A full-field crystal plasticity study on how texture and grain structure influences hydrostatic stress in thermally strained β-Sn films

Abstract

The present study uses full-field thermo-mechanically coupled crystal plasticity to simulate the stress distribution in thermally strained β-Sn films to better understand the conditions causing the generally rare nucleation of whiskers from such films. Following the notion that stress-driven diffusion along the grain boundary network is leading to and supporting whisker formation, the goal is to identify critical factors of crystallographic and/or geometric nature that influence the hydrostatic stress in such films prior to the onset of actual whisker formation. Approximating the film as a periodic structure of around a hundred columnar grains on an isotropic substrate, the simulations reveal a strong spatial variation of hydrostatic stress over distances comparable to the grain size but without apparent long-range gradients, suggesting whisker nucleation to be a phenomenon that depends on specifics within a relatively small neighborhood of grains. Furthermore, neither the grain size distribution nor the presence of oblique surface grains alters the width of the stress distribution by much. In contrast, the variation of hydrostatic stress notably depends on the crystallographic texture of the film, where β-Sn films for which the film normal is aligned with ⟨0 0 1] show a narrower distribution than films with ⟨1 0 0] parallel to the normal. The former film texture, therefore, is predicted to be less prone to whisker formation than the latter.