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Abstract The rheology of the upper mantle impacts a variety of geodynamic processes, including postseismic deformation following great earthquakes and post-glacial rebound. The deformation of upper mantle rocks is controlled by the rheology of olivine, the most abundant upper mantle mineral. The mechanical properties of olivine at steady state are well constrained. However, the physical mechanism underlying transient creep, an evolutionary, hardening phase converging to steady state asymptotically, is still poorly understood. Here, we constrain a constitutive framework that captures transient creep and steady state creep consistently using the mechanical data from laboratory experiments on natural dunites containing at least 94% olivine under both hydrous and anhydrous conditions. The constitutive framework represents a Burgers assembly with a thermally activated nonlinear stress-versus-strain-rate relationship for the dashpots. Work hardening is obtained by the evolution of a state variable that represents internal stress. We determine the flow law parameters for dunites using a Markov chain Monte Carlo method. We find the activation energy $$430\pm 20$$ 430 ± 20 and $$250\pm 10$$ 250 ± 10 kJ/mol for dry and wet conditions, respectively, and the stress exponent $$2.0\pm 0.1$$ 2.0 ± 0.1 for both the dry and wet cases for transient creep, consistently lower than those of steady-state creep, suggesting a separate physical mechanism. For wet dunites in the grain-boundary sliding regime, the grain-size dependence is similar for transient creep and steady-state creep. The lower activation energy of transient creep could be due to a higher jog density of the corresponding soft-slip system. More experimental data are required to estimate the activation volume and water content exponent of transient creep. The constitutive relation used and its associated flow law parameters provide useful constraints for geodynamics applications. Graphical Abstract
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The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law
Abstract. Viscous flow in ice is often described by the Glen flow law – anon-Newtonian, power-law relationship between stress and strain rate with astress exponent n ∼ 3. The Glen law is attributed tograin-size-insensitive dislocation creep; however, laboratory and fieldstudies demonstrate that deformation in ice can be strongly dependent ongrain size. This has led to the hypothesis that at sufficiently lowstresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studiesfind that neither dislocation creep (n ∼ 4) nor grain boundarysliding (n ∼ 1.8) have stress exponents that match the value ofn ∼ 3 in the Glen law. Thus, although the Glen law provides anapproximate description of ice flow in glaciers and ice sheets, itsfunctional form is not explained by a single deformation mechanism. Here weseek to understand the origin of the n ∼ 3 dependence of theGlen law by using the “wattmeter” to model grain size evolution in ice.The wattmeter posits that grain size is controlled by a balance between themechanical work required for grain growth and dynamic grain size reduction.Using the wattmeter, we calculate grain size evolution in two end-membercases: (1) a 1-D shear zone and (2) as a function of depth within anice sheet. Calculated grain sizes match both laboratory data and ice coreobservations for the interior of ice sheets. Finally, we show thatvariations in grain size with deformation conditions result in an effectivestress exponent intermediate between grain boundary sliding and dislocationcreep, which is consistent with a value of n = 3 ± 0.5 over the rangeof strain rates found in most natural systems.
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- Award ID(s):
- 1838410
- PAR ID:
- 10374027
- Date Published:
- Journal Name:
- The Cryosphere
- Volume:
- 15
- Issue:
- 9
- ISSN:
- 1994-0424
- Page Range / eLocation ID:
- 4589 to 4605
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5194/tc-15-4589-2021
