Abstract

The influence of elastic characteristics of phases and their volume content on the distribution of energies of shape and volume changes in a representative volume of a multiphase polycrystal has been studied. The analysis is carried out within the framework of a two-level constitutive model. The connection between microscopic and macroscopic stress and strain tensors is established based on the principles of averaged connections, orthogonality of oscillations of stress and strain tensors, as well as the extremum of discrepancy between macroscopic measures and the corresponding average values of microscopic analogues. A general system of equations is obtained for determining the elasticity constants of a multiphase polycrystal. It is shown that the bulk modulus of elasticity is equal to the geometric mean value of the bulk modulus of elasticity obtained in two limiting versions of the model: uniform stressed and uniform deformed states. Numerical studies of changes in stress invariants, strains and energies of shape/volume change depending on the concentration of phases and their elastic characteristics were carried out. The calculations performed show that the invariants of the stress/strain and strain energy tensors vary depending on the degree of phase concentration according to non-monotonic laws..