A multi-scale, theoretical study of twin nucleation from grain boundaries in polycrystalline hexagonal close packed metals was presented. A key element in the model was a probability theory for the nucleation of deformation twins based on the idea that twins originate from a statistical distribution of defects in the grain boundaries and were activated by local stresses at the grain boundaries. In this work, this theory was integrated into a crystal plasticity constitutive model in order to study the influence of these statistical effects on the microstructural evolution of the polycrystal, such as texture and twin volume fraction. Recently, a statistical analysis of exceptionally large data sets of {10•2} deformation twins was conducted for high-purity Mg (Beyerlein et al., 2010). To demonstrate the significantly enhanced accuracy of the present model over those employing more conventional, deterministic approaches to twin activation, the model was applied to the case of {10•2} twinning in Mg to quantitatively interpret the many statistical features reported for these twins (e.g., variant selection, thickness, numbers per grain) and their relationship to crystallographic grain orientation, grain size, and grain boundary misorientation angle. Notably the model explains the weak relationship observed between crystal orientation and twin variant selection and the strong correlation found between grain size and the number of twins formed per grain. The predictions suggested that stress fluctuations generated at grain boundaries were responsible for experimentally observed dispersions in twin variant selection.

Effect of Microstructure on the Nucleation of Deformation Twins in Polycrystalline High-Purity Magnesium: a Multi-Scale Modeling Study. I.J.Beyerlein, R.J.McCabe, C.N.Tomé: Journal of the Mechanics and Physics of Solids, 2011, 59[5], 988-1003