Screw dislocations in the field theory of elastoplasticity

TL;DR

This paper develops a static elastoplastic field theory for screw dislocations, revealing non-singular stress fields and modified energy formulas that incorporate localized moment stresses and an intrinsic material length.

Contribution

It introduces a microscopic elastoplastic framework for dislocations, linking moment stress to the Nye tensor, and provides new stress and energy calculations for various dislocation configurations.

Findings

Stress fields are non-singular at the dislocation core.

Localized moment stress modifies the core stress distribution.

Derived a modified Eshelby twist formula depending on material length.

Abstract

A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so-called Eshelby twist which depends on a specific intrinsic material length.