Eshelbian dislocation mechanics: $J$-, $M$-, and $L$-integrals of straight dislocations
Abstract
In this work, using the framework of (three-dimensional) Eshelbian dislocation mechanics, we derive the -, -, and -integrals of a single (edge and screw) dislocation in isotropic elasticity as a limit of the -, -, and -integrals between two straight dislocations as they have recently been derived by Agiasofitou and Lazar [Int. J. Eng. Sci. 114 (2017) 16-40]. Special attention is focused on the -integral. The -integral of a single dislocation in anisotropic elasticity is also derived. The obtained results reveal the physical interpretation of the -integral (per unit length) of a single dislocation as the total energy of the dislocation which is the sum of the self-energy (per unit length) of the dislocation and the dislocation core energy (per unit length). The latter can be identified with the work produced by the Peach-Koehler force. It is shown that the dislocation core energy (per unit length) is twice the corresponding pre-logarithmic energy factor. This result is valid in isotropic as well as in anisotropic elasticity. The only difference lies on the pre-logarithmic energy factor which is more complex in anisotropic elasticity due to the anisotropic energy coefficient tensor which captures the anisotropy of the material.
Keywords
Cite
@article{arxiv.1709.01836,
title = {Eshelbian dislocation mechanics: $J$-, $M$-, and $L$-integrals of straight dislocations},
author = {Markus Lazar and Eleni Agiasofitou},
journal= {arXiv preprint arXiv:1709.01836},
year = {2020}
}
Comments
8 pages. arXiv admin note: text overlap with arXiv:1702.00363