THE PEIERLS MODEL FOR DISLOCATION RINGS

The energy of a shear dislocation ring is calculated in the framework of the Peierls model in which the displacement is represented by a den sity of infinitesimal dislocations in the glide plane. This avoids the introduction of an uncertain core cut-off radius r(0) to prevent dive rgence in the usual treatment. The atomic misfit energy in the glide p lane is accounted for explicitly and the influence of the interplanar potential on the ring energy and the core structure is studied. Wherea s spontaneous formation of shear rings in a homogenous stress field ca n be ruled out, the emission of dislocation rings from crack tips in g lide planes not containing the crack front is feasible.