TRANSITION THEORIES OF ELASTIC-PLASTIC DEFORMATION OF METALLIC POLYCRYSTALS

A general approach to the problem of determination of elastoplastic be havior of metallic polycrystals at finite deformation is presented. Th e relation between moving dislocation density and global slip rate for grains is developed. Transition to grain response is obtained by intr oducing the hardening matrix. Field equations for heterogeneous elasto plastic metals are transformed into an integral equation, using Green functions technique. This allows to find the spin of the lattice relat ed to texture formation. Scale transition is achieved by a self-consis tent approximation of the integral equation. New results concerning BC C metals (sheet steel) are presented. They apply to tensile test, Lank ford coefficient, initial and subsequent yield surfaces, and evolution of the internal state of the polycrystal: second-order residual stres s, stored energy and texture evolution.