Equation for estimating the Young's modulus, shear modulus and Vickers hardness of aluminosilicate glasses

The Young's modulus, shear modulus and Vickers hardness of alkali oxide-, alkaline earth oxide- and rare earth oxide-aluminosilicate glasses were measured. For the direct calculation of these properties from the glass composition, semi-empirical equations expressed in terms of the product of the apparent Madelung constant, the ionic packing ratio and the dissociation energy of each glass are presented based on Makishima's theory. The apparent Madelung constant is an empirical parameter which represents the long-range force among the ions in the glass, and the values are calculated using Templeton-Kapustinsky's equation. The experimental results indicate that the calculated values obtained using our proposed equations are in good agreement with the measured values for all types of glass examined in this study.