Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model

The constitutive equations currently used for metallic materials are written on a macroscopic scale, using macroscopic criteria and internal stresses to represent hardening. The granular nature of the material is then not represented. Since it may be critical in some cases, many attempts have already been made to account for it. So a series of modeling have been made in the framework of models having uniform stress or strain in each (crystallographic) phase. As a result, each crystallographic orientation has a different stress–strain state, but the actual microstructure is generally not introduced (Taylor model, self-consistent approach), so that the heterogenity obtained is not realistic. The aim of this work is to have a better evaluation of the heterogenity of stress and strain fields in realistic polycrystalline aggregates. For that purpose, an aggregate model is generated, and computed by finite element technique. The paper is presented in two parts, the first one being devoted to the description of the numerical tools, the second one showing the results at different scales. The present part includes the description of the 3D generator of microstructures, able to define any number of grains in a given 3D volume, with arbitrary shapes, and with a monitoring of the volume fraction of each phase. The result of this code will be taken as a starting point of the modeling, which is performed with a crystallographic model implemented in a parallel finite element code. Typical validation results are shown, with convergence data, on the size of the meshes and on the geometrical realisations of aggregates.