Continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening

TL;DR

This paper extends continuum dislocation theory to include statistically stored dislocations and Taylor hardening, providing new insights into dislocation distribution, size effects, and work hardening in single crystal shear.

Contribution

It introduces a novel continuum dislocation model that incorporates statistically stored dislocations and Taylor hardening effects for single crystals.

Findings

Dislocation distribution in equilibrium state is characterized.

Stress-strain curves show Bauschinger effect and size dependence.

Comparison demonstrates the impact of including statistically stored dislocations.

Abstract

This paper develops the small strain continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening for single crystals. As illustration, the problem of anti-plane constrained shear of single crystal deforming in single slip is solved within the proposed theory. The distribution of geometrically necessary dislocations in the final state of equilibrium as well as the stress-strain curve exhibiting the Bauschinger translational work hardening and the size effect are found. Comparison with the stress-strain curve obtained from the continuum dislocation theory without statistically stored dislocations and Taylor hardening is provided.