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Constraining and size effects in lead-free solder joints

Constraining and size effects in lead-free solder joints. J. Cugnoni 1 , J. Botsis 1 , J.Janczak 2 1 Lab. Applied Mechanics & Reliability, EPFL, Switzerland 2 Füge- und Grenzflächentechnologie, EMPA, Switzerland. Outline. Introduction Global project & goals Constraining effects

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Constraining and size effects in lead-free solder joints

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  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, joel.cugnoni@epfl.ch

  2. 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, joel.cugnoni@epfl.ch

  3. Nature of Irreversible Deformations Objectives Global Project Interface Micro Structure ConstitutiveEquations Thermo-mechanical History Size / ConstrainingEffects Manufacturing Deformation & damage of lead-free solder joints • Plastic constitutive law of Sn-4.0Ag-0.5Cu solder • Variable solder gap width • Effects of constraints • Effects of size ? J.Cugnoni, joel.cugnoni@epfl.ch

  4. Rigid substrates: - impose lateral stresses at the interfaces - additionnal 3D stresses => apparent hardening => constraining effects Plastic deformation of solder: - constant volume - shrinks in lateral directions Solder joint in tension: - stiff elastic substrates - plastic solder (n~=0.5) Constraints in solder joints J.Cugnoni, joel.cugnoni@epfl.ch

  5. FEM Cu Cu Solder Stress field in constrained solder s11 s22 Front surface view 47 MPa 76 MPa 37 MPa 70 MPa Mid-plane view J.Cugnoni, joel.cugnoni@epfl.ch

  6. FEM Cu Cu Solder Stress field in constrained solder Von Mises eq. stress Hydrostatic pressure Front surface view 54 MPa -47 MPa 58 MPa -37 MPa Mid-plane view J.Cugnoni, joel.cugnoni@epfl.ch

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

  8. Methodology In-situ characterization of constitutive parameters Experimental SpecimenProduction TensileTest (DIC) Experimental Load - Displacement Curve Apparent Stress-Strain Curve (Constrained) Constraining Effects Identification Loop Optimization (Least Square Fitting) Stress - Strain Constitutive Law (Unconstrained) Geometry & ConstitutiveModel FEM Simulated Load - Displacement Curve Numerical Simulations J.Cugnoni, joel.cugnoni@epfl.ch

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

  10. ~ +/- 5% scatter => averaging Constrained stress-strain curves J.Cugnoni, joel.cugnoni@epfl.ch

  11. Similar results No clear conclusion Constrained stress-strain curves Identify constitutive properties Stress (Pa) Strain (-) J.Cugnoni, joel.cugnoni@epfl.ch

  12. Imposed displacement & calculated load Cu Simulated load-displacement curve Sn-Ag-Cu Elongation of solder Finite Element Modelling • 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: J.Cugnoni, joel.cugnoni@epfl.ch

  13. 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, joel.cugnoni@epfl.ch

  14. Load - displacement curves Blue: initial load-displ. curve Red: identified load-displ. curveBlack: measured load-displ. curve Relative errors Inverse identification • 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 J.Cugnoni, joel.cugnoni@epfl.ch

  15. Identified constitutive parameters Mechanical properties decreasing for smaller joints due to a visible increase of the porosity: Manufacturing process is also size dependant !! J.Cugnoni, joel.cugnoni@epfl.ch

  16. 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 ?? J.Cugnoni, joel.cugnoni@epfl.ch

  17. + 16 % Constraining effects 2 mm J.Cugnoni, joel.cugnoni@epfl.ch

  18. + 22 % Constraining effects 1 mm J.Cugnoni, joel.cugnoni@epfl.ch

  19. + 30 % Constraining effects 0.5 mm J.Cugnoni, joel.cugnoni@epfl.ch

  20. + 37 % Constraining effects 0.2 mm J.Cugnoni, joel.cugnoni@epfl.ch

  21. decrease of yield & ultimate stress ~7-8 MPa Size effects increase of constraining effects ~ 10 MPa J.Cugnoni, joel.cugnoni@epfl.ch

  22. Constraining effects / gap Constraining effects: ~~ (1/Gap)0.6 R Gap (mm) J.Cugnoni, joel.cugnoni@epfl.ch

  23. 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, joel.cugnoni@epfl.ch

  24. 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, joel.cugnoni@epfl.ch

  25. 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, joel.cugnoni@epfl.ch

  26. Realistic Experiment (DIC) Mixed num-expidentification: realistic properties Design / processvalidation FE Analysis & optimization 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) J.Cugnoni, joel.cugnoni@epfl.ch

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

  28. Results: sp1, 0.2mm joint, global view 20 mm J.Cugnoni, joel.cugnoni@epfl.ch

  29. Results: sp1, 0.2mm joint, displ. distrib. J.Cugnoni, joel.cugnoni@epfl.ch

  30. Results: sp1, 0.2mm joint, strain distrib. J.Cugnoni, joel.cugnoni@epfl.ch

  31. Results: 0.2mm joint, local view 0.2mm J.Cugnoni, joel.cugnoni@epfl.ch

  32. Results: sp3, 1mm joint, displ. distrib. J.Cugnoni, joel.cugnoni@epfl.ch

  33. Results: sp3, 1mm joint, strain distrib. J.Cugnoni, joel.cugnoni@epfl.ch

  34. Results: stress-strain curves J.Cugnoni, joel.cugnoni@epfl.ch

  35. + 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 ESPI measurement for joints J.Cugnoni, joel.cugnoni@epfl.ch

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