Macroscopic stress and strain in a doubly periodic array of dislocation dipoles

Gourgiotis, P.A.; Stupkiewicz, S.

Abstract

It is known that in two-dimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the long-range character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem.

Citation

Gourgiotis, P., & Stupkiewicz, S. (2014). Macroscopic stress and strain in a doubly periodic array of dislocation dipoles. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2171), Article 20140309. https://doi.org/10.1098/rspa.2014.0309

• Journal Article Type: Article
• Acceptance Date: Aug 21, 2014
• Online Publication Date: Sep 17, 2014
• Publication Date: Nov 8, 2014
• Deposit Date: Sep 22, 2016
• Publicly Available Date: Sep 20, 2018
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Electronic ISSN: 1471-2946
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 470
• Issue: 2171
• Article Number: 20140309
• DOI: https://doi.org/10.1098/rspa.2014.0309
• Public URL: https://durham-repository.worktribe.com/output/1374562