Modeling of microstructural stresses of composite materials during phase transformations

Using the method of self-consistent field, we consider the problem of competing influence of structural components on the properties of the matrix arising in the transformation phase. To this end, the problem of determining the average stresses in the elements of the microstructure through the elastic characteristics and the concentrations of the matrix and phase components, as well as free deformations of the phases undergoing volume transformations, is previously solved. As a model, we consider a continuous matrix with isotropic elastic characteristics, into which spherical inclusions are introduced. The introduced inclusions are strongly intermixed and distributed equally. The matrix was assumed to be free from external loads, so the macroscopic stresses are zero. Under certain external influences, inclusions begin to undergo structural transformations with changes in the size and specific volume of the phase components, some of them begin to expand and others contract, which causes stresses in the composite structure that are balanced on a macroscopic scale. Following the method of the generalized self-consistent field, the average stresses over the volume occupied by the i-th dispersed phase are determined from the Eshelby solution on the deformation of a single particle. The collective influence of other dispersed particles is taken into account by the fact that the deformation in the matrix is different from zero and is assumed to be equal to the average deformation in the volume occupied by the matrix phase in the composite material. As a result of the transformations using the Eshelby tensor and the generalized Hooke’s law, which is satisfied by the average stresses and strains in the matrix, a closed system of equations is obtained for determining the average stresses and deformations in the phase components, that are expressed in terms of the elastic characteristics and concentrations of the matrix and phase components as well as deformation of phases undergoing volume transformations.