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Composite)Materials)and)their)use)in) Civil)Infrastructure:)An)Introduction
K.K.#Bajpai Principal#Scientific#Officer Structural#Engineering#Laboratory IIT#Kanpur
Fibre&Composites&– Introduction Definition:&Composites&are&created&by& synthetic&assembly&of&2&or&more&constituents ! !
Reinforcement&phase&(Fibres) Binder&phase&(matrix)
Advantages ! ! ! ! ! !
Corrosion&resistant High&strength&and&stiffness High&Strength/Weight&ratio Very&Low&Coefficient&of&Thermal&Expansion High&Internal&Damping:&Better&NVH&control Material&can&be&designed&in&addition&to&the& structure
Why$fibreous$materials$are$stronger 1.5 Compressive Strength (Kg/cm2)
Imperfections/flaws$in$bulk$ material$are$prone$to$exist Presence$of$flaw$in$a$form$of$ crack$perpendicular$to$ loading$direction Measured$strength$are$much$ smaller$than$theoretical$ values$for$bulk$materials
Andes Straw 1 Ichu grass
0.5
J. Vargas Data
0 -0.5
0
0.5 1 1.5 2 2.5 % Straw or Grass
3
3.5
Material
Density, (g/cc)
Modulus, (GPa)
Tensile, Strength, (GPa)
Yield, Strength, (GPa)
Ratio,of, Modulus,to, Density, (Specific, Modulus)
Ratio,of,Tensile, Strength,to, Density, (Specific, Strength)
Mild%Steel%
7.8
210
0.45.0.83
0.25.0.30
26.9
0.058%– 0.106
Aluminum
2.7
69
0.31
0.275
25.5
0.115
E.Glass%Fiber
2.54
72.4
3.5
..
28.5
1.38
High%Strength% Carbon%Fiber
1.90
240.0
2.5
..
126.0
1.30
High%Modulus% Carbon%Fiber
1.90
390.0
2.1
..
205.0
1.10
Kevlar.49%Fiber
1.50
130.0
2.8
..
87.0
1.87
Fibres'only'can'not'be'used'as' structural'material Embedding'of'fibres'in'a'suitable' material'which'should'be'capable'of ! ! !
Transfer'loads'to'fibres Providing'environmental'protection Providing'protection'from'mechanical' abrasion
Classification Composite.Materials(FRP)
Single-Layer
Multi-Layer
Laminates Continuous-Fibers Unidirectional
Hybrids
Discontinuous-Fibers
Bi; directional
Random
Preferred
Applications
! ! ! !
Aerospace-industry Sporting-goods Automotive Construction
F"16%Use%of%Carbon"Epoxy% Wt.%Savings%23% Boeing%757%Weight% reduction%31%%using%FRP
Applications…
FRP/as/Main/ Reinforcement/ 40%/of/World’s/ steel/production/ used/to/repair/ corrosion/ problems/ Canadian/Society/of/ Civil/Engineers,/2003 !
Huge/scope/for/ FRP/bars
Applications… FRP/bars/as/ replacement/of/ steel/bars
Applications….
FRP0strengthening !
!
Very0effective0in0magnetic0isolation0and0 corrosion0resistance0applications Easy0to0handle/apply0in0strengthening0of0 masonry0structures0
compared0to0traditional0strengthening0 techniques
Benefits…
Un*reinforced/Masonry/(URM)/Infill/Walls/ strengthened/with/FRP/laminates/ !
Subjected/to/loads " In*plane " Out*of*plane
WL/EL !
Remarkable/increase/in/strength/&/ductility !
Ehsani/et/al,/1999/ Hamilton/et/al,/1999 Velazquez/et/al,/2000/ Bajpai/et/al,/2002,/2008
FRP$as$Main$Reinforcement…
Design$philosophy$understood… !
Design$Guidelines$; India
HYSD steel Stress
Mild steel
FRP Stress
Concrete
Concrete Strain
Strain
FRP$Rebars$(CFRP$and$GFRP)
ACI 440.1R-01 "Guide for the Design and Construction of Concrete Reinforced with FRP Bars"
Costs%of%composite%manufacture Material%costs%22 higher%for%composites ! !
Constituent%materials%(e.g.,%fibers%and%resin) Processing%costs%22 embedding%fibers%in%matrix% " not%required%for%metals%Carbon%fibers%order%of%magnitude%
higher%than%aluminum
Design%costs%22 lower%for%composites !
Can%reduce%the%number%of%parts%in%a%complex% assembly%by%designing%the%material%in%combination% with%the%structure
Increased%performance%must%justify%higher% material%costs
Forms&of&Reinforcement&Phase Fibers& ! ! !
cross2section&can&be&circular,&square&or&hexagonal Diameters&22>&~10&µm Lengths&22>&L/D&ratio " 100&22 for&chopped&fiber " much&longer&for&continuous&fiber
Particulate For&sizes&>&1&µm,&strength&of&particle&is&involved&in& load&sharing&with&matrix
Flakes !
flat&platelet&form
Fibers'( Glass Most'widely'used'fiber Uses:'piping,'tanks,'boats,'sporting'goods Advantages ! ! !
low'cost Corrosion'resistance Low'cost'relative'to'other'composites:'
Disadvantages ! ! !
Relatively'low'strength High'elongation Moderate'strength'and'weight
Types: ! !
E(Glass'( electrical,'cheaper S(Glass'( high'strength
Fibers'( Carbon 2nd'most'widely'used'fiber Examples !
aerospace,'sporting'goods,'construction
Advantages ! ! ! !
high'stiffness'and'strength Low'density Intermediate'cost Properties:' " " " "
Standard'modulus:'207(240'Gpa Intermediate'modulus:'240(340'GPa High'modulus:'340(960'GPa' Diameter:'5(8'microns,'smaller'than'human'hair !
Fibers'grouped'into'tows'or'yarns'of'2(12k'fibers
Fibers'(( Carbon'(2) Types'of'carbon'fiber ! !
vary'in'strength'with'processing Trade(off'between'strength'and'modulus
Intermediate'modulus !
PAN'(Polyacrylonitrile)' " fiber'precursor'heated'and'stretched'to'align'structure'
and'remove'non(carbon'material
High'modulus' !
!
made'from'petroleum'pitch'precursor'at'lower' cost'(Pyrolysis'Method) much'lower'strength
Fibers'( Aramid'(Kevlar) Uses:' !
high'performance'replacement'for'glass' fiber
Examples !
Armor,'protective'clothing,'industrial,' sporting'goods
Advantages:' " higher'strength'and'lighter'than'glass " More'ductile'than'carbon
Fibers'( Others Boron ! ! !
High'stiffness,'very'high'cost Large'diameter'( 200'microns Good'compressive'strength
Polyethylene'( trade'name:'Spectra'fiber ! ! ! !
Textile'industry High'strength Extremely'light'weight Low'range'of'temperature'usage
Fibers'(( Others'(2) Ceramic'Fibers'(and'matrices) !
! !
!
Very'high'temperature'applications'(e.g.' engine'components) Silicon'carbide'fiber'( in'whisker'form. Ceramic'matrix'so'temperature'resistance' is'not'compromised Infrequent'use
Matrix'Materials Functions'of'the'matrix ! !
Transmit'force'between'fibers arrest'cracks'from'spreading'between'fibers " do'not'carry'most'of'the'load
! !
hold'fibers'in'proper'oreintation protect'fibers'from'environment
" mechanical'forces'can'cause'cracks'that'allow'
environment'to'affect'fibers
Demands'on'matrix' ! ! ! ! !
Interlaminar'shear'strength Toughness Moisture/environmental'resistance Temperature'properties Cost
Matrices)* Polymeric Thermosets ! ! !
cure)by)chemical)reaction Irreversible Examples " Polyester,)vinylester !
Most)common,)lower)cost,)solvent)resistance
" Epoxy)resins !
Superior)performance,)relatively)costly
Matrices)* Thermoplastics Formed)by)heating)to)elevated)temperature) at)which)softening)occurs ! ! !
Reversible)reaction Can)be)reformed)and/or)repaired)* not)common Limited)in)temperature)range)to)1500C
Examples !
Polypropylene) " with)nylon)or)glass) " can)be)injected** inexpensive
!
Soften)layers)of)combined)fiber)and)resin)and) place)in)a)mold)** higher)costs
Matrices)* Others Metal)Matrix)Composites)* higher) temperature !
e.g.,)Aluminum)with)boron)or)carbon)fibers
Ceramic)matrix)materials)* very)high) temperature !
Fiber)is)used)to)add)toughness,)not) necessarily)higher)in)strength)and)stiffness
Important)Note Composite)properties)are)less)than) that)of)the)fiber)because)of)dilution) by)the)matrix)and)the)need)to) orient)fibers)in)different)directions.)
Material
Density, g/cc (fibre only)
Modulus, GPa (fibre only)
Tensile, Strength, GPa (fibre only)
Yield, Strength, Gpa (fibre only)
Ratio,of, Modulus,to, Density,(fibre only)
Ratio,of,Tensile, Strength,to, Density, (fibre onlt)
Mild%Steel%
7.8
210
0.45.0.83
0.25.0.30
26.9
0.058%– 0.106
Aluminum
2.7
69
0.31
0.275
25.5
0.115
E.Glass%Epoxy (Vf =%57%)
1.97 (2.54)
21.5 (72.0)
0.57 (3.5)
..
10.9 (28.5)
0.26 (1.38)
Carbon%.Epoxy%% (Vf =%58%)
1.54 (1.90)
83.0 (240/390)
0.38 (2.5./2.1)
..
53.5 (126/205)
0.24 (1.30/1.10)
Kevlar.49. Epoxy (Vf =%60%)
1.40 (1.50)
40.0 (130)
0.65 (2.8)
..
29.0 (87)
0.46 (1.87)
Composites
Rule%of%Mixtures%(Unidirectional% Composites:%Longitudinal%Direction) For%a%composite%loaded%along%its%fiber%axis,%we%can% assume%that%the%strain%in%the%fibers%and%the%strain%in%the% matrix%must%be%the%same.%%From%this,%it%is%easy%to%derive% expressions%for%the%elastic%modulus%of%the%composite%as%a% function%of%its%constituents:
where%ECL means%the%modulus%of%the%composite%in%the% longitudinal%direction,%and%the%m%subscript%means%matrix% while%the%f%subscript%means%fiber.%V%means%volume% fraction.
! c = ! f V f + ! m (1 " V f ) Fiber
Composite Stress Matrix
Strain
Unidirectional,Loading,::,Load,sharing,between,fibers,and,matrix
1 0.9 0.8 0.7
Pf / Pc
0.6 0.5 Ef/Em = 1
0.4
Ef/Em = 2 Ef/Em = 5
0.3
Ef/Em = 10 Ef/Em = 20
0.2
Ef/Em = 50 Ef/Em = 100
0.1 0 0
0.1
0.2
0.3
0.4
0.5
Fiber Volume Fraction
0.6
0.7
0.8
Minimum fibre volume fraction (Vmin) Continuing the expression for rule mixture:
! c = ! f V f + ! m (1 " V f )
(1)
If we assume all the fibres fail at the same time (the failure strain of the fibres is less than the matrix), under these conditions the ultimate longitudinal strength (σcu) of composite can be assumed equal to the composite stress at the fibre fracture strain, εf* equation (1)
can
therefore be used to obtain
! cu = ! fuV f + (! m )# (1 " V f ) * f
(2)
Where σfu is ultimate strength of fibres, and (σm_) εf* is the matrix stress at the fibre fracture strain εf*.
Minimum fibre volume fraction (Vmin) Contd…. If the fibre volume fraction is small, i.e. below Vmin, the matrix will be able to support the entire composite when all the fibres break. At the composite strains higher than the fibre fracture strain, the composite will eventually fail when the matrix stress equals its ultimate strength (σ mu). Thus, for fibre volume fraction less than Vmin equation (1) can be written as
! cu = ! mu (1 " V f )
(3)
Now Vmin can be defined as the minimum fibre volume fraction that ensures fibre controlled composite failure. Vmin can be obtained by equating right hand sides of equation (2) and (3). Thus
Vmin =
" mu # (" m )!
* f
" fu + " mu # (" m )!
* f
(4)
Critical fibre volume fraction (Vcrit) The$longitudinal$composite$strengths,$as$predicted$by$equation$ (2)$&$(3)$have$been$plotted$against$fibre$volume$fractions$in$ the$following$figure: σ
" cu = " fuV f + (" m )! (1 # V f ) * f
σcu
εf
ε
Vcrit
! cu = ! mu (1 " V f )
σmu (σm)εf
Vmin
Vf
σfu
σfu
Equation)(2))predicts)composite)strength)that)can)be)lower)or) higher)than)matrix)strength)depending)on)the)fibre)volume) fraction,)however)equation)(3))predicts)composite)strength)that)is) always)less)than)the)strength)of)matrix.) A)critical)fibre)volume)fraction,)Vcrit,)therefore)can)be)defined,)as) follows,)that)must)be)expressed)for)matrix)strengthening:
" cu = " fuV f + (" m )! (1 # V f ) $ " mu * f
Vcrit =
" mu # (" m )! " fu # (" m )!
* f
* f
Rule#of#Mixtures#(Unidirectional# Composites:#Transverse#Direction) If#the#composite#is#loaded#transverse#to# the#fiber,#we#get#a#different#expression# for#stiffness:
Modulus'of'Unidirectional'Composites'as'a' function'of'volume'fraction
Ec''
Ef EcL EcT Em 0
0.1
0.2
0.3
0.4
0.5
Vf
0.6
0.7
0.8
0.9
1
Transverse(Loading(::(Shear(Modulus(and(Poisson’s(Ratio It(may(be(assumed(that(shearing(stress(on(fibers(and(the(matrix(are(equal
The(total(shear(deformation(is(the(sum(of(shear(deformations(of(fibers(and the(matrix
The(shear(deformations(can(be(written(as(the(product(of(corresponding shear(strain(and(the(cumulative(thickness
Transverse#Loading#::#Shear#Modulus#and#Poisson’s#Ratio#contd…
Recognizing#thickness#is#proportional#to#volume#fraction#yields
The#shear#strains#can#be#replaced#by#the#ratios#of#shear#stress#and# appropriate#shear#modulus#as#follows:
Where######is#the#inEplane#shear#modulus#of#the#composite#and######and###### are#the#shear#modulii#of#the#fibers#and#matrix,#respectively.
Or#we#can#simplify#the#above#equation#as:
Transverse(Loading(::(Shear(Modulus(and(Poisson’s(Ratio(contd…
The(major(Poisson’s(ratio(can(be(predicted(using(the(same(model(as(that( used(for(predicting(transverse(Elastic(modulus.((The(rule(of(mixture(for( the(major(Poisson’s(ratio(of(a(unidirectional(composite(can(be(derived(as:
Further,(the(relationship(between(major(and(minor(Poisson’s(ratios(is:
Transverse(loading It(is(pretty(clear(that(loading(the( composite(transverse(to(the(fiber( direction(is(not a(good(idea.((
Transverse(loading This(problem( can(be(reduced( in(a(number(of( ways: !
Make(a( structure( consisting(of( multiple(layers( of(composite,( with(the(fibers( aligned(in( different( directions(in( each(layer.((
Transverse(loading !
Make(a(random(array of(fibers " Reduces(directionality,(but(also( reduces(performance " example:((glass(mats(used(in(boat( construction
!
Design(part(so(stresses(are( always(along(fiber(axis. " Possible(in(some(applications(like( rackets(and(club(shaftsA((not( always(possible
Material(Forms(and(Manufacturing Objectives(of(material(production ! ! ! !
assemble(fibers impregnate(resin shape(product cure(resin(
Manufacturing+, Filament+Winding Highly+automated !
!
low+manufacturing+ costs+if+high+ throughput e.g.,+Glass+fiber+pipe,+ sailboard+masts
Prepregs Prepreg'and'prepreg'layup !
“prepreg”'0 partially'cured'mixture'of'fiber' and'resin " Unidirectional'prepreg'tape'with'paper'backing ! !
!
wound'on'spools Cut'and'stacked
Curing'conditions " Typical'temperature'and'pressure'in'autoclave' is'12002000C,'100'psi
Manufacturing+, Layups compression molding
vacuum+bagging
Manufacturing+– Lay/up+Contd
Advantages: Large+&+Complex+items Minimum+Equipment Low+Tooling+Cost
Resin&transfer&molding&(RTM) Dry6fiber&preform&&placed&in&a&closed& mold,&resin&injected&into&mold,&then& cured Advantages:
High&Quality&&Finish Higher&Dimensional& tolerance
Pultrusion Fiber-and-matrix-are-pulled-through-adie,-like-extrusion-of-metals-88 assembles-fibers,-impregnates-theresin,-shapes-the-product,-and-curesthe-resin-in-one-step. ! Example.-Fishing-rods,-Re8bars !
Pultrusion
Reference'Books/Publications Fiber'Reinforced'Composites By'P.K.'Mallik'(Chapters'1,2,3,&5)
Hand'Book'of'Composites By'George'Lubin''(Chapters'1'&'2)
Analysis'and'Performance'of'Fiber'Composites By'B.D.'Agarwal'and'L.'J.'Broutman'(Chapters'1,2,&3)
FRP'Strengthened'RC'Structures By'J.G.'Teng,'J.F.'Chen,'S.T.'Smith,'&'L.'Lam
StatePofPthePArt'Report'on'Fiber'Reinforced'Plastic' Reinforcement'for'Concrete'Structures Reported'by'ACI'Committee'440
K.K.#Bajpai Principal#Scientific#Officer Structural#Engineering#Laboratory IIT#Kanpur
Fibre&Composites&– Introduction Definition:&Composites&are&created&by& synthetic&assembly&of&2&or&more&constituents ! !
Reinforcement&phase&(Fibres) Binder&phase&(matrix)
Advantages ! ! ! ! ! !
Corrosion&resistant High&strength&and&stiffness High&Strength/Weight&ratio Very&Low&Coefficient&of&Thermal&Expansion High&Internal&Damping:&Better&NVH&control Material&can&be&designed&in&addition&to&the& structure
Why$fibreous$materials$are$stronger 1.5 Compressive Strength (Kg/cm2)
Imperfections/flaws$in$bulk$ material$are$prone$to$exist Presence$of$flaw$in$a$form$of$ crack$perpendicular$to$ loading$direction Measured$strength$are$much$ smaller$than$theoretical$ values$for$bulk$materials
Andes Straw 1 Ichu grass
0.5
J. Vargas Data
0 -0.5
0
0.5 1 1.5 2 2.5 % Straw or Grass
3
3.5
Material
Density, (g/cc)
Modulus, (GPa)
Tensile, Strength, (GPa)
Yield, Strength, (GPa)
Ratio,of, Modulus,to, Density, (Specific, Modulus)
Ratio,of,Tensile, Strength,to, Density, (Specific, Strength)
Mild%Steel%
7.8
210
0.45.0.83
0.25.0.30
26.9
0.058%– 0.106
Aluminum
2.7
69
0.31
0.275
25.5
0.115
E.Glass%Fiber
2.54
72.4
3.5
..
28.5
1.38
High%Strength% Carbon%Fiber
1.90
240.0
2.5
..
126.0
1.30
High%Modulus% Carbon%Fiber
1.90
390.0
2.1
..
205.0
1.10
Kevlar.49%Fiber
1.50
130.0
2.8
..
87.0
1.87
Fibres'only'can'not'be'used'as' structural'material Embedding'of'fibres'in'a'suitable' material'which'should'be'capable'of ! ! !
Transfer'loads'to'fibres Providing'environmental'protection Providing'protection'from'mechanical' abrasion
Classification Composite.Materials(FRP)
Single-Layer
Multi-Layer
Laminates Continuous-Fibers Unidirectional
Hybrids
Discontinuous-Fibers
Bi; directional
Random
Preferred
Applications
! ! ! !
Aerospace-industry Sporting-goods Automotive Construction
F"16%Use%of%Carbon"Epoxy% Wt.%Savings%23% Boeing%757%Weight% reduction%31%%using%FRP
Applications…
FRP/as/Main/ Reinforcement/ 40%/of/World’s/ steel/production/ used/to/repair/ corrosion/ problems/ Canadian/Society/of/ Civil/Engineers,/2003 !
Huge/scope/for/ FRP/bars
Applications… FRP/bars/as/ replacement/of/ steel/bars
Applications….
FRP0strengthening !
!
Very0effective0in0magnetic0isolation0and0 corrosion0resistance0applications Easy0to0handle/apply0in0strengthening0of0 masonry0structures0
compared0to0traditional0strengthening0 techniques
Benefits…
Un*reinforced/Masonry/(URM)/Infill/Walls/ strengthened/with/FRP/laminates/ !
Subjected/to/loads " In*plane " Out*of*plane
WL/EL !
Remarkable/increase/in/strength/&/ductility !
Ehsani/et/al,/1999/ Hamilton/et/al,/1999 Velazquez/et/al,/2000/ Bajpai/et/al,/2002,/2008
FRP$as$Main$Reinforcement…
Design$philosophy$understood… !
Design$Guidelines$; India
HYSD steel Stress
Mild steel
FRP Stress
Concrete
Concrete Strain
Strain
FRP$Rebars$(CFRP$and$GFRP)
ACI 440.1R-01 "Guide for the Design and Construction of Concrete Reinforced with FRP Bars"
Costs%of%composite%manufacture Material%costs%22 higher%for%composites ! !
Constituent%materials%(e.g.,%fibers%and%resin) Processing%costs%22 embedding%fibers%in%matrix% " not%required%for%metals%Carbon%fibers%order%of%magnitude%
higher%than%aluminum
Design%costs%22 lower%for%composites !
Can%reduce%the%number%of%parts%in%a%complex% assembly%by%designing%the%material%in%combination% with%the%structure
Increased%performance%must%justify%higher% material%costs
Forms&of&Reinforcement&Phase Fibers& ! ! !
cross2section&can&be&circular,&square&or&hexagonal Diameters&22>&~10&µm Lengths&22>&L/D&ratio " 100&22 for&chopped&fiber " much&longer&for&continuous&fiber
Particulate For&sizes&>&1&µm,&strength&of&particle&is&involved&in& load&sharing&with&matrix
Flakes !
flat&platelet&form
Fibers'( Glass Most'widely'used'fiber Uses:'piping,'tanks,'boats,'sporting'goods Advantages ! ! !
low'cost Corrosion'resistance Low'cost'relative'to'other'composites:'
Disadvantages ! ! !
Relatively'low'strength High'elongation Moderate'strength'and'weight
Types: ! !
E(Glass'( electrical,'cheaper S(Glass'( high'strength
Fibers'( Carbon 2nd'most'widely'used'fiber Examples !
aerospace,'sporting'goods,'construction
Advantages ! ! ! !
high'stiffness'and'strength Low'density Intermediate'cost Properties:' " " " "
Standard'modulus:'207(240'Gpa Intermediate'modulus:'240(340'GPa High'modulus:'340(960'GPa' Diameter:'5(8'microns,'smaller'than'human'hair !
Fibers'grouped'into'tows'or'yarns'of'2(12k'fibers
Fibers'(( Carbon'(2) Types'of'carbon'fiber ! !
vary'in'strength'with'processing Trade(off'between'strength'and'modulus
Intermediate'modulus !
PAN'(Polyacrylonitrile)' " fiber'precursor'heated'and'stretched'to'align'structure'
and'remove'non(carbon'material
High'modulus' !
!
made'from'petroleum'pitch'precursor'at'lower' cost'(Pyrolysis'Method) much'lower'strength
Fibers'( Aramid'(Kevlar) Uses:' !
high'performance'replacement'for'glass' fiber
Examples !
Armor,'protective'clothing,'industrial,' sporting'goods
Advantages:' " higher'strength'and'lighter'than'glass " More'ductile'than'carbon
Fibers'( Others Boron ! ! !
High'stiffness,'very'high'cost Large'diameter'( 200'microns Good'compressive'strength
Polyethylene'( trade'name:'Spectra'fiber ! ! ! !
Textile'industry High'strength Extremely'light'weight Low'range'of'temperature'usage
Fibers'(( Others'(2) Ceramic'Fibers'(and'matrices) !
! !
!
Very'high'temperature'applications'(e.g.' engine'components) Silicon'carbide'fiber'( in'whisker'form. Ceramic'matrix'so'temperature'resistance' is'not'compromised Infrequent'use
Matrix'Materials Functions'of'the'matrix ! !
Transmit'force'between'fibers arrest'cracks'from'spreading'between'fibers " do'not'carry'most'of'the'load
! !
hold'fibers'in'proper'oreintation protect'fibers'from'environment
" mechanical'forces'can'cause'cracks'that'allow'
environment'to'affect'fibers
Demands'on'matrix' ! ! ! ! !
Interlaminar'shear'strength Toughness Moisture/environmental'resistance Temperature'properties Cost
Matrices)* Polymeric Thermosets ! ! !
cure)by)chemical)reaction Irreversible Examples " Polyester,)vinylester !
Most)common,)lower)cost,)solvent)resistance
" Epoxy)resins !
Superior)performance,)relatively)costly
Matrices)* Thermoplastics Formed)by)heating)to)elevated)temperature) at)which)softening)occurs ! ! !
Reversible)reaction Can)be)reformed)and/or)repaired)* not)common Limited)in)temperature)range)to)1500C
Examples !
Polypropylene) " with)nylon)or)glass) " can)be)injected** inexpensive
!
Soften)layers)of)combined)fiber)and)resin)and) place)in)a)mold)** higher)costs
Matrices)* Others Metal)Matrix)Composites)* higher) temperature !
e.g.,)Aluminum)with)boron)or)carbon)fibers
Ceramic)matrix)materials)* very)high) temperature !
Fiber)is)used)to)add)toughness,)not) necessarily)higher)in)strength)and)stiffness
Important)Note Composite)properties)are)less)than) that)of)the)fiber)because)of)dilution) by)the)matrix)and)the)need)to) orient)fibers)in)different)directions.)
Material
Density, g/cc (fibre only)
Modulus, GPa (fibre only)
Tensile, Strength, GPa (fibre only)
Yield, Strength, Gpa (fibre only)
Ratio,of, Modulus,to, Density,(fibre only)
Ratio,of,Tensile, Strength,to, Density, (fibre onlt)
Mild%Steel%
7.8
210
0.45.0.83
0.25.0.30
26.9
0.058%– 0.106
Aluminum
2.7
69
0.31
0.275
25.5
0.115
E.Glass%Epoxy (Vf =%57%)
1.97 (2.54)
21.5 (72.0)
0.57 (3.5)
..
10.9 (28.5)
0.26 (1.38)
Carbon%.Epoxy%% (Vf =%58%)
1.54 (1.90)
83.0 (240/390)
0.38 (2.5./2.1)
..
53.5 (126/205)
0.24 (1.30/1.10)
Kevlar.49. Epoxy (Vf =%60%)
1.40 (1.50)
40.0 (130)
0.65 (2.8)
..
29.0 (87)
0.46 (1.87)
Composites
Rule%of%Mixtures%(Unidirectional% Composites:%Longitudinal%Direction) For%a%composite%loaded%along%its%fiber%axis,%we%can% assume%that%the%strain%in%the%fibers%and%the%strain%in%the% matrix%must%be%the%same.%%From%this,%it%is%easy%to%derive% expressions%for%the%elastic%modulus%of%the%composite%as%a% function%of%its%constituents:
where%ECL means%the%modulus%of%the%composite%in%the% longitudinal%direction,%and%the%m%subscript%means%matrix% while%the%f%subscript%means%fiber.%V%means%volume% fraction.
! c = ! f V f + ! m (1 " V f ) Fiber
Composite Stress Matrix
Strain
Unidirectional,Loading,::,Load,sharing,between,fibers,and,matrix
1 0.9 0.8 0.7
Pf / Pc
0.6 0.5 Ef/Em = 1
0.4
Ef/Em = 2 Ef/Em = 5
0.3
Ef/Em = 10 Ef/Em = 20
0.2
Ef/Em = 50 Ef/Em = 100
0.1 0 0
0.1
0.2
0.3
0.4
0.5
Fiber Volume Fraction
0.6
0.7
0.8
Minimum fibre volume fraction (Vmin) Continuing the expression for rule mixture:
! c = ! f V f + ! m (1 " V f )
(1)
If we assume all the fibres fail at the same time (the failure strain of the fibres is less than the matrix), under these conditions the ultimate longitudinal strength (σcu) of composite can be assumed equal to the composite stress at the fibre fracture strain, εf* equation (1)
can
therefore be used to obtain
! cu = ! fuV f + (! m )# (1 " V f ) * f
(2)
Where σfu is ultimate strength of fibres, and (σm_) εf* is the matrix stress at the fibre fracture strain εf*.
Minimum fibre volume fraction (Vmin) Contd…. If the fibre volume fraction is small, i.e. below Vmin, the matrix will be able to support the entire composite when all the fibres break. At the composite strains higher than the fibre fracture strain, the composite will eventually fail when the matrix stress equals its ultimate strength (σ mu). Thus, for fibre volume fraction less than Vmin equation (1) can be written as
! cu = ! mu (1 " V f )
(3)
Now Vmin can be defined as the minimum fibre volume fraction that ensures fibre controlled composite failure. Vmin can be obtained by equating right hand sides of equation (2) and (3). Thus
Vmin =
" mu # (" m )!
* f
" fu + " mu # (" m )!
* f
(4)
Critical fibre volume fraction (Vcrit) The$longitudinal$composite$strengths,$as$predicted$by$equation$ (2)$&$(3)$have$been$plotted$against$fibre$volume$fractions$in$ the$following$figure: σ
" cu = " fuV f + (" m )! (1 # V f ) * f
σcu
εf
ε
Vcrit
! cu = ! mu (1 " V f )
σmu (σm)εf
Vmin
Vf
σfu
σfu
Equation)(2))predicts)composite)strength)that)can)be)lower)or) higher)than)matrix)strength)depending)on)the)fibre)volume) fraction,)however)equation)(3))predicts)composite)strength)that)is) always)less)than)the)strength)of)matrix.) A)critical)fibre)volume)fraction,)Vcrit,)therefore)can)be)defined,)as) follows,)that)must)be)expressed)for)matrix)strengthening:
" cu = " fuV f + (" m )! (1 # V f ) $ " mu * f
Vcrit =
" mu # (" m )! " fu # (" m )!
* f
* f
Rule#of#Mixtures#(Unidirectional# Composites:#Transverse#Direction) If#the#composite#is#loaded#transverse#to# the#fiber,#we#get#a#different#expression# for#stiffness:
Modulus'of'Unidirectional'Composites'as'a' function'of'volume'fraction
Ec''
Ef EcL EcT Em 0
0.1
0.2
0.3
0.4
0.5
Vf
0.6
0.7
0.8
0.9
1
Transverse(Loading(::(Shear(Modulus(and(Poisson’s(Ratio It(may(be(assumed(that(shearing(stress(on(fibers(and(the(matrix(are(equal
The(total(shear(deformation(is(the(sum(of(shear(deformations(of(fibers(and the(matrix
The(shear(deformations(can(be(written(as(the(product(of(corresponding shear(strain(and(the(cumulative(thickness
Transverse#Loading#::#Shear#Modulus#and#Poisson’s#Ratio#contd…
Recognizing#thickness#is#proportional#to#volume#fraction#yields
The#shear#strains#can#be#replaced#by#the#ratios#of#shear#stress#and# appropriate#shear#modulus#as#follows:
Where######is#the#inEplane#shear#modulus#of#the#composite#and######and###### are#the#shear#modulii#of#the#fibers#and#matrix,#respectively.
Or#we#can#simplify#the#above#equation#as:
Transverse(Loading(::(Shear(Modulus(and(Poisson’s(Ratio(contd…
The(major(Poisson’s(ratio(can(be(predicted(using(the(same(model(as(that( used(for(predicting(transverse(Elastic(modulus.((The(rule(of(mixture(for( the(major(Poisson’s(ratio(of(a(unidirectional(composite(can(be(derived(as:
Further,(the(relationship(between(major(and(minor(Poisson’s(ratios(is:
Transverse(loading It(is(pretty(clear(that(loading(the( composite(transverse(to(the(fiber( direction(is(not a(good(idea.((
Transverse(loading This(problem( can(be(reduced( in(a(number(of( ways: !
Make(a( structure( consisting(of( multiple(layers( of(composite,( with(the(fibers( aligned(in( different( directions(in( each(layer.((
Transverse(loading !
Make(a(random(array of(fibers " Reduces(directionality,(but(also( reduces(performance " example:((glass(mats(used(in(boat( construction
!
Design(part(so(stresses(are( always(along(fiber(axis. " Possible(in(some(applications(like( rackets(and(club(shaftsA((not( always(possible
Material(Forms(and(Manufacturing Objectives(of(material(production ! ! ! !
assemble(fibers impregnate(resin shape(product cure(resin(
Manufacturing+, Filament+Winding Highly+automated !
!
low+manufacturing+ costs+if+high+ throughput e.g.,+Glass+fiber+pipe,+ sailboard+masts
Prepregs Prepreg'and'prepreg'layup !
“prepreg”'0 partially'cured'mixture'of'fiber' and'resin " Unidirectional'prepreg'tape'with'paper'backing ! !
!
wound'on'spools Cut'and'stacked
Curing'conditions " Typical'temperature'and'pressure'in'autoclave' is'12002000C,'100'psi
Manufacturing+, Layups compression molding
vacuum+bagging
Manufacturing+– Lay/up+Contd
Advantages: Large+&+Complex+items Minimum+Equipment Low+Tooling+Cost
Resin&transfer&molding&(RTM) Dry6fiber&preform&&placed&in&a&closed& mold,&resin&injected&into&mold,&then& cured Advantages:
High&Quality&&Finish Higher&Dimensional& tolerance
Pultrusion Fiber-and-matrix-are-pulled-through-adie,-like-extrusion-of-metals-88 assembles-fibers,-impregnates-theresin,-shapes-the-product,-and-curesthe-resin-in-one-step. ! Example.-Fishing-rods,-Re8bars !
Pultrusion
Reference'Books/Publications Fiber'Reinforced'Composites By'P.K.'Mallik'(Chapters'1,2,3,&5)
Hand'Book'of'Composites By'George'Lubin''(Chapters'1'&'2)
Analysis'and'Performance'of'Fiber'Composites By'B.D.'Agarwal'and'L.'J.'Broutman'(Chapters'1,2,&3)
FRP'Strengthened'RC'Structures By'J.G.'Teng,'J.F.'Chen,'S.T.'Smith,'&'L.'Lam
StatePofPthePArt'Report'on'Fiber'Reinforced'Plastic' Reinforcement'for'Concrete'Structures Reported'by'ACI'Committee'440
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