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

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.

Consistent determination of geometrically necessary dislocation density from simulations and experiments

“…Kroner (Kroner, 1955) and Bilby (Lazar and Pellegrini, 2016) expressed the dislocation density tensor as the negative of the expression adopted by Nye (Eq. 14).…”

Instabilities of High Speed Dislocations

“…Since then, continuum models of increasing complexity have been proposed to describe dislocation glide [11][12][13][14][15][16][17][18]. The limiting speeds of dislocations found in continuum models have been attributed to inadequate treatments of the dislocation core [18,19] and the inherent limitations of the small strain approximation [20][21][22].…”

Mechanical properties of aluminum foams ceramic coated through plasma electrolytic oxidation

“…12. Since the generation and motion of fast dislocations play an important role in technical (engineering) applications, e.g., such as shock loading of solids [29], continuous attention is devoted to various aspects of the fast dislocation motion both in the theoretical studies (e.g., [30][31][32]) and in atomistic studies via molecular dynamics (e.g., [33,34]). Such studies contribute to an understanding of the process and create a base for proposals of verification experiments in future, e.g., via the detection of AE signal from the fast dislocation motion or via measurements of dislocation density [29] and their post-processing analysis.…”