On the three-dimensional spatial correlations of curved dislocation systems

TL;DR

This paper develops a coarse-graining framework using dislocation-dislocation correlation functions to better capture interactions in dislocation systems, with implications for continuum dislocation dynamics modeling.

Contribution

It introduces a method to evaluate spatial correlation functions from discrete dislocation simulations, linking microscopic interactions to mean field descriptions.

Findings

Correlation functions depend weakly on plastic strain

Correlation functions depend strongly on coarse-graining length

Method enables improved continuum modeling of dislocation interactions

Abstract

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a coarse-graining length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow relative positions of dislocation pairs, and thus the strength of their interactions at short range, to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of self-correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain (and, in turn, the total dislocation density), but are seen to depend strongly on the coarse-graining length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.