1. Constraining and size effects in lead-free solder joints
J. Cugnoni1, J. Botsis1, J.Janczak2
1 Lab. Applied Mechanics & Reliability, EPFL, Switzerland
2 Füge- und Grenzflächentechnologie, EMPA, Switzerland
J.Cugnoni,

2. J.Cugnoni, joel.cugnoni@epfl.ch
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
J.Cugnoni,

3. Deformation & damage of lead-free solder joints
Objectives
Plastic constitutive law of Sn-4.0Ag-0.5Cu solder
Variable solder gap width
Effects of constraints
Effects of size
Manufacturing
Size / Constraining Effects
Thermo- mechanical History
Micro Structure
Interface
Nature of Irreversible Deformations
Constitutive Equations
Global Project ?
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4. Constraints in solder joints
Plastic deformation of
solder:
- constant volume
- shrinks in lateral directions
Rigid substrates:
- impose lateral stresses at the interfaces
- additionnal 3D stresses
=> apparent hardening
=> constraining effects
Solder joint in tension:
- stiff elastic substrates
- plastic solder (n~=0.5)
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5. Stress field in constrained solder
Front surface
view
47 MPa
76 MPa Cu
Solder
FEM
37 MPa
70 MPa
Mid-plane view
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6. Stress field in constrained solder
Von Mises
eq. stress
Hydrostatic pressure
Front surface
view
54 MPa
-47 MPa Cu
Solder
FEM
58 MPa
-37 MPa
Mid-plane view
J.Cugnoni,

7. Constitutive law & constraints
Effects of the constraints:
Non-uniform, tri-axial, plasticity dependent, stress field in the solder
Constitutive law of the solder
Independant of geometry, but may depend on characteristic size & porosity
Constraining effects
Apparent stress - strain law of the solder confined in a joint
Depends on constraints (geometry, base materials)
J.Cugnoni,

8. Constitutive law & constraints
3D FEM: includes all the geometrical effects
Apparent stress - strain curve of the solder in a joint
is what we usually measure
depends on geometry
Constitutive law of the solder
is needed for FE simulations
independent of geometry
Inverse numerical identification of a 3D FEM
???
J.Cugnoni,

9. In-situ characterization
Mechanical properties of lead-free solder materials can be process, geometry & size dependant
In-situ characterization of the mechanical properties in real solder joints can provide accurate data for modelling and optimization of solder joints
Stress / strain fields inside real solder joints are very heterogeneous and classical characterization techniques are not suitable (no analytical solution)
By combining the advantages of finite element modelling and in-situ optical strain measurement (digital image correlation), a novell inverse numerical identification procedure can be used to extract accurate constitutive properties of the solder material from a real constrained solder joint
J.Cugnoni,

10. Methodology In-situ characterization of constitutive parameters
Experimental
Specimen Production
Tensile Test (DIC)
Experimental
Load - Displacement
Curve
Apparent
Stress-Strain Curve
(Constrained)
Constraining
Effects
Identification Loop
Optimization
(Least Square
Fitting)
Stress - Strain
Constitutive Law
(Unconstrained)
Geometry &
Constitutive Model
FEM
Simulated
Load - Displacement
Curve
Numerical Simulations
J.Cugnoni,

11. J.Cugnoni, joel.cugnoni@epfl.ch
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 mm/s
Digital Image Correlation:
1.3MPix CCD camera
30x optical microscope
3x2 mm observation region
Displacement resolution 0.2 mm
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12. Constrained stress-strain curves
~ +/- 5% scatter
=> averaging
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13. Constrained stress-strain curves
Similar results
No clear conclusion
Identify
constitutive
properties
Stress (Pa)
Strain (-)
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14. Finite Element Modelling
Imposed displacement & calculated load
3D FEM of 1/8th of the specimen
Copper:
Elastic behaviour:
ECu = 112 GPa, n = 0.3
Solder:
Elasto-plastic with isotropic exponential & linear hardening
Chosen to fit bulk solder plastic response
5 unknown parameters: Cu
Sn-Ag-Cu
Simulated load-displacement curve
Elongation of solder
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15. Inverse identification procedure
Identification parameters:
Objective function: relative difference of load-displ. curves
with Pexp = measured load-displacement curve
and Pnum(a) = simulated load-displacement curve
Levenberg-Marquardt non-linear least square optimization algorithm to solve:
Gradients of objective function by Finite Differences
J.Cugnoni,

16. Inverse identification
Blue: initial load-displ. curve
Red: identified load-displ. curve Black: measured load-displ. curve
Load - displacement curves
Relative errors
Solution time:
4 iterations / 50 FE solutions required to identify the material properties (~1h30)
Accuracy:
max error +/-4% on load – displacement curve
Convergence
Very robust convergence even with bad initial guess of the parameters
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17. Identified constitutive parameters
Mechanical properties decreasing for smaller joints
due to a visible increase of the porosity:
Manufacturing process is also size dependant !!
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18. 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
Porous metal constitutive law ??
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19. Constraining effects 2 mm
+ 16 %
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20. Constraining effects 1 mm
+ 22 %
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21. Constraining effects 0.5 mm
+ 30 %
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22. Constraining effects 0.2 mm
+ 37 %
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23. Size effects decrease of yield & ultimate stress ~7-8 MPa
increase of constraining effects ~ 10 MPa
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24. Constraining effects / gap
Gap (mm)
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25. Plastic deformations: 1mm Gap
Average Strain: 2% Max Strain: 10% 1
Outside
Inside
Two plastic deformation regions:
At the interface on the outside surface
In the center of the joint 2
J.Cugnoni,

26. J.Cugnoni, joel.cugnoni@epfl.ch
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
J.Cugnoni,

27. J.Cugnoni, joel.cugnoni@epfl.ch
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 !!
J.Cugnoni,

28. Constraining & size effects:
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)
Mixed num-exp identification: realistic properties
Design / process validation
FE Analysis & optimization
J.Cugnoni,

29. 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
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30. Results: sp1, 0.2mm joint, global view
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31. Results: sp1, 0.2mm joint, displ. distrib.
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32. Results: sp1, 0.2mm joint, strain distrib.
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33. Results: 0.2mm joint, local view
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34. Results: sp3, 1mm joint, displ. distrib.
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35. Results: sp3, 1mm joint, strain distrib.
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36. Results: stress-strain curves
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37. 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,