Introduction To Mechanical Properties Of Materials.pdf

Introduction to Mechanical Properties of Materials Stress, strain, and deformation

Introduction of Materials in Electronic •

• Component board at rest

•

Component board under increased temperature

•

Component board under mechanical bending / shock / vibration

•

•

Solid materials in electronic products –

Metals, Polymers

–

Ceramics, Semiconductors

Composites are combinations of materials in the first three groups, namely In electronic assemblies, various materials are integrated together, e.g. CTE mismatch

When electronic component boards are loaded a multi-axial stress/strain state is produced.

Stresses/strains produced during use are distributed heterogeneously in the structure.

If the strength of materials is exceeded or the material has been “fatigued” long enough, fracture will take place (ductile fracture, brittle fracture, fatigue fracture, creep rupture etc.)

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Basic Terminology

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Terminology • Application of a force (F) on an area (A) constitutes a stress, the unit of which is normally expressed in N/mm2 = MN/m2 = MPa • A fixed body deforms under the action of the stress and experiences strain • Both strain and stress are defined in tension/compression as well as in shear – When stress acts in tension or compression, it is designated by sigma (σ) – When stress acts in shear, it is designated by tau (τ)

A Page 4

Strain • Very often strain is determined by the extent of deformation divided by the original dimension (normal or engineering strain)

(l − lo ) εn = lo • The true strain is defined as the sum of all the instantaneous engineering strains:

dl → ε = ln(1 + ε n ) dε = l

•

l

εt =

 l  dl   = ln ∫l  lo 

l0

Note that strain is a dimensionless quantity

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Large deformation •

Similarly as with strain, nominal or engineering stress is the force divided by the original area and, true stress by true area (e.g. necking taken into account)

•

With small deformations there is little difference between the true stress and true strain from the engineering stress and strain

•

As the strain becomes large, dilatation becomes more significant and the crosssectional area of the specimen decreases and the true stress can become much larger than the engineering stress

•

Normal and shear stresses have different effects on the fracture mechanics of materials

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Hydrostatic Stress and Poisson’s Ratio • Hydrostatic stress is an isotropic stress that is produced by e.g. the weight of water at a certain depth – Hydrostatic pressure tends to change the volume of the material (resisted by the body's bulk modulus) – Shear (or tensile) stresses tend to deform the material without changing its volume

• Poisson’s ratio – When a material is stretched in one direction, it usually tends to contract in the directions transverse to the direction of stretching. …or vise versa… – Poisson's ratio (ν) is the ratio stretched to contraction – For most materials between 0.0 (cork)and 0.5 (rubber)

Strain Energy • The energy stored in a body due to deformation is called strain energy • The strain energy per unit volume is called strain energy density and is the area underneath the stressstrain curve up to the point of deformation – Units: Nm/m3 or Joules/m3

• Materials are classified based on the amount of energy stored – Brittle material (high strength, low ductility; a) – Ductile material (low strength, high ductility; b) – Elastoplastic material (moderate strength, moderate ductility; c)

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Stress-Strain Responses of Materials • Linear-elastic response

• Plastic response

• Viscoelastic response

• Creep response

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Properties of Different Materials

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Stress-Strain Curve

• When σ < σy, materials deform elastically – Deformation is

Necking begins

σuts σf

σy

• instantaneous • time-independent • recoverable upon release of stress

– Strain is proportional to stress via a proportionality constant i.e. (elastic) modulus – The Hooke’s law is the constitutive equation that relates stress with strain at the elastic region

σ =ε ×E

τ = γ ×G

Stress / [MPa]

• When σ ≥ σy materials deform plastically – Deformation is

εy

εn ε p

• instantaneous • time dependent or independent • is not recoverable upon release of stress

εf

– No such simple relation exist as the Hooke’s law

Strain / []

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Strain Hardening • When stress above σy is applied and subsequently released, permanent strain is produced. • Now, when stress is applied again, higher than σy must be applied for additional strain to occur

σuts

σy Stress / [MPa]

– I.e. the yield stress has increased

εp εy

εn

– This effect is called strain hardening – Any stress above σy is termed flow stress – The engineering stress exhibits a maximum (σuts), where necking begins – The strain to fracture is called the ductility (The “ability” of material to accommodate deformation)

Strain

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Temperature-Dependent Material Properties • Polymers – Glass transition temperature region, Tg – Solid-form transition from a glassy amorphous to viscous amorphous state – This transition is associated with a notable change in mechanical properties – The glass transition temperature range is also sensitive to humidity

• Metals – Homologous temperature TH=T/Tm – Above about 0.3 to 0.4 in the scale of homologous temperatures mechanical properties of metals are different from those below this range – At high homologous temperatures the plastic deformation metals become time–dependent • metals can be deformed plastically even at stress levels below their macroscopic yield stress (creep) • Plastic behavior becomes strain–rate dependent

Material

Melting RT in homol. Temperature Temp. Si 1410 0.18 Cu 1083 0.22 Al 660.3 0.32 SnPb (eut) 183 0.65 SnAgCu (eut) 217 0.60 Pb 327 0.49

With Increasing Temperature • The ability to carry loads is decreased with an increase in temperature • With increasing temperature – – – – –

the values of elastic modulus decrease the values of yield strength and ultimate tensile strength decrease ductility increases strain hardening is less significant strain rate sensitivity is less significant

σuts

σy, T↑

T↑

T↑

T↑

ε

εf

E E, σuts, εf

σuts, T↑ σy

σuts

T

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Effects of Strain-Rate (Time-Dependent) • The plastic behavior of metals at high homologous temperatures is strain–rate dependent – strength increases with increased rate of strain (ε)̇ – ductility is reduced with increased rate of strain Strength (UTS) of four different solders at room temperature

Strength (UTS) of one solder at two different temperatures

90

ε ↑

80 70

σ

Stress [MPa]

ε ↑

T↑

60 50 40 30 20 10

ε

0 0,00001

0,001

0,1 Strain rate [%/s]

10

1000

Note that the unit of strain is [%]; the unitless value of strain has only been multiplied by 100%.

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Mechanisms of Deformation

• • •

The deformation diagrams indicating regions in which the different mechanisms operate Applied stress (σ) is divided by the shear modulus (G) and homologous temperature is used instead of absolute temperature in order to treat different materials equally The presentation is simplified – The yield strength of metals decreases with increasing temperature – The boundaries between the different mechanisms are not exact

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Creep •

When a material is strained to yield point and the load is sustained, the applied stress necessary to maintain the strain falls as a function of time – –

•

Creep is considered significant – – –

•

Initial strain is a combination of elastic and plastic deformation At high homologous temperatures the elastic deformation is gradually translated into permanent plastic deformation by (timedependent) creep

for metals when T > 0.3-0.4×Tm for ceramics when T > 0.4-0.5×Tm for polymers when T > Tg

For Sn-rich lead-free solders:

TmpSn = 232 C = 505K → 0.45 × 505K = 227 K = − 450 C –

Solder based on Sn creep under almost every use conditions

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Measurement of Creep Properties • Creep tests are typically carried out under constant stress (/force) and the strain as a function of time is measured • Creep is commonly presented as strain (ε) as a function of time (t) and the graphs continue until the specimen ruptures

• The three stages of creep: •

Primary creep –

•

Secondary creep –

•

Continuous fall of creep strain rate Constant creep rate

Tertiary creep –

Creep rate increases continuously until rupture

= instantaneous elastic deformation

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Measurement of Creep Properties ε = f (σ, t , T)

(Schubert model, 2001)

• In addition to the applied stress, the creep strain is dependent on time and temperature Page 19

Plastic Deformation of Polymers

Plastic flow and time-dependent creep from the material physics perspective

Chemistry of Polymers Adapted from Fig. 14.1, Callister 7e.

Note: polyethylene is just a long HC - paraffin is short polyethylene

Polymer Additives • To improve mechanical properties, processability, durability, etc. • Fillers – Added to improve tensile strength & abrasion resistance, toughness & decrease cost – e.g. carbon black, silica gel, wood flour, glass, limestone, talc, etc. • Plasticizers – Added to reduce the glass transition temperature (Tg) – Commonly added to PVC - otherwise it is brittle

22

Polymer Additives • Stabilizers – Antioxidants – UV protectants • Lubricants – Added to allow easier processing – “slides” through dies easier • Colorants – Dyes or pigments • Flame Retardants – Cl/F & Br

23

Molecular Structures • Covalent chain configurations and strength:

secondary bonding

Linear

Branched

Cross-Linked

Network

Direction of increasing strength

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Polymer Crystallinity Polymers rarely 100% crystalline • Too difficult to get all those chains aligned crystalline region

• % Crystallinity: % of material

that is crystalline. -- TS and E often increase with % crystallinity. -- Annealing causes crystalline regions to grow. % crystallinity increases.

amorphous region Adapted from Fig. 14.11, Callister 6e. (Fig. 14.11 is from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, John Wiley and Sons, Inc., 1965.)

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Basic Deformation Mechanisms in Polymers • Elastic deformation: Chains elongate elastically, instantly reversible

• Plastic deformation: Chains stretch, rotate, slide and detangle under load

Mechanical Properties of Polymers • i.e. stress-strain behavior of polymers brittle polymer σFS of polymer ca. 10% that of metals

plastic elastomer elastic modulus – less than metal

Strains – deformations > 1 000% possible (for metals, maximum strain ca. 10% or less) 27

Effects of Temperature and Strain Rate on Thermoplastics • Increase in T – Decreases E – Decreases UTS – Increases εf

• Increase in strain rate – Increase E – Increase UTS – Decrease εf

Restoration of Plastically Deformed Metals •

When solder interconnections are deformed plastically, energy is stored in the crystal lattice in the form of defects such as vacancies, interstitial atoms, stacking faults, dislocations, and deformation twins –

•

Measurements have shown that about 1–15% of the energy is stored, and the rest is dissipated irreversibly as heat

The defects produced during plastic deformation are unstable and gradually restored –

The restoration can take place by two mechanisms: •

Recovery (no notable change in the grain structure)

•

Recrystallization (clearly visible even with the resolution of an optical microscope) Restoration

•

Restoration can take place either during deformation (dynamic restoration) or at elevated temperatures after deformation (static restoration)

Recovery

Static Recovery

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Recrystallization

Dynamic Recovery

Static Recrystallization

Dynamic Recrystallization

Recovery, Recrystallization and Grain Growth of Deformed Microstructures

Grain structure recovers slightly

New grains nucleate

Larger grains grow at the expense of the smaller grains

Factors affecting recrystallization: 1. Degree of plastic deformation 2. Temperature 3. Time 4. Original grain size 5.Chemical composition

Case Example: Cold-deformed (left) and Recovery of Cu Dislocation annihilation (dislocations of opposite sign)

Remaining dislocations rearrange

low-energy dislocation configurations

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Polygonization

Case Example: Cold-deformed (left) and Recrystallized Cu Prim. recrystallized

After grain growth

Cracking of Materials • Definition of a fracture: “Fracture is the separation, or fragmentation, of a solid body into two or more parts under the action of stress”

• There are two distinguishable stages of cracking Transgranular cracking

Intergranular cracking

1.) Nucleation of cracks • at dents, pits, voids, or other defects on the surface of material

2.) Propagation of cracks • in polycrystalline materials: – Transgranularly through grains – Intergranularly along grain boundaries Micrographs are the courtesy of Metallurgical Technologies http://www.met-tech.com/metallography.htm Page 33

Classification of Fracture Modes •

Fracture modes of engineering materials are commonly classified into two groups: –

Brittle crack • •

–

Cracks propagate rapidly and show little or no plastic deformation before fracture Brittle cracks, unlike ductile cracks, do not usually need an increase of applied stress to continue their growth once they are nucleated

Ductile crack • •

Demonstrates large amounts of plastic deformation both before crack initiation and propagation as well as during the propagation in front of the crack tip Crack moves slowly and will usually not extend unless an increased stress is applied

A crack surface showing brittle nature of propagation Page 34

A crack surface showing ductile nature of propagation

Fatigue • Even ductile materials can crack when they are placed repeatedly under loads smaller than the fracture strength! – Fatigue is a cumulative structural damage that occurs when a material is subjected to repeated loading – The maximum stress values are less than the ultimate tensile strength limit, and sometimes even below the yield strength limit of the material

• Fatigue life is influenced by a variety of factors – – – – –

the applied stress temperature presence of oxidizing or inert chemicals residual stresses etc.

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Fatigue • Fatigue is commonly divided into two categories: – Stress controlled fatigue (flawless material under repeatedly applied stress levels below yield) – Strain controlled fatigue (applied stress exceeds either locally or “globally” the yield strength) Cracking of a flawless material - No crack nucleates at time zero - Nucleation of cracks essential

"High cycle fatigue" - σ < σy - N > 104 f - E.g. elastic vibration

•

Cracking of a distorted material - Material contains crack nucleates - Plastic deformation at the tip of the cracks  strain controlled state even if macroscopically strain controlled  propagation of cracks essential "Low cycle fatigue" - σ > σy - N < 104 f - E.g. thermomechanical cycles

Fatigue of electronic assemblies can take place isothermally under cyclic mechanical load but most often it is caused by changes of temperature and the “thermal mismatch” of adjoining materials

Fatigue in Solder Interconnections •

Cracking of SnPb solder interconnections in solders typically proceeds by the following steps: 1) Change of the appearance of solder interconnections 2) Formation of voids on the surface of solder interconnections 3) Nucleation of crack is enhanced by the voids 4) Electrical failure of solder interconnections

•

Cracking of lead-free solders are typically missing at least the first step (appearance is “duller”)

As soldered: SnPb solder

Step 1: a) 40x b) 500x

Step 2: Formation of voids

Step 3: Nucleation of cracks

a)

Step 4: Failed interconect

b)

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Fatigue in Solder Interconnections •

The nature of fatigue in solder interconnections are complex because – Operation temperature of the devices is relatively high (high homologous temperature) – Solders are very soft and ductile (as compared to structural materials) • Significant plastic deformation takes place during loading • The creep rate of solders is relatively fast

– Microstructures of solder interconnections change during their lifetime – Interconnections (micro)structures are heterogenious: interconnections are layered structures composed of both relatively soft (e.g. solders) as well as hard materials (e.g. intermetallic compounds) right next to each other

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– There is a difference in the rate of strain energy accumulation between the opposite interfacial regions

As Soldered At failure

• Changes of microstructure were first observed in the strain concentration regions

3500 Cycles

2000 Cycles

1000 Cycles

Evolution of Microstructures in the Course of Thermal Cycling

Evolution of Microstructures during Cycling •

500 cycles

Experimental results – Thermal cycling (0℃ -125℃, 20 minute cycle time) – Average cycles to failure about 6000 cycles

1000 cycles

•

1500 cycles

2500 cycles

3000 cycles

5000 cycles

6000 cycles

Relatively good agreement between the simulated microstructures and the observed microstructures in terms of – incubation time of recrystallization – expansion of recrystallized region – growth rate of the recrystallized area fraction

Cracking of Solder Interconnections

• The network of high-angle grain boundaries extends through the interconnections and provides favorable paths for cracks to propagate intergranularly

Thermal Cycling Tests •

Purpose: To simulate changes in temperature of ambient atmosphere

•

Methods: air-to-air or fluid-to-fluid test chambers depending on the required rate of temperature change –

Test profile determined by values of upper and lower temperatures, dwell time, and rate of change (or transition time) between the temperatures •

•

IEC 68-2-14N standard: - 45 °C / + 125 °C, 15 min dwell time

Single vs. multiple chamber structures –

–

Single chamber: •

Slow rates of temperature change (< 20 ºC/minute)

•

Good control of the rate of temperature change

•

For high thermal masses

Multiple chamber: •

Rapid rate of temperature change (>20 ºC/minute)

•

Rate determined by the thermal mass

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Power Cycling Tests •

Many products are continuously exposed to temperature fluctuations caused by internally generated heat during normal use – Thermal cycling tests are being replaced by operational/power cycling tests to simulate better the internal heat production during normal operation – Includes the effects of electrical current (electromigration)

•

No standardized tests procedures yet available

a 3G terminal device during normal opera

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