Evaluation of the effect of considering elastic anisotropy on the response of polycrystals with tetragonal and HCP lattices

In recent years, much attention has been paid to polycrystalline material multilevel models based on physical theories of elastoviscoplasticity. In many applied works, based on the assumption of a uniform distribution of crystallite orientations, it is assumed that the representative macrovolume of polycrystalline metals and alloys can be considered as elastic-isotropic at the macrolevel. A similar assumption was taken in some works (especially at an early stage in the development of multilevel models) for crystallites, despite the fact that at the grain level the materials in question have a pronounced anisotropy of elastic properties. The purpose of the proposed work is to assess the differences in stress-strain state characteristics (especially residual mesostresses) at isothermal loads of the representative volume of polycrystals due to considering the anisotropy of elastic properties of its crystallites with HCP and tetragonal lattices (as compared to the data obtained for material with isotropic elastic properties obtained using different averaging procedures – Voigt, Reuss and Hill). The results of a stress-strain analysis for a simple shear (up to accumulated deformation of 50%) of polycrystalline samples are given. The study used a statistical two-level constitutive model based on the geometrically nonlinear physical theory of elastoviscoplasticity. In these constitutive models, one of the main relations is an elastic law written in a velocity relaxation form in terms of stress and strain rate measures independent on the choice of a reference system (or on an imposed rigid motion).