Elastic–Plastic Mechanical Behavior Analysis of a Nb₃Sn Superconducting Strand with Initial Thermal Damage

Round 1

Reviewer 1 Report

 

The manuscript by Z. Zhichao and S. Lifan entitled “Elastic-plastic mechanical behavior analysis of a Nb3Sn super-conducting strand with initial temperature damage” proposed to study the influence of filament fractures caused by thermal stress on the mechanical properties of Nb₃Sn superconducting strands. The manuscript presents the available studies on the mechanical properties of the Nb₃Sn strands.  A hierarchical homogenization model is presented and described.

Some important aspects are important to be reinforced in order to help the reader to clarify the message of the article:

- What is the importance or the advantages of the hierarchical homogenization model of EAS-Nb3Sn strands described in the article respect to other models already used and presented in the literature?

- The title does not seem to represent the content of the article as “the initial temperature damage” is not clearly studied in the text. A deeper discussion or analysis about the temperature damage would be expected.

- The comparison between the numerical simulations and the available experimental data is presented in figure 13 and no discussion is done respect to other simulations presented in this reference and others. Also a deep discussion about the origin of the differences with the experimental data will be useful and the possibility to improve the agreement.

- an English check will help the reader to better take profit of the manuscript

Author Response

Dear Reviewer:

Thank you for your letter and for the reviewers’ comments concerning our manuscript ‘Elastic-plastic mechanical behavior analysis of a Nb₃Sn superconducting strand with initial temperature damage’ (ID: applsci-1808901). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding of great significance to our research. We have carefully studied the comments and made corrections which we hope are met with approval. Revised sections are marked in blue in the paper. The main corrections in the paper and the responses to the reviewer’s comments are as follows:

Comment No. 1: What is the importance or the advantages of the hierarchical homogenization model of EAS-Nb₃Sn strands described in the article respect to other models already used and presented in the literature?

Response: Thank you very much for your comments. The main contributions of the hierarchical homogenization model are reflected in the following three aspects. First, hierarchical homogenization model is computationally efficient. There are several previous numerical studies investigate the elastic-plastic behaviours of EAS-Nb₃Sn strand. However, we have to say they are computationally expensive. Because the size of fiber is much smaller than that of EAS-Nb₃Sn strand, this results the numerical methods for the fully macroscale models is too large, and each individual run can take several days. In the paper, the hierarchical homogenization model takes about half an hour for each individual run. Next, plasticity models are considered in the hierarchical homogenization model. To simplify, the constitutive relationships of these materials are simplified as elastic model. For example, the fiber bundle are asumued as elastic in in Wang’s work [7]. Eventually, the Nb₃Sn fiber is prone to brittle fracture, then fractures caused by the initial thermal stress are considered to study the effect of temperature on the elastic-plastic behaviours. To make it more clear, we have changed some wording, see:

Page 3, line 20-26.

Page 16, line 21-23;

Page 17, line 2-20.

 

Comment No. 2: The title does not seem to represent the content of the article as “the initial temperature damage” is not clearly studied in the text. A deeper discussion or analysis about the temperature damage would be expected.

Response: Thanks for your comments. In the manuscript, Fig. 9 and Fig. 11 inllustrate the difference of the effective constitutive parameters of level 1 and level 2 both with and without considering the initial temperature damage. Fig. 14 inllustrate the stress-strain curves both with and without considering the initial temperature damage. Several discussions about the temperature damage were given in the original manusript (page 12, line 6-14; page 14, line 5-6; page 16, 6-18). As the reviewer’s comment, we also think that a deeper discussion is necessary. We supplement the discussion as following:

Page 12, line 14-19;

Page 13, line 1-5;

Page 13, line 15-20

 

Comment No. 3: The comparison between the numerical simulations and the available experimental data is presented in figure 13 and no discussion is done respect to other simulations presented in this reference and others. Also a deep discussion about the origin of the differences with the experimental data will be useful and the possibility to improve the agreement.

Response: Thanks for your advise. A deep discussion about the origin of the differences with the experimental data are given in the manuscript, see page 15, line 23-32.

 

Comment No. 4: an English check will help the reader to better take profit of the manuscript.

Response: Thanks for your advise. English are improvement. We will continue to improve the writing of the manuscript before the article is published. Please see the revised manuscript.

Reviewer 2 Report

Manuscript  review "Elastic-plastic mechanical behavior analysis of Nb3Sn superconducting strand with initial temperature damage"

The first fragment of the introduction must be corrected with the comments below. In some places the authors write untruth! English needs improvement.

- "The starting materials of Nb3Sn low superconductivity metal alloys, Bi-2223 high temperature superconductors (HTS) and AxC60 organic superconductors contain more than 5,000 superconducting materials [1]". This sentence needs to be corrected and it has to be done historically. HTS are not only Bi-2223 superconductors, but also others: Tl-Ba-Ca-Cu-O, RE-Ba-Cu-O, MgB2, Ba-K-Bi-O, and other Bi-Sr-Ca- Cu-O!!! The authors should know that well and I expect it!

- "Even Bi (BiSrCaCuO) and Y (YBCO) based high-temperature superconducting materials have attracted more attention, high cost and increased complexity in recent years during work in low temperatures prevented the wide use of HTS technology. There should be: "Based on Bi (Bi-Sr-Ca-Cu-O [X1 - e.g. 10.1007 / s10948-017-4047-z]) and RE (REBCO [2], as well as with the participation of several RE [3, X2, X3 , e.g. 10.3390 / ma14133503, 10.1002 / pssa.201700888) and Tl-based (Tl-Ba-Ca-Cu-O, e.g. [XXX - see literature]) high-temperature superconducting materials are becoming more and more popular in recent years". I leave the correct justification to the Authors. The authors also write untruth, LN is cheaper than helium!

- "high costs and increased complexity of the process working in low temperatures prevented the widespread use of HTS technology ”. I leave the correct justification to the Authors. The authors also write untruth, LN is cheaper than helium! Uses Explanation Below: "Superconducting tapes are used without and with a stabilizer as windings in transormers and superconducting electromagnets, superconducting current limiters (please check which ones are used for what). Did the authors forget about it or don't they know?

- Then I ask the authors to check what currents are in HTS, in superconducting tapes and in the Nb3Sn superconductor. "106 A/cm2" - these are the higher currents already in the HTS mass samples. On Nb3Sn, I agree that there is a high second field. The authors should also refer to this issue extensively, there are many works in the Polish group on this subject.

- Besides, I am asking you to correct typos in many places where dots appear after Fig, spaces after the equal sign, etc.

- Conclusions related to the supported results.

At the moment, the work requires a thorough improvement. Introduction. Only then can I consider it in terms of publishing it in the journal. Simulation deserves an advantage.

Author Response

Dear Reviewer:

 

Thank you for your letter and for the reviewers’ comments concerning our manuscript ‘Elastic-plastic mechanical behavior analysis of a Nb₃Sn superconducting strand with initial temperature damage’ (ID: applsci-1808901). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding of great significance to our research. We have carefully studied the comments and made corrections which we hope are met with approval. Revised sections are marked in blue in the paper. The main corrections in the paper and the responses to the reviewer’s comments are as follows:

Comment No. 1: "The starting materials of Nb₃Sn low superconductivity metal alloys, Bi-2223 high temperature superconductors (HTS) and AxC60 organic superconductors contain more than 5,000 superconducting materials [1]". This sentence needs to be corrected and it has to be done historically. HTS are not only Bi-2223 superconductors, but also others: Tl-Ba-Ca-Cu-O, RE-Ba-Cu-O, MgB₂, Ba-K-Bi-O, and other Bi-Sr-Ca- Cu-O!!! The authors should know that well and I expect it!

Response: Thank you so much for your comment. As the reviewer mentioned, there are severl different HTS superconductors, include Tl-Ba-Ca-Cu-O, RE-Ba-Cu-O, MgB₂, Ba-K-Bi-O, and other Bi-Sr-Ca- Cu-O. We take a deeper insight into those HTS superconductors, and the formulation are corrected. Diverse classes of superconducting materials are introduced in next next sentence.

See page 1, line 26-32: “Since the discovery of superconductivity more than 100 years ago, many diverse classes of superconducting materials have been found and subsequently studied in detail. Based on the different superconducting transition temperature, the superconding materials can be classified into the low temperature superconductors (LTS) which are represented by metals, alloys and metal alloy materials such as Nb₃Sn, NbTi, et al., and the high temperature superconductors (HTS). To date, more than 5000 uperconducting materials that have been discovered or synthesized all over the world [1].”

 

Comment No. 2: "Even Bi (BiSrCaCuO) and Y (YBCO) based high-temperature superconducting materials have attracted more attention, high cost and increased complexity in recent years during work in low temperatures prevented the wide use of HTS technology. There should be: "Based on Bi (Bi-Sr-Ca-Cu-O [X1 - e.g. 10.1007 / s10948-017-4047-z]) and RE (REBCO [2], as well as with the participation of several RE [3, X2, X3 , e.g. 10.3390 / ma14133503, 10.1002 / pssa.201700888) and Tl-based (Tl-Ba-Ca-Cu-O, e.g. [XXX - see literature]) high-temperature superconducting materials are becoming more and more popular in recent years". I leave the correct justification to the Authors. The authors also write untruth, LN is cheaper than helium!

Response: Thank you. We fully agree with the reviewers’ opinion. We have followed the reviewers’ suggestion to reviewe the high-temperature superconducting materials.

See page 1, line 32-35: “Based on Bi (Bi-Sr-Ca-Cu-O [2, 3] ), Tl (Tl-Ba-Ca-Cu-O [4]), Re (Re-Ba-Cu-O [5] as well as with the participation of several Re [6] ), and Y (Y-Ba-Cu-O [7]) high-temperature superconducting materials are becoming more and more popular in recent years.”

 

Comment No. 3: "high costs and increased complexity of the process working in low temperatures prevented the widespread use of HTS technology ”. I leave the correct justification to the Authors. The authors also write untruth, LN is cheaper than helium! Uses Explanation Below: "Superconducting tapes are used without and with a stabilizer as windings in transormers and superconducting electromagnets, superconducting current limiters (please check which ones are used for what). Did the authors forget about it or don't they know?

Response: Thank you so much for your advise. We agree that the options in the original manuscript are inappropriate. To gain an in-depth understanding of this part of knowledge, we have reading relevant literature including the works of Polish group, American group, and China group. Thank you very much for reminding us of this aspect. We have removed it from the revised manuscript, and modifications were made as suggested by the reviewers.

See page 1, line 35-43: “HTS superconducting tapes are used without and with a stabilizer as windings in transormers and superconducting electromagnets, superconducting current limiters. Compared with HTSs, Nb₃Sn low-temperature superconducting materials are widely used in the core of large high-field magnets because of their mature and simple preparation, high critical magnetic field (H_c2»25T), critical current [8] and stable mechanical properties in low-temperature environments. However, even today, after thousands of papers devoted to the materials have been published, understanding their nonlinear mechanical behavior remains a challenge.”

 

Comment No. 4: Then I ask the authors to check what currents are in HTS, in superconducting tapes and in the Nb₃Sn superconductor. "106 A/cm2" - these are the higher currents already in the HTS mass samples. On Nb₃Sn, I agree that there is a high second field. The authors should also refer to this issue extensively, there are many works in the Polish group on this subject.

Response: Thank you. Our statement was not precise in the original manuscript. The high critical magnetic field of Nb₃Sn is about 25T. The critical current is not a constant, but a function of the magnetic field, temperature and strain. The ITER community adopted a modern scaling relation that was derived elsewhere for the description of axial strain experiments on Nb₃Sn wires.

The letters in above equation are explained in the reference [8]. We have modified the the presentation in the revised manuscript.

See page 1, line 37-43: “Compared with HTSs, Nb₃Sn low-temperature superconducting materials are widely used in the core of large high-field magnets because of their mature and simple preparation, high critical magnetic field (H_c2»25T), critical current [8] and stable mechanical properties in low-temperature environments. However, even today, after thousands of papers devoted to the materials have been published, understanding their nonlinear mechanical behavior remains a challenge.”

 

Comment No. 5: Besides, I am asking you to correct typos in many places where dots appear after Fig, spaces after the equal sign, etc.

Response: Thanks for reminding us. The clerical errors are modified. See the revised manuscript, letters in blue. See the manuscript.

 

Comment No. 6: Conclusions related to the supported results.

Response: Thanks for your advise. we have revisited our conclusions so they are based on consistent results.

See page 17, line 10-24.

Author Response File: Author Response.pdf

Reviewer 3 Report

In this work, they presented a hierarchical homogenized model to maximize computational efficiency.

 

In this article, the effects of Nb3Sn filament breakage caused by mechanical loads and large thermal stresses on the mechanical behavior of ropes were investigated. Here, Curtin-Zhou's theory of damage was extended to consider the initial damage caused by thermal and mechanical action, and a hierarchical homogenized model was presented.

 

The novelty of the study should be emphasized more.

Details of the experimental analysis should be included.

Load cases are mentioned, but details are not available.

 

Author Response

Dear Reviewer:

Thank you for your letter and for the reviewers’ comments concerning our manuscript ‘Elastic-plastic mechanical behavior analysis of a Nb₃Sn superconducting strand with initial temperature damage’ (ID: applsci-1808901). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding of great significance to our research. We have carefully studied the comments and made corrections which we hope are met with approval. Revised sections are marked in blue in the paper. The main corrections in the paper and the responses to the reviewer’s comments are as follows:

Comment No. 1: The novelty of the study should be emphasized more.

Response: Thank you so much for your advise. According to the reviewer's opinion, we have modified the manuscript including the introduction, conclusion and writing.

See page 3, line 21-27;

page 9, line 18-22;

page 16, line 21-23;

page 17, line 2-20.

 

Comment No. 2: Details of the experimental analysis should be included.

Response: Thank you. The experimental results for Nb₃Sn strand are cited from literature [10]. Numerical simulations are implemente in this work to analisys the nonlineral mechanical behaviors of the strand, details of the experimental analysis are shown in cited literature. We think that the experimental results are belivable, then the details are not introduced in our manuscript.

 

Comment No. 3: Load cases are mentioned, but details are not available.

Response: Thanks for your reminder. We have introduced the loads case more detailed in the manuscript. As shown in the flow chart (Fig. 6), boundary conditions fo level 1 and level 2 RVE to calculate the effective properties are consistent with existing literature [32]. Moreover, the axial strain ε_z,  to level 2 RVE and  to the level 1 RVE are as following. In the model, the length of the strand is L=20mm in Fig.4. At left end of the strand, we fixed the axial displacement of each piont u_z=0, the displacement components perpendicular to are free. At right end of the strand, we fixed the displacement of each piont u_z=L×ε_z, other displacement components are set as free enabling the average axial strain is equal to ε_z. Then, the volune average strain tensor  of the effective superconducting region (yellow region in Fig.6) are calculated. At the surfaces of the level 2 RVE, the displacements components of each points are given in the form of . In which, x_j (j=1, 2, 3) are the x, y and z coordinate values. u_i (i=1, 2, 3) represente the displacements along x, y and z directions. Similarly, the volune average strain tensor  of the effective fiber bundle are applied to the Level 1 RVE by setting the surface displacements piontwise, . x_j and u_i are the x, y and z coordinate values and displacements in the corresponding directions.

See page 8, line 34-43;

page 9, line 1-10, line 17-20.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

After reviewing the authors' corrections to the manuscript "Elastic-plastic mechanical behavior analysis of a Nb3Sn super- 2 conducting strand with initial thermal damage", I recommend the paper for publication in Applied Sciences MDPI.

Nevertheless, there are a few minor things that need to be corrected in order to make the manuscript good:

- p. 1, lines 34 and 35 - should be RE not Re (Re - may be confused with Rhenium). This should be corrected (should be capital letter E).

- in many places in the manuscript - degrees K, there should be a number space K, e.g. 30 K, no 30K

- p. 1 line 41 - Hc2 ~ 25 T and also the number of space T

- p. 17, line 11 - a dot is missing. It seems to me that the numbering of points (1), (2), (3) can be deleted. I leave it to the authors.

Author Response

Dear reviewer:

Thank you for your decision and constructive comments on my manuscript. We have carefully considered the suggestion of Reviewer and make some changes. The red part that has been revised according to your comments. Revision notes, point-to-point, are given as follows:

 

Response to comment of Reviewer

Comment No. 1: p. 1, lines 34 and 35 - should be RE not Re (Re - may be confused with Rhenium). This should be corrected (should be capital letter E).

Response: Thank you very much for this reminder. Re in the manuscript should be RE,

It has been corrected in the revised manuscript, see page 1, lines 34 and 35 in red font.

 

Comment No. 2: in many places in the manuscript - degrees K, there should be a number space K, e.g. 30 K, no 30K

Response: Thank you. We have corrected it (in red font color).

See page 1, lines 9, 10, 41;

page 2, lines 6 and 7;

page 3, lines 9 and 33;

page 4, lines 14, 18;

page 5, line 6;

page 10, lines 14, 21, 24;

page 11, line 3;

page 12, lines 3, 7;

page 13, lines 13, 21, 24;

page 15, lines 2, 15;

page 16, lines 8, 9, 14, 16, 18

 

Comment No. 3: p. 1 line 41 - H_c2 ~ 25 T and also the number of space T

Response: Thank you. We have corrected it (in red font color).

See page1 line 41.

 

Comment No. 4: p. 17, line 11 - a dot is missing. It seems to me that the numbering of points (1), (2), (3) can be deleted. I leave it to the authors.

Response: Thank you. The numbering of points (1), (2), (3) are deleted, see page17, line 8. The dot is added in line 11.

Author Response File: Author Response.pdf