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

2021 ◽  
Vol 15 (9) ◽  
pp. 4589-4605
Author(s):  
Mark D. Behn ◽  
David L. Goldsby ◽  
Greg Hirth
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Stress Exponent ◽  
Ice Sheets ◽  
Grain Boundary Sliding ◽  
Dislocation Creep ◽  
Ice Flow ◽  
Size Evolution ◽  
Boundary Sliding ◽  
Flow Law

Abstract. Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain rate with a stress exponent n ∼ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ∼ 4) nor grain boundary sliding (n ∼ 1.8) have stress exponents that match the value of n ∼ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ∼ 3 dependence of the Glen law by using the “wattmeter” to model grain size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone and (2) as a function of depth within an ice sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

scholarly journals The role of grain-size evolution on the rheology of ice: Implications for reconciling laboratory creep data and the Glen flow law

2020 ◽  
Author(s):  
Mark D. Behn ◽  
David L. Goldsby ◽  
Greg Hirth
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Stress Exponent ◽  
Ice Sheets ◽  
Grain Boundary Sliding ◽  
Dislocation Creep ◽  
Ice Flow ◽  
Size Evolution ◽  
Boundary Sliding ◽  
Flow Law

Abstract. Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain-rate with a stress exponent n ~ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain-size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ~ 4) nor grain boundary sliding (n ~ 1.8) have stress exponents that match the value of n ~ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ~ 3 dependence of the Glen law by using the wattmeter to model grain-size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone, and (2) as a function of depth within an ice-sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

Inferring ice rheology in Antarctic ice shelves from remotely sensed observations

2021 ◽  
Author(s):  
Joanna Millstein ◽  
Brent Minchew
Keyword(s):  
Stress Exponent ◽  
Ice Sheets ◽  
Remotely Sensed ◽  
Creep Mechanism ◽  
Surface Velocity ◽  
Dislocation Creep ◽  
Ice Flow ◽  
Ice Shelves ◽  
Creep Mechanisms ◽  
Flow Law

<p>Glaciers and ice sheets flow as a consequence of ice rheology. At the temperatures and pressures found on Earth, several creep mechanisms allow glacier ice to flow as a non-Newtonian (shear-thinning) viscous fluid. The semi-empirical constitutive relation known as Glen’s Flow Law is often used to describe ice flow and to provide a simple expression for an effective viscosity that decreases with increasing stress and deformation rate. Glen’s Flow Law is a power-law relation between effective strain rate and deviatoric stress, with two parameters defining the rheology of ice: a rate factor, A, and stress exponent, n. The rate factor depends on features such as temperature and grain size, while the stress exponent is primarily representative of the creep mechanism. Neither A nor n are well constrained in natural ice, and the stress exponent is typically assumed to be n = 3 everywhere. Here, we take advantage of recent improvements in remotely sensed observations of surface velocity and ice shelf thickness to infer the values of A and n in Antarctic ice shelves. We focus on areas of ice shelves that flow in a purely extensional regime, where extensional stresses are proportional to observed ice thickness, drag at the base of the ice is negligible, and extensional strain-rates are calculated from the gradients of observed surface velocity fields. In this manner, we use independent observational data to derive spatially dependent constraints on the rate factor A and stress exponent n in Glen's Flow Law. The robust spatial variability provides insights into the creep mechanisms of ice, thereby capturing rheological properties from satellite observations. Our analysis indicates that n ≈ 4 in most fast-flowing areas in an extensional regime, contrary to the prototypical value of n = 3. This finding implies higher non-linearity in ice flow than typically prescribed, influencing calculations of mass flux and the response of ice sheets to perturbations. Additionally, This result suggests that dislocation creep is the dominant creep mechanism in extensional regimes of Antarctic ice shelves, indicative of tertiary creep. This analysis unites theoretical work and synoptic-scale observations of ice flow, providing insights into the rheology and stress-states of ice shelves in Antarctica.</p>

scholarly journals Strain localization in ultramylonitic marbles by simultaneous activation of dislocation motion and grain boundary sliding (Syros, Greece)

2015 ◽  
Vol 7 (3) ◽  
pp. 2663-2695
Author(s):  
A. Rogowitz ◽  
J. C. White ◽  
B. Grasemann
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Strain Localization ◽  
Grain Boundary Sliding ◽  
Dislocation Creep ◽  
Angle Distribution ◽  
Fine Grained ◽  
Boundary Triple ◽  
Boundary Sliding ◽  
The Cross

Abstract. Extreme strain localization occurred in the center of the cross-cutting element of a flanking structure in almost pure calcite marbles from Syros, Greece. At the maximum displacement of 120 cm along the cross-cutting element evidence of grain size sensitive deformation mechanisms can be found in the ultramylonitic marbles, which are characterized by (1) an extremely small grain size (∼3 μm), (2) grain boundary triple junctions with nearly 120° angles, (3) a weak crystallographic preferred orientation with very low texture index (J=1.4), (4) a random misorientation angle distribution curve and (5) the presence of small cavities. Using transmission electron microscopy a deformation sequence is observed comprising, first recrystallization by bulging resulting in the development of the fine-grained ultramylonite followed by the evolution of a high dislocation density (∼1013 m−2) with ongoing deformation of the fine-grained ultramylonite. The arrangement of dislocations in the extremely fine grain sized calcite differs from microstructures created by classical dislocation creep mediated by combined glide and thermally activated climb. Instead, it exhibits extensive glide and dislocation networks characteristic of recovery accommodated by cross-slip and network-assisted dislocation movement without formation of idealized subgrain walls. The enabling of grain boundary sliding to dislocation activity is deemed central to initiating and sustaining strain softening and is argued to be an important strain localization process in calcite rocks, even at high strain rate (10−9 s−1) and low temperature (300 °C).

scholarly journals Strain localization in ultramylonitic marbles by simultaneous activation of dislocation motion and grain boundary sliding (Syros, Greece)

Solid Earth ◽  
2016 ◽  
Vol 7 (2) ◽  
pp. 355-366 ◽  
Author(s):  
A. Rogowitz ◽  
J. C. White ◽  
B. Grasemann
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Strain Localization ◽  
Grain Boundary Sliding ◽  
Dislocation Creep ◽  
Angle Distribution ◽  
Fine Grained ◽  
Boundary Triple ◽  
Boundary Sliding ◽  
The Cross

Abstract. Extreme strain localization occurred in the centre of the cross-cutting element of a flanking structure in almost pure calcite marbles from Syros, Greece. At the maximum displacement of 120 cm along the cross-cutting element, evidence of grain size sensitive deformation mechanisms can be found in the ultramylonitic marbles, which are characterized by (1) an extremely small grain size ( ∼  3 µm), (2) grain boundary triple junctions with nearly 120° angles, (3) a weak crystallographic preferred orientation with very low texture index (J = 1.4), (4) a random misorientation angle distribution curve and (5) the presence of small cavities. Using transmission electron microscopy, a deformation sequence is observed comprising recrystallization dominantly by bulging, resulting in the development of the fine-grained ultramylonite followed by the development of a high dislocation density ( ∼  1013 m−2) with ongoing deformation of the fine-grained ultramylonite. The arrangement of dislocations in the extremely fine-grain-sized calcite differs from microstructures created by classical dislocation creep mediated by combined glide and thermally activated climb. Instead, it exhibits extensive glide and dislocation networks characteristic of recovery accommodated by cross-slip and network-assisted dislocation movement without formation of idealized subgrain walls. The enabling of grain boundary sliding to dislocation activity is deemed central to initiating and sustaining strain softening and is argued to be an important strain localization process in calcite rocks, even at a high strain rate ( ∼  10−9 s−1) and low temperature (300 °C).

scholarly journals Dislocation-accommodated grain boundary sliding as the major deformation mechanism of olivine in the Earth’s upper mantle

2015 ◽  
Vol 1 (9) ◽  
pp. e1500360 ◽  
Author(s):  
Tomohiro Ohuchi ◽  
Takaaki Kawazoe ◽  
Yuji Higo ◽  
Ken-ichi Funakoshi ◽  
Akio Suzuki ◽  
...  
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Upper Mantle ◽  
Laboratory Data ◽  
Grain Boundary Sliding ◽  
Dislocation Creep ◽  
Softening Effect ◽  
Water Fugacity ◽  
Boundary Sliding

Understanding the deformation mechanisms of olivine is important for addressing the dynamic processes in Earth’s upper mantle. It has been thought that dislocation creep is the dominant mechanism because of extrapolated laboratory data on the plasticity of olivine at pressures below 0.5 GPa. However, we found that dislocation-accommodated grain boundary sliding (DisGBS), rather than dislocation creep, dominates the deformation of olivine under middle and deep upper mantle conditions. We used a deformation-DIA apparatus combined with synchrotron in situ x-ray observations to study the plasticity of olivine aggregates at pressures up to 6.7 GPa (that is, ~200-km depth) and at temperatures between 1273 and 1473 K, which is equivalent to the conditions in the middle region of the upper mantle. The creep strength of olivine deforming by DisGBS is apparently less sensitive to pressure because of the competing pressure-hardening effect of the activation volume and pressure-softening effect of water fugacity. The estimated viscosity of olivine controlled by DisGBS is independent of depth and ranges from 1019.6to 1020.7Pa·s throughout the asthenospheric upper mantle with a representative water content (50 to 1000 parts per million H/Si), which is consistent with geophysical viscosity profiles. Because DisGBS is a grain size–sensitive creep mechanism, the evolution of the grain size of olivine is an important process controlling the dynamics of the upper mantle.

Mechanical Properties of Novel Nanocrystalline Materials

2001 ◽  
Author(s):  
J. Narayan ◽  
H. Wang ◽  
A. Kvit
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Nanocrystalline Materials ◽  
High Surface ◽  
Grain Boundary Sliding ◽  
Boundary Shear ◽  
Functionally Gradient ◽  
Boundary Sliding ◽  
First Time ◽  
Critical Grain Size

Abstract We have synthesized nanocrystalline thin films of Cu, Zn, TiN, and WC having uniform grain size in the range of 5 to 100 nm. This was accomplished by introducing a couple of manolayers of materials with high surface and have a weak interaction with the substrate. The hardness measurements of these well-characterized specimens with controlled microstructures show that hardness initially increases with decreasing grain size following the well-known Hall-Petch relationship (H∝d−½). However, there is a critical grain size below which the hardness decreases with decreasing grain size. The experimental evidence for this softening of nanocrystalline materials at very small grain sizes (referred as reverse Hall-Petch effect) is presented for the first time. Most of the plastic deformation in our model is envisioned to be due to a large number of small “sliding events” associated with grain boundary shear or grain boundary sliding. This grain-size dependence of hardness can be used to create functionally gradient materials for improved adhesion and wear among other improved properties.

scholarly journals Hierarchical creep cavity formation in an ultramylonite and implications for phase mixing

Solid Earth ◽  
2017 ◽  
Vol 8 (6) ◽  
pp. 1193-1209 ◽  
Author(s):  
James Gilgannon ◽  
Florian Fusseis ◽  
Luca Menegon ◽  
Klaus Regenauer-Lieb ◽  
Jim Buckman
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Finite Strain ◽  
Grain Boundary Sliding ◽  
Large Strains ◽  
Cavity Formation ◽  
Phase Mixing ◽  
Transient Phenomena ◽  
Boundary Sliding

Abstract. Establishing models for the formation of well-mixed polyphase domains in ultramylonites is difficult because the effects of large strains and thermo-hydro-chemo-mechanical feedbacks can obscure the transient phenomena that may be responsible for domain production. We use scanning electron microscopy and nanotomography to offer critical insights into how the microstructure of a highly deformed quartzo-feldspathic ultramylonite evolved. The dispersal of monomineralic quartz domains in the ultramylonite is interpreted to be the result of the emergence of synkinematic pores, called creep cavities. The cavities can be considered the product of two distinct mechanisms that formed hierarchically: Zener–Stroh cracking and viscous grain-boundary sliding. In initially thick and coherent quartz ribbons deforming by grain-size-insensitive creep, cavities were generated by the Zener–Stroh mechanism on grain boundaries aligned with the YZ plane of finite strain. The opening of creep cavities promoted the ingress of fluids to sites of low stress. The local addition of a fluid lowered the adhesion and cohesion of grain boundaries and promoted viscous grain-boundary sliding. With the increased contribution of viscous grain-boundary sliding, a second population of cavities formed to accommodate strain incompatibilities. Ultimately, the emergence of creep cavities is interpreted to be responsible for the transition of quartz domains from a grain-size-insensitive to a grain-size-sensitive rheology.

Strain localisation during diffusion creep: influence of grain coarsening and grain boundary sliding

2020 ◽  
Author(s):  
John Wheeler ◽  
Lynn Evans ◽  
Robyn Gardner ◽  
Sandra Piazolo
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Earth Pressure ◽  
Grain Boundary Sliding ◽  
Mechanical Anisotropy ◽  
Limited Attention ◽  
Diffusion Creep ◽  
Pressure Solution ◽  
Grain Coarsening ◽  
Boundary Sliding

<p>Diffusion creep and the wet low temperature version, pressure solution, are major deformation mechanisms in the Earth. Pressure solution operates in many metamorphosing systems in the crust and may contribute to slow creep on fault surfaces. Diffusion creep prevails in areas of the upper mantle deforming slowly, and possibly in most of the lower mantle. Both mechanisms contribute to localisation since small grain sizes can deform faster.</p><p>However, there has been limited attention paid to the evolution of microstructure during diffusion creep. In some experiments grains coarsen; in some but not all experiments grains remain rather equant. We have developed a grain-scale numerical model for diffusion creep, which indicates that those processes are very important in influencing evolving strength. Our models illustrate three behaviours.</p><ol><li>Strain localises along slip surfaces formed by aligned grain boundaries on all scales. This affects overall strength.</li> <li>Diffusion creep is predicted to produce elongate grains and then the overall aggregate has intense mechanical anisotropy. Thus strength during diffusion creep, and localisation on weak zones, is influenced not just by grain size but by other aspects of microstructure.</li> <li>Grain coarsening increases grain size and strength. Our most recent work shows how it interacts with ongoing deformation. In particular grain growth can lead to particular grain shapes which are directly related to strain rate, and influence strength. Consequently, understanding localisation during diffusion creep must encompass the effects of diffusion itself, grain boundary sliding and grain coarsening.</li> </ol>

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