Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum plasticity theory

TL;DR

This paper develops a mesoscale continuum theory for multiple slip dislocation systems, incorporating correlation functions and entropic forces to improve understanding of crystal plasticity beyond single-slip models.

Contribution

It introduces a statistical framework for multiple slip dislocation dynamics using correlation functions and BBGYK equations, extending previous single-slip theories.

Findings

Derived approximate pair correlation functions for multiple-slip dislocation systems.

Identified the role of correlation-induced entropic forces in dislocation interactions.

Compared the new theory with phenomenological models, highlighting improvements.

Abstract

Due to recent successes of a statistical-based nonlocal continuum crystal plasticity theory for single-glide in explaining various aspects such as dislocation patterning and size-dependent plasticity, several attempts have been made to extend the theory to describe crystals with multiple slip systems using ad-hoc assumptions. We present here a mesoscale continuum theory of plasticity for multiple slip systems of parallel edge dislocations. We begin by constructing the Bogolyubov-Born-Green-Yvon-Kirkwood (BBGYK) integral equations relating different orders of dislocation correlation functions in a grand canonical ensemble. Approximate pair correlation functions are obtained for single-slip systems with two types of dislocations and, subsequently, for general multiple-slip systems of both charges. The effect of the correlations manifests itself in the form of an entropic force in addition to the external stress and the self-consistent internal stress. Comparisons with a previous multiple-slip theory based on phenomenological considerations shall be discussed.