Phase field microelasticity theory of dislocation dynamics in a polycrystal: model and three-dimensional simulations

A three-dimensional multidislocation system in a polycrystal under applied stress is treated as a particular case of the phase field microelasticity theory of multivariant stress-induced martensitic transformations in polycrystals. This approach reduces the problem of the evolution of a dislocation system to a solution of the nonlinear integrodifferential Ginzburg-Landau equation. In this formalism, the elastic interaction between dislocations and the elastic coupling between grains are taken into consideration through exact analytical solution of the elasticity problem. The dislocation reactions, such as multiplication and annihilation, are taken into account automatically. The dislocations are 'free' to choose the optimal evolution path. Examples of three-dimensional computer simulations are considered.