SECTION 4.2 – Elastoplasticity of Metallic Polycrystals by the Self-Consistent Model

This chapter describes the elastoplasticity of metallic polycrystals by the self-consistent model. The self-consistent model constitutes a simple way of predicting the effective behavior of inhomogeneous media, especially for metallic polycrystals, for which it may be considered a “good” approximation. In the case of elastoplasticity, self-consistent modeling allows one to take into account texture transformations, development of second-order internal stresses, intragranular hardening, and so forth. All these phenomena are strongly path-dependent. In the case of metallic polycrystals, the development or use of a self-consistent model requires the following: (1) the characterization of the microstructure: shape, size, and orientation of the grains, orientation of the lattices; (2) the definition of elastic moduli of the single crystal; and (3) the definition of the mechanisms: number and orientation of the slip systems, associated Burgers vector, and the parameters describing the inelastic behavior. Some of these values are well established from metallographic experiments on single crystals. Other material parameters are measured on single crystals or identified by inverse methods using experimental results on a polycrystals.