A phase field study focuses on the transverse propagation of deformation twinning for hexagonal-closed packed crystals

The thickening mechanism of the deformation twinning (DT) has been frequently studied in numerous researches and the transverse propagation of that is beginning to trigger the attention of scholars. Recently, some researchers report that the twin front of {101¯2} mode of Magnesium is composed of a conjugate twin plane and prismatic/basal (PB) planes, and the combined mobility of these planes rule the overall kinetics of twin propagation. Focusing on that, a continuum phase field model is proposed to investigate the equilibrium shape of tensile twins and the kinetics of the twin front. A new form of surface free energy is introduced in this model for the purpose of describing the orientation-dependent properties of twin boundaries. The simulations well reproduce the PB interfaces and the results indicate that the anisotropic surface energy plays a dominant role in forming the irregular facets on the twin front. A generalized energy-momentum tensor is derived and analyzed for shear loading in order to investigate the equilibrium and mobility of twin boundaries, and the simulations show that the configurational forces distributed on the PB interfaces are smaller than that on the other twin planes, which implies that the growth of twin is beneficial for the formation of PB interfaces. The simulations also indicate that the anisotropic twin boundary energy is not responsible for the large aspect ratio nature of twins, which may be governed by the competition between thickening mechanism and transverse propagation mechanism of the DT.