Field Dislocation Mechanics, Conservation of Burgers vector, and the augmented Peierls model of dislocation dynamics

TL;DR

This paper develops dissipative models for dislocation dynamics in elastic bodies, emphasizing Burgers vector conservation, and compares them with the augmented Peierls model, addressing limitations related to reference configuration dependence.

Contribution

It introduces reduced models that explicitly conserve Burgers vector during dislocation evolution and compares them with the augmented Peierls model, highlighting their differences and limitations.

Findings

Reduced models account for space-time Burgers vector conservation.

Comparison reveals differences with the augmented Peierls model.

Discussion of limitations related to reference configuration dependence.

Abstract

Dissipative models for the quasi-static and dynamic response due to slip in an elastic body containing a single slip plane of vanishing thickness are developed. Discrete dislocations with continuously distributed cores can glide on this plane, and the models are developed as special cases of a fully three-dimensional theory of plasticity induced by dislocation motion. The reduced models are compared and contrasted with the augmented Peierls model of dislocation dynamics. A primary distinguishing feature of the reduced models is the a-priori accounting of space-time conservation of Burgers vector during dislocation evolution. A physical shortcoming of the developed models as well as the Peierls model with regard to a dependence on the choice of a distinguished, coherent reference configuration is discussed, and a testable model without such dependence is also proposed.