The energy of a shear dislocation ring was calculated within the framework of the Peierls model, in which the displacement was represented by a density of infinitesimal dislocations in the glide plane. This avoided the introduction of an uncertain core cut-off radius in order to prevent the usual divergence. The atomic misfit energy in the glide plane was accounted for explicitly, and the effect of the interplanar potential upon the ring energy and the core structure was studied. It was concluded that, whereas the spontaneous formation of shear rings in an homogenous stress field could be ruled out, the emission of dislocation rings from crack tips in glide planes which did not contain the crack front was possible.

The Peierls Model for Dislocation Rings. G.Schoeck: Czechoslovak Journal of Physics, 1995, 45[11], 991-1002