The Forces Exerted on Dislocations and the Stress Fields Produced by Them

M. Peach and J. S. Koehler
Phys. Rev. 80, 436 – Published 1 November 1950
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Abstract

It is shown that the force dF exerted on a line element νdσ of a dislocation with Burgers vector f by a stress τ is given by dF=ν×(f·τ)dσ. An analogy is drawn between the behavior of a closed line dislocation in a stress field and the behavior of a closed current-carrying loop in a field of magnetic induction. Then formulas for the stress components caused at any point of an infinite elastically isotropic crystal by a line element of a general Burgers dislocation are deduced from Burger's expressions for the displacements (see Sec. III(C)). These formulas bear a close analogy to the Biot-Savart formula of electromagnetic theory. Both of these results taken together constitute a complete system for the investigation of the mutual interaction of dislocations in an infinite elastically isotropic crystal.

  • Received 4 May 1950

DOI:https://doi.org/10.1103/PhysRev.80.436

©1950 American Physical Society

Authors & Affiliations

M. Peach and J. S. Koehler*

  • Carnegie Institute of Technology, Pittsburgh, Pennsylvania

  • *This research constitutes a portion of a thesis submitted by M. O. Peach in partial fulfillment of the requirements for the degree of Doctor of Science at Carnegie Institute of Technology. This work was supported in part by ONR.

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Issue

Vol. 80, Iss. 3 — November 1950

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