SINGLE-CRYSTAL GRADIENT APPROACH TO PLASTICALLY DEFORMED POLYCRYSTAL

This study presents gradient theory for plastically deformed polycrystal using single crystal approach. The theory is developed with a view to approximate material behavior of the polycrystalline solid at infinitesimal length scale. Each grain of the polycrystal is treated as a single crystal such that the plastic distortion at point of the body is approximated by net slip of system of slips (shear strains) across slip-planes contained in an individual grain. The microscopic stresses, micro force balance, constitutive laws and viscoplastic flow rule which characterize the plastic behavior at points of the polycrystal are transformed into their equivalents on the system of slip-planes such that each slip-plane is governed by its microscopic stresses, microscopic force balance, constitutive laws and plastic flow rules. In addition, the inequality which relates the initial yield strengths of polycrystalline and monocrystalline materials is highlighted. Finally, the proposed theory is assumed to be suitable for polycrystals which are almost single crystals.