1 Deformation and damage of lead free materials and joints J. Cugnoni*, A. Mellal*, Th. J. J. Botsis* * LMAF / EPFL EMPA Switzerland Project funded by OFES (CH) Cost 531 Mid-Term Meeting, Lausanne,

LMAF / EPFL 2 Objectives and tasks Objectives: Manufacturing Size / Constraining Effects Thermo- mechanical History Micro Structure Interface Nature of Irreversible Deformations Constitutive Equations

LMAF / EPFL 3 Validation and Comparison with SnPb Complete Characterization of SnAgCu Investigations on Size Effects Effects of Constraints Objectives and tasks Modelling Experimental Finite Element Model Constitutive Law Type Mixed Num. / Exp. Identification Micro Structure Analysis Optical Strain Measurement Design of Experiments

LMAF / EPFL 4 Mechanical characterization Elasto-plastic constitutive law : Characterization: should be carried out on real solder joints (size and constraining effects) should be carried out on real solder joints (size and constraining effects) temperature, strain rate and joint thickness are independent parameters and must be changed temperature, strain rate and joint thickness are independent parameters and must be changed a correlation between thermal history, microstructure and constitutive behaviour must be found a correlation between thermal history, microstructure and constitutive behaviour must be found

LMAF / EPFL 5 Lead-free solders specimens Bulk solder specimen: Solder bar from manufacturer glued in special fixtures, 25 x 6 mm cylinder Solder bar from manufacturer glued in special fixtures, 25 x 6 mm cylinder Idealized joint specimen: Dimension: 120 x 20 x 1 mm, joint thickness from 0.1 to 1 mm Dimension: 120 x 20 x 1 mm, joint thickness from 0.1 to 1 mm Solder: ECOREL Sn-4.0Ag-0.5Cu Solder: ECOREL Sn-4.0Ag-0.5CuProduction: joint cast in a special fixture, temperature cycle: heated at 40 K/min up to melting point, held 60s in liquid phase, and then rapid cooling of the jig (water). joint cast in a special fixture, temperature cycle: heated at 40 K/min up to melting point, held 60s in liquid phase, and then rapid cooling of the jig (water).

LMAF / EPFL 6 Mechanical characterization of constrained joints Objectives characterize the stress - strain law of lead- free solders in a real joint (constrained) characterize the stress - strain law of lead- free solders in a real joint (constrained) optical strain measurement technique to measure the real strains of the solder only (not the average strains of the joint) optical strain measurement technique to measure the real strains of the solder only (not the average strains of the joint) Optical measurement technique a grid of fine dots (pitch = 0.2 mm) glued on the surface or the natural pattern of the material is used a grid of fine dots (pitch = 0.2 mm) glued on the surface or the natural pattern of the material is used the deformation of the surface pattern is observed through a microscope (24x) and recorded by a high resolution video camera (1.3 MPixels) at 1 frame per second the deformation of the surface pattern is observed through a microscope (24x) and recorded by a high resolution video camera (1.3 MPixels) at 1 frame per second custom made video extensometry (Matlab) by motion tracking based on a Normalized Cross Correlation (NCC) or Digital Image Correlation (DIC) algorithm custom made video extensometry (Matlab) by motion tracking based on a Normalized Cross Correlation (NCC) or Digital Image Correlation (DIC) algorithm Resolution: displacement 0.2  m, strain 0.01% Resolution: displacement 0.2  m, strain 0.01%

LMAF / EPFL 7 Bulk solder properties Preliminary results: specimens of pure solder produced in several ways specimens of pure solder produced in several ways important effects of thermal history and processing important effects of thermal history and processing properties must be characterized "in-situ" properties must be characterized "in-situ"

LMAF / EPFL 8 Mechanical characterization of constrained joints Preliminary results: Solder joint properties showing the constraining effects: Solder joint properties showing the constraining effects: Yield stress, ultimate stress and ultimate strain are modified by the constraints Properties must be determined in the most realistic conditions Crack !

LMAF / EPFL 9 Cracking

10 A first modelling approach The elasto-visco-plastic model (Garofalo) of classical lead solders (Shi et al., 1999 ) has been adapted to lead-free solders: yield stress and Young's modulus adjusted for lead-free solders yield stress and Young's modulus adjusted for lead-free solders hardening parameters from the classical lead solders hardening parameters from the classical lead solders Young modulus (GPa) Poisson’s ratio Elastic behavior Plasticity Yield stress = 32.5 (MPa) Linear hardening up to rupture: Ultimate stress = 33 (MPa) Ultimate strain = 0.02 (-) Creep behavior A = (sec -1 ) B = (MPa -1 ) n = 3.3 Q = (J mol -1 ) R=8.314 (J mol -1 K -1 )

LMAF / EPFL 11 A first modelling approach Finite element simulation of real experiments to test the "adjusted" constitutive law: modelling of both copper and solder joint modelling of both copper and solder joint real recorded (extensometer) displacements are applied to the FEM => simulated loads real recorded (extensometer) displacements are applied to the FEM => simulated loads Constitutive law shows a good agreement with experiments for thick joints (1mm) but must be improved for thin joints (0.15 mm) Constitutive law shows a good agreement with experiments for thick joints (1mm) but must be improved for thin joints (0.15 mm)

LMAF / EPFL 12 Bulk solder properties? Finite element model of an ideal joint based on the constitutive law of the bulk solder specimen (Abaqus) Plastic law: Von Mises yield surface, exponential hardening

LMAF / EPFL 13 Plastic strain field

LMAF / EPFL 14 Von Mises stress field

LMAF / EPFL 15 Bi-axial stresses Bi axial stress ratio:  11 /  22 Elastic Plastic

LMAF / EPFL 16 Constitutive law and constraints Effects of the constraints: Non-uniform, bi-axial, plasticity dependent, stress field in the solder Non-uniform, bi-axial, plasticity dependent, stress field in the solder Constitutive law Apparent stress - strain law Independant of constraints, but may depend on characteristic size Depends on constraints (geometry, base materials) Constraining effects

LMAF / EPFL 17 Mixed num./exp. identification Identify constitutive properties even with very complex stress / strain field => use a finite element model instead of a simple analytical solution Mixed num. / exp. identification of the constitutive parameters Initial guess x = x 0 Numerical Solution S num (x) Identified parameters x Experimental data S exp Error norm  (S num,S exp ) Parameter updating x ( minimization of  )  >  min  <  min DIC measurement (Matlab) : load - displacement curve Non linear least squares optimization (Matlab Optim Toolbox) Parametric FEM (Matlab - Abaqus) Bulk solder data

LMAF / EPFL 18 Convergence

LMAF / EPFL 19 Initial guess / identified solution Initial guessIdentified solutionParam  0 (MPa) Q inf (MPa) b (-) Initial Final Execution time ~ 1h, ~ 50 FE solutions We can determine the real constitutive parameters of the solder inside a constrained joint

LMAF / EPFL 20 Future work Characterization of the solder Identify the elasto-visco-plastic constitutive parameters with our mixed numerical-experimental identification procedure and an optical strain measurement Identify the elasto-visco-plastic constitutive parameters with our mixed numerical-experimental identification procedure and an optical strain measurement at a given strain rate and room temperature, with variable joint thickness (size / constraining effects) at different strain rates and temperatures investigate the constraining and size effects Comparison with bulk solder properties at different strain rates / temperatures Comparison with bulk solder properties at different strain rates / temperatures Microstructure evolution (in collaboration with EMPA, Switzerland) Correlate the mechanical properties with the microstructure of the solder Correlate the mechanical properties with the microstructure of the solder Evaluate the evolution of micro structure and mechanical properties in function of the thermal history Evaluate the evolution of micro structure and mechanical properties in function of the thermal history