Theoretical analysis of the channel die compression test—I. General considerations and finite deformation of F.C.C. crystals in stable lattice orientations

Abstract

An extensive theoretical investigation of f.c.c. crystals under [110] loading in the channel die compression test is presented. Two lattice orientations known from experiment to be stable relative to the channel axes, through large deformations, are investigated for each of four hardening laws. These are Taylor's classical isotropic hardening rule, a 2-parameter empirical rule from the metallurgical literature, the “simple theory” of anisotropic latent hardening( Havner and Shalaby, Proc. R. Soc. A 358,47 (1977)), and a modification of the simple theory proposed by pfirce et al., Acta Met. 30, 1087 (1982). Predictions of active systems, equal multiple-slip and consequent lattice stability, finite shape change, and lateral constraint stress are the same for all theories, corresponding to minimum rate of plastic work, and are in general agreement with experiments on copper crystals by Wonsiewicz and Chin, Met. Trans. 1, 2715 (1970) and Wonsiewicz et al., Met. Trans. 2, 2093 (1971). The predictions of latent hardening differ among the theories, however, depending upon whether there is relative rotation of material and lattice. The potential significance of experimental studies of latent hardening in these particular stable lattice orientations is emphasized.