An anisotropic, viscoplastic power law for face-centred cubic crystals: comparative evaluations in the Goss and Brass orientations of channel die compression

Abstract

An anisotropic, viscoplastic power law is introduced and applied to analysis of the Goss and Brass orientations, and compared with predictions from rate-independent theory and experiment. The structure of the new power law is so chosen that it has the capability of approaching rate-independent results for lattice rotation and crystal shearing, after finite rotation about the load axis, in the range of unstable lattice orientations in (110) channel die compression. (Rate-independent predictions of shear and lattice rotation are in good to very good agreement with experiments on aluminium and copper in that range, whereas classicisotropicpower-law results are not.) It is established that, for sufficiently large power-law exponentn, the new anisotropic, elasto-viscoplastic theory predicts: (i) lattice stability in each of the Goss and Brass orientations, consistent with both experiment and rate-independent theory; (ii) zero crystal shear in the Goss orientation, also consistent with both; (iii) finite shear in the Brass orientation, in very good agreement with experiment and rate-independent theory; and (iv) a lateral-constraint stress that remains essentially elastic in both orientations, as predicted by rate-independent theory and close to experimental measurements for aluminium and copper in the Brass orientation.