Line tension of a dislocation moving through an anisotropic crystal

TL;DR

This paper extends the analysis of dislocation line tension to moving dislocations in anisotropic crystals, revealing velocity-dependent stability behaviors and predicting dislocation instabilities near shear wave speeds.

Contribution

It provides a new analytical framework for understanding how dislocation line tension varies with velocity in anisotropic media, including complex behaviors near shear wave speeds.

Findings

Line tension diverges at shear wave speed in isotropic cases.

Edge dislocation line tension changes sign at ~80% of shear wave speed.

Anisotropic effects significantly influence dislocation stability near wave speeds.

Abstract

Plastic deformation, at all strain rates, is accommodated by the collective motion of crystalline defects known as dislocations. Here, we extend an analysis for the energetic stability of a straight dislocation, the so-called line tension ($\Gamma$), to steady-state moving dislocations within elastically anisotropic media. Upon simplification to isotropy, our model reduces to an explicit analytical form yielding insight into the behavior of $\Gamma$ with increasing velocity. We find that at the first shear wave speed within an isotropic solid, the screw dislocation line tension diverges positively indicating infinite stability. The edge dislocation line tension, on the other hand, changes sign at approximately $80\%$ of the first shear wave speed, and subsequently diverges negatively indicating that the straight configuration is energetically unstable. In anisotropic crystals, the dependence of $\Gamma$ on the dislocation velocity is significantly more complex; At velocities approaching the first shear wave speed within the plane of the crystal defined by the dislocation line, $\Gamma$ tends to diverge, with the sign of the divergence strongly dependent on both the elastic properties of the crystal, and the orientation of the dislocation line. We interpret our analyses within the context of recent molecular dynamics simulations (MD) of the motion of dislocations near the first shear wave speed. Both the simulations and our analyses are indicative of instabilities of nominally edge dislocations within fcc crystals approaching the first shear wave speed. We apply our analyses towards predicting the behavior of dislocations within bcc crystals in the vicinity of the first shear wave speed.