A crystal plasticity modeling considering volume fraction of deformation twinning

A crystal plasticity model incorporating deformation twinning is proposed. To reproduce the mechanical behaviors induced by deformation twinning, we require a criterion for initiating deformation twinning, a reorientation of the crystal lattice, and a constitutive relation of mixed state for a untwinned and twinned regions. In the proposed model, deformation twinning is activated by a resolved shear stress on a twinning plane. The crystal lattice is naturally reoriented within the crystal plasticity framework. We also consider the volume fraction of twinning and derive a constitutive equation by superposing the untwinned and twinned states, which is computed at a reasonable computational cost. The model is implemented in a finite element-based crystal plasticity framework. In numerical analyses of polycrystalline pure magnesium, the proposed model reproduces the mechanical behaviors induced by deformation twinning, such as the different flow stresses under tension and compression. The model also exhibits a characteristic behavior of twinning; namely, the convergence of the volume fraction of twinning in several material points to a value below 100%. Comparisons with a previously proposed model are also presented.