A constitutive model for hcp materials deforming by slip and twinning

A crystal-mechanics-based constitutive model, which accounts for both slip and twinning, has been developed for polycrystalline hcp materials. The model has been implemented in a finite-element program. The constitutive model is evaluated for the room-temperature deformation of the magnesium alloy AZ31B. By using comparisons between model predictions and macroscopically-measured stress-strain curves and texture evolution, we have deduced information about the dominant slip and twinning systems active at room temperature, and the values of the single-crystal parameters associated with slip and twin system deformation resistances. Our calculations show that the two main crystallographic mechanisms: (i) slip on basal (0001) 〈11 2 0〉, prismatic {10 1 0} 〈11 2 0〉, and pyramidal {10 1 1} 〈11 2 0〉 systems, and (ii) twinning on pyramidal {10 1 2} 〈 1 011〉 systems, play the dominant role in the deformation of magnesium at room temperature. However, to match the observed stress-strain curves, it is found necessary to account for non-crystallographic grain boundary related effects. We approximately account for these grain-boundary region accommodation effects by adding a suitably-weighted isotropic term to the flow rule. The isotropic plasticity term serves the important function of bounding the stress levels in the numerical calculations; it does not contribute to the crystallographic texture evolution. Overall, we show that a simple non-hardening crystal-mechanics-based constitutive model is able to reproduce the experimentally-measured stress–strain curves and crystallographic texture evolution in simple tension and compression on specimens made from an initially-textured rod, as well as plane strain compression experiments on specimens made from an initially-textured plate.