Three-dimensional shape and stress field of a deformation twin in magnesium

While the three-dimensional (3D) shape and stress field of a twin in hexagonal close-packed (HCP) metals have attracted considerable interest in recent years due to their substantial impact on internal stress and mechanical properties, a detailed understanding of their variation with twin size is still lacking. An analytical model that is not restricted by spatial scale is developed in this work by considering the effects of anisotropic twin boundary energy, elastic strain energy and plastic relaxation to predict the 3D shape with the minimum energy, and the stress field, of an isolated ellipsoidal twin of different sizes. The model is applied to Mg with a focus on the {101¯2} twin type. The analytical calculation results show that the nucleation of the nano-sized twin embryos is facilitated by the stress field near structural defects such as dislocations. During the expansion of this nano-sized twin embryo, the interplay between the elastic strain energy and interfacial energy changes the length of the twin along the twin shear (forward) direction from being shorter to longer than that along the lateral direction. In contrast to the current understandings, the maximum shear stress on the twin plane along the twin shear direction occurs at the lateral, rather than the forward, side of the twin. At the forward side, the maximum shear stress occurs at a distance ahead of the twin tip and this distance increases with increasing twin thickness.