A Two-Level Elasto-Viscoplastic Model: Application to the Analysis of the Crystal Anisotropy Influence

Multilevel (mainly two-level) crystal plasticity models have been widely used for studying processes of inelastic deformation of polycrystalline materials over the last 15-20 years. Anisotropy of plastic strain in crystallites is usually taken into account at the mesoscale, while their elastic properties are often considered as isotropic. The purpose of this study is to assess the differences in the stress-strain characteristics (especially residual mesoscopic stress) by taking into account the anisotropy of elastic properties of materials calculated for the isothermal deformation of polycrystals with various types of crystallite lattice symmetry within a representative macroscopic volume. To this end, our results are compared with the data obtained for a material with isotropic elastic properties using the Voigt-Reuss-Hill averaging procedures. The results of the analysis for the stress-strain state of polycrystalline samples with fcc, bcc, and hcp lattices obtained in a simple shear test (up to the accumulated strain of 50%) are presented. The statistical two-level constitutive model, constructed within the geometrically nonlinear elasto-viscoplasticity theory, is used for calculations. In such constitutive models, the main fundamental relation is the law of elasticity written in the rate relaxation form in terms of the measures of the stress and strain rates, being independent of the chosen reference frame (or of the superimposed rigid motion). It is shown that the analysis of the anisotropy effect has a noticeable impact on the characteristic macroscopic volume stress-strain state only in the initial deformation stage. Subsequently, for deformations exceeding 1-1.5%, the difference becomes insignificant. At the same time, the results of calculating the residual mesoscopic stress (i.e., the stress after unloading the representative macroscopic volume), which has a significant effect on the strength characteristics of materials, with allowance for the crystal anisotropy turned out to be significantly different from those obtained under the hypothesis of isotropy.