Crystal Rotations under Conditions of Imposed Strain and the Influence of Twinning and Cross-Slip

Slip rotations in cubic crystals under conditions of imposed strain are not, in general, uniquely determined, since several equivalent sets of slip systems are available to produce the particular shape change. However, it is shown that for certain crystal orientations undergoing deformation by rolling only four systems are required to operate and in these cases the slip rotations are determined unambiguously. Two orientation ranges, those having 〈110〉 and 〈111〉 transverse directions, are considered and the rate of crystal rotation determined as a function of orientation. It is shown that orientations of the types {1110}〈112〉, {110}〈001〉, and near-{4,4,11}〈11,11,8〉 are stable for f.c.c. crystals and {112}〈110〉, {001}〈110〉, and near-{11,11,8}〈4,4,11〉 for b.c.c. crystals. The predictions of this limited analysis allow the various mechanistic theories of rolling texture formation in f.c.c. metals to be assessed. It is concluded that both twinning and cross-slip are required to account for the full range of textures obtained in f.c.c. metals over a range of stacking-fault energy.