Deformation Behavior and Constitutive Equation of 42CrMo Steel at High Temperature

Round 1

Reviewer 1 Report

Methodology is very typical and microstrucutre characterization are also very outdated. Constitutive equation for 42CrMo steel data would be useful for some readers anyway. As a paper, this is marginal and new information or insight on materials is very limited. English is poor.

This paper contains limited new information. 

Methodology to obtain constititive equations is very typical. Microstructure characterization is based on old approaches and it looks like opitical micrographs.

Even there is no information about how to obatain those microstructure. 

If possible, use EBSD for microstructure characterization. There are a lot of typos and inappropriate sentences and thus English should be polished further before submission.

Author Response

Dear Editors and Reviewers,

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled "Deformation behavior and constitutive equation of 42CrMo steel at high temperature" ID (metals-1375247 ). Those comments are all valuable and helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval.

Revised portion are marked in the yellow in the paper.

Below is our response to their comment.

Responds to the reviewers’ comments:

        1.Response to comment: Methodology to obtain constititive equations is very typical.  

• Response: We have added a new constitutive model, the back propagation artificial neural network (BP ANN) model, to predict the flow behavior of 42CrMo at elevated temperatures. Also, we added the discussion of the thermal processing map to guide the subsequent HR process.

        2.Response to comment: Microstructure characterization is based on old approaches and it looks like opitical micrographs. Even there is no information about how to obatain those microstructure. If possible, use EBSD for microstructure characterization.

• Response: we are sorry for our vague expression in Fig.10 and Fig.11. The microstructure are the results of the sample after being corroded by supersaturated picric acid solution. We added a description in line 236 on page 9. We believe that the austenite grain results can prove the occurrence of recrystallization behavior.

        3.There are a lot of typos and inappropriate sentences and thus English should be polished further before submission.

Response: We have carefully corrected our manuscript according to your comment. Thank you for your careful comments.

We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

We appreciate for Editors/Reviewers’ warm work earnestly and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestion.

Best regards,

Zhicheng Cheng

Reviewer 2 Report

Dear Authors,

Major remarks

1. Literature review should be revised concerning the world literature.
2. English style/grammar should be carefully revised in the whole paper.
3. Introduction should provide more information about the motivation of the study.
4. References for the equations taken from the literature should be given in the paper.
5. Less important mathematical transformations such as (11)-(20) should be given in the Appendix.
6. The style of the paper is poor. Very often there is no connection between text and equations (i.e. lines 97-113 and 139-159, 176, 187-195, etc.).
7. How many samples were tested for particular loading conditions? What about repetition and verification of the particular experiments presented in the paper?
8. Lines 84-88 – Why this part is not given in the introduction?
9. There are missing legends in the figures.
10. The captions should be corrected (i.e. see figure 5 or 7 and “s-1”).
11. What is “C1” in eq. (24) and how it can be calculated?

Other minor remarks:

-line 224 “z” – should be capital

Kind Regards,

Author Response

Dear Editors and Reviewers,

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled "Deformation behavior and constitutive equation of 42CrMo steel at high temperature" ID (metals-1375247 ). Those comments are all valuable and helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval.

Revised portion are marked in the yellow in the paper.

Below is our response to their comment.

Responds to the reviewers’ comments:

        1.Response to comment: Literature review should be revised concerning the world literature.

• Response: We have revised the content of the literature review section based on your suggestions.

        2.Response to comment: English style/grammar should be carefully revised in the whole paper.

• Response: We have carefully corrected our manuscript according to your comment. Thank you for your careful comments.

        3. Response to comment: Introduction should provide more information about the motivation of the study.

• Response: We have revised the introduction to highlight the research motivation of this article.

       4. Response to comment: References for the equations taken from the literature should be given in the paper.

• Response: The important formulas in the article have been added with relevant literature citations based on your suggestions

        5. Response to comment: Less important mathematical transformations such as (11)-(20) should be given in the Appendix. The style of the paper is poor. Very often there is no connection between text and equations (i.e. lines 97-113 and 139-159, 176, 187-195, etc.). Lines 84-88 – Why this part is not given in the introduction?

• Response: We have put the unimportant formulas, i.e. friction correction part formulas, and Arrhenius part formulas, into the appendix based on your suggestions.

        6. Response to comment: How many samples were tested for particular loading conditions? What about repetition and verification of the particular experiments presented in the paper?

• Response: Two sets of thermal compression experiments were performed for each process parameter. Therefore, the experiment is repeatable.

        7.Response to comment: There are missing legends in the figures.

• Response: We carefully examined and revised all the legends to prevent wrong expressions.

8. Response to comment: The captions should be corrected (i.e. see figure 5 or 7 and “s-1”).

• Response: We are sorry for our incorrect spelling of caption and we have revised it.

        9.Response to comment: What is “C1” in eq. (24) and how it can be calculated?

• Response: We are sorry for our incorrect expression of equation and we have deleted it.

We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

We appreciate for Editors/Reviewers’ warm work earnestly and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestion.

Best regards,

Zhicheng Cheng.

Reviewer 3 Report

Dear Authors,
Please find the comments in the attached file.

Comments for author File: Comments.pdf

Author Response

Dear Editors and Reviewers,

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled "Deformation behavior and constitutive equation of 42CrMo steel at high temperature" ID (metals-1375247 ). Those comments are all valuable and helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval.

Revised portion are marked in the yellow in the paper.

Below is our response to their comment.

Responds to the reviewers’ comments:

1. Response to comment: When heating the sample to 1200℃ or higher at a rate of 10 ℃/s，stabilizing the temperature for 10s dose not provide a uniform temperature distribution in the sample.

• Response: We have conducted more than 2 sets of experiments for each temperature and strain. It is found that when the temperature is greater than 1300 ℃ and the strain rate is less than 0.01 s^-1, long-term heat preservation would lead to the failure of the sample melting or the falling of the thermocouple. And too long holding time could lead to carburizing. Therefore, after repeated attempts, we chose this holding time.

        2.Response to comment: at least should be given in the article: grain boundary maps, grain size distribution, misorientation angle.

• Response: We are sorry for our vague expression in Fig.10 and Fig.11. The microstructure are the results of the sample after being corroded by supersaturated picric acid solution. We added a description in line 236 on page 9. We believe that the austenite grain results can prove the occurrence of recrystallization behavior.

        3.Response to comment: Why are there such large differences between the experimental results and the presented constitutive model for lower strain rates, despite the variation of parameters (Eq.20)? How much is the R parameter in these cases?

• Response: The Arrhenius equation has low accuracy for high-temperature and low-strain flow stress prediction. We have added literature citations in the article.“A few researches show that the Arrhenius-type constitutive equation has a large error between the predicted value and the actual value at the high temperature and low strain rate.” (line 149-151)
• We have added a new constitutive model, the back propagation artificial neural network (BP ANN) model, to predict the flow behavior of 42CrMo at elevated temperatures and low strain rate. The R value of each model is calculated in section 3.2.3.

        4.Response to comment: Please add more discussion to the manuscript, it’s better to cite literature to support your discussions. Missing is at least a reference to Hall-Petch relation. No references to literature according to generally accepted principles.

• Response: We added the discussion of the thermal processing map to guide the subsequent HR process. Also, the important formulas in the article have been added with relevant literature citations based on your suggestions.

5. Response to comment: What does the caption under figures 4 and 5 -0.05 mean?

• Response: We are sorry for our incorrect expression of figure legends. We used fig.4 and fig.5 to illustrate the derivation of Arrhenius constitutive model with strain of 0.05. Now this part has been deleted.

6. Response to comment: The beginning of figure 7 should be at the point = 0, = 0.

• Response: We have modified the figure according to your suggestion

7. Response to comment: A parenthesis is used in equation (10). Continue to follow this convention

• Response: We readjust the formula according to your suggestion.

We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

We appreciate for Editors/Reviewers’ warm work earnestly and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestion.

Best regards,

Zhicheng Cheng.

Round 2

Reviewer 1 Report

After revision, ANN parts are included. Overall, it looks more interesting. 

There are still unclear parts below: 

Lines from 98 to 123, three main characteristics of the curves are unclear.

“(1) At a high strain rate level ( ?̇ >1s-1 ), with the strain increase, the stress value rises, 99 showing a typical work hardening characteristic.” It is untrue

“(2) The flow stress curves at low strain rates and high temperatures show dynamic 101 recrystallization (DRX) behavior. In the initial stage, with the increase of strain, stress increases because of work hardening. Then the softening effect is gradually strengthened, and thus the flow stress reaches its peak. In the third stage, the flow softening effect caused by dynamic recovery (DRV) and DRX is greater than that caused by work hardening (WH), resulting in a rapid decrease of flow stress. In the fourth stage, when the deformation reaches a specific value, the competition between WH and dynamic softening reaches a dynamic equilibrium” it is too vague. Explanation on strain-stress curve is unclear. Specify strain rates and temperature range.

“3) Flow stress curve changed from a single peak to multiple peaks when ?̇ changed from 0.01s-1 to 0.001s-1 .

• The curves show a single peak at high strain rates and low temperatures because the DRX rate is so slow that the first round of DRX is not completed when the second round of DRX has begun. 2) The curves show multiple peaks at a low strain rate and elevated temperature. The reason is that the second round of DRX takes place after the first round of DRX is completed at high temperatures and low strain rates. The curve reaches its first peak when the flow stress decreases because of the first round of DRX. The growth of each new DRX grain is terminated by boundary impingement. Then, As the deformation continues, WH leads to an increase in the curve. Due to the deformation of newly formed recrystallized grains, the dislocation density does not reach the critical density of DRX. With the increase of dislocation density, the second round of DRX begins to form a second peak. Such complex WH and softening of DRX superimposed alternately, and the curve periodically appears multiple peaks until equilibrium[23,24]” Explanation on strain-stress curve is unclear. Specify strain rates and temperature range.

Line 164: “. The hidden layer contains 10 neurons, which is equivalent to material parameters in constitutive equation fitting. ” It is unclear.

Author Response

1. Response to comment: Lines from 98 to 123, three main characteristics of the curves are unclear.

“(1) At a high strain rate level ( ?̇ >1s-1 ), with the strain increase, the stress value rises, 99 showing a typical work hardening characteristic.” It is untrue

“(2) The flow stress curves at low strain rates and high temperatures show dynamic 101 recrystallization (DRX) behavior. In the initial stage, with the increase of strain, stress increases because of work hardening. Then the softening effect is gradually strengthened, and thus the flow stress reaches its peak. In the third stage, the flow softening effect caused by dynamic recovery (DRV) and DRX is greater than that caused by work hardening (WH), resulting in a rapid decrease of flow stress. In the fourth stage, when the deformation reaches a specific value, the competition between WH and dynamic softening reaches a dynamic equilibrium” it is too vague. Explanation on strain-stress curve is unclear. Specify strain rates and temperature range.

“3) Flow stress curve changed from a single peak to multiple peaks when ?̇ changed from 0.01s-1 to 0.001s-1 .

• The curves show a single peak at high strain rates and low temperatures because the DRX rate is so slow that the first round of DRX is not completed when the second round of DRX has begun. 2) The curves show multiple peaks at a low strain rate and elevated temperature. The reason is that the second round of DRX takes place after the first round of DRX is completed at high temperatures and low strain rates. The curve reaches its first peak when the flow stress decreases because of the first round of DRX. The growth of each new DRX grain is terminated by boundary impingement. Then, As the deformation continues, WH leads to an increase in the curve. Due to the deformation of newly formed recrystallized grains, the dislocation density does not reach the critical density of DRX. With the increase of dislocation density, the second round of DRX begins to form a second peak. Such complex WH and softening of DRX superimposed alternately, and the curve periodically appears multiple peaks until equilibrium[23,24]” Explanation on strain-stress curve is unclear. Specify strain rates and temperature range.

 Response: We have revised the description of this part to make it easier to understand. And the strain rate range is marked in the text. 

2. Response to comment: “The hidden layer contains 10 neurons, which is equivalent to material parameters in constitutive equation fitting. ” It is unclear. 

Response: We are sorry for our vague expression, and we have modified this sentence to make it easier to understand.

Revised portion are marked in the yellow in the paper.

Reviewer 2 Report

Dear Authors,

My remarks:

1. Line 126 :” strain compensated Arrhenius constitutive equation”, I think “strain-compensated…” will be better. See also line 92 (peak strain corresponding).
2. Figure 6, 7: Figures are blurred and should be corrected.
3. There are missing captions for figure 8a and 8b. Please provide more detailed description and discussion of the results given in Figures 8a and 8b.
4. Lines 205-212: Variables should be italic in the text.
5. Line 214: “When m=1…. dissipation process” please check grammar.

Kind Regards,

Author Response

1. Response to comment: Line 126 :” strain compensated Arrhenius constitutive equation”, I think “strain-compensated…” will be better. See also line 92 (peak strain corresponding).

Response: We have revised the relevant statement based on your suggestions.

2.Response to comment: Figure 6, 7: Figures are blurred and should be corrected.

Response: We have adjusted the number font size in the figure for a clearer display according to your comment. Thank you for your careful comments.

3. Response to comment: There are missing captions for figure 8a and 8b. Please provide more detailed description and discussion of the results given in Figures 8a and 8b.

Response: We have added the caption for figure 8a and 8b. Also detailed references to R and AARE values are added.

4. Response to comment: Lines 205-212: Variables should be italic in the text.

Response: We have revised the font of the variables in the text.

5. Response to comment: Line 214: “When m=1…. dissipation process” please check grammar.

Response: We have revised the sentence: “J takes the maximum value J_max, when m =1, under the ideal linear dissipation process.”

Reviewer 3 Report

Dear Authors,

You have not answered the basic comment I made in my previous review:

When heating the sample to 1200℃ or higher at a rate of 10 ℃/s，stabilizing the temperature for 10s does not provide a uniform temperature distribution in the sample.

Proper planning and execution of research often requires meeting mutually contradictory requirements. In my opinion, you have failed to meet them.

Author Response

1. Response to comment: You have not answered the basic comment I made in my previous review:

When heating the sample to 1200℃ or higher at a rate of 10 ℃/s，stabilizing the temperature for 10s does not provide a uniform temperature distribution in the sample.

Proper planning and execution of research often requires meeting mutually contradictory requirements. In my opinion, you have failed to meet them.

Response: We detected the temperature of center and surface of the same sample by dual channel thermocouple. Temperature difference is less than 5℃, which meets the requirement of uniform temperature distribution.

Round 3

Reviewer 3 Report