Plastic Deformation

· A straight dislocation line in a stress-free elastically isotropic material will be the configuration of minimum energy.
· In a stress field, a dislocation line pinned at both ends will bow out and reach an equilibrium curvature under the combined action of the line tension, T, and the force per unit length due to the stress: F = τb.

From: Hull, "Introduction to Dislocations," Pergamon (1965)

· For the loop in equilibrium: 2T sin(dθ/2) ~ 2T(dθ /2) = τb ds = τb R dθ. i.e. T = τb R
· The line tension, T = G b² , and substituting this in the expression for R gives: G b²= τb R , so that: Equilibrium Radius = R = (G b/τ).