j.cugnoni, [email protected] 1 constraining and size effects in lead-free solder joints j....

J.Cugnoni, [email protected] 1

Constraining and size effects in lead-free solder joints

J. Cugnoni1, J. Botsis1, J.Janczak2

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


Outline

Introduction Global project & goals Constraining effects In-situ characterization by inverse numerical methods

Experimental Test setup Results: Constrained stress-strain curves of SnAgCu joints

Numerical Modelling & inverse identification method Identified constitutive laws (unconstrained) Constraining & size effects

Conclusion


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


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


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


Methodology

SpecimenProduction

TensileTest (DIC)

Geometry &

ConstitutiveModel

FEM

ExperimentalLoad - Displacement

Curve

SimulatedLoad - Displacement

Curve

Apparent Stress-Strain Curve

(Constrained)

Optimization(Least Square

Fitting) Stress - StrainConstitutive Law (Unconstrained)

Identification Loop

ConstrainingEffects

Experimental

In-situ characterization of constitutive parameters

Numerical Simulations


Experimental setup

Tensile tests: Sn-4.0Ag-0.5Cu solder 0.2 to 2.0 mm gap width Instron 5848 Microtester 2kN load cell Displacement ramp 1 m/s

Digital Image Correlation: 1.3MPix CCD camera 30x optical microscope 3x2 mm observation region Displacement resolution 0.2 m


Constrained stress-strain curves

Constrained stress-strain curve, 0.2 mm gap

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 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Strain (-)

Str

ess

(Pa)

J7C-A

J7C-B

J7C-C

J8C-B

J9C-A

J9C-B

J9C-C

J11C-A

J12C-C

J12C-A

~ +/- 5% scatter=> averaging


Average constrained 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

1mm

1mmReinf

0.5mm

0.2mm

2mm

Constrained stress-strain curves

Similar results No clear conclusion

Identifyconstitutiveproperties

Strain (-)

Str

ess

(P

a)


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 & calculated load

Simulated load-displacement

curve


Inverse identification procedure

Identification parameters:

Objective function: relative difference of load-displ. curves

with Pexp = measured load-displacement curve and Pnum() = simulated load-displacement curve

Levenberg-Marquardt non-linear least square optimization algorithm to solve:

Gradients of objective function by Finite Differences

]~

,)~

log()log(,~

,~,~

[ 00 KKbbQQEE yyss α

200,..,2,,1,1

,)(

)(1

nPn

withn

i

expi

expexp

numexp

i PP

αPPαε

2

2)(

2

1)(),(min kkkk FwithFthatsuchFind

kαεααα

α


Inverse identification

Convergence Very robust convergence

even with bad initial guess of the parameters

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

Black: measured load-displ. curve

Load - displacement curves

Relative errors

Convergence graph

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 1 2 3 4 5

Iteration

Rel

ativ

e p

aram

ete

r va

lue

0.01

0.1

1

10

Err

or n

orm

alpha1

alpha2

alpha3

alpha4

alpha5

F(alpha)

Solution time: 4 iterations / 50 FE solutions

required to identify the material properties (~1h30)

Accuracy: max error +/-4% on load –

displacement curve


Identified constitutive stress-strain curves of the solder in 0.2, 0.5, 1.0 & 2.0 mm joints

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 0.01 0.02 0.03 0.04 0.05 0.06

0.2mm

0.5mm

1mm

2mm

Identified constitutive parameters

Mechanical properties decreasing for smaller jointsdue to a visible increase of the porosity:

Manufacturing process is also size dependant !!


Fractography & Porosity

Metallography after testing Fractography

Porosity:

• Responsible for the scatter in exp. data

• Concentrated at the interface: critical !!

• Size of pores ~constant for all gap widths => more influence in thinner joints

Porosity:

• Responsible for the scatter in exp. data

• Concentrated at the interface: critical !!

• Size of pores ~constant for all gap widths => more influence in thinner joints Porous metal constitutive law ??Porous metal constitutive law ??


Constraining effects 2 mm

Constrained & unconstrained 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 0.01 0.02 0.03 0.04 0.05 0.06

Strain (-)

Str

ess

(Pa)

Unconstrained 2mm

Constrained 2mm

+ 16 %


Constraining effects 1 mm

Constrained & Unconstrained 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 0.01 0.02 0.03 0.04 0.05 0.06

Strain (-)

Str

ess

(Pa)

Unconstrained 1mm

Constrained 1mm

+ 22 %


Constraining effects 0.5 mm


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 0.01 0.02 0.03 0.04 0.05 0.06

Strain (-)

Str

ess

(Pa)

Unconstrained 0.5mm

Constrained 0.5mm

+ 30 %


Constraining effects 0.2 mm


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 0.01 0.02 0.03 0.04 0.05 0.06

Strain (-)

Str

ess

(Pa)

Unconstrained 0.2mm

Constrained 0.2mm

+ 37 %


0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0.2 mm 0.5 mm 1 mm 2 mm

Ultimate stress

Yield stress (0.2%)

Constraining effects

Size effects

decrease of yield & ultimate stress ~7-8 MPa

increase of constraining effects ~ 10 MPa


Constraining effects on ultimate stress wrt gap

y = 0.2521x-0.5528

R2 = 0.9891

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

50.0%

0 0.5 1 1.5 2 2.5 3

ConstrainingEffect

Puissance (ConstrainingEffect)

Constraining effects / gap

nedunconstraiu

nedunconstraiu

dconstraineuR

Constraining effects: ~~ (1/Gap)0.6

Gap (mm)

R


Plastic deformations: 1mm Gap

Inside

Outside

Two plastic deformation regions:1) At the interface on the outside surface2) In the center of the joint

Average Strain: 2%Max Strain: 10%

1

2


Conclusions

In-situ characterization by optical measurement & inverse numerical method: Versatile & powerfull:

real joints (geometry & processing) highly heterogeneous stress fields in test specimens

Can determine real constitutive properties from constrained materials:

provide geometry-independant mechanical properties ideal for further modelling & optimization of joints / packages

A general tool for characterization of small size & thin layer materials produced with realistic processing and geometry conditions


Conclusions

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

In the present case, ult. stress decreases by 13% from 2 mm to 0.2 mm joints due to increased porosity in thinner joints.

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

Constraining effects: Constraining effects are size dependant ~(1/Gap)0.6

Up to 37% of additionnal hardening due to constraints Constrained & constitutive properties are NOT equivalent Apparent stress-strain curves are geometry dependant !!


Future developments

Constraining & size effects: Microstructure analysis /

measure porosity Additionnal test with 0.1mm

and 2mm gap widths Improvement of manufacturing

quality / porosity Industrial aspects:

Apply the in-situ characterization method (DIC / mixed num./exp. Identification) to a real industrial 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


STSM: ESPI measurements

Pr. Karalekas, Univ. Piraeus, Greece, STSM at EPFL

Incremental loading by step of 9 microns

Measurement of global incremental displacement field by phase difference between the n-th & n+1-th load state

Reconstruction of the total displacement field by summation of the increments

Theoretical sensitivity: ~ 0.7 microns


Results: sp1, 0.2mm joint, global view

20 mm


Results: sp1, 0.2mm joint, displ. distrib.


Results: sp1, 0.2mm joint, strain distrib.


Results: 0.2mm joint, local view

0.2mm


Results: sp3, 1mm joint, displ. distrib.


Results: sp3, 1mm joint, strain distrib.


Results: stress-strain curves

Constrained stress-strain curve, 0.2 mm gap

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 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Strain (-)

Str

ess

(Pa) J7C-A

J7C-B

J7C-C

J8C-B

ESPI SP1

ESPI SP2


ESPI measurement for joints

+ Sensitivity independant

from magnification: excellent for global observations

Full field measurement Monitoring of the damage

evolution

- Decorrelation when

increasing magnification: not suitable for local measurements

Very sensitive to out of plane displacements: decorrelates

Incremental loading not suitable with creep

In general: difficult to master, takes a lot of time

j.cugnoni, [email protected] 1 constraining and size effects in lead-free solder joints j....

Documents

solder joints solder

constrained solder

solder constitutive

real solder joints

plastic deformation

constraining effects

geometrical effects

stress field