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Abstract
Rate-independent crystal plasticity theory and a classic viscoplastic power-law are investigated, contrasted and compared for finite deformation analysis of fcc crystals in channel die compression, including full consideration of lattice straining. Both experiment-based anisotropic and isotropic (Taylor) hardenings are evaluated in rate-independent theory; and an unlimited range of power-law exponent n is considered in viscoplasticity. The focus is on predictions of lateral constraint stress, lattice rotation and crystal shear, and their comparison with experiment. General elastic-plastic equations (for both theories) are given for the range of unstable lattice orientations in (1 1 0) compression (‘range I’) and evaluated before and after a finite rotation of the lattice about the load axis. Equations also are given and evaluated for the ‘Brass’ orientation. It is shown that the theories can be in close agreement at the onset of finite deformation in range I, but that viscoplasticity gives results (for any n) after finite rotation that are in sharp contrast to rate-independent theory. The latter’s predictions for crystal shear and lattice rotation are in good to very good agreement with finite deformation experiments on aluminium and copper. The inclusion of lattice elasticity is found to have a negligible effect in range I. In contrast, for finite deformation in the stable Brass orientation, elastic-viscoplastic theory can be made to agree very closely with rate-independent theory and with experiment.
Acknowledgement
I thank my colleague Dr Jie Yu for her numerical solution of the differential equation for anisotropic constraint stress in Al, range I and for the final, computer-generated Figures and .