On the dynamics of curved dislocation ensembles

TL;DR

This paper develops a systematic approach to derive the dynamics of curved dislocation systems in crystal plasticity, extending existing models for parallel edge dislocations to more complex curved configurations using a phase field formalism.

Contribution

It introduces a new method for deriving evolution equations for curved dislocation ensembles, incorporating a dipole approximation and generalizing phase field models.

Findings

Derived closed set of evolution equations for curved dislocation densities.

Extended phase field formalism to include curved dislocation dynamics.

Provided a framework for modeling complex dislocation systems in materials science.

Abstract

To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse-graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long standing issue if a similar procedure can be established for curved dislocation systems. An important prerequisite for such a theory has recently been established through a density-based kinematic theory of moving curves. In this paper, an approach is presented for a systematic derivation of the dynamics of systems of curved dislocations in a single slip situation. In order to reduce the complexity of the problem a dipole like approximation for the orientation dependent density variables is applied. This leads to a closed set of kinematic evolution equations of total dislocation density, the GND densities, and the so-called curvature density. The analogy of the resulting equations with the edge dislocation model allows one to generalize the phase field formalism and to obtain a closed set of dynamic evolution equations.