Low‐frequency shear attenuation in polycrystalline olivine: Grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology

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Abstract

The high‐temperature (1200–1285°C) torsional dynamic attenuation (10 −3 –10 0 Hz) and unidirectional creep behavior of a fine, uniform grain sized ( d ≈ 3 μm) olivine (∼Fo 92 ) aggregate have been measured. In all cases, the material is found to be mechanically linear (i.e., γ( t ), γ ∝ σ xy 1 ), indicating that diffusional processes dominate the deformation kinetics in these experiments. The creep response displays a large decelerating transient in the strain rate leading to a nominally constant “steady state.” The attenuation behavior displays a band in Q G −1 that is moderately dependent on frequency ( Q G −1 ≈ f −0.35 ) and temperature with −1.5<log( Q G −1 )<0.5. The creep and attenuation behaviors are accurately represented by a compliance function based on the Andrade model of viscoelasticity, which incorporates a power law description of anelastic strain (i.e., γ α ∝ t n with n ≈ ½), and its Laplace transform, respectively. The uniformity of the material and the nature of its dynamic response allow the argument that the power law transient has a physical interpretation: because the attenuation band is not associated with a range of grain sizes or a distribution of lattice dislocations, the transient term describes the intrinsic transient in diffusional creep, which arises due to the evolution of tractions on the grain boundaries and is effected by chemical diffusion within a diminishing potential. Employing the rheological model of Raj [1975] for the intrinsic transient, we demonstrate that the “high‐temperature background” absorption can be predicted from the creep response; a master curve description of the attenuation results. Comparison of these data to those of previous investigators, and contemplating their application to the upper mantle, raises the suggestion, explored in this paper, that the subgrain size may prove the critical microstructural variable effecting the broad attenuation band seen in all experiments as well as in the upper mantle.

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