Application of phase field microelasticity theory of phase transformations to dislocation dynamics: Model and three-dimensional simulations in a single crystal

A three-dimensional (3D) multi-dislocation system in an elastically anisotropic crystal under applied stress is considered as a particular case of the phase field microelasticity theory of multivariant stress-induced martensitic transformations. This approach reduces the problem of evolution of a dislocation system to a solution of the nonlinear integrodifferential Ginzburg-Landau equation. In this formalism, the elastic interaction between dislocations is taken into account through exact analytical solution of the elasticity problem. The dislocation reactions, such as multiplication/annihilation, are taken into account automatically. The dislocations are 'free' to choose the optimal evolution path. Examples of 3D computer simulation of dislocation dynamics are considered.