Uniformly-moving non-singular dislocations with elliptical core shape in anisotropic media

TL;DR

This paper introduces a regularized model for steadily-moving dislocations with elliptical cores in anisotropic media, providing explicit solutions and analyzing effects on fields, forces, and Mach cone angles across velocities.

Contribution

It develops a novel anisotropic regularization of dislocation fields with explicit solutions applicable at any velocity, including super-sound speeds.

Findings

Fields are differentiable everywhere for finite core parameters.

Mach-cone angles are insensitive to core aspect ratio at high velocities.

A new expression for the radiative force and the concept of least-radiation velocity are proposed.

Abstract

To allow for `relativistic'-like core contraction effects, an anisotropic regularization of steadily-moving straight dislocations of arbitrary orientation is introduced, with two scale parameters $a_\parallel$ and $a_\perp$ along the direction of motion and transverse to it, respectively. The dislocation core shape is an ellipse. When $a_\perp/a_\parallel\to 0$, the model reduces to the Peierls-Eshelby dislocation, the fields of which are non-differentiable on the slip plane. For finite $a_\parallel$ and $a_\perp$, fields are everywhere differentiable. Applying the author's so-called `causal' Stroh formalism to the model, explicit expressions for the regularized fields in anisotropic elasticity are derived for any velocity. For faster-than-wave velocities, Mach-cone angles are found insensitive to the ratio $a_\parallel/a_\perp$, as must be. However, the larger $a_\parallel$, the weaker the intensity of the cone branches. An expression is given for the radiative dissipative force opposed to motion. From this expression, it is inferred that the concept of a `radiation-free' intersonic velocity can, when not applicable, be replaced by that of a `least-radiation' velocity.