The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law
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 deformatio...
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ftdoajarticles:oai:doaj.org/article:063f7f11ff394fe58f26d5e4645b4742 2023-05-15T16:39:23+02:00 The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law M. D. Behn D. L. Goldsby G. Hirth 2021-09-01T00:00:00Z https://doi.org/10.5194/tc-15-4589-2021 https://doaj.org/article/063f7f11ff394fe58f26d5e4645b4742 EN eng Copernicus Publications https://tc.copernicus.org/articles/15/4589/2021/tc-15-4589-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-4589-2021 1994-0416 1994-0424 https://doaj.org/article/063f7f11ff394fe58f26d5e4645b4742 The Cryosphere, Vol 15, Pp 4589-4605 (2021) Environmental sciences GE1-350 Geology QE1-996.5 article 2021 ftdoajarticles https://doi.org/10.5194/tc-15-4589-2021 2022-12-31T10:24:04Z 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. Article in Journal/Newspaper ice core Ice Sheet The Cryosphere Directory of Open Access Journals: DOAJ Articles The Cryosphere 15 9 4589 4605 |
institution |
Open Polar |
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Directory of Open Access Journals: DOAJ Articles |
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ftdoajarticles |
language |
English |
topic |
Environmental sciences GE1-350 Geology QE1-996.5 |
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Environmental sciences GE1-350 Geology QE1-996.5 M. D. Behn D. L. Goldsby G. Hirth The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
description |
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. |
format |
Article in Journal/Newspaper |
author |
M. D. Behn D. L. Goldsby G. Hirth |
author_facet |
M. D. Behn D. L. Goldsby G. Hirth |
author_sort |
M. D. Behn |
title |
The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law |
title_short |
The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law |
title_full |
The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law |
title_fullStr |
The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law |
title_full_unstemmed |
The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law |
title_sort |
role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the glen flow law |
publisher |
Copernicus Publications |
publishDate |
2021 |
url |
https://doi.org/10.5194/tc-15-4589-2021 https://doaj.org/article/063f7f11ff394fe58f26d5e4645b4742 |
genre |
ice core Ice Sheet The Cryosphere |
genre_facet |
ice core Ice Sheet The Cryosphere |
op_source |
The Cryosphere, Vol 15, Pp 4589-4605 (2021) |
op_relation |
https://tc.copernicus.org/articles/15/4589/2021/tc-15-4589-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-4589-2021 1994-0416 1994-0424 https://doaj.org/article/063f7f11ff394fe58f26d5e4645b4742 |
op_doi |
https://doi.org/10.5194/tc-15-4589-2021 |
container_title |
The Cryosphere |
container_volume |
15 |
container_issue |
9 |
container_start_page |
4589 |
op_container_end_page |
4605 |
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1766029724423815168 |