constraining and size effects in lead-free solder joints
DESCRIPTION
Constraining and size effects in lead-free solder joints. J. Cugnoni 1 , J. Botsis 1 , V. Sivasubramaniam 2 , J. Janczak-Rusch 2 1 Lab. Applied Mechanics & Reliability, EPFL, Switzerland 2 Füge- und Grenzflächentechnologie, EMPA, Switzerland. Nature of Irreversible Deformations. Objectives. - PowerPoint PPT PresentationTRANSCRIPT
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
J.Cugnoni, [email protected] 2
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
J.Cugnoni, [email protected] 3
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
J.Cugnoni, [email protected] 4
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
J.Cugnoni, [email protected] 5
Stress field in constrained solder
11 22Front surface
view
Mid-plane view
Cu
Cu
Solder
FEM47 MPa 76 MPa
70 MPa37 MPa
J.Cugnoni, [email protected] 6
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
J.Cugnoni, [email protected] 7
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
J.Cugnoni, [email protected] 8
Parametric FE study: Results
=> 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
J.Cugnoni, [email protected] 9
Parametric FE study: Results
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.
J.Cugnoni, [email protected] 10
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
J.Cugnoni, [email protected] 11
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
J.Cugnoni, [email protected] 12
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
J.Cugnoni, [email protected] 13
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
J.Cugnoni, [email protected] 14
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
J.Cugnoni, [email protected] 15
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
J.Cugnoni, [email protected] 16
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
J.Cugnoni, [email protected] 17
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
J.Cugnoni, [email protected] 18
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 !!
J.Cugnoni, [email protected] 19
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 %
J.Cugnoni, [email protected] 20
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
Constraining effects 1.2 mm
+ 22 %
J.Cugnoni, [email protected] 21
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
Constraining effects 0.7 mm
+ 30 %
J.Cugnoni, [email protected] 22
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
Constraining effects 0.5 mm
+ 37 %
J.Cugnoni, [email protected] 23
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
Constraining effects 0.25 mm
+ 78 %
J.Cugnoni, [email protected] 24
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
J.Cugnoni, [email protected] 25
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
J.Cugnoni, [email protected] 27
Damage mechanisms
Thick Joint G>1= small triaxiality
FE model
Fractography
DIC measurements
plastic damage & void growth in center => crack
J.Cugnoni, [email protected] 28
Damage mechanisms
Thin joint G<0.5= High triaxiality
FE model
DIC measurements
Fractographyvoid growth& crack at interface
J.Cugnoni, [email protected] 29
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
J.Cugnoni, [email protected] 30
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
J.Cugnoni, [email protected] 31
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