How to determine limiting velocities of dislocations in anisotropic crystals

TL;DR

This paper reviews methods to determine the limiting velocities of dislocations in anisotropic crystals, clarifying existing confusion and providing efficient computational approaches for arbitrary dislocation types.

Contribution

It offers a concise overview and systematic methods for calculating dislocation limiting velocities in general anisotropic crystals, addressing gaps in existing literature.

Findings

Provides explicit expressions for limiting velocities in anisotropic crystals.

Clarifies the relationship between limiting velocities and shear wave speeds.

Offers analytical and numerical methods for computation.

Abstract

In the continuum limit, the theory of dislocations in crystals predicts a divergence in the elastic energy of the host material at a crystal geometry dependent limiting (or critical) velocity $v_c$. Explicit expressions for $v_c$ are scattered throughout the literature and are available in analytic form only for special cases with a high degree of symmetry. The fact that in some cases (like pure edge dislocations in fcc) $v_c$ happens to coincide with the lowest shear wave speed of a sound wave traveling parallel to the dislocation's gliding direction has led to further confusion in the more recent literature. The aim of this short review therefore is to provide a concise overview of the limiting velocities for dislocations of arbitrary character in general anisotropic crystals, and how to efficiently compute them, either analytically or numerically.