A nice pedagogical paper from Eshelby

March 2, 2007

A simple derivation of the elastic field of an edge dislocation

J D Eshelby 1966 Brit. J. Appl. Phys. Vol. 17 1131 — 1135


The elastic field of an edge dislocation is found in a simple manner by making use of the relation between an edge dislocation and a `wedge’ dislocation made by inserting or removing a narrow wedge of material.


Eshelby, using his usual cutting and welding operations, motivates a simple derivation for the displacement around an edge dislocation in an infinite isotropic material, which, to use his own expression, have the rather forbidding expression:

u = \frac{b}{2 \pi} \left( \tan^{-1} \frac{y}{x} + \frac{1}{2(1-\sigma)} \frac{xy}{r^{2}}\right)

v = \frac{b}{2 \pi} \left( \frac{1-2\sigma}{2(1-\sigma)} \ln \frac{1}{r} + \frac{1}{2(1-\sigma)} \frac{y^{2}}{r^{2}}\right)

Not surprisingly, the idea of the wedge dislocation itself seems to have its origins in his 1951 paper in Phil. Trans. A (Vol. 244, 87–112).

The four page paper is a pleasure to read; I am enjoying the experience thoroughly. Once I finish, I will find some time to summarise the details of the derivation in this page.

In the meanwhile, have fun, if you have access to British Journal of Applied Physics.


One Response to “A nice pedagogical paper from Eshelby”

  1. […] 4th, 2007 In the previous post, I talked about a nice pedagogical paper of Eshelby in which he describes a simple derivation of […]

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