Mixing Rules of Young's Modulus, Thermal Expansion Coefficient and Thermal Conductivity of Solid Material with Particulate Inclusion

This analyzed a Young's modulus (E), a thermal expansion coefficient (TEC, ${\beta}$) and a thermal conductivity (${\kappa}$) of the material with simple cubic particulate inclusion using two model structures: a parallel structure and a series structure of laminated layers. The derived ${\beta}$ equations were applied to calculate the ${\beta}$ value of the W-MgO system. The accuracy was higher for the series model structure than for the parallel model structure. Young's moduli ($E_c$) of sintered porous alumina compacts were theoretically related to the development of neck growth of grain boundary between sintered two particles and expressed as a function of porosity. The series structure model with cubic pores explained well the increased tendency of $E_c$ with neck growth rather than the parallel structure model. The thermal conductivity of the three phase system of alumina-mullite-pore was calculated by a theoretical equation developed in this research group, and compared with the experimental results. The pores in the sintered composite were treated as one phase. The measured thermal conductivity of the composite with 0.5-25% porosity (open and closed pores) was in accordance with the theoretical prediction based on the parallel structure model.