Grain Structure Rearrangement by Means the Advanced Statistical Model Modified for Describing Dynamic Recrystallization

The study of grain and defect structure evolution in materials subjected to thermomechanical processing is still an urgent problem because the state of a structure substantially determines the physical and mechanical macro properties of polycrystals and polycrystalline products. Significant changes in the structure of polycrystalline materials are associated with the process of dynamic recrystallization (DRX). To investigate DRX, an extended statistical model of inelastic deformation with internal variables is proposed, which takes into consideration contact interactions between neighboring grains. We constructed a geometric image of the grain structure by applying a Laguerre polyhedron in order to describe such interactions in the statistical framework. During the recrystallization simulation, this image is being reconstructed as new recrystallized grains emerge. This leads to the problem of establishing correspondence between an initial grain structure and a reconstructed structure with the required statistical consistency. To provide such consistency, an optimization problem is formulated to preserve the stress and strain parameters and the recrystallization driving force from changes in a statistical sense. This problem is posed with respect to the distributions of differences in defect-stored energy, mutual misorientation angles between grains and sizes of these grains. A genetic algorithm is applied for resolution. By the example of simulating inelastic deformation of a representative volume element (a macrosample analogue) of polycrystalline copper, the influence of the mentioned distributions on the material response upon structure reconstruction is shown. Reasonable values for the objective weights and the genetic algorithm parameters were obtained. This paper presents a detailed description of the grain structure correspondence establishment method, the formulation of the optimization problem and the algorithm to resolve it.