Plastic Deformation

· If F is the force per unit length acting on the dislocation due to the external shear stress, τ , the work done per unit length of dislocation in the virtual displacement δx is: Work = Fδx.
· The work done by the external force, F_E , in this virtual displacement of the dislocation line is: F_E (b δx/d) = τ(d x L)(b δx/d).
· The "internal" and "external" work measure the same quantity so that:
(F δx)L =τ(d x L)(b δx/d), or:
Force per Unit length acting on the Dislocation = F = τb .
· This result for a straight dislocation has been generalized by Peach & Koehler to a dislocation loop in a general stress field given by the tensor Σ.