A probabilistic twin nucleation model for HCP polycrystalline metals

This article presents a basic probabilistic theory for the nucleation of deformation twins in hexagonal close packed (HCP) metals. Twin nucleation is assumed to rely on the dissociation of grain boundary defects (GBDs) under stress into the required number of twinning partials to create a twin nucleus. The number of successful conversion events is considered to follow a stochastic Poisson process where the rate is assumed to increase with local stress. From this concept, the probability distribution for the critical stress to form a twin nucleus is derived wherein the parameters of the distribution are related to properties of the GBDs. The theory is implemented into a multi-scale constitutive model for HCP metals in order to test its predictive capability against measurements made previously on pure zirconium deformed at 76 and 300 K.