Two-level elastic-viscoplastic model: application to the analysis of the crystal anisotropy influence

Multilevel crystal plasticity models have been widely used to study the processes of inelastic deformation of polycrystalline materials over the last 15-20 years. Anisotropy of plastic strains in crystallites is usually taken into account at the mesoscale, while their elastic properties are often assumed to be isotropic. The objective of this work is to assess the differences in the stress-strain characteristics (especially, residual mesoscopic stresses) by taking into account the anisotropy of elastic properties of materials calculated for the isothermal deformation of polycrystals with various types of crystallitelattice symmetry within a representative macrovolume. For this purpose, the results obtained by the authors were compared with the data received for the material with isotropic elastic properties and obtained 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 sheartest(up to the accumulated strain of 50%) are presented. The statistical two-level model developed on the basis of the geometrically nonlinear elasto-viscoplasticity theoryis used to perform calculations. In such constitutive models, the main fundamental relation is the elastic law written in the rate relaxation form in terms of the measures of the stress rates and strain rates, being independent of the choice of a reference frame (or superimposed rigid motion). It is shown that the analysis of the anisotropy effect has a noticeable impacton the characteristic macrovolume stress-strain state only at the initial stage of deformation. Subsequently, for deformations exceeding 1-1.5%, the difference becomes insignificant. At the same time, the results of calculations of the residual mesoscopic stresses (i.e., the stresses after unloading a representative macrovolume), which have a significant effect on the strength characteristics of materials, taking into account the crystallite anisotropy, turned out to be significantly different from those obtained under the isotropy hypothesis.