Quasi-linear correlation between shear and young’s moduli in some polycrystalline ceramics

Abstract

This work aims to investigate the correlation between the shear modulus and the Young’s modulus of some pore-free polycrystalline ceram-ics. Our study shows that the shear modulus correlates quasi-linearly with the Young’s modulus. The best fit was obtained using the linear model. The fit of the shear modulus G as a function of the Young modulus E obeys this linear expression: G = 0.43E - 7.7 (where both G and E are expressed in GPa). The coefficient of the correlation was found at around 0.994. Our expression was used to predict the shear modulus G of some other polycrystalline ceramics, especially: Dy2O3, Er2O3, and Y2O3 materials, which are estimated at around 65.6, 72.4, and 51.8 GPa, respectively. We attempt also to estimate the Vickers hardness of our materials of interest using an empirical expression of the literature. Unfortunately our predicted results are larger than those reported previously in the literature.