Simulation of dislocations on the mesoscopic scale. I. Methods and examples

Abstract

Peach–Koehler theory is implemented to simulate the motion of arbitrarily configured interacting dislocations, located on arbitrary glide planes and having any allowed Burgers vector. The self-interaction is regularized by a modified Brown procedure, which remains stable and loses accuracy in a well-controlled manner as atomic dimensions are approached. The method is illustrated by applying it to several examples of single and interacting dislocations in an fcc slip system. The critical strain for the propagation of a dislocation in a capped layer is calculated and found to be in excellent agreement with theory. Dislocations in a layer with a free surface are studied to test simplified methods for modeling the dislocation–surface interaction. Frank–Read sources are simulated in an infinite medium and in a strained layer. The latter are seen to give rise to the characteristic pileup structures often observed experimentally. The interaction between two initially straight dislocations on intersecting glide planes is studied as a function of relative angle and initial separation. It is found that an attractive instability occurs for a well-defined range of relative angles, and that this range depends only weakly on the initial separation. While this suggests that the detailed calculation of such interactions could be replaced by a simple set of interaction rules specifying their outcome, a variety of factors limiting the usefulness of such rules can be identified. It is further determined that, when an attractive instability occurs, the configuration assumed by the dislocations as they near each other bears little resemblance to any simple starting configuration. This suggests that calculations of the type presented here could provide a useful starting point for atomistic calculations of interacting dislocations.