Chemo-thermo-mechanically Coupled Crystal Plasticity Simulation of Stress Evolution in Thermally Strained β-Sn Films

Abstract

Whisker formation in tin films is a mode of stress relaxation, but the exact conditions causing them are yet to be established. In this work, a three-dimensional full-field chemo-thermo-mechanically coupled crystal plasticity simulation of thermally strained tin films was performed to evaluate the stress evolution and connect it to the redistribution of vacancies. Spatial heterogeneity in the hydrostatic stress along the grain boundary network (that served as the primary conduit for mass transport) was observed, which became more homogeneous towards the film surface. Normal and shear tractions on the columnar grain boundaries were evaluated as they might be crucial to breaking of the oxide layer (formed on the film surface) especially when inclined grain boundaries are present. With such an advanced multi-physics framework, several crystallographic and geometrical factors influencing whisker formation can be analyzed thereby leading to a better understanding of the factors modulating the nucleation and growth of such whiskers.