MATERIAL RATE DEPENDENCE AND LOCALIZED DEFORMATION IN CRYSTALLINE SOLIDS
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Nonuniform deformations of rate dependent single crystals subject to tensile loading are analyzed numerically. The crystal geometry is idealized in terms of a planar double slip model. In addition to allowing the effects of material rate sensitivity to be explored, the present rate dependent formulation permits the analysis of a range of material strain hardening properties and crystal geometries that could not be analyzed within a rate independent framework. Two crystal geometries are modeled. One is a planar model of an f.c.c. crystal undergoing symmetric primary-conjugate slip. For this geometry, a direct comparison with a previous rate independent calculation shows that material rate sensitivity delays shear band development significantly. Our present rate dependent formulation also enables a more complete exploration of the effects of high (i.e. greater than Taylor) latent hardening ratios on "patchy" slip development. In particular we show that strong latent hardening and patchy slip can give rise to kinematical constraints that prevent shear bands from propagating completely across the gage section. The second geometry models a b.c.c. crystal oriented so that there is approximately a double mode of slip with the slip systems inclined by more than 45 to the tensile axis. This calculation displays the formation of a localized band of conjugate slip. The lattice rotations accompanying this mode eventually lead to a decrease in the resolved shear stress on the more active system in the band so that the bands do not accumulate large strains and catastrophic shear bands do not form. The implications of material rate sensitivity for uniqueness are also discussed with reference to implications for the prediction of mechanical properties of polycrystals. 1983.