Dislocation mediated variant selection for secondary twinning in compression of pure titanium

Abstract By compression along the normal direction of rolled pure titanium sheet, primary { 11 2 ¯ 2 } type compression twins were observed, followed by secondary { 10 1 ¯ 2 } extension twins. The latter can be classified into three groups according to their misorientation with respect to the parent matrix grains: 41.34° around 5 143 ¯ > (Group I), 48.44° around 5 ¯ 50 3 ¯ > (Group II), and 87.85° around 7 43 ¯ 0 > (Group III). The experimental observations revealed the following activity frequency of these groups: Group II is the most frequent followed by Group I, and only a few secondary twins can be seen for Group III. When the classical Schmid factor (SF) analysis is applied, the smallest activity is predicted for Group III, in agreement with the experimental observations. However, the SF based criterion fails to distinguish between Group I and Group II variants. Similarly, the twin-shear accommodation based variant selection model proposed earlier for titanium [Qin and Jonas, Acta Mater. 75 (2014) 198–211] is not effective because the easiest accommodation by prismatic slips favors Group III variants which are nearly absent in the experiment. A possible explanation can be based on the smallest inclination angle of the secondary twinning habit plane with respect to the primary one, proposed by Barnett et al. [Acta Mater. 56 (2008) 5–15] which clearly favors Group II. It cannot make distinction between variants of the same group but can predict the right variants if complemented with the SF criterion. In the present work a new approach is proposed in order to disclose the preference for Group II variant over Group I. It is based on the special twinning geometry that applies to Group II; the intersection line of the primary and secondary twin planes lies in an active prismatic plane in the primary twin. Consequently, dislocation reactions are possible for the selection of secondary twin variant in Group II. Namely, prismatic type dislocations in the primary twin can produce partial dislocations that activate the corresponding secondary twin variant. Nevertheless, a further selection rule has to be applied to choose one out of the two possible Group II variants; this is based on the higher Schmid factor of the two secondary variants. By contrast, pyramidal dislocations would be required for the formation of Group I twins, which is less likely due to their relatively high critical resolved shear stress.