A phase field model for the motion of prismatic dislocation loops by both climb and self-climb

Abstract

We study the sharp interface limit and the existence of weak solutions of a phase field model for climb and self-climb of prismatic dislocation loops in periodic settings. The model is set up in a Cahn–Hilliard/Allen–Cahn framework featured with degenerate phase-dependent diffusion mobility with an additional stabilizing function. Moreover, a nonlocal climb force is added to the chemical potential. We introduce a notion of weak solutions for the nonlinear model. The existence result is obtained by approximations of the proposed model with nondegenerate mobilities. Lastly, the numerical simulations are performed to validate the phase field model and the simulation results show a big difference for the prismatic dislocation loops in the evolution time and the pattern with and without self-climb contribution.