Accuracy and convergence of parametric dislocation dynamics

Abstract

In the parametric dislocation dynamics (PDD), closed dislocation loops are described as an assembly of segments, each represented by a parametric space curve. Their equations of motion are derived from an energy variational principle, thus allowing large-scale computer simulations of plastic deformation. We investigate here the limits of temporal and spatial resolution of strong dislocation interactions. The method is demonstrated to be highly accurate, with unconditional spatial convergence that is limited to distances of the order of interatomic dimensions. It is shown that stability of dislocation line shape evolution requires very short time steps for explicit integration schemes, or can be unconditionally stable for implicit time integration schemes. Limitations of the method in resolving strong dislocation interactions are established for the following mechanisms: dislocation generation, annihilation, dipole and junction formation, pileup evolution.