Creep and fracture of warm columnar freshwater ice

Gharamti, Iman E.; Dempsey, John P.; Polojärvi, Arttu; Tuhkuri, Jukka

doi:https://doi.org/10.5194/tc-15-2401-2021

Articles | Volume 15, issue 5

https://doi.org/10.5194/tc-15-2401-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-15-2401-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 15, issue 5

Research article

|

27 May 2021

Research article |

| 27 May 2021

Creep and fracture of warm columnar freshwater ice

Iman E. Gharamti, John P. Dempsey, Arttu Polojärvi, and Jukka Tuhkuri

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Final revised paper (published on 27 May 2021)
Preprint (discussion started on 03 Sep 2020)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Deformation of ice', Anonymous Referee #1, 06 Oct 2020
- AC1: 'Authors' replies to RC1', Iman El Gharamti, 30 Nov 2020
RC2: 'Review of Gharamti et al.', Anonymous Referee #2, 18 Oct 2020
- AC2: 'Authors' replies to RC2', Iman El Gharamti, 30 Nov 2020

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Publish subject to revisions (further review by editor and referees) (02 Dec 2020) by Jürg Schweizer

AR by Mario Ebel on behalf of the Authors (14 Jan 2021) Author's response Manuscript

ED: Referee Nomination & Report Request started (18 Jan 2021) by Jürg Schweizer

RR by Anonymous Referee #1 (02 Feb 2021)

Suggestions for revision or reasons for rejection

The purpose of the work described in the revised manuscript was to assess the time-dependent behavior of freshwater ice, including effects of creep and cyclic loading on fracture properties. To that end a joint experimental-modelling approach was adopted. Experiments were performed by prying open the sides of through-thickness notches that had been cut into large (3 x 6 meter), floating plates of warm (-0.3 C), S2 freshwater ice and then by measuring notch width versus time—the method the authors used (Gharamti et al. 2021) to explore whether size and/or loading rate affect the fracture toughness of the same material. The modelling part of the work was based on Schapery’s constitutive theory for creep of polymeric material loaded uniaxially. Two findings: (i) creep and cycling sequences had no clear effect on failure load; and (ii) unlike in all past work where both recoverable (anelastic/delayed elastic/viscoelastic strain) and non-recoverable (viscoplastic) deformation have been found to contribute to creep of ice, significant viscoelasticity was not detected.

Finding (i) , with one proviso, is worth publishing. Earlier work (Rist et al. (1996, Annals of Glaciology, vol. 23, p.284), not referenced in this manuscript, hinted at an effect; now there appears not to be one. The proviso, in keeping with the stated objective of assessing fracture properties, is that this finding should be presented in terms of a fracture property, namely fracture toughness. Failure load is insufficient. The finding was presented in that way in the original manuscript (original Fig4). Why the change?

Finding (ii) is troubling. Prior work , correctly cited, revealed that viscoelasticity contributes to the creep of ice. Now, no significant anelasticity is detected. Why not? The authors point to differences in specimen size, temperature and grain size, although how those factors could account for the difference is not made clear. Instead, could the explanation reside in the experiment and analysis itself? Unravelling the various contributions to time-dependent deformation, even when experiments are made under uniaxial states of stress, is not easy. Here, the stress state is only approximately uniaxial and the unravelling is performed through mathematical manipulation to optimally fit model to data—a procedure the authors justify with the statement (lines 160-2): “This approach of fitting a model with experimental data is common in fracture models with several parameters. Pure experimental methods to establish these parameters has proven extremely difficult….”. To conclude (lines 344-5) from this rather tortuous approach, justified by what could be read as an excuse, that the response of the ice was overall elastic-viscoplastic is questionable. The conclusion is not credible. Worse, it muddies the picture of the time-dependent deformation of ice.

Referee Report: PDF

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RR by Anonymous Referee #2 (22 Feb 2021)

Suggestions for revision or reasons for rejection

The authors responded to most of the reviewers’ comments fairly well and made several improvements to the paper. I have a couple more minor revisions/comments for the authors below. Overall, I recommend accepting this for publication after revisions.

Major Comments

While I recognize the novelty of the experimental studies and the usefulness of the collected data to the Cryosphere community, I still feel that the authors did not go far enough in terms of explaining how this data or the Schapery model can be used. Please add specific discussion about how this experimental data can be used by modelers and/or any planned future work.

The major finding is that viscoelasticity of S2 columnar ice is not significant because there is no delayed elastic recovery observed in the experiments (Figs. 7b and 8b). Therefore, the authors conclude that ice samples showed elastic-viscoplastic material behavior. The other reviewer seemed to be critical about this. The authors explanation “Further studies are needed to confirm this result and to find explanations for the behavior” is honestly a bit underwhelming. Could the authors instead explain what sort of further studies are necessary to confirm and find explanations. Can the authors test smaller colder samples and do a quick check? Considering that is a significant conclusion, it is essential that the authors unequivocally establish this.

Minor Comments

Page 1, line 15 – I appreciate the authors for clarify that they interest is freshwater ice sheets and not sea ice floes or Antarctic/Greenland glaciers or ice shelves. While the motivation for the experimental study is clear now, please clarify what the motivation is for calibrating the Schapery model instead of a cohesive zone model.

Page 6, line 189 – The authors referenced the work of Elices et al. (2002) that is entitled “Cohesive zone model: advantages, limitations, challenges.” I am not sure how this paper is an appropriate citation for their argument about using indirect fitting methods. Please clarify and if you are using a specific argument/conclusion from Elices et al. (2002) put it in quotes.

Page 7, line 220 – Equation (11) is the main equation that relates CMOD with the applied load P. While the model agrees well with experimental data, wouldn’t it be a better idea to calibrate a cohesive zone model and calibrate its parameters, so that it can be used for predicting ice fracture under realistic cases such as those mentioned in the first paragraph of the introduction.

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ED: Publish subject to revisions (further review by editor and referees) (03 Mar 2021) by Jürg Schweizer

AR by Iman El Gharamti on behalf of the Authors (13 Apr 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (19 Apr 2021) by Jürg Schweizer

RR by Anonymous Referee #2 (20 Apr 2021)

ED: Publish as is (21 Apr 2021) by Jürg Schweizer

Short summary

We study the creep and fracture behavior of 3 m × 6 m floating edge-cracked rectangular plates of warm columnar freshwater S2 ice under creep/cyclic-recovery loading and monotonic loading to fracture. Under the testing conditions, the ice response was elastic–viscoplastic; no significant viscoelasticity or major recovery was detected. There was no clear effect of the creep/cyclic loading on the fracture properties: failure load and crack opening displacements at crack growth initiation.