A THEORETICAL INVESTIGATION OF FINITELY DEFORMING F.C.C. CRYSTALS IN THE CHANNEL DIE COMPRESSION TEST (FACE, CENTERED, CUBIC

A theoretical analysis dealing with the finite deformation of partially constrained crystals is introduced.;A family of highly symmetric orientations of f.c.c. crystals in the channel die compression test that has been studied experimentally is analyzed here based upon the theory of finite deformation. Predictions of the behavior of crystals such as the combination of active slip systems, shape change, rotation of lattice axes with respect to die axes, and latent hardening are made and compared with results in the experimental literature. Four different hardening theories are adopted in this analysis. These theories are the isotropic Taylor's rule, Havner's anisotropic, rotation-dependent "simple theory," the "2-parameter rule" introduced in the metallurgical literature, and the "P-A-N rule" proposed by Peirce, Asaro and Needleman.;This study includes a first-order (rate problem) analysis for three different orientations and a second-order analysis for the unstable lattice orientation. For the second and third crystal orientations considered here the deformation modes obtained from the first-order constitutive inequalities are found to be nonunique. However, uniqueness is obtained for the second orientations, according to each of the four hardening theories, when a postulate of minimum plastic work-rate is applied. The minimum incremental work based upon a second-order analysis for the third orientation gives nonunique solutions for both Taylor's rule and the "simple theory"; it affects the first-order solutions for Taylor's rule but not for the "simple theory.".;A largely qualitative comparison between theoretical and experimental work is made. Among the hardening theories considered in this study, Taylor's rule, the "2-parameter rule," and the "P-A-N rule" all partially predict the experimental results. The "simple theory" is the only one which is qualitatively consistent with experimental results for all three orientations considered.