Grain Structure Refinement Description in the Two-Level Statistical Crystal Plasticity Model

Abstract

As both self-consistent and direct multilevel models (suggesting solution of boundary value problems at the meso-level) are extremely resource intensive, nowadays statistical crystal plasticity models are supposed to be the most promising ones for modeling technological processes of thermo-mechanical treatment of materials. The statement of a boundary value problem at the current configuration in the rate form is preferable, as it is convenient for applying numerical methods. In this case, step-by-step solution with redefining the computational domain configuration (including contacting surfaces) is possible. The two-level (macro- and meso-level) statistical constitutive model for describing deformation of polycrystalline metals and alloys, being formulated in terms of the actual configuration in the rate form, is proposed. The flexible coordinate system at the meso-level is connected with the symmetry elements of the crystallites, which determines appropriate choice of the corotational derivative in the constitutive relation. The approximate model for describing grain structure refinement on the basis of considering the amount of accumulated inelastic deformation as an integral characteristic of the defect structure state is included into the model. The results of the test calculations for describing loading processes, being relevant for equal-channel angular pressing, are given.