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

A Probabilistic Twin Nucleation Model for HCP Polycrystalline Metals. I.J.Beyerlein, C.N.Tomé: Proceedings of the Royal Society A, 2010, 466[2121], 2517-44