A composite viscoelastic model for incorporating grain boundary sliding and transient diffusion creep; correlating creep and attenuation responses for materials with a fine grain size

Abstract

A new viscoelastic creep function that incorporates both the effects of elastically-accommodated grain boundary sliding (GBS) and transient diffusion creep is proposed. It is demonstrated that this model can simultaneously describe both the transient microcreep curves and the shear attenuation/modulus dispersion in a fine-grained (d ∼ 5 µm) peridotite (olivine + 39 vol. % orthopyroxene) specimen. Low-frequency shear attenuation, , and modulus dispersion, G(ω), spectra were measured in a one-atmosphere reciprocating torsion apparatus at temperatures of 1200 ≤ T ≤ 1300°C and frequencies of 10^−2.25 ≤ f ≤ 10⁰ Hz. Reciprocating tests were complemented by a series of small stress (τ ∼ 90 kPa) microcreep experiments at the same temperatures. In contrast to previous models where the parameters of viscoelastic models are derived by fitting the Laplace transform of the creep function to measured attenuation spectra, the parameters are derived solely from the fit of the creep function to the experimental microcreep curves using different published expressions for the relaxation strength of elastically-accommodated GBS. This approach may allow future studies to better link the large dataset of steady-state creep response to the dynamic attenuation behavior.

Keywords:

• anelasticity
• internal friction
• grain boundary sliding
• diffusion creep

Acknowledgements

This work was supported financially, in part, by the National Science Foundation Division of Earth Sciences Program in Geophysics, Grant EAR-0609869; that support is gratefully acknowledged. Additionally, the authors would like to thank Joe Bunton for his help with reconditioning the reciprocating torsion apparatus and David Goldsby for numerous stimulating discussions about the dynamics of grain boundary sliding.

Notes

1. “Peridotite” is a rock name for the refractory mineral assemblage that constitutes the upper mantle of Earth (under ocean basins, ∼10–400 km depth). The primary mineral is a ferromagnesian orthosilicate, olivine (“ol:” [Mg,Fe]₂SiO₄); less abundant minerals, but important mechanically (e.g. 5), are a ferromagnesian metasilicate, orthopyroxene (“opx:” [Mg,Fe]SiO₃), and a calcium-ferromagnesian metasilicate, clinopyroxene (“cpx:” [Ca,Mg,Fe]SiO₃). Interpreting seismological data re the structure of the mantle is first-order dependent on the viscoelastic response of peridotite; developing responsible energetics models of plate tectonics is first-order dependent on the plastic response of peridotite. Application of these experimental rheology data to natural conditions requires, at minimum, extrapolation in grain size from the micrometer grain sizes used in laboratory studies to the millimeter-to-centimeter grain sizes observed in natural peridotite.