2.1.1.2

1-2

120° C

G803/145-4

10139-302-03

Z 2.1.1.3

1-2

125° C

G815/V913

DASA

Z 2.1.1.4

1-2

125° C

G814/V913

10139-450-01

Z 2.1.1.5

1-2

120° C

7781/V913

10516-022-04

Z 2.1.2.1

1

125° C

F155/T120

DASA-BAE

Z 2.1.2.2

1

1 generation high strength nd

2 generation intermediary modulus

Prepreg carbon fabrics EPOXY

st

1 generation high strength

Prepreg glass fabrics

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

CLASSIFICATION OF BY TYPE OF FIBROUS MATERIALS/RESIN MATRICES RESIN

TYPE OF MATERIAL

Prepreg Kevlar

EPOXY

Prepreg glass - carbon hybrid fabrics

Prepreg quartz - polyester hybrid fabrics

© AEROSPATIALE - 1999

CURING TEMPERATURE

TRADENAME OF MATERIAL

PQ

CHAPTER

PAGES

125° C

7788/54/M14

10139-142-00

Z 2-1-3-1

1-2

125° C

796/95/M14

10139-140-00

Z 2-1-3-2

1-2

120° C

ES36D/90285

10139-143-02

Z 2-1-3-3

1-2

120° C

ES36D/90120

Z 2-1-3-4

1-2

120° C

ES36D/91581

10139-142-05

Z 2-1-3-5

1-2

175° C

VICOTEX 108/788

10139-162-01

Z 2-1-3-6

1-2

120° C

VICOTEX 145.2/788

10139-142-01

Z 2-1-3-7

1-2

125° C

VICOTEX 145.4/796

10139-140-03

Z 2-1-3-8

1-2

125° C

VICOTEX 145.4/914

10139-143-03

Z 2-1-3-9

1-2

120° C

KEVLAR economic 285 + GENIN 90285/ES36D EPOXY resin

10139-143-01

Z 2-1-3-10

1

120° C

KEVLAR economic 285 + BROCHIER 1454/914 resin

10139-143-00

Z 2-1-3-11

1

125° C

G973/913

10056-300-01

Z 2.1.4.1

1-7

125° C

ES03/3752

10056-300-02

Z 2.1.4.2

1-2

125° C

M14/1237

Z 2.1.5.1

1-2

MTS 006 Iss. B

Composite stress manual

CLASSIFICATION OF BY TYPE OF FIBROUS MATERIALS/RESIN MATRICES

RESIN

TYPE OF MATERIAL

CURING TEMPERATURE

TRADENAME OF MATERIAL

PQ

CHAPTER

PAGES

Prepreg carbon fabrics

140° C

G803/40/V200

10139-500-01

Z 2.2.1.1

1

Prepreg glass fabrics

180° C

240/38/644

10056-72-01

Z 2.2.2.1

1

135° C

250/44/769

10056-074-01

Z 2.2.2.2

1

135° C

VICOTEX 250/788

10139-182-01

Z 2.2.3.1

1-2

135° C

VICOTEX 250/796

10139-180-01

Z 2.2.3.2

1-2

125° C

EHA 250-33-50 or EHA 250-33-60

Z 2.2.3.3

1

70° C - 90° C

G806 + T120/5052-9390-9396-501

Z 2.2.4.1

1-2

Z 2.2.4.2

1-2

Prepreg Kevlar PHENOLIC

Wet lay-up glass - carbon hybrid fabrics

10139-024-01 10057-002-00

Prepeg glass - carbon hybrid fabrics

© AEROSPATIALE - 1999

135° C - 150° C

G874/V250

MTS 006 Iss. B

10056-200-01

Composite stress manual

CLASSIFICATION OF BY TYPE OF FIBROUS MATERIALS/RESIN MATRICES RESIN

TYPE OF MATERIAL

Wet lay-up carbon fabrics

EPOXY

© AEROSPATIALE - 1999

CURING TEMPERATURE

TRADENAME OF MATERIAL

PQ

CHAPTER

PAGES

80° C

G803/501

10053-080-01 (r)

Z 2.4.1.1

1-2

90° C

G806/501

10139-024-01

Z 2.4.1.2

1-2

90° C

G806/5052

10139-024-01

Z 2.4.1.3

1-2

90° C

G806/9396

10139-024-01

Z 2.4.1.4

1-2

70° C

G814/501

Z 2.4.1.5

1-2

Wet lay-up glass fabrics

70° C

1581/501

10057-004-00/01

Z 2.4.2.1

1

Prepreg Kevlar

120° C

181 + EPOXY resin

10139-142-00

Z 2.4.3.1

1

RTM

150° C

G1151/RTM6

10139-701-00

Z 3.1.1

1-2

150° C

G986/RTM6

10139-702-00

Z 3.1.2

1-2

180° C

E4049/RTM6

10139-701-00

Z 3.1.3

1-2

120° C

GB305/DA3200 (*)

Z 3.1.4

1-2

150° C

GF630/RTM6

Z 3.1.5

1-2

120° C

GB305/XB5142 (*)

Z 3.1.6

1-2

120° C

HF360/LY564-1 + HY2954 (*)

10056-350-00

Z 3.1.7

1-2

120° C

GF520/LY564-1 + HY2954 (*)

10039-700-01

Z 3.1.8

1-2

MTS 006 Iss. B

10139-701-00

Composite stress manual

CLASSIFICATION OF BY TYPE OF FIBROUS MATERIALS/RESIN MATRICES

RESIN

TYPE OF MATERIAL

CURING TEMPERATURE

Injected thermoplastic

PQ

CHAPTER

PAGES

10058-514-01

Z 4.1.1.1

1

RYTON R04

Z 4.1.4.1

1

IXEF 1022

Z 4.1.5.1

1

IXEF C36

Z 4.1.5.2

1

ULTEM 2310

THERMOPLASTIC

Long-fiber thermoplastics

TRADENAME OF MATERIAL

390° C

APC2 (AS4/PEEK)

10139-951-00

Z 5.1.1.1

1

300° C

CD282/PEI DE TENCATE

10139-950-00

Z 5.1.2.1

1-2

(*): do not use (r): resin only

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

CLASSIFICATION OF CORE MATERIALS (HONEYCOMB AND FORMS) IN ALPHABETICAL ORDER Chapters 9 and 10

TRADENAME OF MATERIAL 5052 - F40 - 2.1 (Flex - Core) 5052 - F40 - 2.5 (Flex - Core) 5052 - F40 - 3.1 (Flex - Core) 5052 - F40 - 4.1 (Flex - Core) 5052 - F40 - 5.7 (Flex - Core) 5052 - F80 - 4.3 (Flex - Core) 5052 - F80 - 6.5 (Flex - Core) 5052 - F80 - 8.0 (Flex - Core) 5056 - F40 - 2.1 (Flex - Core) 5056 - F40 - 3.1 (Flex - Core) 5056 - F40 - 4.1 (Flex - Core) 5056 - F80 - 4.3 (Flex - Core) 5056 - F80 - 6.5 (Flex - Core) 5056 - F80 - 8.0 (Flex - Core) ACG - 1/4 - 4.8 ACG - 3/8 - 3.3 ACG - 1/2 - 2.3 ACG -3/4 - 1.8 ACG - 1 - 1.3 CR III 2024 - 3/16 - 3.5 CR III 2024 - 1/8 - 5.0 CR III 2024 - 1/8 - 6.7 CR III 2024 - 1/8 - 8.0 CR III 2024 - 1/8 - 9.5 CR III 2024 - 1/4 - 2.8 CR III 5052 - 1/16 - 6.5 CR III 5052 - 1/16 - 9.5 CR III 5052 - 1/16 - 12.0

© AEROSPATIALE - 1999

CHAPTER

PAGE

Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3

18 18 18 19 19 20 20 20 32 32 32 33 33 33 1 1 1 2 2 3 3 3 4 4 4 5 5 5

TRADENAME OF MATERIAL CR III 5052 - 1/16 - 13.8 CR III 5052 - 3/32 - 4.3 CR III 5052 - 3/32 - 6.3 CR III 5052 - 1/8 - 3.1 CR III 5052 - 1/8 - 4.5 CR III 5052 - 1/8 - 6.1 CR III 5052 - 1/8 - 8.1 CR III 5052 - 1/8 - 12.0 CR III 5052 - 1/8 - 22.1 CR III 5052 - 5/32 - 2.6 CR III 5052 - 5/32 - 3.8 CR III 5052 - 5/32 - 5.3 CR III 5052 - 5/32 - 6.9 CR III 5052 - 5/32 - 8.4 CR III 5052 - 3/16 - 2.0 CR III 5052 - 3/16 - 3.1 CR III 5052 - 3/16 - 4.4 CR III 5052 - 3/16 - 5.7 CR III 5052 - 3/16 - 6.9 CR III 5052 - 3/16 - 8.1 CR III 5052 - 1/4 - 1.6 CR III 5052 - 1/4 - 2.3 CR III 5052 - 1/4 - 3.4 CR III 5052 - 1/4 - 4.3 CR III 5052 - 1/4 - 5.2 CR III 5052 - 1/4 - 6.0 CR III 5052 - 1/4 - 7.9 CR III 5052 - 3/8 - 1.0

MTS 006 Iss. B

CHAPTER

PAGE

Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3

6 6 6 7 7 7 8 8 8 9 9 9 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 15

Composite stress manual

CLASSIFICATION OF CORE MATERIALS (HONEYCOMB AND FORMS) IN ALPHABETICAL ORDER Chapters 9 and 10

TRADENAME OF MATERIAL CR III 5052 - 3/8 - 1.6 CR III 5052 - 3/8 - 2.3 CR III 5052 - 3/8 - 3.0 CR III 5052 - 3/8 - 3.7 CR III 5052 - 3/8 - 4.2 CR III 5052 - 3/8 - 5.4 CR III 5052 - 3/8 - 6.5 CR III 5056 - 1/16 - 6.5 CR III 5056 - 1/16 - 9.5 CR III 5056 - 3/32 - 4.3 CR III 5056 - 3/32 - 6.3 CR III 5056 - 1/8 - 3.1 CR III 5056 - 1/8 - 4.5 CR III 5056 - 1/8 - 6.1 CR III 5056 - 1/8 - 8.1 CR III 5056 - 5/32 - 2.6 CR III 5056 - 5/32 - 3.8 CR III 5056 - 5/32 - 5.3 CR III 5056 - 5/32 - 6.9 CR III 5056 - 3/16 - 2.0 CR III 5056 - 3/16 - 3.1 CR III 5056 - 3/16 - 4.4 CR III 5056 - 3/16 - 5.7 CR III 5056 - 3/16 - 8.1 CR III 5056 - 1/4 - 1.6 CR III 5056 - 1/4 - 2.3 CR III 5056 - 1/4 - 3.4 CR III 5056 - 1/4 - 4.3

© AEROSPATIALE - 1999

CHAPTER

PAGE

Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3

15 16 16 16 17 17 17 21 21 22 22 23 23 23 24 24 24 25 25 26 26 26 27 27 27 28 28 28

TRADENAME OF MATERIAL CR III 5056 - 1/4 - 5.2 CR III 5056 - 1/4 - 6.0 CR III 5056 - 1/4 - 7.9 CR III 5056 - 3/8 - 1.0 CR III 5056 - 3/8 - 1.6 CR III 5056 - 3/8 - 2.3 CR III 5056 - 3/8 - 3.0 CR III 5056 - 3/8 - 5.4 HRH10 - 1/8 - 1.8 HRH10 - 1/8 - 3.0 HRH10 - 1/8 - 4.0 HRH10 - 1/8 - 5.0 HRH10 - 1/8 - 6.0 HRH10 - 1/8 - 8.0 HRH10 - 1/8 - 9.0 HRH10 - 3/16 - 1.5 HRH10 - 3/16 - 1.8 HRH10 - 3/16 - 2.0 HRH10 - 3/16 - 3.0 HRH10 - 3/16 - 4.0 HRH10 - 3/16 - 4.5 HRH10 - 3/16 - 6.0 HRH10 - 1/4 - 1.5 HRH10 - 1/4 - 2.0 HRH10 - 1/4 - 3.1 HRH10 - 1/4 - 4.0 HRH10 - 3/8 - 1.5 HRH10 - 3/8 - 2.0

MTS 006 Iss. B

CHAPTER

PAGE

Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.3 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1

29 29 29 30 30 30 31 31 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7

Composite stress manual

CLASSIFICATION OF CORE MATERIALS (HONEYCOMB AND FORMS) IN ALPHABETICAL ORDER Chapters 9 and 10

TRADENAME OF MATERIAL HRH10 - 3/8 - 3.0 HRH10/OX - 3/16 - 1.8 HRH10/OX - 3/16 - 3.0 HRH10/OX - 3/16 - 4.0 HRH10/OX - 1/4 - 3.0 HRH10 - F35 - 2.5 (Flex - Core) HRH10 - F35 - 3.5 (Flex - Core) HRH10 - F35 - 4.5 (Flex - Core) HRH10 - F50 - 3.5 (Flex - Core) HRH10 - F50 - 4.5 (Flex - Core) HRH10 - F50 - 5.0 (Flex - Core) HRH10 - F50 - 5.5 (Flex - Core) HRP - 3/16 - 4.0 HRP - 3/16 - 5.5 HRP - 3/16 - 7.0 HRP - 3/16 - 8.0 HRP - 3/16 - 12.0 HRP - 1/4 - 3.5 HRP - 1/4 - 4.5 HRP - 1/4 - 5.0 HRP - 1/4 - 6.5 HRP - 3/8 - 2.2 HRP - 3/8 - 3.2 HRP - 3/8 - 4.5 HRP - 3/8 - 6.0 HRP - 3/8 - 8.0 HRP/OX - 1/4 - 4.5 HRP/OX - 1/4 - 5.5

© AEROSPATIALE - 1999

CHAPTER

PAGE

Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.1 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2

7 8 8 8 9 10 10 10 11 11 12 12 1 1 1 2 2 3 3 3 4 5 5 5 6 6 7 7

TRADENAME OF MATERIAL HRP/OX - 1/4 - 7.0 HRP/OX - 3/8 - 3.2 HRP/OX - 3/8 - 5.5 HRP - F35 - 2.5 (Flex - Core) HRP - F35 - 3.5 (Flex - Core) HRP - F35 - 4.5 (Flex - Core) HRP - F50 - 3.5 (Flex - Core) HRP - F50 - 4.5 (Flex - Core) HRP - F50 - 5.5 (Flex - Core) ROHACELL 31 A ROHACELL 51 A ROHACELL 71 A ROHACELL 51 WF ROHACELL 71 WF ROHACELL 110 WF ROHACELL 200 WF

MTS 006 Iss. B

CHAPTER

PAGE

Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 9.2 Z 10 Z 10 Z 10 Z 10 Z 10 Z 10 Z 10

7 8 8 9 9 9 10 10 10 1 1 1 2 2 3 3

Composite stress manual

MATERIAL CHARACTERISTICS Glossary Definitions of the main characteristics of the unidirectional fiber El (daN/mm2)

Longitudinal modulus of elasticity

Et (daN/mm2)

Transverse modulus of elasticity

Glt (daN/mm2)

Shear modulus

νlt ep (mm)

Poisson coefficient Ply thickness

Rlt (hb)

Allowable longitudinal tensile strength

Rlc (hb)

Allowable longitudinal compression strength

Rtt (hb)

Allowable transverse tensile strength

Rtc (hb)

Allowable transverse compression strength

S (hb)

Allowable in-plane shear strength

τinter (hb)

Allowable interlaminar shear strength

c Km

Compression bearing stress coefficient

K mt

Tensile bearing stress coefficient

K ct

Hole compression coefficient

K tt

Hole tensile coefficient

σm (hb)

Allowable bearing strength

K flexion t

Pure bending hole coefficient

κc

Damage tolerance reduction coefficient for Rlc

κt

Damage tolerance reduction coefficient for Rlt

κs

Damage tolerance reduction coefficient for S

εadm. comp. (µd)

Allowable damage tolerance compression strain

εadm. tract. (µd)

Allowable damage tolerance tensile strain

γadm. cisail. (µd)

Allowable damage tolerance shear

Tg dry (° C)

Glass transition temperature in dry environment

Tg wet (° C)

Glass transition temperature in wet environment

Cθ (µd/° C)

Thermal expansion coefficient

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

DEFINITION of Tg Typical diagram of the determination of Tg-onset and Tg-peak

E' (Gpa) elastic modulus

E" (Gpa) viscoelastic modulus point L point M

tangent A point C ∆E

∆T

β

Tan Delta

tangent B

Tg-onset Tg-loss Tg-peak

Temperature (° C)

(cf. AITM 1-0003, index 2)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

MATERIAL CHARACTERISTICS Glossary Definitions of the main characteristics of honeycomb

T W direction

L direction

Ec (daN/mm2)

Compressive modulus direction T

Rc (hb)

Compressive strength direction T

Gl (daN/mm2)

Shearing modulus direction L

Gw (daN/mm2)

Shearing modulus direction W

sl (hb)

Shear strength direction L

sw (hb)

Shear strength direction w

* Preliminary values are obtained from testing one or two blocks of honeycomb type and often only one or two specimens for each point or condition tested. ** Predicted values indicate that no mechanical tests have been performed.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon tapes

Resin % 34 % Curing 180° C Surface density 200 gr/m2 El (daN/mm2)

T = 20° C

Aged wet T = 106° C

13000

13000

13000

Et (daN/mm )

465

465

465

Glt (daN/mm2)

465

465

465

νlt

0.35

0.35

0.35

ep (mm)

0.13

0.13

0.13

Rlt (hb)

120

120

120

Rlc (hb)

- 100

- 84

- 78.9

Rtt (hb)

5

5

5

Rtc (hb)

- 12

- 12

- 12

S (hb)

7.5

6.75

6.3

τinter (hb)

4.5

4.05

3.8

c Km

T300/914 (1)

T300/914 (1)

T300/914 (1)

K mt

T300/914 (2)

T300/914 (2)

T300/914 (2)

K ct

T300/914 (3)

T300/914 (3)

T300/914 (3)

K tt

New

T300/914E (4) T300/914E (4) T300/914E (4)

σm (hb)

T300/914 (5)

T300/914 (5)

T300/914 (5)

K flexion t

0.9

0.9

0.9

κc

T300/914 (6)

T300/914 (6)

T300/914 (6)

κt

T300/914 (6)

T300/914 (6)

T300/914 (6)

κs

T300/914 (6)

T300/914 (6)

T300/914 (6)

εadm. comp. (µd)

T300/914 (7)

εadm. tract. (µd)

T300/914 (7)

γadm. cisail. (µd)

T300/914 (7)

Tg onset dry (° C)

120° C

Tg onset wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

1.1.1

PREPREG CARBON TAPE T300/914 Aged wet T = 70° C

2

Z

95° C 1 (longi.)

40 (transv.)

MTS 006 Iss. B

95° C

References

440.233/89

581.0162/98

432.0026/96

1/10

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 2/10

SHEET T300/914 (1)

0.45

0.4

0.35

0.3

0.25 c

Km 0.2

0.15

0.1

0.05

0 0

5

10

15

20

25 σm

© AEROSPATIALE - 1999

MTS 006 Iss. B

30

35

40

45

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 3/10

SHEET T300/914 (2)

0.2

0.18

0.16

0.14

0.12

t

Km

0.1

0.08

0.06

0.04

0.02

0 0

5

10

15

20

25 σm

© AEROSPATIALE - 1999

MTS 006 Iss. B

30

35

40

45

50

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 4/10

SHEET T300/914 (3)

1

0.9

0.8

0.7

0.6

c

Kt

0.5

0.4

0.3

0.2

0.1

0 0

© AEROSPATIALE - 1999

1

2

3 E/G

MTS 006 Iss. B

4

5

6

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 5/10

SHEET T300/914 (4)

0.8

0.7

∅ 3.2 0.6 ∅ 4.8 0.5 ∅ 6.35 ∅ 7.9 t

Kt

0.4

∅ 9.52 ∅ 11.1

0.3

0.2

0.1

0 0

© AEROSPATIALE - 1999

1

2

3 E/G

MTS 006 Iss. B

4

5

6

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 6/10

SHEET T300/914 (5) 50

47.5

45

42.5

σm

40

37.5

35

32.5

30 0.8

1

1.2

1.4 ∅/e

© AEROSPATIALE - 1999

MTS 006 Iss. B

1.6

1.8

2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 7/10

SHEET T300/914 (6) 1

0.9

0.8

0.7

0.6

K

0.5

Ks

0.4

Kt Kc 0.3

0.2

0.1

0 0

1000

2000

3000

4000 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

5000

6000

7000

8000

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 8/10

SHEET T300/914 (7)

15000

12500

10000

7500

γa (s)

5000

εa (t)

µd 2500

0

εa (c)

- 2500

- 5000

- 7500 0

1000

2000

3000

4000 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

5000

6000

7000

8000

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 9/10

SHEET T300/914 (8)

0.5

0.45

0.4

0.35

0.3

do (t) 0.25

0.2

0.15

0.1

0.05

0 0

2

4

6

8 ∅ mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

10

12

14

16

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.1.1 10/10

SHEET T300/914 (9)

0.5

0.45

0.4

0.35

0.3

do (c) 0.25

0.2

0.15

0.1

0.05

0 0

2

4

6

8 ∅ mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

10

12

14

16

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon tapes

Resin % 35 % Curing 180° C Surface density 200 gr/m2

CARBON TAPE T300/N5208 PL/112/79 New

Aged

T = 20° C

T = 70° C

2

14000

14000

2

Et (daN/mm )

500

500

Glt (daN/mm2)

500

500

νlt

0.35

0.35

ep (mm)

0.13

0.13

Rlt (hb)

120

108

Rlc (hb)

- 100

- 90

Rtt (hb)

5

4.5

Rtc (hb)

- 12

- 10.8

S (hb)

6.5

8.85

c Km

0.1

0.1

K mt

0.1

0.1

K ct

0.765

0.765

K tt

0.6

0.6

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

1.1.2 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon tapes Resin % 34 % Curing 180° C Surface density 200 gr/m2

New

Aged

T = 20° C

T = 70° C

El (daN/mm2)

13000

13000

Et (daN/mm2)

465

465

Glt (daN/mm2)

465

465

νlt

0.35

0.35

ep (mm)

0.13

0.13

Rlt (hb)

132

132

Rlc (hb)

- 100

- 84

Rtt (hb)

5

5.5

Rtc (hb)

- 12

- 12

S (hb)

8.33

7.5

Z

1.1.3

CARBON TAPE HTA EH25 References

440.337/91 440.346/93

τinter (hb) c Km

K mt K ct

581.0162/98

K tt σm (hb) K flexion t

40 0.9

0.9

κc κt κs

432.0026/96

εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg onset dry (° C)

172° C

Tg onset wet (° C) Tg peak dry (° C) Tg peak wet (° C)

109° C 187° C 137° C

Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon tapes

Resin % Curing 180° C Surface density 145 gr/m2 (sec)

CARBON TAPE T800H - DA508T 528-082/90-03 New

Aged

T = 20° C

T = 70° C

2

16200

16200

2

Et (daN/mm )

580

580

Glt (daN/mm2)

580

580

νlt

0.35

0.35

ep (mm)

0.135

0.135

Rlt (hb)

190

190

Rlc (hb)

- 100

- 84

Rtt (hb)

11

11

Rtc (hb)

- 12

- 12

S (hb)

11

10

El (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

1.2.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon tapes

Resin % Curing 190° C/ 7 bars Surface density 145 gr/m2 (sec)

CARBON TAPE IM7/977-2 480.387/92-02 New

Aged

T = 20° C

T = 70° C

2

16200

16200

2

Et (daN/mm )

580

580

Glt (daN/mm2)

580

580

νlt

0.35

0.35

ep (mm)

0.135

0.135

Rlt (hb)

190

190

Rlc (hb)

- 100

- 84

Rtt (hb)

11

11

Rtc (hb)

- 12

- 12

S (hb)

11

10

c Km

T300/914 (1)

T300/914 (1)

K mt

T300/914 (2)

T300/914 (2)

K ct

T300/914 (3)

T300/914 (3)

K tt

T300/914 (4)

T300/914 (4)

σm (hb)

50

50

El (daN/mm )

τinter (hb)

K flexion t κc κt κs εadm. comp. (µd)

IM7/977-2 (1)

εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

1.2.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon tapes

1.2.2 2/2

SHEET IM7/977-2 (1)

BVID = 1 mm

E = 50 J

- 2600

- 2650

- 2700

- 2750

εa (c)

- 2800

- 2850

- 2900

- 2950

- 3000 0

20

40

60 Number of plies

© AEROSPATIALE - 1999

MTS 006 Iss. B

80

100

120

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % Curing 180° C Surface density

New T = 20° C

PREPREG CARBON FABRIC (equiv. tape) G803/914 440.353/87 Aged wet T = 70° C

2

11500

11500

2

Et (daN/mm )

500

500

Glt (daN/mm2)

500

500

νlt

0.35

0.35

ep (mm)

0.15

0.15

Rlt (hb)

96.4

85.8

Rlc (hb)

- 89.5

- 76

Rtt (hb)

5

5

Rtc (hb)

- 10

- 10

S (hb)

9.4

6.5

τinter (hb)

5.6

3.9

c Km

0.25

0.25

K mt

0.25

0.25

K ct

0.85

0.85

K tt

0.65

0.65

σm (hb)

40

40

K flexion t

0.9

0.9

El (daN/mm )

κc κt κs

G803/914 (1) G803/914 (1) * G803/914 (1) G803/914 (1) * G803/914 (1) G803/914 (1) *

εadm. comp. (µd)

G803/914 (2)

εadm. tract. (µd)

G803/914 (2)

γadm. cisail. (µd)

G803/914 (2)

Tg dry (° C)

120° C

Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

95° C 1 (longi.)

Z

40 (transv.)

MTS 006 Iss. B

2.1.1.1 1/4

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % 42 % Curing 180° C Surface density 490 gr/m2

New T = 20° C

PREPREG CARBON FABRIC (fabric) G803/914 440.353/87 Aged wet T = 70° C

2

6027

6027

2

Et (daN/mm )

6027

6027

Glt (daN/mm2)

500

500

νlt

0.0292

0.0292

ep (mm)

0.3

0.3

Rlt (hb)

49

43.7

Rlc (hb)

- 46.3

- 39.3

Rtt (hb)

49

43.7

Rtc (hb)

- 46.3

- 39.3

S (hb)

9.4

6.5

τinter (hb)

5.6

3.9

c Km

0.25

0.25

K mt

0.25

0.25

K ct

0.85

0.85

K tt

0.65

0.65

σm (hb)

40

40

K flexion t

0.9

0.9

El (daN/mm )

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C)

120° C

Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

95° C 3.1

Z

3.1

MTS 006 Iss. B

2.1.1.1 2/4

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon fabric

2.1.1.1 3/4

SHEET G803/914 (1)

1

0.9

0.8

0.7

κs*

0.6

κt κ

κc* κc

0.5

κs 0.4

0.3

0.2

0.1

0 0

200

400

600

800

1000 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

1200

1400

1600

1800

2000

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon fabric

2.1.1.1 4/4

SHEET G803/914 (2)

14000

12000

10000

8000

6000

γa (s) εa (t)

4000 µd 2000

0

- 2000 εa (c) - 4000

- 6000

- 8000 0

200

400

600

800

1000 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

1200

1400

1600

1800

2000

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % Curing 180° C Surface density

New

CARBON FABRIC (equiv. tape) HTA7 (6K) EH25 440.027/94 Aged

T = 20° C

T = 70° C

2

11500

11500

2

Et (daN/mm )

500

500

Glt (daN/mm2)

500

500

νlt

0.35

0.35

ep (mm)

0.15

0.15

Rlt (hb)

96.4

85.8

Rlc (hb)

- 89.5

- 76

Rtt (hb)

5

5

Rtc (hb)

- 10

- 10

S (hb)

9.4

6.5

c Km

0.25

0.25

K mt

0.25

0.25

K ct

0.85

0.85

K tt

0.65

0.65

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % 42 % Curing 180° C Surface density 490 gr/m2

New

CARBON FABRIC (fabric) HTA7 (6K) EH25 440.027/94 Aged

T = 20° C

T = 70° C

2

6027

6027

2

Et (daN/mm )

6027

6027

Glt (daN/mm2)

500

500

νlt

0.0292

0.0292

ep (mm)

0.3

0.3

Rlt (hb)

49

43.7

Rlc (hb)

- 47.7

- 39.7

Rtt (hb)

49

43.7

Rtc (hb)

- 47.7

- 39.7

S (hb)

9.4

6.5

c Km

0.25

0.25

K mt

0.25

0.25

K ct

0.85

0.85

K tt

0.65

0.65

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % Curing 120° C Surface density

New T = 20° C

CARBON FABRIC (equiv. tape) G803/145-4 Hurel Dubois (25 S 002 10388) Aged wet T = 70° C

2

11000

11000

2

Et (daN/mm )

500

500

Glt (daN/mm2)

500

500

νlt

0.35

0.35

ep (mm)

0.15

0.15

Rlt (hb)

95

95

Rlc (hb)

- 67

- 20.1

Rtt (hb)

10

10

Rtc (hb)

-5

- 1.5

S (hb)

6.5

6.5

c Km

0.2

0.2

K mt

0.2

0.2

K ct

0.85

0.85

K tt

0.6

0.6

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.3 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % 42 % Curing 120° C Surface density 490 gr/m2

New T = 20° C

CARBON FABRIC (fabric) G803/145-4 Hurel Dubois (25 S 002 10388) Aged wet T = 70° C

2

5777

5777

2

Et (daN/mm )

5777

5777

Glt (daN/mm2)

500

500

νlt

0.0304

0.0304

ep (mm)

0.3

0.3

Rlt (hb)

49.6

49.6

Rlc (hb)

- 34.6

- 10.4

Rtt (hb)

49.6

49.6

Rtc (hb)

- 34.6

- 10.4

S (hb)

6.5

6.5

c Km

0.2

0.2

K mt

0.2

0.2

K ct

0.85

0.85

K tt

0.6

0.6

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.3 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % Curing 125° C Surface density

CARBON FABRIC (equiv. tape) G815/913 DA - DAN 1208 Aged T = 80° C

2

El (daN/mm )

9450

Et (daN/mm2)

500

Glt (daN/mm2)

336

νlt

0.35

ep (mm)

0.175

Rlt (hb)

100

Rlc (hb)

- 64

Rtt (hb)

4.2

Rtc (hb)

- 3.3

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.4 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % 35 % Curing 125° C Surface density 540 gr/m2

CARBON FABRIC (fabric) G815/913 DA - DAN 1208 Aged T = 80° C

2

5001

2

Et (daN/mm )

5001

Glt (daN/mm2)

336

νlt

0.0352

ep (mm)

0.35

Rlt (hb)

42.28

Rlc (hb)

- 32.28

Rtt (hb)

42.28

Rtc (hb)

- 32.28

S (hb)

4

El (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.4 2/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon fabric

Resin % Curing 125° C/1h30/3.5 bars Surface density

New T = 20° C

CARBON FABRIC (equiv. tape) G814/913 440.104/92 Aged Aged Aged T = 80° C T = 20° C T = 80° C Hurel Dubois

2

10700

9700

9000

9800

2

Et (daN/mm )

400

400

400

400

Glt (daN/mm2)

400

380

320

400

νlt

0.35

0.35

0.35

0.35

ep (mm)

0.115

0.115

0.115

0.115

Rlt (hb)

83

77

77

73

Rlc (hb)

- 72

- 55

- 44

- 38.4

Rtt (hb)

3.5

3.5

3.5

4.5

Rtc (hb)

- 3.5

- 3.5

- 2.5

- 6.5

S (hb)

6

3.4

3.4

5

c Km

0.25

0.25

0.25

0.25

K mt

0.25

0.25

0.25

0.25

K ct

0.85

0.85

0.85

0.85

K tt

0.65

0.65

0.65

0.65

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

2.1.1.5 1/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon fabric

Resin % 50 % Curing 125° C/1h30/3.5 bars Surface density 390 gr/m2

New T = 20° C

CARBON FABRIC (fabric) G814/913 440.104/92 Aged Aged Aged T = 80° C T = 20° C T = 80° C Hurel Dubois

2

5572

5072

4722

5122

2

Et (daN/mm )

5572

5072

4722

5122

Glt (daN/mm2)

400

380

320

400

νlt

0.0252

0.0277

0.0298

0.0275

ep (mm)

0.23

0.23

0.23

0.23

Rlt (hb)

41.7

38.7

38.7

37.4

Rlc (hb)

- 36.5

- 27.8

- 22.6

- 20

Rtt (hb)

41.7

38.7

38.7

37.4

Rtc (hb)

- 36.5

- 27.8

- 22.6

- 20

S (hb)

6

3.4

3.4

5

c Km

0.25

0.25

0.25

0.25

K mt

0.25

0.25

0.25

0.25

K ct

0.85

0.85

0.85

0.85

K tt

0.65

0.65

0.65

0.65

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

2.1.1.5 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabric

Resin % Curing 120° C/1h/1.8 bar Surface density

New

GLASS FABRIC (equiv. tape) V913/7781 528/084/94 Aged

T = 20° C

T = 80° C

2

3800

3800

2

Et (daN/mm )

400

280

Glt (daN/mm2)

400

280

νlt

0.35

0.35

ep (mm)

0.115

0.115

Rlt (hb)

51

35

Rlc (hb)

- 44

- 30

Rtt (hb)

7

3.5

Rtc (hb)

-6

-3

S (hb)

7.4

3.7

c Km

0.1

0.1

K mt

0.1

0.1

K ct

0.85

0.85

K tt

0.75

0.75

σm (hb)

30

30

El (daN/mm )

τinter (hb)

K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.2.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabric

Resin % 37 % Curing 120° C/1h/1.8 bar Surface density 476 gr/m2

New

Aged

T = 20° C

T = 80° C

El (daN/mm2)

2118

2054

Et (daN/mm2)

2118

2054

Glt (daN/mm2)

400

280

νlt

0.0667

0.0667

ep (mm)

0.23

0.23

Rlt (hb)

27.8

18.7

Rlc (hb)

- 23.9

- 16.1

Rtt (hb)

27.8

18.7

Rtc (hb)

- 23.9

- 16.1

S (hb)

7.4

3.7

c Km

0.1

0.1

K mt

0.1

0.1

K ct

0.85

0.85

K tt

0.75

0.75

σm (hb)

30

30

GLASS FABRIC (fabric) V913/7781 528/084/94

τinter (hb)

K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.2.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabric

Resin % 38 % Curing 125° C Surface density 184 gr/m2

Aged wet T = 70° C

El (daN/mm2)

2070

2

GLASS FABRIC (fabric) F155/T120

Et (daN/mm )

2070

Glt (daN/mm2)

260

νlt ep (mm)

0.12

Rlc (hb)

36.3 (T = 23° C) - 30.9 (T = 71° C)

Rtt (hb)

36.3

Rtc (hb)

- 30.9

S (hb)

5

Rlt (hb)

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.2.2 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C/3h Surface density El (daN/mm2) 2

KEVLAR (equiv. tape) 788/54/M14 245/AERO/61-A Aged wet T = 70° C 4600

Et (daN/mm )

300

Glt (daN/mm2)

160

νlt

0.35

ep (mm)

0.125

Rlt (hb)

44

Rlc (hb)

- 14.9

Rtt (hb)

4

Rtc (hb)

-4

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 54 % Curing 125° C/3h Surface density 370 gr/m2

Aged wet T = 70° C

El (daN/mm2)

2465

2

KEVLAR (fabric) 788/54/M14 245/AERO/61-A

Et (daN/mm )

2465

Glt (daN/mm2)

160

νlt

0.0429

ep (mm)

0.25

Rlt (hb)

23.1

Rlc (hb)

-8

Rtt (hb)

23.1

Rtc (hb)

-8

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C/3h Surface density El (daN/mm2) 2

KEVLAR (equiv. tape) 796/65/M14 245/AERO/61-A Aged wet T = 70° C 4600

Et (daN/mm )

300

Glt (daN/mm2)

160

νlt

0.35

ep (mm)

0.05

Rlt (hb)

44

Rlc (hb)

- 14.9

Rtt (hb)

4

Rtc (hb)

-4

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 65 % Curing 125° C/3h Surface density 177 gr/m2

Aged wet T = 70° C

El (daN/mm2)

2465

2

KEVLAR (fabric) 796/65/M14 245/AERO/61-A

Et (daN/mm )

2465

Glt (daN/mm2)

160

νlt

0.0429

ep (mm)

0.1

Rlt (hb)

23.1

Rlc (hb)

-8

Rtt (hb)

23.1

Rtc (hb)

-8

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) ES36D/90285 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.3 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 55 % Curing 120° C Surface density 389 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) ES36D/90285 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.3 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) ES36D/90120 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.05

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.4 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 65 % Curing 120° C Surface density 177 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.1

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) ES36D/90120 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.4 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) ES36D/91581 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.5 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 60 % Curing 120° C Surface density 425 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) ES36D/91581 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.5 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 175° C Surface density

KEVLAR (equiv. tape) VICOTEX 108/788 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.6 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 45 % Curing 175° C Surface density 309 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 108/788 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.6 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) VICOTEX 145.2/788 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.7 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 54 % Curing 120° C Surface density 370 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 145.2/788 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.7 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C Surface density

KEVLAR (equiv. tape) VICOTEX 145.4/796 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.05

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.8 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 65 % Curing 125° C Surface density 177 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.1

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 145.4/796 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.8 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C Surface density

KEVLAR (equiv. tape) VICOTEX 145.4/914 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.9 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 54 % Curing 125° C Surface density 380 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 145.4/914 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.9 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density 185 gr/m2 (sec)

KEVLAR ECONOMIC (fabric) 285 + GENIN 90285/ES36D EPOXY RESIN New T = 20° C

2

2580 (warp)

2

2640 (weft)

El (daN/mm ) Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

0.28

Rlt (hb)

46.9 (warp)

Rlc (hb)

- 12.6 (warp)

Rtt (hb)

39.5 (weft)

Rtc (hb)

- 12.5 (weft)

S (hb) τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.3.10 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density 175 gr/m2 (sec)

KEVLAR ECONOMIC (fabric) 285 + BROCHIER 1454/914 EPOXY RESIN New T = 20° C

2

3175 (warp)

2

2340 (weft)

El (daN/mm ) Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

0.28

Rlt (hb)

43.3 (warp)

Rlc (hb)

- 11 (weft)

Rtt (hb)

38.1 (warp)

Rtc (hb)

- 10.2 (weft)

S (hb) τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.3.11 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % Curing 125° C/1h30/2 bars Surface density

New

GLASS - CARBON HYBRID (equiv. tape) G973/913 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

6560

6560

6105

2

Et (daN/mm )

400

400

360

Glt (daN/mm2)

350

350

315

νlt

0.35

0.35

0.35

ep (mm)

0.105

0.105

0.105

Rlt (hb)

54.6

54.6

46.4

Rlc (hb)

- 42.8

- 36

- 23.5

Rtt (hb)

4

4

4

Rtc (hb)

-8

-7

- 4.5

S (hb)

5

5

5

El (daN/mm )

τinter (hb)

G973/913 (1) G973/913 (1) G973/913 (1) * **

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

G973/913 (2) G973/913 (2) G973/913 (2)

σm (hb)

G973/913 (3) G973/913 (3) G973/913 (3) *

K flexion t

0.9

0.9

0.9

κc

G973/913 (4) G973/913 (4) G973/913 (4)

κt

G973/913 (4) G973/913 (4) G973/913 (4)

κs

G973/913 (4) G973/913 (4) G973/913 (4)

εadm. comp. (µd)

G973/913 (5)

εadm. tract. (µd)

G973/913 (5)

γadm. cisail. (µd)

G973/913 (5)

Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.4.1 1/7

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % 54 % Curing 125° C/1h30/2 bars Surface density 372 gr/m2

New

GLASS - CARBON HYBRID (fabric) G973/913 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

3501

3501

3251

2

Et (daN/mm )

3501

3501

3251

Glt (daN/mm2)

350

350

315

νlt

0.0402

0.0402

0.039

ep (mm)

0.21

0.21

0.21

Rlt (hb)

28.1

28.1

24.3

Rlc (hb)

- 22.9

- 19

- 12.4

Rtt (hb)

28.1

28.1

24.3

Rtc (hb)

- 22.9

- 19

- 12.4

S (hb)

5

5

4

El (daN/mm )

τinter (hb)

G973/913 (1) G973/913 (1) G973/913 (1) * **

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

G973/913 (2) G973/913 (2) G973/913 (2)

σm (hb)

G973/913 (3) G973/913 (3) G973/913 (3) *

K flexion t

0.9

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

0.9

2.1.4.1 2/7

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 3/7

SHEET G973/913 (1)

3

2.5 *

2

τinter.

**

1.5

1

0.5

0 0

5

10

15 Number of fabrics

© AEROSPATIALE - 1999

MTS 006 Iss. B

20

25

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Z

2.1.4.1

80

90

4/7

SHEET G973/913 (2) 1

0.9

0.8

0.7

0.6

0.5 t

Kt 0.4

0.3

0.2

0.1

0 0

10

20

30

40

50 % plies à 45°

© AEROSPATIALE - 1999

MTS 006 Iss. B

60

70

100

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 5/7

SHEET G973/913 (3) 60

50

40

*

σm

30

20

10

0 0

10

20

30

40

50 % plies à 45°

© AEROSPATIALE - 1999

MTS 006 Iss. B

60

70

80

90

100

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 6/7

SHEET G973/913 (4) 1

κt

0.9

κs κc

0.8

0.7

κc*

0.6

κ

0.5

0.4

0.3

0.2

0.1

0 0

20

40

60

80

100 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

120

140

160

180

200

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 7/7

SHEET G973/913 (5) 14000

12000

γa (c)

10000

8000

εa (t)

6000

µd

4000

2000

0

- 2000 εa (c*) εa (c) - 4000

- 6000 0

20

40

60

80

100 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

120

140

160

180

200

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % Curing 125° C/1h30/2 bars Surface density

New

GLASS - CARBON HYBRID (equiv. tape) ES03/3752 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

6560

6560

6105

2

Et (daN/mm )

400

400

360

Glt (daN/mm2)

350

350

315

νlt

0.35

0.35

0.35

ep (mm)

0.105

0.105

0.105

Rlt (hb)

54.6

54.6

46.4

Rlc (hb)

- 42.8

- 36

- 23.5

Rtt (hb)

4

4

4

Rtc (hb)

-8

-7

- 4.5

S (hb)

5

5

4

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

0.7

0.7

0.7

0.9

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.4.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % 52 % Curing 125° C/1h30/2 bars Surface density 372 gr/m2

New

GLASS - CARBON HYBRID (fabric) ES03/3752 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

3501

3501

3251

2

Et (daN/mm )

3501

3501

3251

Glt (daN/mm2)

350

350

315

νlt

0.0402

0.0402

0.039

ep (mm)

0.21

0.21

0.21

Rlt (hb)

19.7

19.7

17

Rlc (hb)

- 16

- 13.3

- 8.7

Rtt (hb)

19.7

19.7

17

Rtc (hb)

- 16

- 13.3

- 8.7

S (hb)

3.5

3.5

2.8

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

0.7

0.7

0.7

0.9

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.4.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % Curing 125° C Surface density

CARBON FABRIC (equiv. tape) G815/913 DA - DAN 1208 Aged T = 80° C

2

El (daN/mm )

9450

Et (daN/mm2)

500

Glt (daN/mm2)

336

νlt

0.35

ep (mm)

0.175

Rlt (hb)

100

Rlc (hb)

- 64

Rtt (hb)

4.2

Rtc (hb)

- 3.3

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.4 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabric

Resin % 35 % Curing 125° C Surface density 540 gr/m2

CARBON FABRIC (fabric) G815/913 DA - DAN 1208 Aged T = 80° C

2

5001

2

Et (daN/mm )

5001

Glt (daN/mm2)

336

νlt

0.0352

ep (mm)

0.35

Rlt (hb)

42.28

Rlc (hb)

- 32.28

Rtt (hb)

42.28

Rtc (hb)

- 32.28

S (hb)

4

El (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.1.4 2/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon fabric

Resin % Curing 125° C/1h30/3.5 bars Surface density

New T = 20° C

CARBON FABRIC (equiv. tape) G814/913 440.104/92 Aged Aged Aged T = 80° C T = 20° C T = 80° C Hurel Dubois

2

10700

9700

9000

9800

2

Et (daN/mm )

400

400

400

400

Glt (daN/mm2)

400

380

320

400

νlt

0.35

0.35

0.35

0.35

ep (mm)

0.115

0.115

0.115

0.115

Rlt (hb)

83

77

77

73

Rlc (hb)

- 72

- 55

- 44

- 38.4

Rtt (hb)

3.5

3.5

3.5

4.5

Rtc (hb)

- 3.5

- 3.5

- 2.5

- 6.5

S (hb)

6

3.4

3.4

5

c Km

0.25

0.25

0.25

0.25

K mt

0.25

0.25

0.25

0.25

K ct

0.85

0.85

0.85

0.85

K tt

0.65

0.65

0.65

0.65

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

2.1.1.5 1/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon fabric

Resin % 50 % Curing 125° C/1h30/3.5 bars Surface density 390 gr/m2

New T = 20° C

CARBON FABRIC (fabric) G814/913 440.104/92 Aged Aged Aged T = 80° C T = 20° C T = 80° C Hurel Dubois

2

5572

5072

4722

5122

2

Et (daN/mm )

5572

5072

4722

5122

Glt (daN/mm2)

400

380

320

400

νlt

0.0252

0.0277

0.0298

0.0275

ep (mm)

0.23

0.23

0.23

0.23

Rlt (hb)

41.7

38.7

38.7

37.4

Rlc (hb)

- 36.5

- 27.8

- 22.6

- 20

Rtt (hb)

41.7

38.7

38.7

37.4

Rtc (hb)

- 36.5

- 27.8

- 22.6

- 20

S (hb)

6

3.4

3.4

5

c Km

0.25

0.25

0.25

0.25

K mt

0.25

0.25

0.25

0.25

K ct

0.85

0.85

0.85

0.85

K tt

0.65

0.65

0.65

0.65

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

2.1.1.5 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabric

Resin % Curing 120° C/1h/1.8 bar Surface density

New

GLASS FABRIC (equiv. tape) V913/7781 528/084/94 Aged

T = 20° C

T = 80° C

2

3800

3800

2

Et (daN/mm )

400

280

Glt (daN/mm2)

400

280

νlt

0.35

0.35

ep (mm)

0.115

0.115

Rlt (hb)

51

35

Rlc (hb)

- 44

- 30

Rtt (hb)

7

3.5

Rtc (hb)

-6

-3

S (hb)

7.4

3.7

c Km

0.1

0.1

K mt

0.1

0.1

K ct

0.85

0.85

K tt

0.75

0.75

σm (hb)

30

30

El (daN/mm )

τinter (hb)

K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.2.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabric

Resin % 37 % Curing 120° C/1h/1.8 bar Surface density 476 gr/m2

New

Aged

T = 20° C

T = 80° C

El (daN/mm2)

2118

2054

Et (daN/mm2)

2118

2054

Glt (daN/mm2)

400

280

νlt

0.0667

0.0667

ep (mm)

0.23

0.23

Rlt (hb)

27.8

18.7

Rlc (hb)

- 23.9

- 16.1

Rtt (hb)

27.8

18.7

Rtc (hb)

- 23.9

- 16.1

S (hb)

7.4

3.7

c Km

0.1

0.1

K mt

0.1

0.1

K ct

0.85

0.85

K tt

0.75

0.75

σm (hb)

30

30

GLASS FABRIC (fabric) V913/7781 528/084/94

τinter (hb)

K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.2.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabric

Resin % 38 % Curing 125° C Surface density 184 gr/m2

Aged wet T = 70° C

El (daN/mm2)

2070

2

GLASS FABRIC (fabric) F155/T120

Et (daN/mm )

2070

Glt (daN/mm2)

260

νlt ep (mm)

0.12

Rlc (hb)

36.3 (T = 23° C) - 30.9 (T = 71° C)

Rtt (hb)

36.3

Rtc (hb)

- 30.9

S (hb)

5

Rlt (hb)

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.2.2 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C/3h Surface density El (daN/mm2) 2

KEVLAR (equiv. tape) 788/54/M14 245/AERO/61-A Aged wet T = 70° C 4600

Et (daN/mm )

300

Glt (daN/mm2)

160

νlt

0.35

ep (mm)

0.125

Rlt (hb)

44

Rlc (hb)

- 14.9

Rtt (hb)

4

Rtc (hb)

-4

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 54 % Curing 125° C/3h Surface density 370 gr/m2

Aged wet T = 70° C

El (daN/mm2)

2465

2

KEVLAR (fabric) 788/54/M14 245/AERO/61-A

Et (daN/mm )

2465

Glt (daN/mm2)

160

νlt

0.0429

ep (mm)

0.25

Rlt (hb)

23.1

Rlc (hb)

-8

Rtt (hb)

23.1

Rtc (hb)

-8

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C/3h Surface density El (daN/mm2) 2

KEVLAR (equiv. tape) 796/65/M14 245/AERO/61-A Aged wet T = 70° C 4600

Et (daN/mm )

300

Glt (daN/mm2)

160

νlt

0.35

ep (mm)

0.05

Rlt (hb)

44

Rlc (hb)

- 14.9

Rtt (hb)

4

Rtc (hb)

-4

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 65 % Curing 125° C/3h Surface density 177 gr/m2

Aged wet T = 70° C

El (daN/mm2)

2465

2

KEVLAR (fabric) 796/65/M14 245/AERO/61-A

Et (daN/mm )

2465

Glt (daN/mm2)

160

νlt

0.0429

ep (mm)

0.1

Rlt (hb)

23.1

Rlc (hb)

-8

Rtt (hb)

23.1

Rtc (hb)

-8

S (hb)

4

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) ES36D/90285 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.3 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 55 % Curing 120° C Surface density 389 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) ES36D/90285 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.3 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) ES36D/90120 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.05

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.4 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 65 % Curing 120° C Surface density 177 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.1

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) ES36D/90120 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.4 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) ES36D/91581 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.5 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 60 % Curing 120° C Surface density 425 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) ES36D/91581 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.5 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 175° C Surface density

KEVLAR (equiv. tape) VICOTEX 108/788 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.6 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 45 % Curing 175° C Surface density 309 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 108/788 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.6 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density

KEVLAR (equiv. tape) VICOTEX 145.2/788 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.7 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 54 % Curing 120° C Surface density 370 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 145.2/788 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.7 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C Surface density

KEVLAR (equiv. tape) VICOTEX 145.4/796 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.05

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.8 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 65 % Curing 125° C Surface density 177 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.1

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 145.4/796 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.8 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 125° C Surface density

KEVLAR (equiv. tape) VICOTEX 145.4/914 440.146/85 Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

Et (daN/mm2)

300

Glt (daN/mm2)

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.9 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 54 % Curing 125° C Surface density 380 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

Et (daN/mm2)

2500

Glt (daN/mm2)

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

KEVLAR (fabric) VICOTEX 145.4/914 440.146/85

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.1.3.9 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density 185 gr/m2 (sec)

KEVLAR ECONOMIC (fabric) 285 + GENIN 90285/ES36D EPOXY RESIN New T = 20° C

2

2580 (warp)

2

2640 (weft)

El (daN/mm ) Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

0.28

Rlt (hb)

46.9 (warp)

Rlc (hb)

- 12.6 (warp)

Rtt (hb)

39.5 (weft)

Rtc (hb)

- 12.5 (weft)

S (hb) τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.3.10 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % Curing 120° C Surface density 175 gr/m2 (sec)

KEVLAR ECONOMIC (fabric) 285 + BROCHIER 1454/914 EPOXY RESIN New T = 20° C

2

3175 (warp)

2

2340 (weft)

El (daN/mm ) Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

0.28

Rlt (hb)

43.3 (warp)

Rlc (hb)

- 11 (weft)

Rtt (hb)

38.1 (warp)

Rtc (hb)

- 10.2 (weft)

S (hb) τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.3.11 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % Curing 125° C/1h30/2 bars Surface density

New

GLASS - CARBON HYBRID (equiv. tape) G973/913 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

6560

6560

6105

2

Et (daN/mm )

400

400

360

Glt (daN/mm2)

350

350

315

νlt

0.35

0.35

0.35

ep (mm)

0.105

0.105

0.105

Rlt (hb)

54.6

54.6

46.4

Rlc (hb)

- 42.8

- 36

- 23.5

Rtt (hb)

4

4

4

Rtc (hb)

-8

-7

- 4.5

S (hb)

5

5

5

El (daN/mm )

τinter (hb)

G973/913 (1) G973/913 (1) G973/913 (1) * **

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

G973/913 (2) G973/913 (2) G973/913 (2)

σm (hb)

G973/913 (3) G973/913 (3) G973/913 (3) *

K flexion t

0.9

0.9

0.9

κc

G973/913 (4) G973/913 (4) G973/913 (4)

κt

G973/913 (4) G973/913 (4) G973/913 (4)

κs

G973/913 (4) G973/913 (4) G973/913 (4)

εadm. comp. (µd)

G973/913 (5)

εadm. tract. (µd)

G973/913 (5)

γadm. cisail. (µd)

G973/913 (5)

Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.4.1 1/7

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % 54 % Curing 125° C/1h30/2 bars Surface density 372 gr/m2

New

GLASS - CARBON HYBRID (fabric) G973/913 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

3501

3501

3251

2

Et (daN/mm )

3501

3501

3251

Glt (daN/mm2)

350

350

315

νlt

0.0402

0.0402

0.039

ep (mm)

0.21

0.21

0.21

Rlt (hb)

28.1

28.1

24.3

Rlc (hb)

- 22.9

- 19

- 12.4

Rtt (hb)

28.1

28.1

24.3

Rtc (hb)

- 22.9

- 19

- 12.4

S (hb)

5

5

4

El (daN/mm )

τinter (hb)

G973/913 (1) G973/913 (1) G973/913 (1) * **

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

G973/913 (2) G973/913 (2) G973/913 (2)

σm (hb)

G973/913 (3) G973/913 (3) G973/913 (3) *

K flexion t

0.9

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

0.9

2.1.4.1 2/7

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 3/7

SHEET G973/913 (1)

3

2.5 *

2

τinter.

**

1.5

1

0.5

0 0

5

10

15 Number of fabrics

© AEROSPATIALE - 1999

MTS 006 Iss. B

20

25

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Z

2.1.4.1

80

90

4/7

SHEET G973/913 (2) 1

0.9

0.8

0.7

0.6

0.5 t

Kt 0.4

0.3

0.2

0.1

0 0

10

20

30

40

50 % plies à 45°

© AEROSPATIALE - 1999

MTS 006 Iss. B

60

70

100

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 5/7

SHEET G973/913 (3) 60

50

40

*

σm

30

20

10

0 0

10

20

30

40

50 % plies à 45°

© AEROSPATIALE - 1999

MTS 006 Iss. B

60

70

80

90

100

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 6/7

SHEET G973/913 (4) 1

κt

0.9

κs κc

0.8

0.7

κc*

0.6

κ

0.5

0.4

0.3

0.2

0.1

0 0

20

40

60

80

100 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

120

140

160

180

200

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.1.4.1 7/7

SHEET G973/913 (5) 14000

12000

γa (c)

10000

8000

εa (t)

6000

µd

4000

2000

0

- 2000 εa (c*) εa (c) - 4000

- 6000 0

20

40

60

80

100 Sd 2 mm

© AEROSPATIALE - 1999

MTS 006 Iss. B

120

140

160

180

200

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % Curing 125° C/1h30/2 bars Surface density

New

GLASS - CARBON HYBRID (equiv. tape) ES03/3752 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

6560

6560

6105

2

Et (daN/mm )

400

400

360

Glt (daN/mm2)

350

350

315

νlt

0.35

0.35

0.35

ep (mm)

0.105

0.105

0.105

Rlt (hb)

54.6

54.6

46.4

Rlc (hb)

- 42.8

- 36

- 23.5

Rtt (hb)

4

4

4

Rtc (hb)

-8

-7

- 4.5

S (hb)

5

5

4

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

0.7

0.7

0.7

0.9

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.4.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % 52 % Curing 125° C/1h30/2 bars Surface density 372 gr/m2

New

GLASS - CARBON HYBRID (fabric) ES03/3752 440.399-02 Aged Aged

T = 20° C

T = 20° C

T = 70° C

2

3501

3501

3251

2

Et (daN/mm )

3501

3501

3251

Glt (daN/mm2)

350

350

315

νlt

0.0402

0.0402

0.039

ep (mm)

0.21

0.21

0.21

Rlt (hb)

19.7

19.7

17

Rlc (hb)

- 16

- 13.3

- 8.7

Rtt (hb)

19.7

19.7

17

Rtc (hb)

- 16

- 13.3

- 8.7

S (hb)

3.5

3.5

2.8

c Km

0.2

0.2

0.2

K mt

0.2

0.2

0.2

K ct

1

1

1

K tt

0.7

0.7

0.7

0.9

0.9

0.9

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.4.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg quartz - polyester hybrid fabrics

Resin % Curing 125° C/3h Surface density

Z

QUARTZ - POLYESTER FABRIC (equiv. tape) M14/1237 New

Aged

Aged

Aged

T = 20° C

T = 70° C

T = 70° C

T = - 55° C

El (daN/mm )

1820

1820

Et (daN/mm2)

455

455

Glt (daN/mm2)

193

193

νlt

0.35

0.35

ep (mm)

0.105

0.105

Rlt (hb)

46.5

10

Rlc (hb)

- 26.1

- 10.6

Rtt (hb)

11.63

2.5

Rtc (hb)

- 6.53

- 2.65

S (hb)

8.38

2.51

τinter (hb)

3

1.04

c Km

0.2

0.2

K mt

0.2

0.2

K ct

0.61

0.61

K tt

0.61

0.61

σm (hb)

40

12.8

15.2

18.1

K flexion t

0.9

0.9

2

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

2.1.5.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg quartz - polyester hybrid fabrics

Resin % 48 % Curing 125° C/3h Surface density 342 gr/m2

HYBRIDE QUARTZ - POLYESTER (fabric) M14/1237 New

Aged

Aged

Aged

T = 20° C

T = - 55° C

15.2

18.1

T = 20° C

T = 70° C

2

1150

1150

2

Et (daN/mm )

1150

1150

Glt (daN/mm2)

193

193

νlt

0.14

0.14

ep (mm)

0.21

0.21

Rlt (hb)

28.9

6.66

Rlc (hb)

- 17.7

- 9.89

Rtt (hb)

28.9

6.31

Rtc (hb)

- 17.7

- 6.45

S (hb)

8.38

2.51

τinter (hb)

3

1.04

c Km

0.2

0.2

K mt

0.2

0.2

K ct

0.61

0.61

K tt

0.61

0.61

σm (hb)

40

12.8

K flexion t

0.9

0.9

El (daN/mm )

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.1.5.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % 40 % Curing 140° C/1h30/4.75 bars Surface density 475 gr/m2

PHENOLIC PREPREG CARBON FABRIC (fabric) G803/40/V200

T = 20° C

Aged wet T = 110° C

2

6490

6730

2

Et (daN/mm )

6490

6730

Glt (daN/mm2)

600

406

νlt

0.05

0.05

ep (mm)

0.3

0.3

Rlt (hb)

51

44

Rlc (hb)

- 51

- 30

Rtt (hb)

51

44

Rtc (hb)

- 51

- 30

S (hb)

5

5.9

τinter (hb)

4

2

El (daN/mm )

New

c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.1.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabrics

Resin % 38 % Curing 180° C Surface density 485 gr/m2

Aged wet T = 20° C

El (daN/mm2)

1300

PHENOLIC GLASS FABRIC (fabric) 240/38/644

2

Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

0.1 - 0.3

Rlt (hb)

23

Rlc (hb)

- 23

Rtt (hb)

23

Rtc (hb)

- 23

S (hb) τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.2.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass fabrics

Resin % 44 % Curing

PHENOLIC GLASS FABRIC (fabric) 250/44/759

Surface density 190 gr/m2

Aged wet T = 20° C

El (daN/mm2)

1300

135° C/1h30 or 150° C/1h

Et (daN/mm2) Glt (daN/mm2) νlt ep (mm)

0.1 - 0.3

Rlt (hb)

23

Rlc (hb)

- 23

Rtt (hb)

23

Rtc (hb)

- 23

S (hb) τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.2.2 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin %

KEVLAR (equiv. tape) VICOTEX 250/788 440.146/85

Curing Surface density

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

135° C/1h30 or 150° C/1h

2

300

2

Glt (daN/mm )

230

νlt

0.35

ep (mm)

0.125

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

Et (daN/mm )

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.2.3.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 56 % Curing

KEVLAR (fabric) VICOTEX 250/788 440.146/85

Surface density 386 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

135° C/1h30 or 150° C/1h

2

2500

2

Glt (daN/mm )

230

νlt

0.0423

ep (mm)

0.25

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

Et (daN/mm )

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.2.3.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin %

KEVLAR (equiv. tape) VICOTEX 250/796 440.146/85

Curing surface density

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

4670

135° C/1h30 or 150° C/1h

2

300

2

Glt (daN/mm )

230

νlt

0.35

ep (mm)

0.05

Rlt (hb)

67.5

Rlc (hb)

- 18.7

Rtt (hb)

5

Rtc (hb)

-5

S (hb)

5

Et (daN/mm )

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.2.3.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 60 % Curing

KEVLAR (fabric) VICOTEX 250/796 440.146/85

Surface density 155 gr/m2

Aged T ≥ - 55° C T ≤ 70° C

El (daN/mm2)

2500

135° C/1h30 or 150° C/1h

2

2500

2

Glt (daN/mm )

230

νlt

0.0423

ep (mm)

0.1

Rlt (hb)

35

Rlc (hb)

- 10

Rtt (hb)

35

Rtc (hb)

- 10

S (hb)

5

Et (daN/mm )

τinter (hb) c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.2.3.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin % 50 % or 60% Curing 125° C/3h Surface density 425 gr/m2

KEVLAR (fabric) EHA 250-33-50 or EHA 250-33-60 TN-DE 423-7/83 New T = 80° C

2

2580

2

Et (daN/mm )

2530

Glt (daN/mm2)

207

El (daN/mm )

νlt ep (mm)

0.25

Rlt (hb)

36.6

Rlc (hb)

- 10

Rtt (hb)

36

Rtc (hb)

- 8.8

S (hb) τinter (hb)

2.5

c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.3.3 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Wet lay-up glass - carbon hybrid fabrics

Resin % Curing 90° C (70° C - 501) 2h/1 bar

New

GLASS - CARBON HYBRID (equiv. tape) G806 + T120/5052 - 9390 - 9396 - 501 440.218/94 Aged

Surface density T = 20° C

T = 70° C

El (daN/mm )

10000

10000

Et (daN/mm2)

300

300

Glt (daN/mm2)

300

300

νlt

0.35

0.35

ep (mm)

0.156

0.156

Rlt (hb)

50

40

Rlc (hb)

- 38

- 21

Rtt (hb)

4

4

Rtc (hb)

-7

-4

S (hb)

5

3

2

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.4.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Wet lay-up glass - carbon hybrid fabrics

Resin % 50 % Curing

GLASS - CARBON HYBRID (fabric) G806 + T120/5052 - 9390 - 9396 - 501 440.218/94 Aged

90° C (70° C - 501) 2h/1 bar

New

Surface density 240 gr/m2

T = 20° C

T = 70° C

El (daN/mm )

5167

5167

Et (daN/mm2)

5167

5167

Glt (daN/mm2)

300

170

νlt

0.0204

0.0204

ep (mm)

0.312

0.312

Rlt (hb)

25.6

20.5

Rlc (hb)

- 19.6

- 10.9

Rtt (hb)

25.6

20.5

Rtc (hb)

- 19.6

- 10.9

S (hb)

5

3

2

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.4.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin %

GLASS - CARBON HYBRID (equiv. tape) G874/V250 528/070/90

Curing 135° C/1h30 or 150° C/1h

Aged

Surface density T = 20° C 2

El (daN/mm )

1650

Et (daN/mm2) Glt (daN/mm2) νlt ep (mm)

0.15

Rlt (hb)

20.5

Rlc (hb)

- 18

Rtt (hb) Rtc (hb) S (hb) τinter (hb)

G874/V250 (1) G874/V250 (1)

c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.4.2 1/3

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg glass - carbon hybrid fabrics

Resin % 47 % Curing

GLASS - CARBON HYBRID (fabric) G874/V250 528/070/90

135° C/1h30 or 150° C/1h

Aged

Surface density 325 gr/m2

T = 20° C

2

El (daN/mm )

(825)

Et (daN/mm2)

(825)

Glt (daN/mm2) νlt ep (mm)

(0.4)

Rlt (hb)

(10.2)

Rlc (hb)

(- 9)

Rtt (hb)

(10.2)

Rtc (hb)

(- 9)

S (hb) τinter (hb)

G874/V250 (1) G874/V250 (1)

c Km

0.2

K mt

0.2

K ct

0.85

K tt

0.6

σm (hb)

35

K flexion t

0.9

κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

2.2.4.2 2/3

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg glass - carbon hybrid fabrics

2.2.4.2 3/3

SHEET G874/V250 (1) 2.8

2.4

2

1.6 τinter.

1.2

0.8

0.4

0 0

5

10

15 Number of fabrics

© AEROSPATIALE - 1999

MTS 006 Iss. B

20

25

30

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Wet lay-up carbon fabrics

Resin % Curing 80° C/2h/1 bar Surface density

New

CARBON FABRIC (equiv. tape) G803/501 432.308/96 Aged New Aged

T = 23° C

T = 55° C

T = 70° C

T = 70° C

2

13700

10900

13900

10900

2

Et (daN/mm )

500

500

500

500

Glt (daN/mm2)

313

240

240

240

νlt

0.35

0.35

0.35

0.35

ep (mm)

0.15

0.15

0.15

0.15

Rlt (hb)

111

90

98

86

Rlc (hb)

- 81

- 61

- 64

- 55

Rtt (hb)

5

5

5

5

Rtc (hb)

- 10

- 10

- 10

- 10

S (hb)

7.38

2.96

5.35

2.3

El (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

2.4.1.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Wet lay-up carbon fabrics

Resin % 50 % Curing 80° C/2h/1 bar Surface density 285 gr/m2 (sec)

New

CARBON FABRIC (fabric) G803/501 432.308/96 Aged New Aged

T = 23° C

T = 55° C

T = 70° C

T = 70° C

El (daN/mm )

7128

5727

7228

5727

Et (daN/mm2)

7128

5727

7228

5727

Glt (daN/mm2)

313

240

250

240

νlt

0.0246

0.0307

0.0243

0.0307

ep (mm)

0.3

0.3

0.3

0.3

Rlt (hb)

56

45.66

49.67

44

Rlc (hb)

- 42

- 32

- 33.33

- 28.8

Rtt (hb)

56

45.66

49.67

44

Rtc (hb)

- 42

- 32

- 33.33

- 28.8

S (hb)

7.38

2.96

5.35

2.3

2

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

2.4.1.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % Curing 90° C/2h/1 bar surface density

New

CARBON FABRIC (equiv. tape) G806/501 528/068/94 Aged

T = 20° C

T = 80° C

2

11250

11250

2

Et (daN/mm )

300

300

Glt (daN/mm2)

300

300

νlt

0.35

0.35

ep (mm)

0.078

0.078

Rlt (hb)

97.6

86.9

Rlc (hb)

- 81.6

- 34.4

Rtt (hb)

2.4

2.4

Rtc (hb)

- 10

- 10

S (hb)

7.9

2.04

El (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.1.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % 50 % Curing 90° C/2h/1 bar Surface density 135 gr/m2 (sec)

New

CARBON FABRIC (fabric) G806/501 528/068/94 Aged

T = 20° C

T = 80° C

El (daN/mm )

5792

5792

Et (daN/mm2)

5792

5792

Glt (daN/mm2)

300

300

νlt

0.0182

0.0182

ep (mm)

0.156

0.156

Rlt (hb)

46.2

42.9

Rlc (hb)

- 41.7

- 17.9

Rtt (hb)

46.2

42.9

Rtc (hb)

- 41.7

- 17.9

S (hb)

7.9

2.04

2

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.1.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

Prepreg carbon fabrics

Resin % Curing 90° C/2h/1 bar Surface density

New T = 20° C

CARBON FABRIC (equiv. tape) G806/5052 432.0533/96 issue 1 New Aged Aged wet wet T = 80° C T = 20° C T = 80° C

2.4.1.3 1/2

Aged wet T = 70° C

2

10450

10450

10450

10450

10450

2

Et (daN/mm )

283

283

283

283

283

Glt (daN/mm2)

283

283

283

283

283

νlt

0.35

0.35

0.35

0.35

0.35

ep (mm)

0.078

0.078

0.078

0.078

0.078

Rlt (hb)

105

105

105

93.4

93.4

Rlc (hb)

- 72

- 49

- 71

- 42.3

- 47

Rtt (hb)

6

6

6

6

6

Rtc (hb)

- 10

- 10

- 10

- 10

- 10

S (hb)

9.8

5.75

7.3

4.3

4.8

El (daN/mm )

τinter (hb) c Km

K mt K ct

0.79

0.79

0.79

0.79

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

K tt

0.78

0.78

0.78

0.78

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % 50 % Curing 90° C/2h/1 bar Surface density 135 gr/m2 2

New T = 20° C

CARBON FABRIC (fabric) G806/5052 432.0533/96 issue 1 Aged wet T = 70° C

El (daN/mm )

5383

5383

Et (daN/mm2)

5383

5383

Glt (daN/mm2)

283

283

νlt

0.02

0.02

ep (mm)

0.156

0.156

Rlt (hb)

53.5

47.7

Rlc (hb)

- 37.1

- 24.2

Rtt (hb)

53.5

47.7

Rtc (hb)

- 37.1

- 24.2

S (hb)

9.8

4.8

τinter (hb) c Km

K mt K ct

0.79

0.79

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

K tt

0.78

0.78

(Ø 3.2; E/G = 2.35)

(Ø 3.2; E/G = 2.35)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.1.3 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % Curing 90° C/2h/1 bar Surface density

New

CARBON FABRIC (equiv. tape) G806/9396 432.0533/96 issue 1 Aged

T = 20° C

T = 70° C

2

10450

10450

2

Et (daN/mm )

283

283

Glt (daN/mm2)

283

283

νlt

0.35

0.35

ep (mm)

0.078

0.078

Rlt (hb)

105

93.4

Rlc (hb)

- 72

- 54

Rtt (hb)

6

6

Rtc (hb)

- 10

- 10

S (hb)

9.8

4.8

El (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.1.4 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % 50 % Curing 90° C/2h/1 bar Surface density 135 gr/m2 (sec)

New

CARBON FABRIC (fabric) G806/9396 432.0533/96 issue 1 Aged

T = 20° C

T = 70° C

El (daN/mm )

5383

5383

Et (daN/mm2)

5383

5383

Glt (daN/mm2)

283

283

νlt

0.02

0.02

ep (mm)

0.156

0.156

Rlt (hb)

53.5

47.7

Rlc (hb)

- 37.1

- 27.8

Rtt (hb)

53.5

6

Rtc (hb)

- 37.1

- 10

S (hb)

9.8

4.8

2

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.1.4 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % Curing 90° C/2h/1 bar Surface density

CARBON FABRIC (equiv. tape) G814/501 Aged T = 70° C

2

11250

2

Et (daN/mm )

300

Glt (daN/mm2)

300

νlt

0.35

ep (mm)

0.115

Rlt (hb)

86.9

Rlc (hb)

- 34.4

Rtt (hb)

2.4

Rtc (hb)

- 10

S (hb)

3.4

El (daN/mm )

τinter (hb) c Km

0.25

K mt

0.25

K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.1.5 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg carbon fabrics

Resin % 50 % Curing 70° C/2h Surface density 385 gr/m2 2

CARBON FABRIC (fabric) G814/501 Aged T = 70° C

El (daN/mm )

5792

Et (daN/mm2)

5792

Glt (daN/mm2)

300

νlt

0.0182

ep (mm)

0.23

Rlt (hb)

42.9

Rlc (hb)

- 17.8

Rtt (hb)

42.9

Rtc (hb)

- 17.8

S (hb)

3.4

τinter (hb) c Km

0.25

K mt

0.25

K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.1.5 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Wet Lay-up glass fabrics

Resin % 50 % Curing 70° C/2h/1 bar Surface density 302 gr/m2 (sec)

GLASS FABRIC (fabric) 1581/501 Aged T = 25° C

2

2070

2

Et (daN/mm )

2070

Glt (daN/mm2)

260

El (daN/mm )

νlt ep (mm)

0.3

Rlt (hb)

30

Rlc (hb)

- 25

Rtt (hb)

30

Rtc (hb)

- 25

S (hb)

5

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.2.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Prepreg Kevlar

Resin %

KEVLAR (fabric) 181 + EPOXY RESIN

Curing New Surface density 170 gr/m2 (sec)

T = 20° C

2

El (daN/mm ) Et (daN/mm2) Glt (daN/mm2) νlt ep (mm)

0.28

Rlt (hb)

40

Rlc (hb)

- 10

Rtt (hb)

40

Rtc (hb)

- 10

S (hb) τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

2.4.3.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS

Z

RTM

Resin % Curing 180° C/3h30/2 at 3 bars Surface density

New T = 20° C

RTM (equiv. tape) G1151/RTM6 432.0123/95 & 440.417/94 Aged New Aged T = 20° C T = 70° C T = 70° C (sock) (sock)

2

11200

11200

10200

10200

2

Et (daN/mm )

527

527

480

480

Glt (daN/mm2)

527

527

480

480

νlt

0.35

0.35

0.35

0.35

ep (mm)

0.3

0.3

0.3

0.3

Rlt (hb)

108

108

81

72.1

Rlc (hb)

- 68

- 56

- 65

- 55.2

Rtt (hb)

5

5

5

5

Rtc (hb)

- 10

- 10

- 10

- 10

S (hb)

8.6

6.2

8.8

6.2

c Km

0.25

0.25

0.25

0.25

K mt

0.25

0.25

0.25

0.25

K ct

1 (Ø 4.8)

1 (Ø 4.8)

1 (Ø 4.8)

1 (Ø 4.8)

K tt

0.7 (Ø 4.8)

0.7 (Ø 4.8)

0.7 (Ø 4.8)

0.7 (Ø 4.8)

El (daN/mm )

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

3.1.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

RTM

Resin % 56 % Curing 180° C/3h30/2 at 3 bars Surface density 600 gr/m2 2

New T = 20° C

RTM (fabric) G1151/RTM6 432.0123/95 & 440.417/94 Aged New Aged T = 20° C T = 70° C T = 70° C (sock) (sock)

El (daN/mm )

5892

5892

5366

5366

Et (daN/mm2)

5892

5892

5366

5366

Glt (daN/mm2)

527

527

480

480

νlt

0.0315

0.0315

0.03

0.03

ep (mm)

0.6

0.6

0.6

0.6

Rlt (hb)

54.1

54.1

41.5

37.1

Rlc (hb)

- 35.6

- 29.4

- 34.1

- 28.9

Rtt (hb)

54.1

54.1

41.5

37.1

Rtc (hb)

- 35.6

- 29.4

- 34.1

- 28.9

S (hb)

8.6

6.2

8.8

6.2

c Km

0.25

0.25

0.25

0.25

K mt

0.25

0.25

0.25

0.25

K ct

1 (Ø 4.8)

1 (Ø 4.8)

1 (Ø 4.8)

1 (Ø 4.8)

K tt

0.7 (Ø 4.8)

0.7 (Ø 4.8)

0.7 (Ø 4.8)

0.7 (Ø 4.8)

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

3.1.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 150° C/3h30/2 at 3 bars Surface density

RTM (equiv. tape) G986/RTM6 Aged T = 70° C

2

10299

2

Et (daN/mm )

448

Glt (daN/mm2)

448

νlt

0.35

ep (mm)

0.1675

Rlt (hb)

76.6

Rlc (hb)

- 68.1

Rtt (hb)

4.48

Rtc (hb)

- 8.96

S (hb)

5.8

El (daN/mm )

τinter (hb) c Km

0.25

K mt

0.25

K ct

0.85

K tt

0.65

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.2 1/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 150° C/3h30/2 at 3 bars Surface density 305 gr/m2 2

RTM (fabric) G986/RTM6 Aged T = 70° C

El (daN/mm )

5398

Et (daN/mm2)

5398

Glt (daN/mm2)

448

νlt

0.0292

ep (mm)

0.335

Rlt (hb)

39.1

Rlc (hb)

- 35.5

Rtt (hb)

39.1

Rtc (hb)

- 35.5

S (hb)

5.82

τinter (hb) c Km

0.25

K mt

0.25

K ct

0.85

K tt

0.65

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.2 2/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 180° C Surface density

RTM (equiv. tape) E4049/RTM6 440.417/94 New

Aged

T = 20° C

T = 70° C

2

10200

10200

2

Et (daN/mm )

480

480

Glt (daN/mm2)

480

480

νlt

0.35

0.35

ep (mm)

0.3

0.3

Rlt (hb)

81

72.1

Rlc (hb)

- 65

- 55.2

Rtt (hb)

5

5

Rtc (hb)

- 10

- 10

S (hb)

8.8

6.2

K ct

1 (Ø 4.8)

1 (Ø 4.8)

K tt

0.7 (Ø 4.8)

0.7 (Ø 4.8)

El (daN/mm )

τinter (hb) c Km

K mt

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.3 1/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 180° C surface density 630 gr/m2

RTM (fabric) E4049/RTM6 440.417/94 New

Aged

T = 20° C

T = 70° C

El (daN/mm )

5366

5366

Et (daN/mm2)

5366

5366

Glt (daN/mm2)

480

480

νlt

0.03

0.03

ep (mm)

0.6

0.6

Rlt (hb)

41.5

37.1

Rlc (hb)

- 34.1

- 28.9

Rtt (hb)

41.5

37.1

Rtc (hb)

- 34.1

- 28.9

S (hb)

8.8

6.2

K ct

1 (Ø 4.8)

1 (Ø 4.8)

K tt

0.7 (Ø 4.8)

0.7 (Ø 4.8)

2

τinter (hb) c Km

K mt

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.3 2/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 120° C Surface density

RTM (equiv. tape) GB305/DA3200 440.102/94 New

Aged

T = 20° C

T = 70° C

El (daN/mm )

9800

9800

Et (daN/mm2)

424

424

Glt (daN/mm2)

424

424

νlt

0.35

0.35

ep (mm)

0.15

0.15

Rlt (hb)

178

178

Rlc (hb)

- 40

- 34

Rtt (hb)

8

8

Rtc (hb)

- 10

- 10

S (hb)

5.8

4.8

K ct

1

1

K tt

0.8 (Ø 3.2)

0.65 (Ø 3.2)

2

τinter (hb) c Km

K mt

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.4 1/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 120° C Surface density

RTM (fabric) GB305/DA3200 440.102/94 New

Aged

T = 20° C

T = 70° C

El (daN/mm )

5135

5135

Et (daN/mm2)

5135

5135

Glt (daN/mm2)

424

424

νlt

0.029

0.029

ep (mm)

0.3

0.3

Rlt (hb)

89.3

89.3

Rlc (hb)

- 21

- 17.7

Rtt (hb)

89.3

89.3

Rtc (hb)

- 21

- 17.7

S (hb)

5.8

4.8

K ct

1

1

K tt

0.8 (Ø 3.2)

0.65 (Ø 3.2)

2

τinter (hb) c Km

K mt

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.4 2/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 150° C/3h30/2 at 3 bars Surface density

RTM (equiv. tape) GF630/RTM6 528/082/94 New

Aged

T = 20° C

T = 70° C

2

11000

11000

2

Et (daN/mm )

480

480

Glt (daN/mm2)

480

480

νlt

0.35

0.35

ep (mm)

0.3

0.3

Rlt (hb)

95.5

95.5

Rlc (hb)

- 50

- 39.5

Rtt (hb)

5

5

Rtc (hb)

- 10

- 10

S (hb)

8.8

6.9

El (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.5 1/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 150° C/3h30/2 at 3 bars Surface density

RTM (fabric) GF630/RTM6 528/082/94 New

Aged

T = 20° C

T = 70° C

El (daN/mm )

5766

5766

Et (daN/mm2)

5766

5766

Glt (daN/mm2)

480

480

νlt

0.0293

0.0293

ep (mm)

0.6

0.6

Rlt (hb)

29

29

Rlc (hb)

- 26.2

- 20.7

Rtt (hb)

29

29

Rtc (hb)

- 26.2

- 20.7

S (hb)

8.8

6.9

2

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.5 2/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 120° C Surface density

RTM (equiv. tape) GB305/XB5142 440.102/94 New

Aged

T = 20° C

T = 70° C

2

9800

9800

2

Et (daN/mm )

424

424

Glt (daN/mm2)

424

424

νlt

0.35

0.35

ep (mm)

0.15

0.15

Rlt (hb)

167

167

Rlc (hb)

- 37

- 27

Rtt (hb)

7.5

7.7

Rtc (hb)

- 10

- 10

S (hb)

5.75

4.8

K ct

1

1

K tt

0.8 (Ø 3.2)

0.65 (Ø 3.2)

El (daN/mm )

τinter (hb) c Km

K mt

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.6 1/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM

Resin % Curing 120° C Surface density

RTM (fabric) GB305/XB5142 440.102/94 New

Aged

T = 20° C

T = 70° C

El (daN/mm )

5135

5135

Et (daN/mm2)

5135

5135

Glt (daN/mm2)

424

424

νlt

0.029

0.029

ep (mm)

0.3

0.3

Rlt (hb)

84

84

Rlc (hb)

- 19.3

- 14.3

Rtt (hb)

84

84

Rtc (hb)

- 19.3

- 14.3

S (hb)

5.75

4.8

K ct

1

1

K tt

0.8 (Ø 3.2)

0.65 (Ø 3.2)

2

τinter (hb) c Km

K mt

σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

3.1.6 2/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

RTM Resin % Curing 120° C

New T = 23° C

Surface density El (daN/mm2)

RTM (equiv. tape) HF360/LY564-1 + HY2954 440.171/94 New Aged Aged T = 23° C T = 80° C T = 80° C sock sock effect effect (MEC) (MEC)

6830

6830

6830

6830

2

416

416

416

416

2

Glt (daN/mm )

416

416

416

416

νlt

0.35

0.35

0.35

0.35

ep (mm)

0.16

0.16

0.16

0.16

Rlt (hb)

82.7

70.3

62.9

53.4

Rlc (hb)

- 56.6

- 30.7

- 43

- 23.3

Rtt (hb)

5

5

3.8

3.8

Rtc (hb)

- 10

- 10

- 7.6

- 7.6

S (hb)

7.1

(4.3)

5.4

(3.3)

Et (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

3.1.7 1/2

Composite stress manual

MATERIAL CHARACTERISTICS RTM Resin % Curing 120° C

New T = 23° C

Surface density 360 gr/m2

Z

RTM (fabric) HF360/LY564-1 + HY2954 440.171/94 Aged New Aged T = 80° C T = 23° C T = 80° C sock sock effect effect (MEC) (MEC)

El (daN/mm2)

3644

3644

3644

3644

Et (daN/mm2)

3644

3644

3644

3644

Glt (daN/mm2)

416

416

416

416

νlt

0.0402

0.0402

0.0402

0.0402

ep (mm)

0.32

0.32

0.32

0.32

Rlt (hb)

42.2

36.3

32.2

27.5

Rlc (hb)

- 30

- 16.3

- 22.8

- 12.5

Rtt (hb)

42.2

36.3

32.2

27.5

Rtc (hb)

- 30

- 16.3

- 22.8

- 12.5

S (hb)

7.1

(4.3)

5.4

(3.3)

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

3.1.7 2/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

RTM Resin % Curing 120° C

New T = 23° C

Surface density El (daN/mm2)

RTM (equiv. tape) GF520/LY564-1 + HY2954 440.171/94 New Aged Aged T = 23° C T = 80° C T = 80° C sock sock effect effect (MEC) (MEC)

11400

11400

11400

11400

2

500

500

500

500

2

Glt (daN/mm )

500

500

500

500

νlt

0.35

0.35

0.35

0.35

ep (mm)

0.25

0.25

0.25

0.25

Rlt (hb)

95.4

81.1

72.2

61.6

Rlc (hb)

- 50.2

- 35.1

- 38.1

- 26.7

Rtt (hb)

5

5

3.8

3.8

Rtc (hb)

- 10

- 10

- 7.6

- 7.6

S (hb)

9.4

(5.6)

7.1

(4.3)

Et (daN/mm )

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

3.1.8 1/2

Composite stress manual

MATERIAL CHARACTERISTICS

Z

RTM Resin % Curing 120° C

New T = 23° C

Surface density 520 gr/m2

RTM (fabric) GF520/LY564-1 + HY2954 440.171/94 Aged New Aged T = 80° C T = 23° C T = 80° C sock sock effect effect (MEC) (MEC)

El (daN/mm2)

5977

5977

5977

5977

Et (daN/mm2)

5977

5977

5977

5977

Glt (daN/mm2)

500

500

500

500

νlt

0.0294

0.0294

0.0294

0.0294

ep (mm)

0.5

0.5

0.5

0.5

Rlt (hb)

48.4

41.4

36.8

31.6

Rlc (hb)

- 26.4

- 18.4

- 20

- 14

Rtt (hb)

48.4

41.4

36.8

31.6

Rtc (hb)

- 26.4

- 18.4

- 20

- 14

S (hb)

9.4

(5.6)

7.1

(4.3)

τinter (hb) c Km

K mt K ct K tt σm (hb) K flexion t κc κt κs εadm. comp. (µd) εadm. tract. (µd) γadm. cisail. (µd) Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

3.1.8 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Injected thermoplastics

Resin % 30 % Curing New

Aged

THERMOPLASTIC ULTEM 2310 440.106/92 Aged

T = 20° C

T = 20° C

T = 70° C

1150

1150

1150

Rlt (hb)

14.3

12.5

11.6

Rlc (hb)

- 24.2

- 23.9

c Km

0.17

0.17

0.17

K mt

0.17

0.17

0.17

0.6

0.6

0.6

Surface density 2

El (daN/mm ) 2

Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

Rtt (hb) Rtc (hb) S (hb) τinter (hb)

K ct K tt σm (hb) K flexion t

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

4.1.1.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Injected thermoplastics

Resin % 40 % Curing New

Aged

THERMOPLASTIC RYTON R04 440.106/92 Aged

T = 20° C

T = 20° C

T = 70° C

1450

1450

1450

Rlt (hb)

11.4

10.3

11.2

Rlc (hb)

- 19.6

- 18.6

c Km

0.6

0.6

0.6

K mt

0.6

0.6

0.6

0.59

0.59

0.59

Surface density 2

El (daN/mm ) 2

Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

Rtt (hb) Rtc (hb) S (hb) τinter (hb)

K ct K tt σm (hb) K flexion t

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

4.1.4.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Injected thermoplastics

Resin % 50 % Curing New

Aged

THERMOPLASTIC IXEF 1022 440.106/92 Aged

T = 20° C

T = 20° C

T = 70° C

1100

1100

1100

Rlt (hb)

17.2

8.5

5.2

Rlc (hb)

- 26

- 12.9

c Km

0.09 to 0.57

0.09 to 0.57

0.09 to 0.57

K mt

0.09 to 0.57

0.09 to 0.57

0.09 to 0.57

0.6

0.6

0.6

Surface density 2

El (daN/mm ) 2

Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

Rtt (hb) Rtc (hb) S (hb) τinter (hb)

K ct K tt σm (hb) K flexion t

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

4.1.5.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Injected thermoplastics

Resin % 30 % Curing New

Aged

THERMOPLASTIC IXEF C36 440.106/92 Aged

T = 20° C

T = 20° C

T = 70° C

1500

1500

1500

Rlt (hb)

19

9.9

5.8

Rlc (hb)

- 25.1

- 12.6

c Km

0.13 to 0.25

0.13 to 0.25

0.13 to 0.25

K mt

0.13 to 0.25

0.13 to 0.25

0.13 to 0.25

0.63

0.63

0.63

surface density 2

El (daN/mm ) 2

Et (daN/mm ) Glt (daN/mm2) νlt ep (mm)

Rtt (hb) Rtc (hb) S (hb) τinter (hb)

K ct K tt σm (hb) K flexion t

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

4.1.5.2 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Long fibre thermoplastics

Resin % 32 % Curing 395° C/35mn/2 bars Surface density 213 gr/m2

New

Aged

THERMOPLASTIC APC2 (AS4/PEEK) 581.0053/98 Aged

T = 20° C

T = 70° C

T = 120° C

El (daN/mm )

13400

13400

13400

Et (daN/mm2)

900

900

900

Glt (daN/mm2)

500

500

500

νlt

0.40

0.40

0.40

ep (mm)

0.13

0.13

0.13

Rlt (hb)

150

150

150

Rlc (hb)

- 115

- 100

- 95

Rtt (hb)

11

11

11

Rtc (hb)

- 12

- 12

- 12

S (hb)

10

10

9

c Km

T300/914 (1)

T300/914 (1)

T300/914 (1)

K mt

T300/914 (2)

T300/914 (2)

T300/914 (2)

K ct

T300/914 (3)

T300/914 (3)

T300/914 (3)

K tt

T300/914E (4) T300/914E (4) T300/914E (4)

2

τinter (hb)

σm (hb) K flexion t κc κt κs εadm. comp. (µd)

3300

(6000 mm2)

εadm. tract. (µd)

9000

(6000 mm2)

γadm. cisail. (µd)

3500

(6000 mm2)

Tg dry (° C) Tg wet (° C) Cθ (µd/° C)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

5.1.1.1 1/1

Composite stress manual

MATERIAL CHARACTERISTICS Long fibre thermoplastics

Resin % Curing 300° C/7 bars Surface density

New

THERMOPLASTIC CD282/PEI DE TENCATE (equiv. tape) 432.0015/95 Aged Skydrol

T = 20° C

T = 70° C

T = 70° C

2

11500

11500

11500

2

Et (daN/mm )

500

500

500

Glt (daN/mm2)

400

400

300

νlt

0.35

0.35

0.35

ep (mm)

0.15

0.15

0.15

Rlt (hb)

90

85.8

85.8

Rlc (hb)

- 85

- 76

- 49.5

Rtt (hb)

5

5

5

Rtc (hb)

- 10

- 10

- 10

S (hb)

10

9

3.9

c Km

0.25

0.25

0.25

K mt

0.25

0.25

0.25

K ct

0.85

0.85

0.85

K tt

0.65

0.65

0.65

σm (hb)

40

40

40

K flexion t

0.9

0.9

0.9

El (daN/mm )

τinter (hb)

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

5.1.2.1 1/2

Composite stress manual

MATERIAL CHARACTERISTICS Long fibre thermoplastics

Resin % 42 % Curing 300° C/7 bars Surface density 465 gr/m2

New

THERMOPLASTIC CD282/PEI DE TENCATE (fabric) 432.0015/95 Aged Skydrol

T = 20° C

T = 70° C

T = 70° C

2

6027

6207

5530

2

Et (daN/mm )

6027

6207

5530

Glt (daN/mm2)

400

400

300

νlt

0.03

0.03

0.03

ep (mm)

0.3

0.3

0.3

Rlt (hb)

45.8

43.8

43.8

Rlc (hb)

- 44.3

- 39.7

- 26

Rtt (hb)

45.8

43.9

43.8

Rtc (hb)

- 44.3

- 39.7

- 26

S (hb)

10

9

3.9

c Km

0.25

0.25

0.25

K mt

0.25

0.25

0.25

K ct

0.85

0.85

0.85

K tt

0.65

0.65

0.65

σm (hb)

40

40

40

K flexion t

0.9

0.9

0.9

El (daN/mm )

τinter (hb)

© AEROSPATIALE - 1999

MTS 006 Iss. B

Z

5.1.2.1 2/2

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Hexagonal cell 1/8 inches Curing Volume density 29 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

9.1

HEXCEL NOMEX HONEYCOMB HRH10 - 1/8 - 1.8 Hexcel – september 1989 New T = 23°C 0.065 2.6 1.0 0.052 0.028

Hexagonal cell 1/8 inches

HEXCEL NOMEX HONEYCOMB HRH10 - 1/8 - 3.0 528 – 099/90

Curing New

New

Aged

Volume density 48 Kg/m3

T = 23°C

T = 80°C

T = 80°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

13.8 0.15* 3.2* 2.4 0.075* 0.046

Hexagonal cell 1/8 inches Curing Volume density 64 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

0.15

0.075 0.046

13.8 0.15 3.2 2.4 0.075 0.046

HEXCEL NOMEX HONEYCOMB HRH10 - 1/8 - 4.0 30147 of 21/08/92 New T = 23°C 19.3 0.324 6.3 3.2 0.155 0.076

* ASTA/SOCATA HUREL-DUBOIS use these values increased by 20 %.

© AEROSPATIALE - 1999

MTS 006 Iss. B

1/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Hexagonal cell 1/8 inches Curing Volume density 80 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10 - 1/8 - 5.0 Hexcel – september 1989 New T = 23°C 0.455 7.0 3.7 0.190 0.103

Hexagonal cell 1/8 inches

HEXCEL NOMEX HONEYCOMB HRH10 - 1/8 - 6.0 Hexcel – september 1989

Curing New Volume density 96 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

41.4 0.638 9.0 4.5 0.228 0.117

Hexagonal cell 1/8 inches Curing Volume density 128 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL NOMEX HONEYCOMB HRH10 - 1/8 - 8.0 Hexcel – september 1989 New T = 23°C 53.8 1.0 11.0 6.5 0.276 0.145

MTS 006 Iss. B

9.1 2/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Hexagonal cell 1/8 inches Curing Volume density 144 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10 - 1/8 - 9.0 Hexcel – september 1989 New T = 23°C 62.1 1.241 12.1 7.6 0.293 0.172

Hexagonal cell 3/16 inches

HEXCEL NOMEX HONEYCOMB HRH10 - 3/16 - 1.5 Hexcel – september 1989

Curing New Volume density 24 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

0.059 2.1 1.1 0.041 0.022

Hexagonal cell 3/16 inches Curing Volume density 29 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL NOMEX HONEYCOMB HRH10 - 3/16 - 1.8 Hexcel – september 1989 New T = 23°C 0.072 2.6 1.3 0.052 0.028

MTS 006 Iss. B

9.1 3/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Hexagonal cell 3/16 inches Curing Volume density 32 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10 - 3/16 - 2.0 Hexcel – september 1989 New T = 23°C 7.6 0.097 3.0 1.4 0.062 0.031

Hexagonal cell 3/16 inches

HEXCEL NOMEX HONEYCOMB HRH10 - 3/16 - 3.0 528 – 099/90

Curing New

New

Aged

Volume density 48 Kg/m3

T = 23°C

T = 80°C

T = 80°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

13.8 0.15* 3.2* 2.4 0.075* 0.046

Hexagonal cell 3/16 inches Curing Volume density 64 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

0.15

0.075 0.046

13.8 0.15 3.2 2.4 0.075 0.046

HEXCEL NOMEX HONEYCOMB HRH10 - 3/16 - 4.0 30147 of 21/08/92 New T = 23°C 19.3 0.324 6.3 3.2 0.155 0.076

* ASTA/SOCATA HUREL-DUBOIS use these values increased by 20 %.

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.1 4/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Hexagonal cell 3/16 inches Curing Volume density 72 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10 - 3/16 - 4.5 Hexcel – may 1986 New T = 23°C 0.276 6.5 2.8 0.155 0.076

Hexagonal cell 3/16 inches

HEXCEL NOMEX HONEYCOMB HRH10 - 3/16 - 6.0 Hexcel – september 1989

Curing New Volume density 96 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

0.596 9 4.5 0.255 0.138

Hexagonal cell 1/4 inches Curing Volume density 24 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL NOMEX HONEYCOMB HRH10 - 1/4 - 1.5 Hexcel – september 1989 New T = 23°C 4.1 0.052 2.1 0.9 0.038 0.017

MTS 006 Iss. B

9.1 5/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Hexagonal cell 1/4 inches Curing Volume density 32 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10 - 1/4 - 2.0 Hexcel – september 1989 New T = 23°C 7.6 0.086 2.8 1.4 0.059 0.028

Hexagonal cell 1/4 inches

HEXCEL NOMEX HONEYCOMB HRH10 - 1/4 - 3.1 528 – 099/90

Curing New

New

Aged

Volume density 50 Kg/m3

T = 23°C

T = 80°C

T = 80°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

13.8 0.15* 3.2* 2.4 0.075* 0.046

Hexagonal cell 1/4 inches Curing Volume density 64 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

0.15

0.075 0.046

13.8 0.15 3.2 2.4 0.075 0.046

HEXCEL NOMEX HONEYCOMB HRH10 - 1/4 - 4.0 30147 of 21/08/92 New T = 23°C 19.3 0.324 6.3 3.2 0.155 0.076

* ASTA/SOCATA HUREL-DUBOIS use these values increased by 20 %.

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.1 6/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Hexagonal cell 3/8 inches Curing Volume density 24 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10 - 3/8 - 1.5 Hexcel – september 1989 New T = 23°C 4.1 0.055 2.1 1.0 0.038 0.017

Hexagonal cell 3/8 inches

HEXCEL NOMEX HONEYCOMB HRH10 - 3/8 - 2.0 Hexcel – september 1989

Curing New Volume density 32 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

7.6 0.086 2.6 1.7 0.050 0.025

Hexagonal cell 3/8 inches Curing Volume density 48 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL NOMEX HONEYCOMB HRH10 - 3/8 - 3.0 Hexcel – september 1989 New T = 23°C 11.7 0.186 3.9 2.4 0.110 0.055

MTS 006 Iss. B

9.1 7/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

OX - Core cell 3/16 inches Curing Volume density 29 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10/OX - 3/16 - 1.8 Hexcel – september 1989 New T = 23°C 0.065 1.4 2.1 0.031 0.034

OX - Core cell 3/16 inches

HEXCEL NOMEX HONEYCOMB HRH10/OX - 3/16 - 3.0 528 – 099/90

Curing New Volume density 48 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

9.5 0.16 1.4 3.35 0.053 0.064

OX - Core cell 3/16 inches Curing Volume density 64 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL NOMEX HONEYCOMB HRH10/OX - 3/16 - 4.0 Hexcel – september 1989 New T = 23°C 0.379 2.4 5.2 0.072 0.090

MTS 006 Iss. B

9.1 8/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

OX - Core cell 1/4 inches Curing Volume density 48 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

Z

HEXCEL NOMEX HONEYCOMB HRH10/OX - 1/4 - 3.0 528 – 099/90 New T = 23°C 9.5 0.16 1.4 3.35 0.053 0.064

MTS 006 Iss. B

9.1 9/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Flex - Core cell Curing Volume density 40 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL NOMEX HONEYCOMB HRH10 – F35 – 2.5 Hexcel – october 1992 New T = 23°C 8.3 0.121 2.8 1.7 0.062 0.034

Flex - Core cell

HEXCEL NOMEX HONEYCOMB HRH10 – F35 – 3.5 Hexcel – october 1992

Curing New Volume density 56 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

16.5 0.228 4.1 2.6 0.117 0.062

Flex - Core cell Curing Volume density 72 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL NOMEX HONEYCOMB HRH10 – F35 – 4.5 Hexcel – october 1992 New T = 23°C 22.8 0.331 6.2 3.0 0.159 0.103

MTS 006 Iss. B

9.1 10/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Flex - Core cell Curing Volume density 56 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL NOMEX HONEYCOMB HRH10 – F50 – 3.5 Hexcel – october 1992 New T = 23°C 16.5 0.214 3.8 2.5 0.090 0.052

Flex - Core cell

HEXCEL NOMEX HONEYCOMB HRH10 – F50 – 4.5 Hexcel – october 1992

Curing New Volume density 72 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

22.8 0.324 6.5 3.2 0.172 0.097

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

9.1 11/12

Composite stress manual

MATERIAL CHARACTERISTICS Nomex honeycomb

Flex - Core cell Curing Volume density 80 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL NOMEX HONEYCOMB HRH10 – F50 – 5.0 Hexcel – october 1992 New T = 23°C 25.5 0.372 6.9 3.6 0.207 0.117

Flex - Core cell

HEXCEL NOMEX HONEYCOMB HRH10 – F50 – 5.5 Hexcel – october 1992

Curing New Volume density 88 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

29.0 0.455 7.2 3.9 0.221 0.124

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

9.1 12/12

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Hexagonal cell 3/16 inches Curing Volume density 64 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/16 - 4.0 Hexcel – july 1989 New T = 23°C 39.3 0.331 9.7 4.8 0.145 0.090

Hexagonal cell 3/16 inches

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/16 - 5.5 Hexcel – july 1989

Curing New Volume density 88 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

65.5 0.517 13.1 7.6 0.241 0.138

Hexagonal cell 3/16 inches Curing Volume density 112 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/16 - 7.0 Hexcel – july 1989 New T = 23°C 93.8 0.689 20.7 9.0 0.345

MTS 006 Iss. B

9.2 1/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Hexagonal cell 3/16 inches Curing Volume density 128 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/16 - 8.0 Hexcel – july 1989 New T = 23°C 113.1 0.883 23.4 13.1 0.414 0.255

Hexagonal cell 3/16 inches

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/16 - 12.0 Hexcel – july 1989

Curing New Volume density 192 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

179.3* 1.31 33.1 19.3 0.562 0.362

* Preliminary value

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

9.2 2/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Hexagonal cell 1/4 inches Curing Volume density 56 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL FIBERGLASS HONEYCOMB HRP - 1/4 - 3.5 Hexcel – july 1989 New T = 23°C 31.7 0.276 6.2 3.4 0.117 0.069

Hexagonal cell 1/4 inches

HEXCEL FIBERGLASS HONEYCOMB HRP - 1/4 - 4.5 Hexcel – july 1989

Curing New Volume density 72 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

48.3 0.386 10.3 5.5 0.172 0.107

Hexagonal cell 1/4 inches Curing Volume density 80 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL FIBERGLASS HONEYCOMB HRP - 1/4 - 5.0 Hexcel – july 1989 New T = 23°C 57.9 0.455 13.8 6.9

MTS 006 Iss. B

9.2 3/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Hexagonal cell 1/4 inches Curing Volume density 104 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

Z

HEXCEL FIBERGLASS HONEYCOMB HRP - 1/4 - 6.5 Hexcel – july 1989 New T = 23°C 82.7 0.621 17.2 9.0

MTS 006 Iss. B

9.2 4/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Hexagonal cell 3/8 inches Curing Volume density 35 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/8 - 2.2 Hexcel – july 1989 New T = 23°C 9.0 0.100 4.1 1.4 0.062 0.031

Hexagonal cell 3/8 inches

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/8 - 3.2 Hexcel – july 1989

Curing New Volume density 51 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

26.2 0.241 8.3 3.4 0.110 0.059

Hexagonal cell 3/8 inches Curing Volume density 72 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/8 - 4.5 Hexcel – july 1989 New T = 23°C 44.8 0.379 9.7 5.5 0.179 0.103

MTS 006 Iss. B

9.2 5/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Hexagonal cell 3/8 inches Curing Volume density 96 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/8 - 6.0 Hexcel – july 1989 New T = 23°C 68.9 0.552 17.2 8.3 0.234 0.145

Hexagonal cell 3/8 inches

HEXCEL FIBERGLASS HONEYCOMB HRP - 3/8 - 8.0 Hexcel – july 1989

Curing New Volume density 128 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 103.4* 21.4* 9.0*

* Preliminary values

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

9.2 6/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

OX - Core cell 1/4 inches Curing Volume density 72 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL FIBERGLASS HONEYCOMB HRP/OX - 1/4 - 4.5 Hexcel – july 1989 New T = 23°C 29.6* 0.355 5.5 10.3 0.117 0.131

OX - Core cell 1/4 inches

HEXCEL FIBERGLASS HONEYCOMB HRP/OX - 1/4 - 5.5 Hexcel – july 1989

Curing New Volume density 88 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 44.8* 6.9* 12.4

OX - Core cell 1/4 inches Curing Volume density 112 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL FIBERGLASS HONEYCOMB HRP/OX - 1/4 - 7.0 Hexcel – july 1989 New T = 23°C 57.9* 0.683* 9.7* 13.8*

MTS 006 Iss. B

9.2 7/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

OX - Core cell 3/8 inches Curing Volume density 51 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL FIBERGLASS HONEYCOMB HRP/OX - 3/8 - 3.2 Hexcel – july 1989 New T = 23°C 22.1* 3.1* 6.2*

OX - Core cell 3/8 inches

HEXCEL FIBERGLASS HONEYCOMB HRP/OX - 3/8 - 5.5 Hexcel – july 1989

Curing New Volume density 88 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 41.4* 6.9* 11.7*

* Preliminary values

© AEROSPATIALE - 1999

Z

MTS 006 Iss. B

9.2 8/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Flex - Core cell Curing Volume density 40 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL FIBERGLASS HONEYCOMB HRP - F35 - 2.5 Hexcel – october 1992 New T = 23°C 17.2 0.128 8.3 4.8 0.065 0.038

Flex - Core cell

HEXCEL FIBERGLASS HONEYCOMB HRP - F35 - 3.5 Hexcel – october 1992

Curing New Volume density 56 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

25.5 0.207 10.3 6.9 0.097 0.052

Flex - Core cell Curing Volume density 72 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL FIBERGLASS HONEYCOMB HRP - F35 - 4.5 Hexcel – october 1992 New T = 23°C 33.8 0.324 15.2 8.3 0.152 0.076

MTS 006 Iss. B

9.2 9/10

Composite stress manual

MATERIAL CHARACTERISTICS Fiberglass honeycomb

Flex - Core cell Curing Volume density 56 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL FIBERGLASS HONEYCOMB HRP - F50 - 3.5 Hexcel – october 1992 New T = 23°C 25.5 0.176 11.0 5.5 0.090 0.045

Flex - Core cell

HEXCEL FIBERGLASS HONEYCOMB HRP - F50 - 4.5 Hexcel – october 1992

Curing New Volume density 72 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

33.8 0.345 17.2 9.0 0.138 0.069

Flex - Core cell Curing Volume density 88 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL FIBERGLASS HONEYCOMB HRP - F50 - 5.5 Hexcel – october 1992 New T = 23°C 42.1 0.469 27.6 12.4 0.228 0.124

MTS 006 Iss. B

9.2 10/10

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB ACG - 1/4 - 4.8 Hexcel – december 1988

Perforated hexagonal cell 1/4 inches New Volume density 77 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 102.0 0.434 43.4 21.4 0.231 0.148

HEXCEL ALUMINIUM HONEYCOMB ACG - 3/8 - 3.3 Hexcel – december 1988

Perforated hexagonal cell 3/8 inches New Volume density 53 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 63.4 0.224 27.6 13.8 0.134 0.090

HEXCEL ALUMINIUM HONEYCOMB ACG - 1/2 - 2.3 Hexcel – december 1988

Perforated hexagonal cell 1/2 inches New Volume density 37 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23°C 27.6 0.121 17.2 10.3 0.086 0.048

MTS 006 Iss. B

9.3 1/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB ACG - 3/4 - 1.8 Hexcel – december 1988

Perforated hexagonal cell 3/4 inches New Volume density 29 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 16.5 0.083 11 5.5 0.055 0.041

HEXCEL ALUMINIUM HONEYCOMB ACG - 1 - 1.3 Hexcel – december 1988

Perforated hexagonal cell 1 inches New Volume density 21 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 11* 0.048 9.7* 4.8* 0.038* 0.028*

* Preliminary values

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.3 2/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 3/16 inches Curing Volume density 56 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 2024 - 3/16 - 3.5 Hexcel – july 1988 New T = 23°C 59.3 0.200 37.9 15.9 0.159 0.099

Hexagonal cell 1/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 2024 - 1/8 - 5.0 Hexcel – july 1988

Curing New Volume density 80 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

137.9 0.427 56.5 22.8 0.276 0.172

Hexagonal cell 1/8 inches Curing Volume density 107 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 2024 - 1/8 - 6.7 Hexcel – july 1988 New T = 23°C 206.8 0.676 81.4 31.0 0.414 0.259

MTS 006 Iss. B

9.3 3/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/8 inches Curing Volume density 128 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 2024 - 1/8 - 8.0 Hexcel – july 1988 New T = 23°C 262 0.910 102 37.2 0.531 0.324

Hexagonal cell 1/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 2024 - 1/8 - 9.5 Hexcel – july 1988

Curing New Volume density 152 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

330.9 1.189 117.2 44.1 0.655 0.403

Hexagonal cell 1/4 inches Curing Volume density 45 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 2024 - 1/4 - 2.8 Hexcel – july 1988 New T = 23°C 27.6 0.121 29 13.1 0.097 0.061

MTS 006 Iss. B

9.3 4/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/16 inches Curing Volume density 104 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/16 - 6.5 Hexcel – october 1988 New T = 23°C 189.6* 62.1* 27.6* 0.331* 0.207*

Hexagonal cell 1/16 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/16 - 9.5 Hexcel – october 1988

Curing New Volume density 152 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 289.6** 72.4** 36.5 0.576* 0.359*

Hexagonal cell 1/16 inches Curing Volume density 192 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/16 - 12.0 Hexcel – october 1988 New T = 23°C 448.2* 82.7** 44.8**

* Preliminary values ** Predicted values

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.3 5/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/16 inches Curing Volume density 221 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/16 - 13.8 Hexcel – march 1988 New T = 23°C 448.2* 1.586* 103.4** 51.7** 0.896** 0.517**

Hexagonal cell 3/32 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/32 - 4.3 Hexcel – march 1988

Curing New Volume density 69 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

82.7** 0.303** 42.7** 18.6** 0.2** 0.128**

Hexagonal cell 3/32 inches Curing Volume density 101 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/32 - 6.3 Hexcel – march 1988 New T = 23°C 172.4** 0.655** 68.9** 27.6** 0.365** 0.228**

* Preliminary values ** Predicted values

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.3 6/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/8 inches Curing Volume density 50 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/8 - 3.1 Hexcel – october 1988 New T = 23°C 51.7 0.148 31 15.2 0.107 0.062

Hexagonal cell 1/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/8 - 4.5 Hexcel – october 1988

Curing New Volume density 72 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

103.4 0.279 48.3 21.4 0.196 0.359

Hexagonal cell 1/8 inches Curing Volume density 98 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/8 - 6.1 Rohr – RHR 95-057 New T = 23°C

T = 120°C

0.448 53 21.2 0.310 0.186

0.448 53 21.2 0.279 0.168

* Preliminary values ** Predicted values

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.3 7/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/8 inches Curing Volume density 130 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/8 - 8.1 Hexcel – october 1988 New T = 23°C 241.3 0.758 93.1 37.2 0.462 0.276

Hexagonal cell 1/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/8 - 12.0 Rohr – RHR 85-054 ADD C

Curing New Volume density 192 Kg/m3

T = 23°C

T = 77°C

T = 113°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

1.317 93.1 41.4 0.862 0.517

1.224 91 40.7 0.801 0.481

1.152 89.6 40.0 0.754 0.452

Hexagonal cell 1/8 inches Curing Volume density 354 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/8 - 22.1 Rohr – RHR 95-057 New T = 23°C

T = 120°C

3.103 144.8 68.9 1.724 1.034

3.103 144.8 68.9 1.255 0.503

MTS 006 Iss. B

9.3 8/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 5/32 inches Curing Volume density 42 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 5/32 - 2.6 Hexcel – october 1988 New T = 23°C 37.9 0.110 25.5 13.1 0.083 0.048

Hexagonal cell 5/32 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 5/32 - 3.8 Hexcel – october 1988

Curing New Volume density 61 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

75.8 0.207 38.6 18.2 0.148 0.086

Hexagonal cell 5/32 inches Curing Volume density 85 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 5/32 - 5.3 Hexcel – october 1988 New T = 23°C 134.4 0.369 57.9 24.8 0.255 0.148

MTS 006 Iss. B

9.3 9/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 5/32 inches Curing Volume density 110 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 5/32 - 6.9 Hexcel – october 1988 New T = 23°C 196.5 0.552 78.6 32 0.372 0.226

Hexagonal cell 5/32 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 5/32 - 8.4 Hexcel – october 1988

Curing New Volume density 134 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

255.1 0.814 96.5 38.6 0.476 0.290

© AEROSPATIALE - 1999

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MTS 006 Iss. B

9.3 10/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 3/16 inches Curing Volume density 32 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/16 - 2.0 Hexcel – october 1988 New T = 23°C 23.4 0.069 18.6 9.9 0.055 0.032

Hexagonal cell 3/16 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/16 - 3.1 Hexcel – october 1988

Curing New Volume density 50 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

51.7 0.148 31 15.2 0.107 0.062

Hexagonal cell 3/16 inches Curing Volume density 70 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/16 - 4.4 Hexcel – october 1988 New T = 23°C 100 0.265 46.9 20.7 0.193 0.110

MTS 006 Iss. B

9.3 11/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 3/16 inches Curing Volume density 91 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/16 - 5.7 Hexcel – october 1988 New T = 23°C 151.7 0.414 62.1 26.5 0.283 0.168

Hexagonal cell 3/16 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/16 - 6.9 Hexcel – october 1988

Curing New Volume density 110 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

196.5 0.552 78.6 32 0.372 0.226

Hexagonal cell 3/16 inches Curing Volume density 130 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/16 - 8.1 Rohr - RHR 95-057 New T = 23°C

T = 120°C

0.689 77.2 34.7 0.469 0.276

0.689 77.2 34.7 0.422 0.248

MTS 006 Iss. B

9.3 12/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/4 inches Curing Volume density 26 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/4 - 1.6 Hexcel – october 1988 New T = 23°C 13.8 0.048 14.5 7.6 0.041 0.022

Hexagonal cell 1/4 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/4 - 2.3 Hexcel – october 1988

Curing New Volume density 37 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

31 0.09 22.1 11.2 0.069 0.039

Hexagonal cell 1/4 inches Curing Volume density 54 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/4 - 3.4 Hexcel – october 1988 New T = 23°C 62.1 0.172 34.5 16.5 0.124 0.072

MTS 006 Iss. B

9.3 13/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/4 inches Curing Volume density 69 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/4 - 4.3 Hexcel – october 1988 New T = 23°C 96.5 0.255 45.5 20.5 0.183 0.107

Hexagonal cell 1/4 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/4 - 5.2 Hexcel – october 1988

Curing New Volume density 83 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

131 0.352 56.5 24.4 0.248 0.138

Hexagonal cell 1/4 inches Curing Volume density 96 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/4 - 6.0 Rohr – RHR 95-057 New T = 23°C

T = 120°C

0.414 51.7 24.8 0.303 0.183

0.414 51.7 24.8 0.273 0.164

MTS 006 Iss. B

9.3 14/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/4 inches Curing Volume density 126 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 1/4 - 7.9 Hexcel – october 1988 New T = 23°C 234.4 0.724 89.6 36.4 0.448 0.269

Hexagonal cell 3/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 1.0 Hexcel – october 1988

Curing New Volume density 16 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

6.9 0.014 8.3 4.8 0.022 0.014

Hexagonal cell 3/8 inches Curing Volume density 26 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 1.6 Hexcel – october 1988 New T = 23°C 13.8 0.048 14.5 7.6 0.041 0.022

MTS 006 Iss. B

9.3 15/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 3/8 inches Curing Volume density 37 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 2.3 Rohr – RHR 95-057 New T = 23°C

T = 120°C

0.069 14.8 7.4 0.065 0.038

0.069 14.8 7.4 0.059 0.034

Hexagonal cell 3/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 3.0 Hexcel – october 1988

Curing New Volume density 48 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

48.3 0.138 29.6 14.6 0.1 0.059

Hexagonal cell 3/8 inches Curing Volume density 59 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 3.7 Hexcel – october 1988 New T = 23°C 72.4 0.196 37.9 17.9 0.138 0.079

MTS 006 Iss. B

9.3 16/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 3/8 inches Curing Volume density 67 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 4.2 Rohr – RHR 85-054 ADD C New T = 23°C

T = 77°C

93.1 0.231 32.4 15.9 0.162 0.1

84.8 0.215 30.3 14.5 0.151 0.093

Hexagonal cell 3/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 5.4 Rohr – RHR 95-057

Curing New Volume density 86 Kg/m3

T = 23°C

T = 120°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

0.345 45.2 22.1 0.262 0.157

0.345 45.2 22.1 0.23 0.122

Hexagonal cell 3/8 inches Curing Volume density 104 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB CR III 5052 - 3/8 - 6.5 Hexcel – october 1988 New T = 23°C 182.7 0.517 72.4 30 0.345 0.207

MTS 006 Iss. B

9.3 17/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Flex - Core cell Curing Volume density 34 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB 5052 - F40 - 2.1 Hexcel – march 1988 New T = 23°C 44.8 0.108 12.4 6.9 0.043 0.026

Flex - Core cell

HEXCEL ALUMINIUM HONEYCOMB 5052 - F40 - 2.5 Hexcel – march 1988

Curing New Volume density 40 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 62.1** 16.5** 7.6** 0.065** 0.038**

Flex - Core cell Curing Volume density 50 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB 5052 - F40 - 3.1 Hexcel – march 1988 New T = 23°C 86.2 0.193 22.1 9 0.087 0.052

** Predicted values

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.3 18/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Flex - Core cell Curing Volume density 66 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB 5052 - F40 - 4.1 Hexcel – march 1988 New T = 23°C 127.6 0.29 31 11.7 0.125 0.079

Flex - Core cell

HEXCEL ALUMINIUM HONEYCOMB 5052 - F40 - 5.7 Hexcel – march 1988

Curing New Volume density 91 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

199.9 0.483 46.9 15.9 0.193 0.117

© AEROSPATIALE - 1999

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9.3 19/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Flex - Core cell Curing Volume density 69 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB 5052 - F80 - 4.3 Hexcel – march 1988 New T = 23°C 134.4 0.314 31 12.4 0.135 0.083

Flex - Core cell

HEXCEL ALUMINIUM HONEYCOMB 5052 - F80 - 6.5 Hexcel – march 1988

Curing New Volume density 104 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

213.7 0.507 49.6 16.5 0.212 0.124

Flex - Core cell Curing Volume density 128 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB 5052 - F80 - 8.0 Hexcel – march 1988 New T = 23°C 275.8 0.772 67.6 21.4 0.299 0.179

MTS 006 Iss. B

9.3 20/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/16 inches Curing Volume density 104 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/16 - 6.5 Hexcel – october 1988 New T = 23°C 227.5** 65.5** 26.2**

Hexagonal cell 1/16 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/16 - 9.5 Hexcel – october 1988

Curing New Volume density 152 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 344.7* 75.8* 34.5*

* Preliminary values ** Predicted values

© AEROSPATIALE - 1999

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MTS 006 Iss. B

9.3 21/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 3/32 inches Curing Volume density 69 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/32 - 4.3 Hexcel – march 1988 New T = 23°C 103.4** 0.379** 41.4** 17.2** 0.248** 0.152**

Hexagonal cell 3/32 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/32 - 6.3 Hexcel – march 1988

Curing New Volume density 101 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

241.3* 0.827* 68.9* 24.1* 0.462* 0.265*

* Preliminary values ** Predicted values

© AEROSPATIALE - 1999

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/8 - 3.1 Hexcel – october 1988 Reference Aerospatiale 5056 3.20

Hexagonal cell 1/8 inches Curing New Volume density 50 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 66.9 0.179 31 13.8 0.138 0.076

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/8 - 4.5 Hexcel – october 1988 Reference Aerospatiale 5056 3.28

Hexagonal cell 1/8 inches Curing New Volume density 72 Kg/m3 2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 127.6 0.345 48.3 19.3 0.241 0.141

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/8 - 6.1 Rohr – RHR 95-057 Reference Aerospatiale 5056 3.45

Hexagonal cell 1/8 inches Curing New Volume density 97 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23°C

T = 120°C

0.448 53 21.2 0.359 0.210

0.448 53 21.2 0.323 0.189

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/8 - 8.1 Hexcel – october 1988 Reference Aerospatiale 5056 3.58

Hexagonal cell 1/8 inches Curing New Volume density 130 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 299.9 0.896 98.6 35.2 0.510 0.303

Hexagonal cell 5/32 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 5/32 - 2.6 Hexcel – october 1988

Curing New Volume density 42 Kg/m3 2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 48.3 0.128 24.8 11.7 0.105 0.055

Hexagonal cell 5/32 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 5/32 - 3.8 Hexcel – october 1988

Curing New Volume density 61 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23°C 96.5 0.259 39.3 16.5 0.188 0.107

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 5/32 inches Curing Volume density 85 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 5/32 - 5.3 Hexcel – october 1988 New T = 23°C 165.5 0.448 58.6 22.8 0.300 0.172

Hexagonal cell 5/32 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 5/32 - 6.9 Hexcel – october 1988

Curing New Volume density 110 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

241.3 0.689 81.4 29.6 0.421 0.248

© AEROSPATIALE - 1999

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/16 - 2.0 Hexcel – october 1988 Reference Aerospatiale 5056 4.20

Hexagonal cell 3/16 inches Curing New Volume density 32 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23° C 31 0.083 18.6 9 0.072 0.034

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/16 - 3.1 Rohr – RHR 95-057 Reference Aerospatiale 5056 4.28

Hexagonal cell 3/16 inches Curing New Volume density 50 Kg/m3

T = 23° C T = 120° C

2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

0.148 22.1 11 0.107 0.062

0.148 22.1 11 0.087 0.048

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/16 - 4.4 Hexcel – october 1988 Reference Aerospatiale 5056 4.45

Hexagonal cell 3/16 inches Curing New Volume density 70 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23° C 124.1 0.338 46.9 19 0.234 0.137

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/16 - 5.7 Hexcel – october 1988 Reference Aerospatiale 5056 4.58

Hexagonal cell 3/16 inches Curing New Volume density 91 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 186.2 0.507 64.8 24.8 0.331 0.193

Hexagonal cell 3/16 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/16 - 8.1 Rohr – RHR 95-057

Curing New Volume density 130 Kg/m3

T = 23°C

T = 120°C

0.689 77.2 34.7 0.510 0.296

0.689 77.2 34.7 0.459 0.267

2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/4 - 1.6 Hexcel – october 1988 Reference Aerospatiale 5056 6.20

Hexagonal cell 1/4 inches Curing New Volume density 26 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23°C 20.7 0.055 13.8 8.3 0.054 0.026

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/4 - 2.3 Hexcel – october 1988 Reference Aerospatiale 5056 6.28

Hexagonal cell 1/4 inches Curing New Volume density 37 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 40 0.107 22.1 10.3 0.09 0.043

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/4 - 3.4 Hexcel – october 1988 Reference Aerospatiale 5056 6.48

Hexagonal cell 1/4 inches Curing New Volume density 55 Kg/m3 2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 79.3 0.217 34.5 15.2 0.159 0.09

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/4 - 4.3 Hexcel – october 1988 Reference Aerospatiale 5056 6.58

Hexagonal cell 1/4 inches Curing New Volume density 69 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23°C 118.6 0.321 46.2 18.6 0.224 0.131

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Hexagonal cell 1/4 inches

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/4 - 5.2 Hexcel – october 1988

Curing New Volume density 83 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 158.6 0.445 57.9 22.1 0.293 0.169

Hexagonal cell 1/4 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/4 - 6.0 Rohr – RHR 95-057

Curing New Volume density 96 Kg/m3

T = 23°C

T = 120°C

0.414 51.7 24.8 0.352 0.207

0.414 51.7 24.8 0.316 0.186

2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Hexagonal cell 1/4 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 1/4 - 7.9 Rohr – RHR 95-057

Curing New Volume density 126 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23°C

T = 120°C

0.724 74.5 33.8 0.448 0.269

0.724 74.5 33.8 0.363 0.209

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/8 - 1.0 Hexcel – october 1988 Reference Aerospatiale 5056 9.20

Hexagonal cell 3/8 inches Curing New Volume density 16 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 10.3 0.024 10.3 6.2 0.031 0.017

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/8 - 1.6 Hexcel – october 1988 Reference Aerospatiale 5056 9.28

Hexagonal cell 3/8 inches Curing New Volume density 26 Kg/m3 2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 20.7 0.055 13.8 8.3 0.054 0.026

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/8 - 2.3 Rohr – RHR 95-057 Reference Aerospatiale 5056 9.48

Hexagonal cell 3/8 inches Curing New Volume density 37 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

T = 23°C

T = 120°C

0.069 14.8 7.4 0.091 0.049

0.069 14.8 7.4 0.082 0.044

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Z

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/8 - 3.0 Hexcel – october 1988 Reference Aerospatiale 5056 9.58

Hexagonal cell 3/8 inches Curing New Volume density 48 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

T = 23°C 63.4 0.179 29.6 13.1 0.131 0.069

Hexagonal cell 3/8 inches

HEXCEL ALUMINIUM HONEYCOMB CR III 5056 - 3/8 - 5.4 Rohr – RHR 95-057

Curing New Volume density 86 Kg/m3

T = 23°C

T = 120°C

0.345 45.2 22.1 0.307 0.179

0.345 45.2 22.1 0.276 0.161

2

Ec (daN/mm ) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

MTS 006 Iss. B

9.3 31/33

Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Flex - Core cell Curing Volume density 34 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB 5056 - F40 - 2.1 Hexcel – march 1988 New T = 23°C 44.8 0.125 12.4 6.9 0.051 0.029

Flex - Core cell

HEXCEL ALUMINIUM HONEYCOMB 5056 - F40 - 3.1 Hexcel – march 1988

Curing New Volume density 50 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

86.2 0.227 22.1 9 0.103 0.062

Flex - Core cell Curing Volume density 66 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB 5056 - F40 - 4.1 Hexcel – march 1988 New T = 23°C 127.6 0.333 31 11.7 0.15 0.091

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Composite stress manual

MATERIAL CHARACTERISTICS Aluminium honeycomb

Flex - Core cell Curing Volume density 69 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

Z

HEXCEL ALUMINIUM HONEYCOMB 5056 - F80 - 4.3 Hexcel – march 1988 New T = 23°C 134.4 0.357 32.4 12.4 0.162 0.095

Flex - Core cell

HEXCEL ALUMINIUM HONEYCOMB 5056 - F80 - 6.5 Hexcel – march 1988

Curing New Volume density 104 Kg/m3

T = 23°C

Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

213.7 0.627 50.3 16.5 0.251 0.147

Flex - Core cell Curing Volume density 128 Kg/m3 Ec (daN/mm2) Rc (hb) Gl (daN/mm2) Gw (daN/mm2) Sl (hb) Sw (hb)

© AEROSPATIALE - 1999

HEXCEL ALUMINIUM HONEYCOMB 5056 - F80 - 8.0 Hexcel – march 1988 New T = 23°C 282.7 0.869 68.9 22.1 0.357 0.212

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Composite stress manual

MATERIAL CHARACTERISTICS Foam

Volume density 32 ± 7 Kg/m3 Test standard DIN 53420 Modulus of elasticity E (daN/mm2) Compressive strength Rc (hb) Tensile strength Rt (hb) Bending strength Rf (hb) Shearing modulus G (daN/mm2) Shear strength S (hb) Elongation at break % Dimensional stability at high temperature °C

ROHACELL FOAM 31 A Rohacell Test standard

New T = 23°C

DIN 53457 DIN 53421 DIN 53455 DIN 53423 DIN 53294 DIN 53294 DIN 53455 DIN 53424

2.6 0.03 0.1 0.08 0.8 0.03 3.5 180

Volume density 52 ± 12 Kg/m3 Test standard DIN 53420 Modulus of elasticity E (daN/mm2) Compressive strength Rc (hb) Tensile strength Rt (hb) Bending strength Rf (hb) Shearing modulus G (daN/mm2) Shear strength S (hb) Elongation at break % Dimensional stability at high temperature °C

ROHACELL FOAM 51 A Rohacell Test standard

New T = 23°C

DIN 53457 DIN 53421 DIN 53455 DIN 53423 DIN 53294 DIN 53294 DIN 53455 DIN 53424

4.5 0.07 0.19 0.16 1.3 0.06 4 180

Volume density 75 ± 15 Kg/m3 Test standard DIN 53420 Modulus of elasticity E (daN/mm2) Compressive strength Rc (hb) Tensile strength Rt (hb) Bending strength Rf (hb) Shearing modulus G (daN/mm2) Shear strength S (hb) Elongation at break % Dimensional stability at high temperature °C

© AEROSPATIALE - 1999

Z

ROHACELL FOAM 71 A Rohacell Test standard

New T = 23°C

DIN 53457 DIN 53421 DIN 53455 DIN 53423 DIN 53294 DIN 53294 DIN 53455 DIN 53424

7.5 0.13 0.28 0.25 2.2 0.09 4.5 180

MTS 006 Iss. B

10 1/3

Composite stress manual

MATERIAL CHARACTERISTICS Foam

Volume density 52 ± 12 Kg/m3 Test standard DIN 53420 Modulus of elasticity E (daN/mm2) Compressive strength Rc (hb) Tensile strength Rt (hb) Bending strength Rf (hb) Shearing modulus G (daN/mm2) Shear strength S (hb) Elongation at break % Dimensional stability at high temperature °C

ROHACELL FOAM 51 WF Rohacell Test standard

New T = 23°C

DIN 53457 DIN 53421 DIN 53455 DIN 53423 DIN 53294 DIN 53294 DIN 53455 DIN 53424

4.5 0.04 0.16 0.16 1.4 0.05 3 205

Volume density 75 ± 15 Kg/m3 Test standard DIN 53420 Modulus of elasticity E (daN/mm2) Compressive strength Rc (hb) Tensile strength Rt (hb) Bending strength Rf (hb) Shearing modulus G (daN/mm2) Shear strength S (hb) Elongation at break % Dimensional stability at high temperature °C

© AEROSPATIALE - 1999

Z

ROHACELL FOAM 71 WF Rohacell Test standard

New T = 23°C

DIN 53457 DIN 53421 DIN 53455 DIN 53423 DIN 53294 DIN 53294 DIN 53455 DIN 53424

7.5 0.105 0.22 0.29 2.4 0.1 3 200

MTS 006 Iss. B

10 2/3

Composite stress manual

MATERIAL CHARACTERISTICS Foam

Volume density 110 ± 21 Kg/m3 Test standard DIN 53420 Modulus of elasticity E (daN/mm2) Compressive strength Rc (hb) Tensile strength Rt (hb) Bending strength Rf (hb) Shearing modulus G (daN/mm2) Shear strength S (hb) Elongation at break % Dimensional stability at high temperature °C

ROHACELL FOAM 110 WF Rohacell Test standard

New T = 23°C

DIN 53457 DIN 53421 DIN 53455 DIN 53423 DIN 53294 DIN 53294 DIN 53455 DIN 53424

13.5 0.22 0.37 0.52 4 0.175 3 200

Volume density 205 ± 35 Kg/m3 Test standard DIN 53420 Modulus of elasticity E (daN/mm2) Compressive strength Rc (hb) Tensile strength Rt (hb) Bending strength Rf (hb) Shearing modulus G (daN/mm2) Shear strength S (hb) Elongation at break % Dimensional stability at high temperature °C

© AEROSPATIALE - 1999

Z

ROHACELL FOAM 200 WF Rohacell Test standard

New T = 23°C

DIN 53457 DIN 53421 DIN 53455 DIN 53423 DIN 53294 DIN 53294 DIN 53455 DIN 53424

27 0.64 0.68 1.2 10 0.36 3.5 200

MTS 006 Iss. B

10 3/3

Composite stress manual - Annex

B

Reference documents

C BE 019 : Elaboration du dossier de justification structurale

Documents to be consulted Abbreviations

Terminology

See Lexique Aerospatiale Aéronautique (Aerospatiale Aeronautique Lexicon) List of words defined in the Lexique Aerospatiale Aéronautique (Aerospatiale Aeronautique Lexicon):

Highlights

Issue

Date

Pages modified

A

03/99

All

New document.

B

05/99

All

Mises à jour Chapitres A, F, G, K, L, N, T, V. Complément au chapitre Z. Rajout Chapitre I.

© AEROSPATIALE - 1999

MTS 006 Iss. B

Justification of the changes made

38Ann. page

Composite stress manual - Management Information

NOT

FOR

DISTRIBUTION

List of approval

B

Dept. code

Function

BTE/CC/SC

Head of Department

Key words

Name / First name

Signature

Mr THOMAS

Calculation, Stressing

B Bibliography

-

Distribution list

Dept. code B

Function

Name / First name (if necessary)

BQP/TE

Diderot archives

SIBADE Alain

BQP/TE

BQP/TE Library

SIBADE Alain

BT Technical Library

BOUTET Fernand

BTE/SM/MG

B Distribution list managed in real time by BIO/D (Didocost application)

© AEROSPATIALE - 1999

MTS 006 Iss. B

MI page 1