Analysis of extreme values of stress and strain invariants in multiphase polycrystals

Abstract

The limits of change in stress/strain invariants in the phases of polycrystal-line materials with cubic lattices are investigated. The relationship between the local and macroscopic parameters is established on the basis of the follow-ing principles: averaged connections, orthogonality of fluctuations of the stress and strain tensors, extremum of discrepancy between the macroscopic measures and suitable average values of microscopic analogues. General ex-pressions for extreme values of stress/strain deviator invariants for the pol-ycrystal phases are obtained. The non-monotonic nature of changes in the extreme values of the invariants of stress/strain deviators and volumetric stresses/strains depending on the phase concentration is revealed. In case of a two-phase polycrystal, as the harder phase increases, the invariants first increase, reaching their maximum value at a concentration of less than 5%, and then, monotonically decrease. Volumetric macrostress has a nonlinear effect on the patterns of changes in volumetric stresses in the grains of a pol-ycrystalline material.