Advances in Modelling of Irradiation Creep Using Rate Theory

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 

1. The absence of an abstract section in the article is a significant shortcoming. While it may be acceptable not to provide authors' details for blind peer review, the review process requires abstracts and keywords to enable reviewers to quickly understand the content of the work. Therefore, abstract and keyword sections should be added to the beginning of the article.
2. The caption of Figure 1 is excessively long and includes explanatory and interpretative statements. Figure captions should be concise and descriptive, while detailed explanations and interpretations should be provided in the main text with explicit references to the figure. It is recommended to shorten the caption and move the explanatory content into the manuscript text.

“Suggested Fig. 1. Preferred orientation of the pressure tube and corresponding creep compliance tensor quadrics in the L–T plane.”

3. Upon reviewing the iThenticate report, it was found that the article contained an alarmingly high similarity rate. The report indicates that some sections, almost entire paragraphs in length, were directly copied and pasted from source texts. A striking example of this is the discovery that the heading "Figure 1" was taken verbatim from another study. For such similarities to be acceptable, it is essential that the authors assimilate the information from the sources, rephrase it in their own original words (paraphrase), and appropriately cite each source within the text.
4. The section beginning with the phrase “For large-grained materials... becomes important.” in the last paragraph of page 7 appears to have been copied verbatim from another source, as indicated in the iThenticate report, with the exception of the word “creep”. Furthermore, it appears that no reference is made to the source from which these statements were taken in the relevant section. As is well known, the verbatim copying of text in any work, including the authors' own previously published articles, raises ethical issues. Therefore, instead of directly copying from the literature, the relevant section should be rewritten in the authors' own words and appropriately cited.
5. The same issues are present in the captions for Figures 6, 7, and 16.
6. Authors must carefully review the “Instructions for Authors” section of Metals journal. Citations must be numbered within the text in accordance with the journal's style guidelines as [1], [2], [3], … and each citation must be clearly indicated where it applies.

Author Response

Reviewer #1

1. The absence of an abstract section in the article is a significant shortcoming. While it may be acceptable not to provide authors' details for blind peer review, the review process requires abstracts and keywords to enable reviewers to quickly understand the content of the work. Therefore, abstract and keyword sections should be added to the beginning of the article.  Apologies – an abstract was uploaded separately during the submission.  We will embed an abstract and key words in the text as suggested.
2. The caption of Figure 1 is excessively long and includes explanatory and interpretative statements. Figure captions should be concise and descriptive, while detailed explanations and interpretations should be provided in the main text with explicit references to the figure. It is recommended to shorten the caption and move the explanatory content into the manuscript text.  Yes, we agree and will re-write caption for Figure and other lengthy captions as suggested.

“Suggested Fig. 1. Preferred orientation of the pressure tube and corresponding creep compliance tensor quadrics in the L–T plane.”

1. Upon reviewing the iThenticate report, it was found that the article contained an alarmingly high similarity rate. The report indicates that some sections, almost entire paragraphs in length, were directly copied and pasted from source texts. A striking example of this is the discovery that the heading "Figure 1" was taken verbatim from another study. For such similarities to be acceptable, it is essential that the authors assimilate the information from the sources, rephrase it in their own original words (paraphrase), and appropriately cite each source within the text.  Yes, certain sections of texts were copied verbatim as noted.  Thank you for the note.  In our defense the text was originally generated by the primary author so we were guilty of copying ourselves.  We have revised the copied section to make the text more unique. 
2. The section beginning with the phrase “For large-grained materials... becomes important.” in the last paragraph of page 7 appears to have been copied verbatim from another source, as indicated in the iThenticate report, with the exception of the word “creep”. Furthermore, it appears that no reference is made to the source from which these statements were taken in the relevant section. As is well known, the verbatim copying of text in any work, including the authors' own previously published articles, raises ethical issues. Therefore, instead of directly copying from the literature, the relevant section should be rewritten in the authors' own words and appropriately cited.  Thank you for the note.  In our defense the text was originally generated by the primary author so we were guilty of copying ourselves.  We have revised the copied section to make the text more unique. 
3. The same issues are present in the captions for Figures 6, 7, and 16.  Noted – addressed in revised text.
4. Authors must carefully review the “Instructions for Authors” section of Metals journal. Citations must be numbered within the text in accordance with the journal's style guidelines as [1], [2], [3], … and each citation must be clearly indicated where it applies.  We have re-formatted the references numerically.  While the citation app we are using does not accommodate the same numbering style as indicated, that will be adjusted during the copy-editing by MDPI.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a detailed model for predicting creep strain in Zr-Nb pressure tubes, a topic of significant importance for reactor safety and lifetime assessment. The paper is logically structured and generally well-written. The authors have made a commendable effort to develop a physically-based model that incorporates key microstructural features, and they demonstrate its utility by comparing its predictions to several important experimental and in-service observations.

The primary strength of the work is its focus on linking grain structure variations to macroscopic creep behavior. However, the manuscript could be substantially improved by addressing some minor formatting issues and, by providing justification for key input parameters used in the model, particularly dislocation density.

Minor revisions required:
Missing units on figures 13-15.  Please include the X axis units
Figure 17 is labeled Figure 11
Figure 6 - What is the Z axis showing?
Sub-figure labeling - various figures were missing the "A)" and "B)" delineations.
Double check acronyms - on line 212 "DAD" is used incorrectly

Optional suggestion:
The manuscript uses specific dislocation densities without reference.  Have the authors estimated dislocation densities via TEM or GND from EBSD maps?   Would these values better suit the model?

The reviewer, whose expertise lies more in the domain of empirical creep of FCC metals, finds the modeling approach intriguing and its correlation with grain structure compelling.  The author's efforts in this complex field are appreciated, and I look forward to seeing a revised manuscript that incorporates this feedback.

Author Response

This manuscript presents a detailed model for predicting creep strain in Zr-Nb pressure tubes, a topic of significant importance for reactor safety and lifetime assessment. The paper is logically structured and generally well-written. The authors have made a commendable effort to develop a physically-based model that incorporates key microstructural features, and they demonstrate its utility by comparing its predictions to several important experimental and in-service observations.

The primary strength of the work is its focus on linking grain structure variations to macroscopic creep behavior. However, the manuscript could be substantially improved by addressing some minor formatting issues and, by providing justification for key input parameters used in the model, particularly dislocation density.

Minor revisions required:
Missing units on figures 13-15.  Please include the X axis units corrected in revision done – thank you.
Figure 17 is labeled Figure 11 new figures applied
Figure 6 - What is the Z axis showing?  Caption revised to indicate that the z-axis is the relative creep rate.
Sub-figure labeling - various figures were missing the "A)" and "B)" delineations. Corrected
Double check acronyms - on line 212 "DAD" is used incorrectly Text revised to clarify.  Noted and clarified

Thank you for noting the mistakes in the text.  Note - we have had to revise the document because we have been denied permission to use certain data and have addressed the reviewer comments in the revision.

Optional suggestion:
The manuscript uses specific dislocation densities without reference.  Have the authors estimated dislocation densities via TEM or GND from EBSD maps?   Would these values better suit the model?  We have added an appropriate reference.   We have used X-ray diffraction techniques validated by TEM (M. Griffiths et al. 1992, 2001).  For this work the dislocation densities have been correlated with line broadening by X-ray diffraction using a Fourier transform analysis technique based on the methodology proposed by Warren and Averbach.  We have found that, for complex irradiated microstructures, the best method is to relate the dislocation density directly to the coherent diffracting domain size (M. Griffiths 2023, 2024).  It is an intriguing prospect to use electron diffraction line broadening to determine dislocation densities.  GNDs are specific to crystal misorientation and are only useful as a means of measurement for those dislocations that are in sub-grain boundaries (Malcolm Griffiths 2023).  While sub-grain boundaries exist in pressure tubes they do not factor into the dislocation structure that we deem important for creep, i.e. the network dislocations that can glide and climb and the dislocation loops that harden the material and inhibit creep. 

Bickel, G. A., M. Griffiths, A. Douchant, S. Douglas, O. T. Woo, and A. Buyers. 2011. “Improved Zr-2.5Nb Pressure Tubes for Reduced Diametral Strain in Advanced CANDU Reactors.” Journal of ASTM International 8 (2): 1–14. https://doi.org/10.1520/JAI103521.

Christodoulou, N., A. R. Causey, R. A. Holt, et al. 1996. “Modelling In-Reactor Deformation of Zr-2.5Nb Pressure Tubes in CANDU Power Reactors.” In Zirconium in the Nuclear Industry: Eleventh International Symposium; ASTM 1295, edited by Eds. American Society for Testing and Materials.

Christodoulou, N., A. R. Causey, C. H. Woo, C. N. Tome, R. J. Klassen, and R. A. Holt. 1993. “Modelling the Effect of Texture and Dislocation Structure on Irradiation Creep of Zirconium Alloys.” In Effects of Radiation on Materials:16th International Symposium. ASTM STP 1175, edited by A. S. Kumar, D. S. Gelles, R. K. Nanstad, and E. A. Little.

Griffiths, M. 2023. “X-Ray Diffraction Line Broadening and Radiation Damage.” Materialia 27: 101704,. https://doi.org/10.1016/j.mtla.2023.101704.

Griffiths, M. 2024. “X-Ray Diffraction Line Broadening of Irradiated Zr-2.5Nb Alloys.” Metals 14 (12): 1446. https://doi.org/10.3390/met14121446.

Griffiths, M., G. A. Bickel, R. DeAbreu, and W. Li. 2017. “Irradiation Creep of Zr-Alloys.” In Mechanical and Creep Behavior of Advanced Materials, edited by Indrajit Charit, Yuntian T. Zhu, Stuart A. Maloy, and Peter K. Liaw. The Minerals, Metals & Materials Series. Springer International Publishing. https://doi.org/10.1007/978-3-319-51097-2_13.

Griffiths, M., D. Sage, and R.A. 2001. “Holt and C.N.Tome, Determination of Dislocation Densities in HCP Metals from XRD Line-Broadening Analysis, Proc.” TMS 33: 859–65.

Griffiths, M., J. E. Winegar, J. F. Mecke, and R. A. Holt. 1992. “Determination of Dislocation Densities in HCP Metals Using X-Ray Diffraction and Transmission Electron Microscopy.” Advances in X-Ray Analysis 35: 593–99.

Griffiths, Malcolm. 2023. “Crystal Orientation and Dislocation Slip.” Metals 13 (12): 1950. https://doi.org/10.3390/met13121950.

Osetsky, Y. N., D. J. Bacon, and N. Diego. 2002. “Anisotropy of Point Defect Diffusion in Alpha-Zirconium.” Metall and Mat Trans A 33: 777–82. https://doi.org/10.1007/s11661-002-1007-3.

Osetsky, Yuri, and David Rodney. 2020. “Atomic-Level Dislocation Dynamics in Irradiated Metals.” In Comprehensive Nuclear Materials. Elsevier. https://doi.org/10.1016/B978-0-12-803581-8.00662-7.

Woo, C. H., and U. Gosele. 1983. “Dislocation Bias in an Anisotropic Diffusive Medium and Irradiation Growth.” J. Nucl. Mater 119: 219-228.

 

The reviewer, whose expertise lies more in the domain of empirical creep of FCC metals, finds the modeling approach intriguing and its correlation with grain structure compelling.  The author's efforts in this complex field are appreciated, and I look forward to seeing a revised manuscript that incorporates this feedback.

 

The reviewer is very kind.  Unfortunately, we must revise the article because we have been denied permission to data that we attributed to Type B tubes.  We apologise for this and will incorporate the reviewer’s helpful suggestions in the re-write.  The data we had included was from Type B tubes in a newly refurbished 600 MWe unit.  The tubes exhibited unusually high strain that we had predicted based on microstructure before the tubes had been gauged.  The high creep was sensitive information simply because it showed that the tubes in the refurbished unit exhibited unexpected and abnormal creep behaviour.  Accordingly, the reactor operator and engineering groups involved would not approve use of those data.  It turns out that the TG3 RT1 tubes are a good surrogate because they have similar microstructures and (it turns out) exhibit similar creep behaviour.   By removing the sensitive data on the Type B tubes, the text and figures must be revised, which we have done.  The main thrust of the paper does not change because the new tubes have a similar microstructure to our surrogate TG3 RT1 tubes that were made by a deliberately different fabrication process.   

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript develops a mechanistic rate-theory framework to explain irradiation creep in Zr-2.5Nb pressure tubes, emphasizing the role of grain boundary sink strengths, diffusional anisotropy, and microstructural variability.

1. Thoroughly check the abstract and introduction and point out the novelty clearly in the manuscript.
2. Is this an original article or a review article?
3. A mechanistic model should demonstrate predictive capability, not merely trend agreement. Please mention error quantification, goodness-of-fit, sensitivity analysis, and predictive uncertainty. 
4. Cite all the previous works, even in the figures, in the results section. 
5. "The model treats grain boundaries as biased sinks governed by diffusional anisotropy." Are grain boundaries assumed equivalent? What about LAGb and HAGB? 

6. In equation 18: Why linear in axial position? Why the factor 0.13? Mechanistic models must avoid the appearance of hidden empirical tuning.

7. Please discuss more in detail about Diffusion Anisotropy Treatment, as no temperature dependence is discussed, and no comparison to atomistic simulations is provided.  

8. The paper lacks in-depth discussion. 

Author Response

This manuscript develops a mechanistic rate-theory framework to explain irradiation creep in Zr-2.5Nb pressure tubes, emphasizing the role of grain boundary sink strengths, diffusional anisotropy, and microstructural variability.

1. Thoroughly check the abstract and introduction and point out the novelty clearly in the manuscript. We have restructured the introduction to better explain how and why the rate theory modelling has developed.

 Most historical creep models applied to Zr-2,5Nb pressure tubing have been empirical in nature.  Although the models used for many years by the CANDU industry have been dependent on dislocation slip (Christodoulou et al. 1993, 1996) the authors of published works have omitted to point out that the incorporation of a major, empirically determined, parameter in such models after all other creep anisotropy parameters have been incorporated, essentially makes the models 100% empirical in nature.  The empirical adjustment has been applied because of the inability of the industry-standard models based on slip to account for changes in the grain structure.  Rate theory can accommodate the microstructure and (we believe) works well in the instances we have described.  The submitted text describes how rate theory model can account for observations of  unusually high diametral creep in one refurbished CANDU 600 MWe unit.  Unfortunately, the utility is restricted by contractual obligations with an engineering company involved in qualification of new pressure tubes, and we have been denied permission to use their data (even if we don’t give details of the specific tubes and the unit).  We can however use similar microstructure data from tubes operating in a different reactor design with different operating conditions (temperature specifically) and thus predict how those tubes will behave in a 600 MWe reactor design.  We demonstrate what we anticipate for diametral creep in a 600 MWe design using our model.  Dislocation loop density is important because it is lower in the 600 MWe design and this results in higher creep.  In moving from the 900 MWe to 600 MWe design we have reduced the dislocation loop density and that, coupled with a finer grain structure, results in unusually high diametral creep.  We have predicted this before measurements were available but we are not allowed to make the connection hence the shift to a theoretical assessment of the likely creep for a given, well-characterised, microstructure in a 600 MWe reactor.  We have revised the text to make this clear.

 

2. Is this an original article or a review article? It is both a review and original – the applied part is application of rate theory modelling to recent data.  The model addresses two important aspects of creep behaviour: (i) that arising from the as-fabricated microstructure; and (ii) that arising from the radiation-induced microstructure.  The paper shows how a high creep rate the dependent on the fabricated microstructure and how the creep behaviour changes when the operating conditions, which affect the dislocation loop density.
3. A mechanistic model should demonstrate predictive capability, not merely trend agreement. Please mention error quantification, goodness-of-fit, sensitivity analysis, and predictive uncertainty. We think the reviewer must be thinking of empirical models that depend on fits to a many data and the model is then justified based on statistical grounds.  We have developed statistical models for creep previously and in those cases have included the information that the reviewer mentions (Bickel et al. 2011; M. Griffiths et al. 2017)   In this case we are not at that stage.  However, it is important to make a statement that we can explain why certain creep behaviour is exhibited.  We are limited to “high” or “low” but that is important to know when pressure tubes are being fabricated for multiple units in Canada.  Without necessarily knowing what is the optimum condition in the first instance, having an idea of what to avoid (or at least be concerned about) is beneficial to the industry.

Bickel, G. A., M. Griffiths, A. Douchant, S. Douglas, O. T. Woo, and A. Buyers. 2011. “Improved Zr-2.5Nb Pressure Tubes for Reduced Diametral Strain in Advanced CANDU Reactors.” Journal of ASTM International 8 (2): 1–14. https://doi.org/10.1520/JAI103521.

Griffiths, M., G. A. Bickel, R. DeAbreu, and W. Li. 2017. “Irradiation Creep of Zr-Alloys.” In Mechanical and Creep Behavior of Advanced Materials, edited by Indrajit Charit, Yuntian T. Zhu, Stuart A. Maloy, and Peter K. Liaw. The Minerals, Metals & Materials Series. Springer International Publishing. https://doi.org/10.1007/978-3-319-51097-2_13.

4. Cite all the previous works, even in the figures, in the results section.  Done
5. "The model treats grain boundaries as biased sinks governed by diffusional anisotropy." Are grain boundaries assumed equivalent? What about LAGb and HAGB? We treat LAGBs as dislocation networks and HAGBs as perfect sinks. The LAGBs are then subsumed into the analysis of the network dislocation structure. We have not applied any higher degree of sophistication.
6. In equation 18: Why linear in axial position? Why the factor 0.13? Mechanistic models must avoid the appearance of hidden empirical tuning. Noted – The 0.13 is a scaler that allows for using whole numbers like 30 and 50 when to apply to different reactor types.
7. Please discuss more in detail about Diffusion Anisotropy Treatment, as no temperature dependence is discussed, and no comparison to atomistic simulations is provided. We rely on work conducted by other research ((Woo and Gosele 1983)) and use his guidance.  While Woo relied on some degree of empiricism (deducing that interstitial diffusion must be anisotropic to account for irradiation growth in all circumstances), atomic simulations are limited to showing that interstitial diffusion is anisotropic (preferentially in the basal plane) at low temperatures and the anisotropy diminishes with increasing temperature.  We will include a note to this fact and a referernce (Y. N. Osetsky et al. 2002; Y. Osetsky and Rodney 2020).

   Osetsky, Y. N., D. J. Bacon, and N. Diego. 2002. “Anisotropy of Point Defect Diffusion in Alpha-Zirconium.” Metall and Mat Trans A 33: 777–82. https://doi.org/10.1007/s11661-002-1007-3.

   Osetsky, Yuri, and David Rodney. 2020. “Atomic-Level Dislocation Dynamics in Irradiated Metals.” In Comprehensive Nuclear Materials. Elsevier. https://doi.org/10.1016/B978-0-12-803581-8.00662-7.

   Woo, C. H., and U. Gosele. 1983. “Dislocation Bias in an Anisotropic Diffusive Medium and Irradiation Growth.” J. Nucl. Mater 119: 219-228,

    
8. The paper lacks in-depth discussion.  While some discussion is included in the introduction and methofology sections we have revised the discussion section to be more explanatory but we do not wish to repeat what has already been said in the earlier sections.

 

 

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors appear to have adequately addressed the questions raised and requested revisions during the previous review process.
However, since the iThenticate/plagiarism report for the revised version of the article has not been uploaded/sent to us by the journal system, a technical evaluation of the new similarity rate after the corrections could not be performed. Therefore, authors are advised to check the final status of the article in terms of publication ethics.

Reviewer 3 Report

Comments and Suggestions for Authors

The Manuscript is revised as per the suggestions.