Modeling of intergranular thermal fatigue cracking of a lead-free solder joint in a power electronic module

Fatigue of lead-free solder joints remains the most critical concern in thermo-mechanical reliability of high power modules. Due to size miniaturization requirements, fatigue properties become strongly affected by features of the solder joint microstructure. Phenomenological fatigue models based on effective material properties at macro-scale only grossly predict the engineering lifetime for some specific boundary conditions while ignoring the important effects of the microstructural mechanisms of deformation. In this study, a 3D microstructure-informed model for reproducing the intergranular fatigue crack in the solder joint of a power module is developed. The submodeling technique is applied in order to investigate accurately the critical zone of the solder joint with reasonably reduced computational time. In the submodel, the anisotropic elasticity and crystal plasticity constitutive laws are integrated for the bulk grain material, while the decohesion at grain boundaries is modeled by the cohesive zone approach. The needed crystal plasticity parameters are calibrated using the Berveiller-Zaoui transition rule to fit tensile test data for the so-called InnoLot solder alloy, and physically-based concepts are used to estimate the cohesive zone parameters at the grain scale. Simulations demonstrate how fatigue cracking occurs and propagates at grain boundaries in the solder joint. A criterion is then presented to estimate the fatigue lifetime of the entire solder joint, based on specific quantities predicted numerically.