A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry

TL;DR

This paper develops a general analytical solution for accelerating screw dislocations in anisotropic crystals with reflection symmetry, addressing limitations of previous steady-state models and enabling more realistic dislocation dynamics studies.

Contribution

It derives a comprehensive anisotropic solution for pure screw dislocations in slip systems with reflection symmetry, extending previous special-case analyses.

Findings

Provides a general solution applicable to arbitrary slip systems with reflection symmetry.

Addresses the limitations of steady-state models by including acceleration effects.

Lays groundwork for future studies on mixed dislocations and core regularization.

Abstract

Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain `critical' velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago. A generalization to anisotropic crystals has been attempted for pure screw and edge dislocations only for some special cases. This work aims to fill the gap of deriving a general anisotropic solution for pure screw dislocations applicable to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Further generalizations to arbitrary mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.