Do Reuss and Voigt bounds really bound in high-pressure rheology experiments?

Abstract

Energy dispersive synchrotron x-ray diffraction is carried out to measure differential lattice strains in polycrystalline Fe(2)SiO(4) (fayalite) and MgO samples using a multi-element solid state detector during high-pressure deformation. The theory of elastic modelling with Reuss (iso-stress) and Voigt (iso-strain) bounds is used to evaluate the aggregate stress and weight parameter, α (0≤α≤1), of the two bounds. Results under the elastic assumption quantitatively demonstrate that a highly stressed sample in high-pressure experiments reasonably approximates to an iso-stress state. However, when the sample is plastically deformed, the Reuss and Voigt bounds are no longer valid (α becomes beyond 1). Instead, if plastic slip systems of the sample are known (e.g. in the case of MgO), the aggregate property can be modelled using a visco-plastic self-consistent theory.