Resolving the diffusionless transformation process of twinning in single crystal plasticity theory

Abstract

This paper outlines a single crystal plasticity theory for the mesoscale resolution of the diffusionless transformation process of deformation twinning. Unlike prevalent crystal plasticity models of lattice transformation that characterize volume fraction evolution of coexisting parent and product lattices at a material point, our model alternates between two deformation gradient decompositions, depending on whether or not the lattice is transforming, so that only a single lattice exists at a material point at all times. This approach permits a proper spatiotemporal resolution of the transformation, and further captures its associated residual lattice distortions. Our formulation was implemented as a VUMAT subroutine on the finite element solver ABAQUS\\Explicit and used to model the twinning of a magnesium single crystal that was loaded under compression at different angles. As verified against multiple experiments from the literature, our model successfully characterizes for moderate strain: (a) the anisotropic stress-strain behavior of the Mg crystal, (b) the resulting spatial cross-hatch pattern of spindle shaped twins, and (c) the natural completion times of the twinning transformation. These results indicate that our mesoscale theory is capable of an in-depth spatiotemporal investigation of twinning and can be potentially extended to similar diffusionless transformation processes in single crystals.