In this work, a new supplementary formula was introduced to modify the Kerner model. This supplementary formula enable the Kerner model to predict the thermal expansion coefficient of multi-phase reinforced composites by normalization of the thermal expansion coefficient, bulk modulus, and shear modulus of the reinforcements. For comparison, the modified Kerner model as well as modified Schapery, the rule of mixtures, and Turner models were used to predict the thermal expansion coefficient of multi-phase reinforced composites 6092 Aluminum Alloy/silicon carbide/β-eucryptite. The results confirm the robustness of the modified Kerner model for predicting the thermal expansion coefficient of composites with multi-phase near-spherical inclusions. It may provide a fine selection to predict the thermal expansion coefficient of multi-phase reinforced metal matrix composites which cannot predict efficiently before.

The thermal expansion of a ZrO2-20 mol% Gd2O3 pellet has been systematically investigated using a thermo-mechanical analyzer in the temperature range of 293-1773 K. Variations in the thermal expansion coefficient and density upon temperature change were calculated using the thermal expansion data. The average linear thermal expansion coefficient of the ZrO2-20 mol% Gd2O3 pellet was found to be 9.522 × 10–6 K–1 in the range of 298-1073 K. This value is smaller than that of ZrO2 and larger than that of Gd2O3. Further, with an increase in temperature to 1773 K, the density of ZrO2-20 mol% Gd2O3 pellet was found to decrease to 94.98 % of the initial density at 293 K.