Distributional and regularized radiation fields of non-uniformly moving straight dislocations, and elastodynamic Tamm problem

TL;DR

This paper develops explicit, singularity-free solutions for elastodynamic fields radiated by non-uniformly moving dislocations, applicable at arbitrary speeds, including super-sonic, and demonstrates their application through numerical simulations of the Tamm problem.

Contribution

It introduces a novel regularization method for elastodynamic dislocation fields, enabling accurate modeling of non-uniform, high-speed dislocation motion with explicit integral solutions.

Findings

Solutions produce Mach cones for super-sonic dislocation speeds

Regularized fields are singularity-free and depend on dislocation density

Numerical method efficiently computes fields for complex dislocation motions

Abstract

This work introduces original explicit solutions for the elastic fields radiated by non-uniformly moving, straight, screw or edge dislocations in an isotropic medium, in the form of time-integral representations in which acceleration-dependent contributions are explicitly separated out. These solutions are obtained by applying an isotropic regularization procedure to distributional expressions of the elastodynamic fields built on the Green tensor of the Navier equation. The obtained regularized field expressions are singularity-free, and depend on the dislocation density rather than on the plastic eigenstrain. They cover non-uniform motion at arbitrary speeds, including faster-than-wave ones. A numerical method of computation is discussed, that rests on discretizing motion along an arbitrary path in the plane transverse to the dislocation, into a succession of time intervals of constant velocity vector over which time-integrated contributions can be obtained in closed form. As a simple illustration, it is applied to the elastodynamic equivalent of the Tamm problem, where fields induced by a dislocation accelerated from rest beyond the longitudinal wave speed, and thereafter put to rest again, are computed. As expected, the proposed expressions produce Mach cones, the dynamic build-up and decay of which is illustrated by means of full-field calculations.