Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal–Torsional Ultrasonic Vibrations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

See the attached file.

Comments for author File: Comments.pdf

Author Response

RESPONSE TO REVIEWERS' COMMENTS

“Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal-Torsional Ultrasonic Vibrations”

By T.  Zarrouk, M. Nouari, H Bouali

Manuscript Number: machines-3374486

Dear Editor,

Please, find herewith our responses to the reviewers. Many thanks to them for their comments and valuable suggestions that helped us to improve our manuscript. We hope that we satisfied all required changes and suggested modifications to enhance the quality of our paper. We indicate below how we responded to required and suggested revisions.

All comments, point by point, are described in the manuscript.

Yours Sincerely.

The authors of the paper                           

1. Equations (1) – (3): All parameters need to be properly explained, g., t,

w_n and w. The angular velocities should be drawn in Figures 5 and 6 for better understanding. The designation of the amplitude of longitudinal and torsional oscillations should be unified (see Eq. 3 and Figure 6).

Answers: Thank you for this remark. the parameters of the equation are well identified.

2. Equation (5): You're adding stresses and strains? Is the quantity w the same as in Eq. (3)? In general, the designation and significance of the quantities are unsuitable.

     Answers: Thank you for this remark. Indeed, it is not the same quantity. Therefore, we have changed the quantity in the new version.

3. The meaning of the abbreviations NHC and RUM is often repeated in the text. It is sufficient to define these abbreviations at the beginning of the manuscript and then use them throughout the text.

            Answers: Thank you for this remark. We have done what is necessary.

4. Quantities in the manuscript should be written in italics, as in

             Answers: Thank you for this remark. We have done what is necessary.

5. The quality of some figures (e.g., Figures 1-6) is These include, e.g., the size of the captions (in some cases they are very small), the quotation, the notation of quantities with units, grammatical errors (e.g., rotay motion in Figure 5), etc. They need to be well revised.

Answers: Thank you for this remark. We have done what is necessary.

6. Introduction: Lines 78-80: “In this perspective, several numerical studies available in the literature have focused on the use of longitudinal ultrasonic vibrations to improve the machining of honeycomb structures”. It would be useful to acquaint readers with the specific results of these numerical studies that have already been carried out. That is, to perform a literature search in this area.

Answers: Thank you for this remark. We have done what is necessary.

7. Table 1: Young modulus should be replaced by the term "Young's modulus".

Answers: Thank you for this remark. We have done what is necessary.

8. As with the Nomex paper, it would be useful to give the basic mechanical properties of the high-speed steel from which the ultrasonic circular cutter was made.

Answers: Thank you for this remark. The cutting tool is considered rigid during the numerical simulation. Therefore, its mechanical properties are not assigned.

9. Figures 7-10: Different properties are compared for longitudinal and longitudinal-torsion ultrasonic vibrations using Abaqus/Explicit software. Furthermore, the cutting forces for longitudinal ultrasonic vibrations are compared with experimental It was found that lower cutting forces are generally achieved at lower feed rates and higher rotational speeds. This certainly had a positive effect on the quality of the machined surface, which is one of the purposes of this research. The authors could make microscopic images of the machined surfaces in the case of.    

longitudinal ultrasonic vibrations and thus confirm the above conclusions (i.e., the effect of feed rate and rotational speed on the surface quality). Would this be possible? At least a few examples where the trend of change in surface quality would be evident. This would increase the quality of the article and make it more interesting for readers.

Answers: Thank you for this remark. We cannot present microscopic images. Because the walls of the structure are modeled by shell elements which makes it impossible to present the burrs. Our focus has been on the deformation and tearing of the walls.

10. There are minor deficiencies in the manuscript. For example: Line 188: “A₁ denotes the amplitude associated with the longitudinal vibration”. The amplitude of what quantity? Line 233: “an optimal size of 0.6 mm provided”. Again, optimal size of what quantity? Line 224: “accuracy (See Figure”. It should be (see Figure…). Therefore, it is necessary to thoroughly check the manuscript from the point of view of stylistics and

Answers: Thank you for this remark. We have done what is necessary.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The study is very interesting. However, it does not bring a completely new perspective on the modeling of ultrasonic machining of honeycomb structures. The novelty can be found in the used workpiece or tool material, but I am not completely familiar with the latest developments in this field. I have a few questions and comments for the authors that need to be resolved.

1. The study takes the data for modeling from reference [35]. However, from comparing the curves, it does not seem to me that the force curves in dependence on the speed and feed correspond (compare article 35 and yours). The curves in [35] are more straightforward. Can you explain this?

2. In the study, you assume a reduction in force based on the calculation. The data for verifying the calculation are apparently not available, right?

3. What is the percentage difference between the predicted and real values?

4. In your numerical calculation, you also predict the deformation of the honeycomb structure. Could you compare the simulation results with real photos from [35]?

5. This is just a small thing, but the tool position in Figure 9a and 9b is not the same and it raises the question of how it would look if it were.

6. In Figure 9, I would recommend choosing black font color on the scale.

7. In Figure 5b, you have a typo in the word "rotary"

8. In the conclusion, you present lower tool wear for the longitudinal-torsional case. Is this supported by any literary source, or is it just a speculation. If the latter, the statement in the conclusion should be tempered.

Author Response

RESPONSE TO REVIEWERS' COMMENTS

“Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal-Torsional Ultrasonic Vibrations”

By T.  Zarrouk, M. Nouari, H Bouali

Manuscript Number: machines-3374486

Dear Editor,

Please, find herewith our responses to the reviewers. Many thanks to them for their comments and valuable suggestions that helped us to improve our manuscript. We hope that we satisfied all required changes and suggested modifications to enhance the quality of our paper. We indicate below how we responded to required and suggested revisions.

All comments, point by point, are described in the manuscript.

Yours Sincerely.

The authors of the paper

1. The study takes the data for modeling from reference [35]. However, from comparing the curves, it does not seem to me that the force curves in dependence on the speed and feed correspond (compare article 35 and yours). The curves in [35] are more straightforward. Can you explain this?

Answers: Thank you for this remark. We validated the numerical model by comparing it with experimental results concerning the integration of longitudinal ultrasonic vibrations. Subsequently, we numerically analyzed the impact of combined longitudinal-torsional ultrasonic vibrations on the cutting force components. as for the experimental results are correctly extracted from the article cited in reference [39].

2. In the study, you assume a reduction in force based on the calculation. The data for verifying the calculation are apparently not available, right?

Answers: Thank you for this remark. Our study focused on the integration of ultrasonic vibrations. On the experimental side, only longitudinal ultrasonic vibrations were used. First, we validated the model for this case, then we numerically studied the influence of combined longitudinal and torsional ultrasonic vibrations.

3. What is the percentage difference between the predicted and real values?

Answers: Thank you for this remark. we introduced the optimization rates in percentage in the new version.

4. In your numerical calculation, you also predict the deformation of the honeycomb structure. Could you compare the simulation results with real photos from [35]?

Answers: Thank you for this remark. Indeed, I cannot do it because the results concerning combined vibrations are not established experimentally.

5. This is just a small thing, but the tool position in Figure 9a and 9b is not the same and it raises the question of how it would look if it were.

Answers: Thank you for this remark. you are right, the feed rate is not the same for the two cases treated, that is why we presented the new figure.

6. In Figure 9, I would recommend choosing black font color on the scale.

Answers: Thank you for this remark.  the scale produced by the Abaqus software I cannot modify it.

7. In Figure 5b, you have a typo in the word "rotary".

Answers: Thank you for this remark.  the figure is modified.

8. In the conclusion, you present lower tool wear for the longitudinal-torsional case. Is this supported by any literary source or is it just a speculation. If the latter, the statement in the conclusion should be tempered.

Answers: Thank you for this remark.  Indeed, longitudinal-torsional vibrations minimize cutting forces, thus reducing premature wear of the cutting tool.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. In abstract of the manuscript, the authors mentioned that the cutting force during the machining processes of Nomex honeycomb structure can be reduced, the surface quality can be optimized, and the accumulation of material in front of the cutting tool can be reduced. Unfortunately, the optimization ratio is not specified in detail, and it is recommended to add a clear optimization ratio.

 2. Line 116: The resonant frequency of THU Ultrasonic 850 is 20 kHz, what makes the reviewer confused is that the resonant frequency set at line 296 of the manuscript is 21.26 kHz, which is higher than the resonant frequency of the equipment. Is there any contradiction?

 3. During the actual machining process, the cutting force should fluctuate within a certain range. The cutting force shown in Figure 7 and Figure 8 in the manuscript is a fixed value. Is this fixed value the average cutting force? It is suggested that the author should add explanations to the manuscript.

 4. The accuracy of the finite element model established by the authors was verified through experiments. Unfortunately, only the cutting force was taken as the evaluation index, as shown in Figure 7, and other important indexes such as the quality of the machined surface were not discussed. Therefore, the reliability of the finite element model may need to be further verified.

 5. The Part 2 (Materials and Methods), Part 3 (Ultrasonic Vibration Assisted Milling) and Part 4 (Setting Up the Numerical Model) of the manuscript contain a lot of general knowledge introduction, and it is recommended to delete it appropriately, and Part 3 and part 4 are recommended to be combined.

 6. Figures 7, 8 and 9 in the manuscript were discussed a lot by authors, but the reviewer was confused that some results were difficult to draw from the pictures, such as lines 323 to 342, 368 to 399, 428 to 450 of the manuscript, and more experimental or simulation pictures should be compensated to present the above results.

7. In conclusions of the manuscript, the authors improved the cutting performance of the Nomex honeycomb structure through simulation, unfortunately, the authors did not explain the improvement ratio, such as the optimization ratio of the machined surface quality, the improvement ratio of machining efficiency, etc. It is suggested to supplement the corresponding data.

Author Response

RESPONSE TO REVIEWERS' COMMENTS

“Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal-Torsional Ultrasonic Vibrations”

By T.  Zarrouk, M. Nouari, H Bouali

Manuscript Number: machines-3374486

Dear Editor,

Please, find herewith our responses to the reviewers. Many thanks to them for their comments and valuable suggestions that helped us to improve our manuscript. We hope that we satisfied all required changes and suggested modifications to enhance the quality of our paper. We indicate below how we responded to required and suggested revisions.

All comments, point by point, are described in the manuscript.

Yours Sincerely.

The authors of the paper.

1. In abstract of the manuscript, the authors mentioned that the cutting force during the machining processes of Nomex honeycomb structure can be reduced, the surface quality can be optimized, and the accumulation of material in front of the cutting tool can be reduced. Unfortunately, the optimization ratio is not specified in detail, and it is recommended to add a clear optimization ratio.

Answers: Thank you for this remark. The Abstract is modified in the revised version.

2. Line 116: The resonant frequency of THU Ultrasonic 850 is 20 kHz, what makes the reviewer confused is that the resonant frequency set at line 296 of the manuscript is 21.26 kHz, which is higher than the resonant frequency of the equipment. Is there any contradiction?

Answers: Thank you for this remark. The machine performance is presented in the reference article [35]. However, in order to avoid confusion, we will limit ourselves to the frequency used during the experimental phase.

3. During the actual machining process, the cutting force should fluctuate within a certain range. The cutting force shown in Figure 7 and Figure 8 in the manuscript is a fixed value. Is this fixed value the average cutting force? It is suggested that the author should add explanations to the manuscript.

Answers: Thank you for this remark. In fact, the values ​​of the components of the cutting force are presented as averages. We will subsequently present the formulas highlighting this ambiguity.

4. The accuracy of the finite element model established by the authors was verified through experiments. Unfortunately, only the cutting force was taken as the evaluation index, as shown in Figure 7, and other important indexes such as the quality of the machined surface were not discussed. Therefore, the reliability of the finite element model may need to be further verified.

Answers: Thank you for this remark. Our model has been validated by experimental tests regarding the integration of longitudinal vibrations. However, it is not possible to compare the numerical results in terms of surface quality, because the integration of longitudinal-torsional vibrations has not been carried out experimentally.

5. The Part 2 (Materials and Methods), Part 3 (Ultrasonic Vibration Assisted Milling) and Part 4 (Setting Up the Numerical Model) of the manuscript contain a lot of general knowledge introduction, and it is recommended to delete it appropriately, and Part 3 and part 4 are recommended to be combined.

Answers: Thank you for this remark. We have done what is necessary.

6. Figures 7, 8 and 9 in the manuscript were discussed a lot by authors, but the reviewer was confused that some results were difficult to draw from the pictures, such as lines 323 to 342, 368 to 399, 428 to 450 of the manuscript, and more experimental or simulation pictures should be compensated to present the above results.

Answers: Thank you for this remark. we have done what is necessary.

7. In conclusions of the manuscript, the authors improved the cutting performance of the Nomex honeycomb structure through simulation, unfortunately, the authors did not explain the improvement ratio, such as the optimization ratio of the machined surface quality, the improvement ratio of machining efficiency, etc. It is suggested to supplement the corresponding data.

Answers: Thank you for this remark. we have done what is necessary.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Comments and suggestions for authors are attached.

Comments for author File: Comments.pdf

Author Response

RESPONSE TO REVIEWERS' COMMENTS
“Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal-Torsional Ultrasonic Vibrations”
By T. Zarrouk, M. Nouari, H Bouali
Manuscript Number: machines-3374486
Dear Editor,
Please, find herewith our responses to the reviewers. Many thanks to them for their comments and valuable suggestions that helped us to improve our manuscript. We hope that we satisfied all required changes and suggested modifications to enhance the quality of our paper. We indicate below how we responded to required and suggested revisions. All comments, point by point, are described in the manuscript.
Yours Sincerely.
The authors of the paper
1. Symbols for quantities in equations, figures and handwriting are usually written in different styles. I could give many examples. In all cases, the quantities should be written in a uniform way.
Answers: Thank you for this remark. your comment has been taken into account.
2. Again, I have to say that the quality of some figures (e.g., Figs. 1 and 2) is very poor. This is particularly the case with the dimensioning, which should be done on the basis of the rules of technical drawing. There should be a uniform font height (similar to a manuscript), uniform font styles, correct vertical dimensions (as in graphs), etc. Therefore, they should be properly redrawn to enhance their quality.
Answers: Thank you for this remark. Your kind remark is taken into consideration in the new version.
3. Again, the equation 5: The meanings of quantities and their units are unclear, and it is confusing for the reader. For example, Δ corresponds to the equivalent plastic strain increment. What is the quantity  and ´ including their units? Similarly, in the new equations 6 and 7, the meanings of the quantities are missing. It is necessary that the authors properly explain the meaning of all quantities throughout the manuscript and specify their units (preferably in parentheses) for each quantity.
Answers: Thank you for this remark. your comment has been taken into account.
4. The meaning of the abbreviation RUM should be given at the beginning of the article where the abbreviation is used and not on line 262.
Answers: Thank you for this remark. your comment has been taken into account.
5. One of my recommendations was to conduct a detailed investigation into ultrasonic vibration leading to improved surface quality compared to conventional machining technologies. There is a lot of research in this area. However, the authors only cite their two studies without specific results. I recommend a detailed discussion when applying ultrasonic vibration to surface quality compared to conventional machining technologies, for a variety of materials and their structures (not just honeycomb structures).
Answers: Thank you for this remark. This is presented in the introduction in the new version.
6. Figures 5 and 6: It is recommended to write the values of quantities on the vertical axis (for force) with decimal points instead of lines. Furthermore (and elsewhere in the article), there should be a space between the quantity designation and its unit.
Answers: Thank you for this remark. your comment has been taken into account.
7. I recommended that the authors take microscopic images of the surfaces to confirm their claims regarding the quality of the machined surface (Figures 7-10). Their response was: "We cannot present microscopic images. Because the walls of the structure are modelled by shell elements which makes it impossible to present the burrs. Our focus has been on the deformation and tearing of the walls". However, it would be useful in the future to compare this (i.e. the effect of feed rate and rotational speed on surface quality) using microscopy, e.g. on other more suitable material structures. The authors' arguments should be experimentally verified in some way.
Answers: Thank you for this remark. This is presented as a perspective in the new version.

Reviewer 2 Report

Comments and Suggestions for Authors

The author's answer is acceptable, thank you for the explanation and improvement of the article

There was a recommendation for Fig. 9 (now Fig. 7), which was strangely explained, however, the new design of Fig. 7 looked much better and its readability improved.

It is a pity that the comparison of defects on the honeycomb structure could not be confronted with reality in this study. Hopefully, we will see next time

Are you going to experimentally verify numerical cutting of longitudinal - torsional ultrasonic vibrations in the future?

I believe that future work should be mentioned in the conclusions. Can you add this detail? I assume that you have not solved everything yet.

Author Response

RESPONSE TO REVIEWERS' COMMENTS
“Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal-Torsional Ultrasonic Vibrations”
By T. Zarrouk, M. Nouari, H Bouali
Manuscript Number: machines-3374486
Dear Editor,
Please, find herewith our responses to the reviewers. Many thanks to them for their comments and valuable suggestions that helped us to improve our manuscript. We hope that we satisfied all required changes and suggested modifications to enhance the quality of our paper. We indicate below how we responded to required and suggested revisions.
All comments, point by point, are described in the manuscript.
Yours Sincerely.
The authors of the paper
• There was a recommendation for Fig. 9 (now Fig. 7), which was strangely explained, however, the new design of Fig. 7 looked much better and its readability improved.
Answers: Thank you for this remark. Section analysis is changed in the new version.
• It is a pity that the comparison of defects on the honeycomb structure could not be confronted with reality in this study. Hopefully, we will see next time.
Answers: Thank you for this remark. This remark is modified in the conclusion for the new version.
• Are you going to experimentally verify numerical cutting of longitudinal - torsional ultrasonic vibrations in the future?
Answers: Thank you for this remark. indeed, we hope to continue in this direction to validate the numerical model and treat other cases experimentally.
• I believe that future work should be mentioned in the conclusions. Can you add this detail? I assume that you have not solved everything yet.
Answers: Thank you for this remark. Conclusion is modified by adding your important remark.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors modified the manuscript with reference to the reviewer's comments. Unfortunately, the quality of the manuscript is still significantly short of the standards of international journals. The obvious problems are as follows:

 1.In abstract and conclusion of the manuscript, the authors mentioned that the optimization ratio of cutting force and accumulation of material in front of the cutting tool was 28% and 30%, respectively. However, the source and solution of these two data were not found in results and discussion of the manuscript, and even these two data were not found. Therefore, the reviewer is very confused about how the authors obtained the above optimization ratio.

 2. In the first review, the reviewer mentioned that some results were difficult to draw from the figures, and more experimental or simulation pictures should be compensated to present the above results. Unfortunately, most of the revisions only modified the text and did not significantly improve the quality of the manuscript. For example, Line 319 to 322, the two conclusions cannot be drawn from the manuscript, and more figures and analysis are needed to present the above conclusions.

3. Section 5.4: The authors improved the quality of the machined surface by means of simulation, unfortunately, the evaluation index and the improvement ratio of machined surface quality are not explained.

Author Response

RESPONSE TO REVIEWERS' COMMENTS
“Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal-Torsional Ultrasonic Vibrations”
By T. Zarrouk, M. Nouari, H Bouali
Manuscript Number: machines-3374486
Dear Editor,
Please, find herewith our responses to the reviewers. Many thanks to them for their comments and valuable suggestions that helped us to improve our manuscript. We hope that we satisfied all required changes and suggested modifications to enhance the quality of our paper. We indicate below how we responded to required and suggested revisions.
All comments, point by point, are described in the manuscript.
Yours Sincerely.
The authors of the paper.
1.In abstract and conclusion of the manuscript, the authors mentioned that the optimization ratio of cutting force and accumulation of material in front of the cutting tool was 28% and 30%, respectively. However, the source and solution of these two data were not found in results and discussion of the manuscript, and even these two data were not found. Therefore, the reviewer is very confused about how the authors obtained the above optimization ratio.
Answers: Thank you for this remark. The rates have been correctly calculated and are now presented in the updated version. The calculation of the rates for the cutting force components was performed from the numerical results, while the estimation of the material accumulation rate was based on visual observation with the naked eye.
2. In the first review, the reviewer mentioned that some results were difficult to draw from the figures, and more experimental or simulation pictures should be compensated to present the above results. Unfortunately, most of the revisions only modified the text and did not significantly improve the quality of the manuscript. For example, Line 319 to 322, the two conclusions cannot be drawn from the manuscript, and more figures and analysis are needed to present the above conclusions.
Answers: Thank you for this remark. We have tried to update the conclusion based on the manuscript.
3. Section 5.4: The authors improved the quality of the machined surface by means of simulation, unfortunately, the evaluation index and the improvement ratio of machined surface quality are not explained.
Answers: Thank you for this remark. The analysis and optimization of the machined surface quality was carried out based on visual observation with the naked eye.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors of the paper have carried out appropriate revisions based on my recommendations. The quality of the article has improved. However, I have additional recommendations to improve the quality of this article:

1. The introduction has been only partially corrected. It is more a matter of language and stylistic changes. It is too general. It is more or less just a statement that ultrasonic vibration-assisted machining achieves better results compared to conventional manufacturing technologies. The results of the previous research should be specified in detail (e.g. percentage reduction in cutting force, reduction in burrs, etc.). In addition, the introduction highlights in yellow many words that have remained the same compared to the previous version of the article. The authors should have highlighted in yellow only the new changes in the introduction. This is then misleading to the reviewers.

2. The quality of some of the figures (especially figures 1 and 2) is again insufficient. The font size should be the same (see Figure 1: L=40mm, h=1.83mm). Furthermore, the notation of all quantities should be done in the same way with spaces (e.g. in Figure 1: t = 0.13 mm, L = 40 mm, etc.). The same way in Figure 2. The quantity T´ is written in two ways in Figure 2 (i.e., T´ and T´).  Again, the labeling of quantities should be the same in figures, equations, and text.

3. Equation 4 has been corrected. However, the units of quantities are again missing. Are the damage parameter and increment of the equivalent plastic strain dimensionless quantities? And is the plastic failure stress in MPa? Then it is very confusing. Please add the appropriate units to the manuscript. Same for equations 5 and 6.

4. Other formal deficiencies in the manuscript could be mentioned.

From the above, it is clear that careful proofreading and appropriate additions still need to be made. Otherwise, the quality of the article for potential readers of Machines journal is significantly reduced.

Author Response

RESPONSE TO REVIEWERS' COMMENTS

“Numerical Modeling and Optimization of Nomex Honeycomb Core Milling: Influence of Longitudinal and Longitudinal-Torsional Ultrasonic Vibrations”

By T.  Zarrouk, M. Nouari, H Bouali

Manuscript Number: machines-3374486

Dear Editor,

Please, find herewith our responses to the reviewers. Many thanks to them for their comments and valuable suggestions that helped us to improve our manuscript. We hope that we satisfied all required changes and suggested modifications to enhance the quality of our paper. We indicate below how we responded to required and suggested revisions.

All comments, point by point, are described in the manuscript.

Yours Sincerely.

The authors of the paper

1. The introduction has been only partially corrected. It is more a matter of language and stylistic changes. It is too general. It is more or less just a statement that ultrasonic vibration-assisted machining achieves better results compared to conventional manufacturing technologies. The results of the previous research should be specified in detail (e.g. percentage reduction in cutting force, reduction in burrs, etc.). In addition, the introduction highlights in yellow many words that have remained the same compared to the previous version of the article. The authors should have highlighted in yellow only the new changes in the introduction. This is then misleading to the reviewers.

Answers: Thank you for your constructive comments. I would like to point out that the introduction has been enriched with specific and relevant examples related to the topic at hand, in order to better contextualize the topic and illustrate its importance. Regarding the literature studies, you are right to point out the lack of mention of the optimization percentage. However, it should be noted that in the cited articles, most do not explicitly mention this percentage. Regarding the use of yellow, I have indeed reserved it to highlight the changes and rewordings requested by the reviewers. This is to facilitate reading and to ensure that all suggestions have been taken into account.

2. The quality of some of the figures (especially figures 1 and 2) is again insufficient. The font size should be the same (see Figure 1: L=40mm, h=1.83mm). Furthermore, the notation of all quantities should be done in the same way with spaces (e.g. in Figure 1: t = 0.13 mm, L = 40 mm, etc.). The same way in Figure 2. The quantity T´ is written in two ways in Figure 2 (i.e., T´ and T´).  Again, the labeling of quantities should be the same in figures, equations, and text.

Answers: I sincerely thank you for this important remark. The figure and the necessary elements have been corrected in the new version of the manuscript. I have taken care to ensure that all the required changes have been made and are now in line with expectations.

3. Equation 4 has been corrected. However, the units of quantities are again missing. Are the damage parameter and increment of the equivalent plastic strain dimensionless quantities? And is the plastic failure stress in MPa? Then it is very confusing. Please add the appropriate units to the manuscript. Same for equations 5 and 6.

Answers: I would like to thank you very much for this pertinent remark. I have corrected the sentence and the relationship is now correct. Furthermore, all the quantities mentioned in equation (4) are indeed dimensionless, as you pointed out. In addition, I have also changed the necessary units of the quantities in equations (5) and (6) to ensure consistency and clarity.

4. Other formal deficiencies in the manuscript could be mentioned.

      Answers: A general check was carried out within the requested deadline

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Since the authors had fully revised the manuscript in accordance with the reviewer's comments, the reviewer agrees to accept the manuscript.

Author Response

I would like to sincerely thank the reviewer for his contribution to the evaluation of our article.