Elastic fields of stationary and moving dislocations in finite samples

TL;DR

This paper derives integral formulas for elastic displacement and stress fields caused by stationary or moving dislocation loops in finite, anisotropic samples, providing a general framework that includes specific geometries like half-spaces and thin plates.

Contribution

It introduces a general method to compute elastic fields of dislocations in finite samples, valid for anisotropic media, with explicit line integral representations for stress fields.

Findings

Derived integral expressions for elastic fields in finite samples.

Established stress field independence from slip plane choice.

Explicitly calculated vector potentials for specific geometries.

Abstract

Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the stress fields, a line integral representation is found, thus showing rigorously the independence of the stress fields with respect to the choice of slip planes. In the stationary case the line integral representation involves calculating a "vector potential" dependent on the specific geometry of the sample. Two examples of geometries, isotropic half space and thin plate, are shown where the "vector potential" has been explicitly determined. With this general method one recovers some earlier specific results in these geometries.