ANALYSIS OF TWO APPROACHES TO DETERMINING THE ELASTICITY CONSTANTS OF POLYCRYSTALLINE MATERIALS

Abstract

The article compares the results deriving from the relations of transition from microtensions and deformations to macrotensions and deformations proposed by E. Kroner with the respective relations obtained within the structural model built on the basis of Hill relations and principles: average connections; orthoganality of stress and strain tensor fluctuations; the extreme discrepancy of the macroscopic measure with the mean value of the appropriate microscopic analog. It is shown that the macroscopic shear modulus obtained in E.Kroner's model is greater than or equal to the respective value obtained in V.Marina's model. An inequality between the anisotropy coefficient of the cubic lattice of polycrystalline materials and Poisson's ratio is established. Relations are analyzed by which objective macroscopic measures of the energy of volume and shape change in the field of reversible stresses are determined.