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

Jiuhua Chen, Li Li, Tony Yu, Hongbo Long, Donald Weidner, Liping Wang and Michael Vaughan

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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, 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 However, when the sample is plastically deformed, the Reuss and Voigt bounds are no longer valid (α becomes beyond 1).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.


PACS

62.50.-p High-pressure effects in solids and liquids

62.20.D- Elasticity

83.60.La Viscoplasticity; yield stress

83.50.-v Deformation and flow

62.20.F- Deformation and plasticity

61.05.cp X-ray diffraction

Subjects

Fluid dynamics

Condensed matter: structural, mechanical & thermal

Dates

Issue 25 (28 June 2006)

Received 17 February 2006, in final form 4 May 2006

Published 8 June 2006



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