Numerical Analysis of Deformation Twin Behavior. Small Static Twin Lamellas

Abstract

A detailed numerical analysis has been made of the energies and equilibrium configurations of deformation twin lamellae under various conditions of applied stress and twin boundary energies. Exact expressions have been used for the self‐energies and interaction energies associated with the various partial dislocations comprising the twin lamellae using isotropic elasticity theory developed for circular glide dislocation loops. It has been found that as the applied stress and/or twin boundary energy is increased, the size of the stable twin lamella as well as the number of dislocation loops comprising it decreases. Accompanying this size decrease is a correspondingly smaller energy for activation. In this respect it is found that the critical step in the formation of a twin lamella is the activation of the first loop which requires the formation of a stacking fault. Subsequent loop nucleation on adjacent planes, which increases the twin thickness, occurs spontaneously.