Comparison of the minimum plastic spin and rate sensitive slip theories for loading of symmetrical crystal orientations

The plastic loading of face-centred cubic crystals along directions of symmetry leads to ambiguities in slip system selection. A solution to this problem has been proposed (Fuh & Havner, Proc. R. Soc. Lond. A 427, 193-239 (1989)) by postulating that the operating slip combination is the one which corresponds to the minimum plastic spin (MPS). A comparison is made between the MPS and rate-dependent slip theories. The predictions obtained are identical for the following cases: (i) (110) loading in channel die compression (with one exception) and (ii) all the multiple slip orientations in uniaxial tension. In the case of [100] pure plane strain compression, there is agreement for the four slip-system orientations, but not when six systems are required in the MPS analysis. It is shown that the symmetry of the slip distributions called for by the MPS and rate sensitive approaches is responsible for the broad equivalence between the predictions of the two theories. In each of the examples discussed, the number of operating slip systems is determined by symmetry considerations, leading to the operation of two, four, six or eight slip-systems, rather than by the number of prescribed constraints.