Elastic behavior of random polycrystals composed of anisotropic α-quartz (SiO_2) under pressure

摘要

This work presents several sets of results for granular media all composed of quartz (SiO_2) and all having grains with trigonal (six constant) elastic symmetry. In some cases, the samples had significant amounts of external pressure (up to 20 GPa) applied to the quartz samples while the elastic constants were being either measured or simulated. In other examples, the temperatures ranged from room temperature down to values approaching absolute zero. In addition to the traditional Voigt and Reuss bounds on effective isotropic bulk and shear moduli, the Hashin-Shtrikman bounds of these elastic moduli have also been computed in all these examples. We find that the Hashin-Shtrikman bounds provide a significant tightening of the traditional bounds on the moduli in most cases. Rarely, the Hashin-Shtrikman upper bounds for shear modulus may coincide with Voigt estimates of the shear modulus. More typically we find the HS bounds on both shear and bulk modulus are so close that their averaged values (called here the "self-consistent average" estimates) for both bulk and shear modulus values are tightly constrained by the HS bounds themselves. In contrast, the traditional VRH (Voigt-Reuss-Hill) estimates of the moduli often lie outside of the HS bounds, thus giving reasons for doubting the accuracy of VRH estimates in general - and especially for pressurized samples. Of the eight scenarios considered in the paper, four have substantial confining pressures (10 or 20 GPa), and four have zero confining pressure. One general distinction arising in these particular data sets is observed: when the confining pressure is negligible, the VRH estimates are found always to lie inside the Hashin-Shtrikman bounds. In contrast, when the confining pressure is P=10 GPa or higher the VRH estimates of bulk and shear moduli both lie outside the Hashin-Shtrikman bounds.