Comparative evaluation of a viscoplastic power-law and rate-independent crystal plasticity in channel die compression

General equations in (1 1 0) channel die compression are derived for a viscoplastic power-law, and comparative evaluations made with rate-independent theory and experiment. The latter theory has been shown in a series of papers (2007–2012) to predict well the finite-deformation experimental behavior (1966–2007) of fcc crystals in this family of orientations, and to give a rational basis for the elastoplastic transition that precedes the onset of finite multiple-slip. It is established analytically that, during this elastoplastic transition, the power-law equations in the limit of unbounded exponent n are identical with the rate-independent equations for lateral stress-rate and (very small) lattice rotation-rate. Moreover, results for aluminum and copper agree very closely for large n in four initial orientations investigated numerically. At the onset of finite deformation (in general when four or more systems are equally stressed) the respective results for stress-rate differ sharply, with the exception of the experimentally stable Brass orientation. When lattice elasticity is included in the power-law in this orientation (with an n of 100 or greater), it predicts results essentially indistinguishable from rate-independent theory for both aluminum and copper, in good agreement with experiment. In two orientations near the ends of the range, the power-law lattice rotation-rates at the onset of finite deformation for large n also agree closely with the rate-independent results. However, in the specific orientation from which there is large lattice rotation, the power-law significantly under-predicts rate-independent and experimental results after large strains, whatever the value of exponent n.

► Equations are derived for a viscoplastic power-law in channel die compression.
► Crystal orientations spanning the range of (1 1 0) compression are analyzed.
► Comparisons with rate-independent theory and experiment are presented.
► The power-law can agree as closely as is desired in the elastoplastic transition.
► There are significant differences in certain orientations after finite deformation.