A physically based phenomenological model for deformation twinning in magnesium alloy

A partial differential equation is developed that captures the evolution of key characteristics of tensile twinning in magnesium base alloys. The objective is to provide a framework for ascertaining the effects of hardening – due to grain refinement, precipitation and dislocation substructure – on twin volume fraction, thickness and length. The model is developed with the help of observations made on alloy AZ31. It is shown that it is necessary to consider the nucleation of twins at locations where neighbouring twins impinge on the grain boundary. The model provides a reasonable approximation for the role of grain size on twinning. It predicts a period of low apparent work hardening following yielding and shows that this should be more extensive for finer grain sizes, in agreement with experiment. Finally, some predictions are made on the effect of changing the resistance to twinning.