On phase transitions in a domain of material inhomogeneity. I. Phase transitions of an inclusions in a homogeneous external field

Abstract

We pose and study the problem on an inclusion experiencing a phase transition in a homogeneous external stress field transferred by a matrix. The matrix is formed by a linear-elastic material. The inclusion material admits phase transitions under strain, and the passage from one phase state into another, as well as two-phase states, is determined by the energy preference considerations and the possible existence of two-phase states. For the simplest problem we consider the problem of phase transitions in a cylindrical inclusion under homogeneous plane strain conditions. In the space of strains, we construct the domains of existence of the inclusion one-phase states and the switching surfaces between the one-phase states. We study the possibility of the inclusion two-phase states, prove the characteristic properties of axisymmetric two-phase strains, and examine their stability. We also demonstrate the scale effect, namely, the influence of the relative dimensions of the inclusion and the body on the inclusion phase state. In the second part of the paper, we study the interaction between an inclusion experiencing phase transitions and a crack.