Deformation & damage of lead-free solder joints COST 531 Final Meeting, 17th-18th May 2007, Vienna 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

Outline Overview of the project: Global goals & achievements Global goals & achievements Methods & developments: Experimental techniques Experimental techniques Modelling Modelling Key results Elasto-plastic characterization of SAC405 Elasto-plastic characterization of SAC405 Constraining & size effects Constraining & size effects Ductile failure: effect of voids Ductile failure: effect of voidsFuture Bridging the length scales & the disciplines Bridging the length scales & the disciplines

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 Size & constraining effects Tensile / shear joints Tensile / shear joints Effect of microstructure: Effect of porosity content Effect of porosity content Failure mechanisms: Ductile fracture Ductile fracture Studied system: SAC 405 / Cu substrates SAC 405 / Cu substrates

Methods & developments: overview Elasto-plastic characterization of SAC 405 Effects of voids on the reliability of joints Investigations on Size Effects Effects of Constraints Modelling Experimental Finite Element Model Constitutive Law Type Inverse Num. / Exp. Identification Micro Structure Analysis Optical Strain Measurement Design of Experiments

Key results: overview Manufacturing Size / Constraining Effects Thermo- mechanical History Micro Structure Interface Nature of Irreversible Deformations Constitutive Equations Global Project

Thoughts about the future…. Short term: Time / temperature dependent properties. Interfacial failure: cohesive elements Mid-Long term: Bridging the length scales & disciplines Meso Micro Macro Thermodynamics, phase diagrams Diffusion, interfaces, solidification, microstructure Continuum mechanics, damage, fracture… Homogenization Solidification / diffusion simulation ? Need more transversal research !!

Tensile & shear specimens 9.5 mm 1 mm 2 mm 4 mm 8 mm g w L t Tensile specimen L=120 mm, w=20 mm, t=1mm, g=[0.25, 0.5, 0.75, 1.2, 2.4] mm Solder cross section = 20x1 mm2 Shear specimen joint cross section=2x2 mm2 Shear specimen L=120mm, joint cross section=2x2 mm2 Optimized for stress uniformity & simple manufacturing thickness=2mm

Digital Image Correlation & micro-level measurements Why optical strain measurements??  non-invasive measurements at a small scale DIC Principle: Determine displacement for max correlation btw reference & deformed states dx,dy r(x,y) d(x,y) Advantages: + Versatile & simple to setup + Robust in most cases Drawbacks: - Resolution limited by pixel size - Need a random pattern Reference imageDeformed image Applications: Local strain field measurements, small scale material characterization Finite Element validation & parameter identification Fracture analysis, damage evolution

Digital Image Correlation Why optical strain measurements??  non-invasive measurements at a small scale DIC algorithms developments: Tensile joints: Small strains, small translations Small strains, small translations High accuracy is needed High accuracy is needed Spatial Correlation with cubic spline resampling Spatial Correlation with cubic spline resampling Shear joints: Extremely large strains, large displacement Extremely large strains, large displacement Need excellent robustness Need excellent robustness Incremental FFT-based correlation Incremental FFT-based correlation Advantages / Drawbacks + Versatile & simple to setup + Versatile & simple to setup + Robust in most cases + Robust in most cases - Resolution limited by pixel size - Resolution limited by pixel size - Need a random pattern - Need a random pattern 4 mm

ESPI measurements (STSM, D. Karalekas) Work done with Dr.Karalekas,Univ. Piraeus, Greece during a STSM at EPFL Advantages: Sensitivity independant from magnification: excellent for global observations Sensitivity independant from magnification: excellent for global observations Full field measurement Full field measurementDrawbacks: Decorrelation Decorrelation Problems with creep tests Problems with creep testsApplication: Evaluate boundary conditions Evaluate boundary conditions Full field displacement measurement on assemblies Full field displacement measurement on assemblies 20 mm

DIC & shear testing: displacements => Extract the real boundary conditions for FE analysis & identification

DIC & shear testing: shear strain  xy

Finite Element modelling Modelling? why??  Models have the power of generalization of knowledge FE models Advantages: Versatility: Complex geometries, multi- components, multi-physics Ability to extrapolate knowledge gained on simple test cases to much more complex designs & geometries !! Multi-scale modelling (homogenization) Drawback: Requires an extensive & reliable set of parameters => huge characterization task Combining Experiments & Numerical simulation is of prime importance

Inverse num.-exp. identification Specimen Production Tensile Test (DIC) Geometry & Boundary Conditions FEM Experimental Load – Displacement / Stress-Strain response Simulated Load – Displacement / Stress-Strain response Global / local response of the specimen Optimization (Least Square Fitting) Modelling parameters: Constitutive law, failure model Identification Loop Geometric & structural effects Experimental In-situ characterization of constitutive parameters Numerical Simulations

Constraining effects: Tensile & shear solder joints

Constraints in tensile solder joints Solder joint in tension: - stiff elastic substrates - plastic solder ( ~=0.5) Plastic deformation of solder: - constant volume => solder shrinks in lateral directions Rigid substrates: - impose lateral stresses at the interfaces - hydrostatic stresses => apparent hardening => constraining effects

Parametric FE study: Results => Constraining effects are due to the the triaxiality (hydrostatic part) of the stress field in the solder induced by the substrate

Parametric FE study: Results Constraining effects are inversely proportionnal to the gap to thickness ratio G in tensile joints

Constraining effects : experimental results Q = (  u joint -  u solder ) /  u solder Constraining effects Q: ~1/G

Shear: constraining effects Parametric FE simulation of shear joint response Pure shear = isochoric deformation => no significant effects of constraints !!

Shear: Gap – ultimate stress relationship Shear: No significant effect of solder gap on ultimate stress

Apparent stress - strain response of the solder in a joint is what we usually measure depends on geometry Constitutive law & engineering response 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

Size effects: Tensile & Shear solder joints

Identified elasto-plastic law / size effects Mechanical properties decreasing for smaller joints: combination of scale effects & porosity Manufacturing process is also size dependant Tensile joints

Identified elasto-plastic law / size effects Tensile / shear joints: - similar elasto-plastic behaviours - similar size effects (manufacturing?) Shear joints Size effect

Deformation & damage mechanisms in lead-free solder joints

Microstructure & Fractography Microstructure before testing Fractography 2.4mm 0.7mm 0.5mm (vacuum) Pores: created during manufacturing and grow with plastic deformation introduces large scatter in experimental data => model void !! If porosity cannot be eliminated => Include it in models as a « random » variable

Porous metal plasticity: Gurson-Tvergaard model Porosity content is an internal variable of the model: f= density ratio = 1- void_fraction Yield surface Yield function without pores Hydrostatic pressure Effect of voids Evolution of porosity Growth Nucleation

Shear joint response & porous metal plasticity Plastic Yielding Void growth Void nucleation Ult. strain Changes in initial porosity %

Ductile failure simulation Porous metal plasticity model can 1.Predict the progressive ductile failure of metal up to rupture 2.Simulate shear band formation & localization 3.Introducing « random » initial porosity => statistical estimate of the failure strain in a given assembly Plastic Yielding Void growth Void nucleation Ult. strain