The two-level elastic-viscoplastic model: analysis of the influence of crystallite orientation distribution in the reference configuration and the complexity of loading on the behavior of polycrystalline materials

Components and structural elements used in modern technology are often exposed to significant loads in wide ranges of high and low temperature and deformation rates, high stresses and loading rates.. All these factors, as well as complex loading schemes that must be considered when designing structures of different sizes - from miniature to large-scale -, put forward increased requirements for the properties of materials. A significant part of the structures used in various industries are made of polycrystalline metals and alloys. The physical and mechanical properties of polycrystalline aggregates in finished products depend on their phase and component composition, meso- and microstructure, including the orientation of crystallites (grains, subgrains), symmetry properties of subgrains, and on the initial (residual) stresses that occur during their manufacturing. Experimenting with full-scale structures requires considerable material and time expenditures, therefore mathematical modeling approaches are applied, especially for designing structures and their manufacturing processes. Mathematical modelling provides an opportunity to describe processes in any materials with this or that degree of accuracy. Constitutive relations (or constitutive models) are the most important element of the mathematical models developed for solving these problems. Currently, the most promising among these models are multilevel models based on the introduction of internal variables and crystal plasticity. When analyzing the elastic-plastic deformation of various products, the isotropic constitutive relations are often used to simplify the analysis of the elastic component of deformations. The present work is devoted to the study of errors arising when the anisotropic elastic properties of crystallites are replaced by the corresponding isotropic properties of the materials with BCC, FCC and HCP lattices for different laws of orientation distribution of crystallites in a polycrystalline aggregate in the reference configuration. Using the two-level model based on the elastic-viscoplastic crystal plasticity, a series of numerical experiments on simple shear loading, sequences of two simple loads and cyclic deformation were performed to analyze the evolution of the stress-strain state and to estimate the residual stresses in crystallites.