Prediction of internal stresses during growth of first- and second-generation twins in Mg and Mg alloys

The present work is dedicated to the development of a mean-field continuum mechanics method capable of predicting internal stresses in parent and twin phases during first- and second-generation twinning. For that purpose, a generalized Tanaka–Mori scheme in heterogeneous elastic media with plastic incompatibilities is developed. The work is applied to the case of first- and second-generation twinning in hexagonal close packed magnesium. In the case of first-generation twinning, the model is capable of predicting the trends in the development of back-stresses within the twin domain. A parametric study is performed to explain the roles of grain and twin shape and of relative volume twin volume fractions on the magnitude and directions of the back-stresses. In addition, applying the methodology to the case of second-generation twinning allows identification, in exact agreement with experimental observations, of the most likely second-generation twin variants to grow in a primary twin domain.