Dislocation-density dynamics for modeling the cores and Peierls stress of curved dislocations

Abstract

Although continuum dislocation models can describe dislocation cores, they are generally incapable of describing the Peierls stress, due to the invariance of the misfit energy and a lack of means to trigger configurational changes in the dislocation core as the dislocation moves. In this work, a dislocation-density dynamics framework for modeling dislocations at an 'intensive' resolution scale finer than the dislocation core is established. In this approach, the inter-dislocation elastic interaction is accounted for via Mura's formula after singularity removal, and the interaction within the dislocation core is modeled by introducing a phenomenological formalism of the lattice misfit stress to balance the elastic interaction between dislocation contents, leading to not only a stable width of the dislocation as it travels, but also the expected Peierls stress. This framework is implemented numerically by using a divergence-preserving finite-volume method for curved dislocations gliding on 2D slip planes in general. Simulation examples of various dislocation mechanisms, including shrinkage and expansion of dislocation loops, the Frank-Read source, and Orowan looping, are given. The simulated results exhibit excellent preservation of continuity of dislocation densities during their evolution, while the detailed core structures and Peierls stress are clearly elucidated.