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1. Test of the Effective Stress Law for Semibrittle Deformation Using Isostatic and Triaxial Load Paths

   https://doi.org/10.1029/2020JB021326  

   Ding, J.; Chester, F. M.; Chester, J. S. (May 2021, Journal of Geophysical Research: Solid Earth)

   Abstract For brittle friction and rock deformation, the coefficientαin the general effective stress relationσ^e = σ − αP_pcan be approximated as unity with sufficient accuracy. However, it is uncertain ifαdeviates from unity for semibrittle flow when both brittle and intracrystalline‐plastic deformation is involved. We conducted triaxial and isostatic compression experiments on synthetic salt‐rocks (∼300 ppm water) at room temperature to test the effective stress relation in the semibrittle regime using silicone oil and argon gas as pore fluids. Confining and pore pressures were cycled while their difference (differential pressure) was kept constant, such that changes in the mechanical behavior would indicate deviation ofαfrom unity. Microstructural observations were used to determine the dependence ofαon true area of grain contact from asperity yielding. In triaxial compression experiments, semibrittle flow involves grain boundary cracking and sliding, and intragranular dislocation glide and cracking. Flow strength remains constant for changes in pore fluid pressure of more than two orders of magnitude. In isostatic compression experiments, samples show combined processes of microcracking, grain boundary sliding, dislocation glide, and fluid‐assisted grain boundary migration recrystallization. Volumetric strain depends directly on the differential pressures (i.e.,αequals one). Analysis of grain‐contact area in both experiments indicates thatαis independent of the true area of contact defined by plastic yielding at grain boundaries. The observation ofαeffectively equals one may be explained by operation of pressure‐independent intracrystalline‐plastic mechanisms and transmission of pore pressure at grain boundaries through thin fluid films. 

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2. Ductile Deformation of the Lithospheric Mantle

   https://doi.org/10.1146/annurev-earth-031621-063756  

   Warren, Jessica M.; Hansen, Lars N. (May 2023, Annual Review of Earth and Planetary Sciences)

   The strength of lithospheric plates is a central component of plate tectonics, governed by brittle processes in the shallow portion of the plate and ductile behavior in the deeper portion. We review experimental constraints on ductile deformation of olivine, the main mineral in the upper mantle and thus the lithosphere. Olivine deforms by four major mechanisms: low-temperature plasticity, dislocation creep, dislocation-accommodated grain-boundary sliding (GBS), and diffusion-accommodated grain-boundary sliding (diffusion creep). Deformation in most of the lithosphere is dominated by GBS, except in shear zones—in which diffusion creep dominates—and in the brittle-ductile transition—in which low-temperature plasticity may dominate. We find that observations from naturally deformed rocks are consistent with extrapolation of the experimentally constrained olivine flow laws to geological conditions but that geophysical observations predict a weaker lithosphere. The causes of this discrepancy are unresolved but likely reside in the uncertainty surrounding processes in the brittle-ductile transition, at which the lithosphere is strongest. ▪ Ductile deformation of the lithospheric mantle is constrained by experimental data for olivine. ▪ Olivine deforms by four major mechanisms: low-temperature plasticity, dislocation creep, dislocation-accommodated grain-boundary sliding, and diffusion creep. ▪ Observations of naturally deformed rocks are consistent with extrapolation of olivine flow laws from experimental conditions. ▪ Experiments predict stronger lithosphere than geophysical observations, likely due to gaps in constraints on deformation in the brittle-ductile transition. 

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3. Grain size effect on strain localization, slip-grain boundary interaction and damage in the Alloy 718 Ni-based superalloy at 650 °C

   https://doi.org/10.1016/j.msea.2024.146927  

   Jullien, Malo; Black, RL; Stinville, JC; Legros, Marc; Texier, Damien (October 2024, Materials Science and Engineering: A)

   Grain size effects on the early plastic strain localization and slip transfer at grain boundaries were investigated for the Alloy 718 Ni-based superalloy at 650C. Three microstructures with different grain sizes underwent monotonic tensile tests at 650C, both in air and under vacuum, until rupture. All the microstructure variants exhibit fully intragranular fracture under vacuum and partially intergranular fracture in air. In this latter case, predominant intergranular fracture mode was found in the fine-grain microstructures. Interrupted tensile tests were also conducted under vacuum with ex-situ SEM high-resolution digital image correlation (HR-DIC) measurements to assess in-plane kinematics fields at the microstructure scale. Out-of-plane displacement jumps were obtained using laser scanning confocal microscopy. Both crystallographic slip within grains and near twin boundaries (TBs) and morphological sliding happening at grain boundaries (GBs) were documented. Statistical analysis of all plastic events aimed at quantifying strain localization distribution as a function of the microstructure. The fine-grain microstructure was found to have extensive strain localization at grain boundaries, while the coarse-grain microstructure is more prone to intragranular slip development and slip localization near TBs. Different scenarios of slip band/grain boundary interactions were evidenced. 

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4. Relating strain localization and Kaiser effect to yield surface evolution in brittle rocks

   https://doi.org/10.1093/gji/ggaa130  

   Gajst, Hannah; Shalev, Eyal; Weinberger, Ram; Marco, Shmuel; Zh, Wenlu; Lyakhovsky, Vladimir (June 2020, Geophysical Journal International)

   null (Ed.)

   SUMMARY The yield surfaces of rocks keep evolving beyond the initial yield stress owing to the damage accumulation and porosity change during brittle deformation. Using a poroelastic damage rheology model, we demonstrate that the measure of coupling between the yield surface change and accumulated damage is correlated with strain localization and the Kaiser effect. Constant or minor yield surface change is associated with strong strain localization, as seen in low-porosity crystalline rocks. In contrast, strong coupling between damage growth and the yield surface leads to distributed deformation, as seen in high-porosity rocks. Assuming that during brittle deformation damage occurs primarily in the form of microcracks, we propose that the measured acoustic emission (AE) in rock samples correlates with the damage accumulation. This allows quantifying the Kaiser effect under cyclic loading by matching between the onset of AE and the onset of damage growth. The ratio of the stress at the onset of AE to the peak stress of the previous loading cycle, or Felicity Ratio (FR), is calculated for different model parameters. The results of the simulation show that FR gradually decreases in the case of weak coupling between yield surface and damage growth. For a strong damage-related coupling promoting significant yield surface change, the FR remains close to one and decreases only towards the failure. The model predicts that a steep decrease in FR is associated with a transition between distributed and localized modes of failure. By linking the evolving yield surface to strain localization patterns and the Kaiser effect, the poroelastic damage rheology model provides a new quantitative tool to study failure modes of brittle rocks. 

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5. The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law

   https://doi.org/10.5194/tc-15-4589-2021  

   Behn, Mark D.; Goldsby, David L.; Hirth, Greg (January 2021, The Cryosphere)

   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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