GEOMETRICAL EFFECTS IN THE INHOMOGENEOUS DEFORMATION OF DUCTILE SINGLE-CRYSTALS

Non-uniform deformation in ductile single crystals is studied using a simple model for a crystal undergoing symmetric double slip in tension. The model, when interpreted in terms of the crystallography of face-centred or body-centred cubic crystals, demonstrates, in particular, that shear bands may form when the slip plane workhardening rates are positive and, thus, without either ideal plasticity or strain softening. Localized plastic flow is viewed as a shearing bifurcation in the uniform tensile deformation of the crystal model and the critical stresses and workhardening rates for localized shear are worked out. The importance of yield vertexes and geometrical softening phenomena related to lattice rotations during deformation are given special attention in the development of the constitutive laws and in the results for the critical conditions for localized shear. © 1979.