Continuum model for dislocation dynamics in a slip plane

In this paper, we present a continuum model for dislocation dynamics in a slip plane, which accurately incorporates both the long-range interaction and the local line tension effect of dislocations. Unlike the continuum models in the literature using dislocation densities, we use the disregistry across the slip plane to represent the continuous distribution of dislocations in the slip plane, which has the advantage of including the orientation dependence of dislocations in a very simple way. The continuum dislocation dynamics model is validated by linear instability analysis of a uniform dislocation array to small perturbations and comparisons of the results with those of the discrete dislocation dynamics model. Numerical examples for the evolution of distributions of dislocations and plastic slips in a slip plane are presented.