Variant selection during secondary and tertiary twinning in pure titanium

Three generations of twins were identified by electron backscatter diffraction techniques in pure titanium subjected to uniaxial compression at room temperature. Many primary contraction twins were observed as the initial texture was favourable for their formation. Numerous secondary extension twins formed within the primary contraction twins and some tertiary contraction twins within the secondary extension twins. The orientations of these three generations of twins were determined and their associated Schmid factors (SFs) were calculated. The formation of the twin variants selected in each generation and the absence of certain potential variants are explained by rotating the twinning displacement gradient tensor expressed in the twin system reference frame into the crystal reference frame of the relevant neighbouring grain. The presence of the observed secondary and tertiary twins is accounted for in terms of the ease of imposing the required accommodation strains on their neighbours. The results show that secondary twins can form even with low SFs as long as their accommodation takes place by prismatic or basal glide. However, the formation of certain second and third generation potential high SF twins was impeded when this would have required accommodation by the most difficult deformation mode: pyramidal glide.