constraining and size effects in lead-free solder joints

J.Cugnoni, [email protected] 1

Constraining and size effects in lead-free solder joints

J. Cugnoni1, J. Botsis1, V. Sivasubramaniam2, J. Janczak-Rusch2

1 Lab. Applied Mechanics & Reliability, EPFL, Switzerland2 Füge- und Grenzflächentechnologie, EMPA, Switzerland


Deformation & 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

Plastic constitutive law of Sn-4.0Ag-0.5Cu solder

Variable solder gap width

Effects of constraints

Effects of size


Constraints in solder joints

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

Plastic deformation ofsolder:- constant volume- shrinks in lateral directions

Rigid substrates:- impose lateral stresses at the interfaces - additionnal 3D stresses=> apparent hardening=> constraining effects


Parametric FE study

Goal: study the constraining effects as a

function of geometry

Method: parametric FE simulation of 30 joint

geometries with the same materials parameters:

gap to thickness ratio G = g / t width to thickness ratio W = w / t

indicators: constraining effect ratio

Q = (ujoint - u

solder) / usolder

triaxiality ratio R = p / m

g

w

L

t


Stress field in constrained solder

11 22Front surface

view

Mid-plane view

Cu

Cu

Solder

FEM47 MPa 76 MPa

70 MPa37 MPa


Stress field in constrained solder

Von Miseseq. stress

Hydrostatic pressureFront surface

view

Mid-plane view

Cu

Cu

Solder

FEM54 MPa -47 MPa

58 MPa -37 MPa


Parametric 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 of the stress field in the solder induced by the substrate



=> Constraining effects are inversely proportionnal to the gap to thickness ratio G (asymptotic effect in the form of 1/G)

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



0.050.1

0.20.5

12

12

510

200

1

2

3

4

5

6

Con

stra

inin

g e

ffe

ct r

atio

, Q

G = g / tW

= w

/ t

Constraining effects as a function of geometry

Constraining effects are: strongly dependent on the

gap to thickness ratio G for G<0.5

slightly affected by the width to thickness ratio W for W<2.


Apparent stress - strain curve of the

solder in a joint

is what we usually measure

depends on geometry

Constitutive law & constraints

Constitutive law of the solder

is needed for FE simulations

independent of geometry

3D FEM:includes all the

geometrical effects

???Inverse numerical identification of a

3D FEM


In situ characterization method

SpecimenProduction

TensileTest (DIC)

Geometry FEM

ExperimentalLoad - Displacement

Curve

SimulatedLoad - Displacement

Curve

Apparent engineering stress-strain response

of the joint

Optimization(Least Square

Fitting) Constitutive stress-strain law

of the solder

Identification Loop

ConstrainingEffects

Experimental

In-situ characterization of constitutive parameters

Numerical Simulations


Experimental setup

Tensile tests: Sn-4.0Ag-0.5Cu solder production: 1-2 min at 234°C

(heating rate 3-4°C/min) and rapid cooling in water

0.25 to 2.4 mm gap width Displacement ramp 0.5 m/s

Digital Image Correlation: is used to determine the

displacement "boundary condition" near the solder layer

gauge length =~ 1.5 x solder gap Displacement res. up to 0.1 m


micro - Digital Image Correlation

micro-DIC measurements: Requirements:

DIC needs medium & high frequency details in each sub images => random pattern

micro-measurements: spacial & displacement resolution limited mainly by the pattern

no change in magnification & no loss of focus => difficult with optical microscopy

Pattern created by: rough polishing (contrast in reflexion, uniform light field) spray paint (best results for global measurements) Inkjet printing (in progress)

2 - 4 mm


Digital Image Correlation algorithm

DIC algorithm: Features:

Custom developed in Matlab & C Based on linear / cubic sub-pixel

interpolation Displacement and derivatives

(optional) Optimization:

original "brute" search simplex or gradient based optimizer hybrid "pyramidal" search &

gradient optimizer hybrid FFT-based DSC & gradient

fine search Performance:

up to 0.02 pixel displacement resolution (ideal pattern) 4 mm


Experimental stress-strain curves of the tested joints

0.0E+00

1.0E+07

2.0E+07

3.0E+07

4.0E+07

5.0E+07

6.0E+07

7.0E+07

8.0E+07

9.0E+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

2.40 mm

Bulk Specimen

Constrained stress-strain curves

Similar results for G > 0.5

Identifyconstitutiveproperties

Clear hardening for G < 0.5

Constraining & scale effects=>

can't compare these curves


Finite Element Modelling

3D FEM of 1/8th of the specimen

Copper: Elastic behaviour:

ECu = 112 GPa, = 0.3

Solder: Elasto-plastic with isotropic

exponential & linear hardening

Chosen to fit bulk solder plastic response

5 unknown parameters:

ppypy KbQ ))exp(1()( 0

Cu

Sn-Ag-Cu

KbQE ys and,,,, 0

Elongation of solder

Imposed displacement from testing

Simulated load-displacement

curve


Inverse identification procedure

Identification parameters:

Objective function (): difference of measured and simulated load-displacement curves

non-linear least square optimization algorithm to solve:

]~

,)~

log()log(,~

,~,~

[ 00 KKbbQQEE yyss α

2

2)(

2

1)(),(min kkkk FwithFthatsuchFind

kαεααα

α

Blue: initial load-displ. curveRed: identified load-displ. curve

Black: measured load-displ. curve

Load - displacement curves Solution time: 50 FE solutions required to

identify the material properties (~2h)

Accuracy: max error +/-4% on load –

displacement curve


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 constitutive parameters

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

!! Manufacturing process is also size dependant !!

Removed constraining effects => can compare with bulk specimenBulk specimen appears much softer

!! In-situ characterization !!


g=2.40 mm, G=g/t=2.71

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

8.00E+07

0 0.01 0.02 0.03 0.04 0.05 0.06

strain (-)

stre

ss (

Pa)

constitutive

constrained

Constraining effects 2.4 mm

+ 15 %


g=1.20 mm, G=g/t=1.33

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

8.00E+07

0 0.01 0.02 0.03 0.04 0.05 0.06

strain (-)

stre

ss (

Pa)

constitutive

constrained


+ 22 %


g=0.70 mm, G=g/t=0.77

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

8.00E+07

0 0.01 0.02 0.03 0.04 0.05 0.06

strain (-)

stre

ss (

Pa)

constitutive

constrained


+ 30 %


g=0.50 mm, G=g/t=0.58

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

8.00E+07

0 0.01 0.02 0.03 0.04 0.05 0.06

strain (-)

stre

ss (

Pa)

constitutive

constrained


+ 37 %


g=0.25 mm, G=g/t=0.28

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

8.00E+07

0 0.01 0.02 0.03 0.04 0.05 0.06

strain (-)

stre

ss (

Pa)

constitutive

constrained


+ 78 %


Constraining and size effects

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0.25 mm 0.50 mm 0.70 mm 1.20 mm 2.40 mm

Gap width

Str

ess

(Pa)

Ultimate stressEng. Yield stressEffects of Constraints

Size effects

decrease of yield & ultimate stress ~10 MPa

constraining effects ~ 35 MPa


Microstructure & Fractography

Microstructure before testing Fractography

2.4mm

0.7mm

0.5mm (vacuum)Pores:

• created during manufacturing and grows with plastic deformation

• introduces large scatter in experimental data => modelling?

• interacts with the interfaces => critical defect!!

• size of pores ~ constant for all gap but more influence in thinner joints


Damage mechanisms

Thick Joint G>1= small triaxiality

FE model

Fractography

DIC measurements

plastic damage & void growth in center => crack


Damage mechanisms

Thin joint G<0.5= High triaxiality

FE model

DIC measurements

Fractographyvoid growth& crack at interface


Conclusions

Constraining effects: Proportionnal to triaxility of the stress field in the solder Inversely proportionnal to the gap to thickness ratio G Can completely modify the solder joint response:

in an ideal case, ultimate stress increased by a factor of 6 compared to the ult. stress of the solder material itself

Must be taken into account in Characterization & Design

In-situ characterization method: A versatile & powerful technique for characterization of small

size & thin layer materials produced with realistic processing and geometry conditions

Can determine actual constitutive properties from constrained materials


Conclusions

Size & scale effects in lead-free solders Actual constitutive properties are size dependant:

In the present case, ult. stress decreases by 20% from 2.4mm to 0.2mm joints due to effects of porosity.

material scale effects & the "scaling" of the production methods have a combined influence.

Constraining effects: Constraining effects are size dependant ~(1/G) with G=g/t Up to 80% of additionnal hardening due to plastic constraints solder joint response & constitutive properties are NOT equivalent stress-strain response solder joint curves are geometry dependant

=> should not be compared for diff. geometries


Future developments

In-situ characterization: Apply to shear tests Extend to identification of

visco-elasto-plasticity with damage

Reduced object size Industrial aspects:

Apply the in-situ characterization method to an industrial electronic package (for example BGA)

Determination of the mechanical properties of a solder joint under realistic loading conditions (power-cycles)

Realistic Experiment (DIC)

Design / processvalidation

FE Analysis & optimization

Mixed num-expidentification:

realistic properties

constraining and size effects in lead-free solder joints

Documents

solder gap displacement

ratio w

leadfree solder jointsj

constraining effect

resultsconstraining

size effects

geometrical effects

ratio g asymptotic effect