Non-uniform plastic deformations of crystals undergoing anti-plane constrained shear

TL;DR

This paper develops a thermodynamic dislocation theory to analyze non-uniform plastic deformations in crystals under anti-plane constrained shear, providing insights into energy densities, dislocation densities, and stress-strain behavior.

Contribution

It introduces a novel thermodynamic dislocation model that accounts for configurational temperature and redundant dislocations in non-uniform crystal plasticity.

Findings

Derived asymptotically exact energy density for moderate dislocation densities

Predicted stress-strain curves consistent with experimental observations

Quantified dislocation densities during non-uniform deformation

Abstract

The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the averaging procedure. This energy density is extrapolated to the cases of extremely small or large dislocation densities. By incorporating the configurational temperature and the density of redundant dislocations, we develop the thermodynamic dislocation theory for non-uniform plastic deformations and use it to predict the stress-strain curves and the dislocation densities.