Morphological evolution of grain boundaries under lateral strains

Abstract

A theory for the lateral strain-induced grain boundary instability is proposed by considering two crucial factors, namely, the dependence of the boundary energy on coincidence sites and the differences in elastic responses of the grain and the boundary regions. In contrast to the Asaro-Tiller-Grinfeld instability, where strains, however small, lead to breakup of the interfaces and the amplitudes of the perturbations are only a function of wavelength and time, we find that there exists a critical strain for the grain boundary instability to occur which is due to the periodicity of coincidence site lattices, and the growth rate of perturbations is dependent on the amplitude. These theoretical predictions are validated by the phase field crystal simulations in two dimensions. In addition, the amplitude-dependent growth rate gives rise to two distinct outcomes for the late stage evolution predicted by the proposed theory, namely, the grain boundary structural transformation and the dislocation emission, as seen in the phase field crystal simulations. Not only is the predicted oscillatory behavior of the growth rate observed in simulations, but also the phase diagram predicted by the theory is in quantitative agreement with the phase field crystal simulations.