A dislocation-based model for twin growth within and across grains.

A computational method is presented for representing twins via two-dimensional dislocation statics in an isotropic elastic solid. The method is compared with analytical approximations of twin shape and is used to study how twins evolve within grains subjected to an arbitrary external shear stress. Twin transfer across grains is then studied using the same computational method. The dislocation-based model for twin growth gives the following dependencies: twin thickness increases linearly with grain size and external stress, and increases substantially as the grain is able to traverse multiple grain boundaries with low misorientation angles; the model also predicts that twin transfer becomes less prominent across grain boundaries with high misorientation angles. These predictions are consistent with experimentally measured extension twin growth in magnesium polycrystals. This study suggests that representing twins via discrete dislocations provides a physically reasonable approximation of twinning that can be naturally incorporated into existing dislocation statics and dynamics codes.