Deformation & damage Deformation & damage of lead-free solder jointsof lead-free solder joints

COST 531 Final Meeting,COST 531 Final Meeting,

17th-18th May 2007, Vienna17th-18th May 2007, Vienna

J. CugnoniJ. Cugnoni11, J. Botsis, J. Botsis11, , V. SivasubramaniamV. Sivasubramaniam22, J. Janczak-Rusch, J. Janczak-Rusch22

1 1 Lab. Applied Mechanics & Reliability, EPFL, SwitzerlandLab. Applied Mechanics & Reliability, EPFL, Switzerland22 Füge- und Grenzflächentechnologie, EMPA, Switzerland Füge- und Grenzflächentechnologie, EMPA, Switzerland

OutlineOutline

Overview of the project:Overview of the project: Global goals & achievementsGlobal goals & achievements

Methods & developments:Methods & developments: Experimental techniquesExperimental techniques ModellingModelling

Key resultsKey results Elasto-plastic characterization of SAC405Elasto-plastic characterization of SAC405 Constraining & size effectsConstraining & size effects Ductile failure: effect of voidsDuctile failure: effect of voids

FutureFuture Bridging the length scales & the disciplinesBridging the length scales & the disciplines

Deformation & damage of lead-free solder jointsDeformation & damage of lead-free solder joints

Manufacturing

Siz

e / C

onst

rain

ing

Effe

cts

Thermo-

mechanical H

istory

Micro S

tructure

Inte

rface

Nature of Irreversible Deformations

ConstitutiveEquations

Global Project

?

Objectives

Size & constraining effectsSize & constraining effects Tensile / shear jointsTensile / shear joints

Effect of microstructure:Effect of microstructure: Effect of porosity contentEffect of porosity content

Failure mechanisms:Failure mechanisms: Ductile fractureDuctile fracture

Studied system:Studied system: SAC 405 / Cu substratesSAC 405 / Cu substrates

Methods & developments: overviewMethods & developments: overview

Elasto-plastic

characterization of SAC 405Effe

cts

of v

oids

on

the

relia

bilit

y of

join

ts

Inve

stig

atio

ns o

n Siz

e Effe

cts

Effects of Constraints

Modelling

Experimental

Finite Element Model

Constitutive LawType

Inverse Num. / Exp.Identification

Micro StructureAnalysis

OpticalStrain

Measurement

Designof

Experiments

Key results: overviewKey results: overview

Manufacturing

Siz

e / C

onst

rain

ing

Eff

ects

Thermo-

mechanical H

istory

Micro S

tructure

Inte

rfac

e

Nature of Irreversible Deformations

ConstitutiveEquations

Global Project

Thoughts about the future….Thoughts about the future….

Short term:Short term:Time / temperature dependent properties.Time / temperature dependent properties.Interfacial failure: cohesive elementsInterfacial failure: cohesive elements

Mid-Long term:Mid-Long term:

Bridging the length scales & disciplinesBridging the length scales & disciplines

Meso

Micro

Macro

Thermodynamics, phase diagrams

Diffusion, interfaces, solidification, microstructure

Continuum mechanics, damage, fracture…

Homogenization

Solidification /diffusion simulation ?

Need more transversal research !!

Tensile & shear specimensTensile & shear specimens

9.5 mm

1 mm

2 mm

4 mm

8 mm

g

w

L

t

Tensile specimenTensile specimenL=120 mm, w=20 mm, t=1mm, g=[0.25, 0.5, 0.75, 1.2, 2.4] mmL=120 mm, w=20 mm, t=1mm, g=[0.25, 0.5, 0.75, 1.2, 2.4] mmSolder cross section = 20x1 mm2Solder cross section = 20x1 mm2

Shear specimenShear specimenL=120mm, joint cross section=2x2 mm2joint cross section=2x2 mm2Optimized for stress uniformity Optimized for stress uniformity & simple manufacturing& simple manufacturing

thickness=2mm

Digital Image CorrelationDigital Image Correlation

Why optical strain measurements??Why optical strain measurements?? non-invasive measurements at a non-invasive measurements at a

small scalesmall scale

DIC algorithms developments:DIC algorithms developments:Tensile joints:Tensile joints:

Small strains, small translationsSmall strains, small translations High accuracy is neededHigh accuracy is needed Spatial Correlation with cubic Spatial Correlation with cubic

spline resamplingspline resamplingShear joints:Shear joints:

Extremely large strains, large Extremely large strains, large displacementdisplacement

Need excellent robustnessNeed excellent robustness Incremental FFT-based correlationIncremental FFT-based correlation

Advantages / DrawbacksAdvantages / Drawbacks + Versatile & simple to setup+ Versatile & simple to setup + Robust in most cases+ Robust in most cases - Resolution limited by pixel size- Resolution limited by pixel size - Need a random pattern- Need a random pattern

4 mm

ESPI measurements (STSM, D. Karalekas)ESPI measurements (STSM, D. Karalekas)

Work done with Dr.Karalekas,Univ. Work done with Dr.Karalekas,Univ. Piraeus, Greece during a STSM at EPFLPiraeus, Greece during a STSM at EPFL

Advantages:Advantages: Sensitivity independant from Sensitivity independant from

magnification: excellent for global magnification: excellent for global observationsobservations

Full field measurementFull field measurement

Drawbacks:Drawbacks: Decorrelation Decorrelation Problems with creep tests Problems with creep tests

Application: Application: Evaluate boundary conditions Evaluate boundary conditions Full field displacement measurement on Full field displacement measurement on

assembliesassemblies

20 mm

Finite Element modellingFinite Element modelling

Modelling? why??Modelling? why?? Models have the power of Models have the power of

generalization of knowledgegeneralization of knowledge

FE modelsFE modelsAdvantages: Advantages:

Versatility: Complex geometries, multi-Versatility: Complex geometries, multi-components, components, multi-physicsmulti-physicsAbility to Ability to extrapolateextrapolate knowledge gained knowledge gained on simple test cases to much more on simple test cases to much more complex designs & geometries !!complex designs & geometries !!Multi-scaleMulti-scale modelling (homogenization) modelling (homogenization)

Drawback:Drawback:Requires an extensive & reliable set of Requires an extensive & reliable set of parameters parameters => huge characterization task=> huge characterization task

Combining Experiments & Combining Experiments & Numerical simulation is of prime Numerical simulation is of prime

importanceimportance

Inverse num.-exp. identificationInverse num.-exp. identification

SpecimenProduction

TensileTest (DIC)

Geometry & BoundaryConditions

FEM

ExperimentalLoad – Displacement /Stress-Strain response

SimulatedLoad – Displacement /Stress-Strain response

Global / local responseof the specimen

Optimization(Least Square

Fitting) Modelling parameters:Constitutive law,

failure model

Identification Loop

Geometric &structural effects

Experimental

In-situ characterization of constitutive parameters

Numerical Simulations

Constraining effects:Constraining effects:

Tensile & shear solder jointsTensile & shear solder joints

Constraints in tensile solder jointsConstraints in tensile solder joints

Solder joint in tension: - stiff elastic substrates- plastic solder (~=0.5)

Plastic deformation ofsolder:- constant volume=> solder shrinks in lateral directions

Rigid substrates:- impose lateral stresses at the interfaces - hydrostatic stresses=> apparent hardening=> constraining effects

Parametric FE study: ResultsParametric FE study: Results

Correlation between Constraining Effect ratio & Triaxiality ratio of stress field

y = 0.9686x - 0.4707

R2 = 0.9938

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8

Triaxiality ratio, R

Co

ns

tr. e

ffe

ct r

ati

o, Q

=> Constraining effects are due to the the triaxiality (hydrostatic part) of the stress field in the solder induced by the substrate

Parametric FE study: ResultsParametric FE study: Results

Constraining effects are inversely proportionnal to the gap to thickness ratio G in tensile joints

Constraining effect ratio in function of Gap / Thickness ratio

0

1

2

3

4

5

6

7

8

- 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

Gap / Thickness ratio, G

Co

ns

tra

inin

g e

ffe

ct

rati

o, Q

Q = 0.151G-1.3

R2 = 0.988

Shear: constraining effectsShear: constraining effects

0

5

10

15

20

25

30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

eng. shear strain [-]

no

m.

sh

ea

r s

tre

ss

[M

Pa

]

1mm

0.75mm

0.35mm

Parametric FE simulation of shear joint response

Pure shear = isochoric deformation => no significant effects of constraints !!

Shear: Gap – ultimate stress relationshipShear: Gap – ultimate stress relationship

Shear: Shear: No significant effect of solder gap on ultimate stress No significant effect of solder gap on ultimate stress

Ultimate shear stress as a function of gap

y = 0.236x + 21.339

0

5

10

15

20

25

30

0.3 0.5 0.7 0.9 1.1 1.3Gap (mm)

Ult.

she

ar s

tres

s

Size effects:Size effects:

Tensile & Shear solder jointsTensile & Shear solder joints

Identified constitutive stress-strain curves

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

strain (-)

stre

ss (

Pa)

0.25 mm

0.50 mm

0.70 mm

1.20 mm

2.00 mm

Bulk Specimen

Identified elasto-plastic law / size effectsIdentified elasto-plastic law / size effects

Mechanical properties decreasing for smaller joints:combination of scale effects & porosity

Manufacturing process is also size dependant

Tensile joints

Identified elasto-plastic law / size effectsIdentified elasto-plastic law / size effects

Tensile / shear joints: - similar elasto-plastic behaviours- similar size effects (manufacturing?)

Shear joints

Size effect

Deformation & damage mechanisms in lead-free Deformation & damage mechanisms in lead-free solder jointssolder joints

Microstructure & FractographyMicrostructure & Fractography

Microstructure before testing Fractography

2.4mm

0.7mm

0.5mm (vacuum)Pores:

• created during manufacturing and grow with plastic deformation

• introduces large scatter in experimental data => model void !!

If porosity cannot be eliminated

=> Include it in models as a « random » variable

Porous metal plasticity: Gurson-Tvergaard modelPorous metal plasticity: Gurson-Tvergaard model

Porosity content is an internal variable of the model: Porosity content is an internal variable of the model: f= density ratio = 1- void_fractionf= density ratio = 1- void_fraction

01)(2

3cosh2

)(2

321

2

fq

pqfq

plyply

eq

Yield surface

Yield function without pores Hydrostatic pressure

Effect of voids

Evolution of porosity

nuclgr fff

I:)1( plgr ff Growth

eqpl

eqplnucl Af )(

2

2

1exp

2)(

N

Neqpl

N

Neqpl ss

fA

Nucleation

Shear joint response & porous metal plasticityShear joint response & porous metal plasticity

Plastic Yielding Void

growth Void nucleation

Ult. strain

Changes in initial porosity %

Ductile failure simulationDuctile failure simulation

Porous metal plasticity model can 1. Predict the progressive ductile failure of metal up to rupture2. Simulate shear band formation & localization3. Introducing « random » initial porosity => statistical estimate of the failure

strain in a given assembly

Plastic Yielding

Void growth

Void nucleation

Ult. strain