## 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

Abstract:

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.

Notes:

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.