Self-stress and equilibrium shapes of dislocation loops

Abstract
The equilibrium shape of dislocation loops can be found by a relaxation technique. The applied stress is balanced by the self-stress as obtained from variational considerations. The principal-value stress plus an arc-lengthening term is augmented by a contribution stemming from the dislocation core. This definition is invariant with respect to the choice of the inner cut-off radius and non-singular spreading of the dislocation core. Elastic anisotropy and dissociation of the dislocation are fully taken into account. In agreement with experimental results, it is predicted that small loops are rounder than are large loops.