Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach

TL;DR

This paper develops a collective-variable theoretical framework to model the dynamics of rectilinear edge dislocations, capturing core-width effects and analyzing subsonic to transonic transitions with good agreement to atomistic simulations.

Contribution

It introduces a novel complex-valued equation of motion for dislocations that incorporates core-width dynamics and history dependence, advancing understanding of dislocation motion and transitions.

Findings

The transition is governed by a loading-dependent dynamic critical stress.

The equation predicts a delayed bifurcation at the subsonic-transonic transition.

Results align well with atomistic simulations on tungsten.

Abstract

A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to account for core-width generalized stacking-fault energy effects. The degrees of freedom of the solution of the latter equation are reduced by means of the collective-variable method, well known in soliton theory, which we reformulate in a way suitable to the problem at hand. Through these means, two coupled governing equations for the dislocation position and core width are obtained, which are combined into one single complex-valued equation of motion, of compact form. The latter equation embodies the history dependence of dislocation inertia. It is employed to investigate the motion of an edge dislocation under uniform time-dependent loading, with focus on the subsonic/transonic transition. Except in the steady-state supersonic range of velocities---which the equation does not address---our results are in good agreement with atomistic simulations on tungsten. In particular, we provide an explanation for the transition, showing that it is governed by a loading-dependent dynamic critical stress. The transition has the character of a delayed bifurcation. Moreover, various quantitative predictions are made, that could be tested in atomistic simulations. Overall, this work demonstrates the crucial role played by core-width variations in dynamic dislocation motion.