| Many experimental evidences indicate that deformation localization can occur in the positive work hardening regime without introducing material imperfections or strain softening. The mechanisms of this phenomenon are attributed to non-Schmid effects, material rotation, and inhomogeneous deformation (slip). To account for effects of material rotation and inhomogeneous slip on deformation localization of ductile crystal, a gradient dependent crystal plasticity is established in this dissertation by formulating a slip gradient dependent Schmid law and an orientation gradient dependent evolution equation for the slip system. The possible unsymmetrical deformation mode is properly considered in this theory by adopting a single slip configuration. This theory is then applied to study the initiation condition and the corresponding spatial characteristics of deformation bands (kink and shear bands) by using linear stability analysis. Existing experimental data is compared with the theoretic predications that gives a way to estimate value of gradient coefficient of the crystal.; For polycrystalline solids, there are also sufficient evidences that deformation localization can occur under condition of "nearly homogeneous" deformation and positive work hardening. It has been found that crystallographic texture, especially the texture inhomogeneity, resulting from the rotation of grains into preferred orientations, imparts a strong directionality to the stress-strain response and stability of plastic flow of polycrystalline solids. In the present study, a texture gradient polycrystal plasticity is developed by using scale invariance approach to describe the local plastic flow of a crystallite, a statistical approach (Inhomogeneous Orientation Distribution Function) to consider the orientation state of grains in a polycrystalline aggregate, and an appropriate averaging procedure to account for effects of inhomogeneous texture development on macroscopic constitutive relations of polycrystals. The linear stability analysis for the instability of polycrystals in simple shearing is performed which establishes the essential relation between the deformation localization, anisotropic plastic flow and the inhomogeneous development of texture. |
