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

Energy dispersive synchrotron x-ray diffraction is carried out to measure differential lattice strains in polycrystalline Fe2SiO4 ( 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, alpha ( 0 <= alpha <= 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 However, when the sample is plastically deformed, the Reuss and Voigt bounds are no longer valid ( alpha becomes beyond 1).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.