Micromechanical model for describing intergranular fatigue cracking in a lead-free solder alloy

Abstract

Solder joints possess a small thickness of the order of a few grains but they remain one of the key concerns in thermo-mechanical reliability of high-power electronic systems. Fatigue lifetime of solder joints subjected to thermal and mechanical loading cycles is generally predicted based on phenomenological and macroscopic fatigue models that use the effective material properties as inputs. Such semi-empirical models will thus only provide a gross estimation of the engineering lifetime for some specific boundary and loading conditions while ignoring the deformation mechanisms at micro-scale. Microscopic analysis of fractured solder joints points rather to crack propagation at grain boundaries. Therefore, a 3D microstructure-informed model is developed in this study for reproducing the intergranular fatigue crack in the solder joint of a power module. The submodeling technique has been applied in order to only investigate the critical zone of the solder joint. A global model of the whole module is first simulated to obtain the inputs for a submodel focused on the zone of interest where failure is expected to develop. The submodel simultaneously makes use of the cohesive zone and the crystal plasticity theories to represent decohesion at grain boundaries and plastic slips in the grains of the solder joint, respectively. The needed crystal plasticity parameters were fitted out with the help of the Berveiller-Zaoui homogenization scheme using experimental data, while the parameters for the cohesive zone model were estimated from some physical quantities. Simulations of repeated thermo-mechanical loading on the power module demonstrate how cracking occurs at grain boundaries in the solder joint of the submodel. In addition, it is shown that the crack propagation rate is almost constant during the whole loading time. This suggests an ability of the present approach to give a fatigue lifetime estimate for the entire solder joint by extrapolating some specific computed quantities from the local model.