Sequential double extension twinning in a magnesium alloy: Combined statistical and micromechanical analyses

A statistical analysis is conducted on sequential (10-12)-(10-12) double extension twinning in a Mg AZ31 alloy obtained after two mutually perpendicular successive compressions. Indeed, primary twins form during the first compression, which produce secondary twins during the second compression. Here, ``sequential double twinning'' is adopted to describe this twinning mechanism, which is different from classic double twinning obtained during monotonic loading. Double extension twins, no matter sequential or classic ones, can be classified into Groups I-IV according to their misorientations with respect to the parent grain. In the present study, the majority of the sequential double extension twins have relatively high Schmid factors (SFs) and a misorientation of 60 degrees with respect to the parent grain (Group III). However, the classical SF based analysis fails to explain why secondary twin variants in Group III are preferred over their nearest orientated neighbors in Group IV, since their SF differences are negligible. Therefore, a static double inclusion model is developed to analytically compute the elastic energy in a final configuration of sequential double twinning. The model well explains the predominance of secondary twins in Group III by a noticeable greater decrease of free energy after secondary twinning.