Numerical simulation of dynamics of dislocation arrays and long-range stress fields of nonplanar dislocation arrays

We present a simulation method for the dynamics of dislocation arrays. In this numerical method, dislocation arrays are considered as continuous surfaces in three dimensions, and the level set representation is used for these dislocation array surfaces. The level set representation of the surfaces has the advantage of automatically handling the topological changes occurring during the evolution, and simple implementation using standard accurate finite difference schemes on a uniform grid. The driving force of the evolution of the dislocation array surfaces comes from both the long-range interaction of the constituent dislocations and their local curvature effect. The long-range interaction, which is expressed by a complicated integral over the whole dislocation array surface, is calculated efficiently using the fast Fourier transform (FFT) method. Simulations are performed for dislocation arrays bypassing different particles under applied stress and are compared with those of a single dislocation. The long-range nature of the stress fields of nonplanar infinite dislocation arrays is discussed, and is shown to be essentially different from that by a single dislocation. Examples also show that such long-range stress fields may contribute to the formation of inhomogeneities of dislocation distributions.