J.Cugnoni, 1 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

J.Cugnoni, Deformation & damage of lead-free solder joints Manufacturing Size / Constraining Effects Thermo- mechanical History Micro Structure Interface Nature of Irreversible Deformations Constitutive Equations 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, Constraints in solder joints Solder joint in tension: - stiff elastic substrates - plastic solder ( ~=0.5) 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

J.Cugnoni, 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 = (  u joint -  u solder ) /  u solder triaxiality ratio R = p /  m g w L t

J.Cugnoni, Stress field in constrained solder  11  22 Front surface view Mid-plane view Cu Solder FEM 47 MPa76 MPa 70 MPa37 MPa

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

J.Cugnoni, Parametric FE study: Results => Constraining effects are due to the the triaxiality of the stress field in the solder induced by the substrate

J.Cugnoni, Parametric FE study: Results => Constraining effects are inversely proportionnal to the gap to thickness ratio G (asymptotic effect in the form of 1/G)

J.Cugnoni, Parametric FE study: Results 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, 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, In situ characterization method Specimen Production Tensile Test (DIC) GeometryFEM Experimental Load - Displacement Curve Simulated Load - Displacement Curve Apparent engineering stress-strain response of the joint Optimization (Least Square Fitting) Constitutive stress-strain law of the solder Identification Loop Constraining Effects Experimental In-situ characterization of constitutive parameters Numerical Simulations

J.Cugnoni, 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, 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) mm

J.Cugnoni, 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, Constrained stress-strain curves Similar results for G > 0.5 Identify constitutive properties Clear hardening for G < 0.5 Constraining & scale effects => can't compare these curves

J.Cugnoni, Finite Element Modelling 3D FEM of 1/8th of the specimen Copper:  Elastic behaviour: E Cu = 112 GPa,  = 0.3 Solder:  Elasto-plastic with isotropic exponential & linear hardening  Chosen to fit bulk solder plastic response  5 unknown parameters: Cu Sn-Ag-Cu Elongation of solder Imposed displacement from testing Simulated load- displacement curve

J.Cugnoni, Inverse identification procedure Identification parameters: Objective function  (  ):  difference of measured and simulated load-displacement curves non-linear least square optimization algorithm to solve: Blue: initial load-displ. curve Red: 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, 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 specimen Bulk specimen appears much softer !! In-situ characterization !!

J.Cugnoni, Constraining effects 2.4 mm + 15 %

J.Cugnoni, Constraining effects 1.2 mm + 22 %

J.Cugnoni, Constraining effects 0.7 mm + 30 %

J.Cugnoni, Constraining effects 0.5 mm + 37 %

J.Cugnoni, Constraining effects 0.25 mm + 78 %

J.Cugnoni, Size effects decrease of yield & ultimate stress ~10 MPa constraining effects ~ 35 MPa

J.Cugnoni, Microstructure & Fractography Microstructure before testing Fractography 2.4mm 0.7mm0.5mm (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, Constraining effects / gap Q = (  u joint -  u solder ) /  u solder Constraining effects Q: ~1/G

J.Cugnoni, Damage mechanisms Thick Joint G>1 = small triaxiality FE model Fractography DIC measurements plastic damage & void growth in center => crack

J.Cugnoni, Damage mechanisms Thin joint G<0.5 = High triaxiality FE model DIC measurements Fractography void growth & crack at interface

J.Cugnoni, 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, 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, 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 / process validation FE Analysis & optimization Mixed num-exp identification: realistic properties