A continuum model for distributions of dislocations incorporating short-range interactions

TL;DR

This paper develops a continuum model for dislocation distributions in crystals that incorporates short-range interactions using asymptotic analysis, improving the accuracy of dislocation dynamics simulations.

Contribution

It introduces a novel continuum description of short-range dislocation interactions based on asymptotic analysis, enhancing the modeling of dislocation dynamics.

Findings

The continuum model accurately captures anisotropic dislocation interactions.

The model ensures strong stability properties similar to discrete models.

Validation shows good agreement with discrete dislocation simulations.

Abstract

Dislocations are the main carriers of the permanent deformation of crystals. For simulations of engineering applications, continuum models where material microstructures are represented by continuous density distributions of dislocations are preferred. It is challenging to capture in the continuum model the short-range dislocation interactions, which vanish after the standard averaging procedure from discrete dislocation models. In this study, we consider systems of parallel straight dislocation walls and develop continuum descriptions for the short-range interactions of dislocations by using asymptotic analysis. The obtained continuum short-range interaction formulas are incorporated in the continuum model for dislocation dynamics based on a pair of dislocation density potential functions that represent continuous distributions of dislocations. This derived continuum model is able to describe the anisotropic dislocation interaction and motion. Mathematically, these short-range interaction terms ensure strong stability property of the continuum model that is possessed by the discrete dislocation dynamics model. The derived continuum model is validated by comparisons with the discrete dislocation dynamical simulation results.