The inhomogeneity of plastic-deformation in ductile single-crystals

A discrete slip model which characterizes the inhomogeneity of material properties in ductile single crystals is proposed in this paper. Based on this model rate-dependent finite element investigations are carried out which consider the finite deformation, finite rotation, latent hardening effect and elastic anisotropy. The calculation clearly exhibits the process from microscopic inhomogeneous and localized deformation to necking and the formation of LSBS and reveals several important features of shear localization. For example, the inhomogeneous deformation is influenced by the imperfections and initial non-uniformities of material properties. The inhomogeneous deformation may either induce necking which results in the lattice rotation and leads to geometrical softening, which in turn promotes the formation of CSBS, or induces heavily localized deformation. The microscopic localized deformation eventually develops into the LSBS and results in a failure. These results are in close agreement with experiment. Our calculations also find that the slip lines on the specimen's surface at necking become curved and also find that if the necking occurs before the formation of LSBS, this band must be misoriented from the operative slip systems. In this case, the formation of LSBS must involve non-crystallographic effects. These can also be indirectly confirmed by experiment. All these suggest that our present discrete slip model offers a correct description of the inhomogeneous deformation characterization in ductile crystals.