Homogenization of the thermoelastic properties of silicon nitride

The main contribution of this paper is the numerical homogenization of the effective thermoelastic properties of silicon nitride based on the temperature-dependent thermoelastic data of the two phases. Silicon nitride consists of two phases: rod-like β-Si3N4 grains (approximately 90 vol.%) and the glassy phase formed by the sintering additives. Due to its microstructure, silicon nitride has a high crack and thermal shock resistance. The homogenization is performed with the finite element method, where a new type of periodic boundary conditions is used that is applicable to non-conforming finite element meshes. The periodic microstructures considered are generated by means of a statistical microstructure generator. The temperature-dependent material properties on the microscale are experimental results taken from the literature. The effective properties obtained are compared to experimental data from the literature and to new experiments. The numerically determined local fields are discussed and different measures of triaxiality are examined.