Negative Thermomechanical Effects in Granular Composites with Incompatible Thermomechanical Parameters of Their Components

Abstract

Within the framework of the theory of thermoelasticity, the problem of the generation of additional internal thermal stresses in a composite material with granular fillers under the influence of temperature is posed. Using the spherical inclusion model applied in the theory of composites, constitutive equations are formulated, and their analytical closed-form solutions are constructed. It is shown that the internal thermal stresses initiated in the system have a localized character, are proportional to the values of the elastic moduli of the materials of each phase and the difference between their coefficients of linear thermal expansion, and decrease in inverse proportion to the cube of the radial coordinate. With the help of specific applied examples, it has been established that even at relatively moderate values of temperature changes, these stresses can reach limit values that contribute to the initiation of internal latent localized defects and cracks in the system. The cases of thermally stressed states of a spherical inclusion coated with a layer of another material, an inclusion with a cavity, and a spherical pore are also considered.