An integrated crystal plasticity–phase field model for spatially resolved twin nucleation, propagation, and growth in hexagonal materials

Abstract

Typical hexagonal engineering materials, such as magnesium and titanium, deform extensively through shear strains and crystallographic re-orientations associated with the nucleation, propagation, and growth of twins. To accurately predict their deformation behavior it is, therefore, critical for constitutive models to incorporate these mechanisms. In this work an integrated approach for modeling the concurrent dislocation mediated plasticity and heterogeneous twinning behavior in hexagonal materials is presented. A dislocation density-based crystal plasticity model is employed to predict the heterogeneous distribution of stress, strain and dislocation activity and is coupled to a phase field model for the description of the nucleation, propagation, and growth of {1¯012} tensile twins. A stochastic model is used to nucleate twins at grain boundaries, and their subsequent propagation and growth are driven by the Ginzburg–Landau relaxation of the system free energy which includes the orientation dependent twin interfacial energy and the elastic strain energy. Application of this novel and fully coupled model to the cases of magnesium single crystal, bicrystal, and polycrystal deformation is shown to demonstrate its predictive capability. Numerical simulations predict, in accordance with experimental observations, twin nucleation at grain boundaries followed by twin propagation into the grain interior and subsequent transverse twin thickening. Through this new combination of modeling approaches it is possible to systematically study the twin induced strain fields, the stress distribution along twin boundaries, and the spatial evolution of dislocation density within twins and parent grains.