Stress anisotropy in opposed anvil high−pressure cells

Abstract

When materials such as sodium chloride are introduced into a piston−cylinder (or other) chamber it is commonly assumed that the state of stress for small loads is nonhydrostatic; as the load is increased, and the mean normal pressure greatly exceeds the yield stress (at zero pressure), it is commonly assumed that the state of stress approaches hydrostatic pressure. In other words it is assumed that as the mean normal pressure becomes arbitrarily large, the deviatoric stresses become negligible. It is shown in the present paper that this is an erroneous assumption. Specifically it is shown that as the mean normal pressure becomes arbitrarily large, the ratios of the deviatoric stresses to the mean normal pressure approach finite values. The present analysis also shows that as the mean normal pressure is increased, the difference of pressure deduced from interplanar spacing measurements (on a cubic crystal) for planes lying normal to the piston motion to the pressure deduced from interplanar spacing measurements for planes lying parallel to the direction of piston motion, divided by the mean normal pressure, approaches a constant value. Lattice parameter measurements with the incident beam normal to the direction for piston motion underestimate the mean normal pressure, the error decreasing to a constant value as the mean normal pressure is increased. More importantly, this analysis leads to a method of measuring yield stresses as a function of pressure at high pressures using x−ray measurement of lattice spacings of planes of the appropriate orientation.