Analytical model of thermal stresses in two- and three-component materials II

The paper deals with an analytical model of thermal stresses in isotropic solid continuum represented by periodically distributed isotropic spherical particles in an isotropic infinite matrix, with or without an isotropic spherical envelope on the particle surface. The isotropic multi-particle-(envelope)-matrix system to represent a model system regarding the analytical modelling is applicable to two and three types of two- and three-component isotropic materials, respectively. The thermal stresses as functions of microstructural parameters (particle volume fraction, particle radius, inter-particle distance, envelope thickness) originate during a cooling process as a consequence of the difference in thermal expansion coefficients. The analytical modelling based on fundamental equations of mechanics of solid continuum represents a combination of different mathematical techniques applied to the equilibrium and compatibility equations, where a solution for a radial stress, and consequently for tangential and shear stresses is obtained. Finally, as an application example, the analytical model of the thermal stresses in the multi-particle-matrix system is applied to the SiC-Si3N4 ceramics representing a two-component material which consists of SiC particles and Si3N4 matrix.