Optimal Design of Functionally Graded Parts
Round 1
Reviewer 1 Report
I consider the review to be interesting and to contain interesting information and conclusions. The article processing method suits me. In my opinion this is a well-written, well-organized and well-illustrated paper. The title is adequate for the contribution. The content of the main section is presented clearly. Processing of the sources and conclusions of the literature is comprehensible and meets the standards of a review article. The authors provide a detailed description and analysis of the results obtained by researchers over 25 years. All aspects related to the topic of the article were discussed. The supporting figures and tables are appropriate. In terms of content and form, I consider the article to be suitable for publication in the MDPI Metals.
Minor remarks:
- Perhaps the authors consider that a table listing the signs and symbols used in the article would be useful. Also, in my opinion, comparative tables such as Table 1 for the other chapters in the article would be very useful.
- Figures 3 and 4 could be in colour and better quality.
- The article should be written according to the requirements of the journal.
Author Response
We are thankful to the reviewers for their valuable comments and suggestions, which have greatly improved the original manuscript. We have tried to do our best to address the comments and respond to the points raised. Changes in the revised manuscript are marked in red.
Response to reviewer #1:
Comment 1: “Perhaps the authors consider that a table listing the signs and symbols used in the article would be useful. Also, in my opinion, comparative tables such as Table 1 for the other chapters in the article would be very useful.”
Response: We added a table, listing the signs and symbols, to the introduction section in the revised manuscript. Also, we added a table to the “Representation Techniques” section in the manuscript that outlines different models and their properties for functionally graded materials.
Comment 2: “Figures 3 and 4 could be in colour and better quality.”
Response: We agree with you, but these figures are taken from the literature and are originally in black and white. Unfortunately, they cannot be converted to color figures with higher quality.
Comment 3: “The article should be written according to the requirements of the journal.”
Response: We reformatted the article to comply with the requirements of the journal according to your comment.
Once again, we would like to express our gratitude to you for your time reviewing our manuscript and your thoughtful comments and suggestions.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this paper, the optimal design methods of functionally graded materials with complex material composition distributions are reviewed for the first time, including the related research works on homogenization methods, material representation techniques, finite element methods and optimization algorithms, and manufacturing. In addition, some current problems and future developments in FGM structural design methods are summarized. Overall, the presented work is good and is within the scope of Metals Journal. Authors are encouraged to address the following minor issues that need to be addressed before the consideration of paper.
1. Section 3.1, the description of the ROM can help to understand this method by introducing the calculation formula of material properties.
2. Section 4.4, more information on how to employ b-spline basis function to obtain the volume fraction distribution of FGM should be provided. In addition, the piece-wise cubic interpolation function can also realize the modeling based on control points. For details, please refer to: Composite Structures, 214, 83-102(2019).
3: In Section 5.1, the author mentioned the researches on modeling FGM structures with commercial software. Currently, COMSOL Multiphysics can also define the material properties of FGM through analytic functions to analyze the mechanical behavior of FGM structures. The author can add related research.
4: This study is concerned with the FGM. In this regard, authors are invited to strengthen the literature review by incorporating the following recent literature at the micron scale of FGM: International Journal of Applied Mechanics Vol. 13, No. 5, 2150057 (2021); Composite Structures 278, 114554 (2021).
Author Response
We are thankful to the reviewers for their valuable comments and suggestions, which have greatly improved the original manuscript. We have tried to do our best to address the comments and respond to the points raised. Changes in the revised manuscript are marked in red.
Response to reviewer #2:
Comment 1: “Section 3.1, the description of the ROM can help to understand this method by introducing the calculation formula of material properties.”
Response: We added the calculation formula of material properties for the description of ROM in Section 3.1 according to your comment.
Comment 2: “Section 4.4, more information on how to employ b-spline basis function to obtain the volume fraction distribution of FGM should be provided. In addition, the piece-wise cubic interpolation function can also realize the modeling based on control points. For details, please refer to: Composite Structures, 214, 83-102(2019).”
Response: We added some more literatures for the explanation of b-spline basis function to obtain the volume fraction distribution of FGMs in Section 4.4. The literature on piece-wise cubic interpolation function is also provided according to your comment.
Comment 3: “In Section 5.1, the author mentioned the researches on modeling FGM structures with commercial software. Currently, COMSOL Multiphysics can also define the material properties of FGM through analytic functions to analyze the mechanical behavior of FGM structures. The author can add related research.”
Response: We added some literatures on COMSOL Multiphysics to define the material properties of FGM structures in Section 5.1 according to your comment.
Comment 4: “This study is concerned with the FGM. In this regard, authors are invited to strengthen the literature review by incorporating the following recent literature at the micron scale of FGM: International Journal of Applied Mechanics Vol. 13, No. 5, 2150057 (2021); Composite Structures 278, 114554 (2021).”
Response: We added the recent literature at the micron scale of FGMs to Section 2.4.
Once again, we would like to thank you for your careful review of our manuscript and thoughtful comments and suggestions.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper provides a comprehensive literature review of FGMs. My comments are as follows:
Any particular reasons/grounds how the years are segmented in section 2? Why 2002? 2009? 2015?
The finite element model was first introduced in section 3.6, then section 5 specifically and more comprehensively introduces the finite element analysis approaches. Actually section 3.6 covers more about the application of RVE in Finite element model, while section 4 more specifically and comprehensively introduces the Representation techniques. I think section 3.6 should be reorganised into section 4 and section 5.
Please include a bit more relevant literature about using Finite element analysis approaches for the simulation of FGMs, such as in the aerospace industry: Preparation and thermodynamic analysis of the porous ZrO2/(ZrO2+Ni) functionally graded bolted joint; Load distribution in threads of porous metal–ceramic functionally graded composite joints subjected to thermomechanical loading.
Table 1 is a bit wordy. Perhaps using simple symbols to replace “Yes’ or ‘No’
Fig. 13 has a rather low quality, please try to improve it. Also, there two ‘(a) and ‘(b)’, replace with (c) and (d) and add figure captions.
There should be a comparison of different models, either in the format of Table or Text, about their advantages, disadvantages and applications. This is like a summary and will provide important reference value for this review paper.
Author Response
We are thankful to the reviewers for their valuable comments and suggestions, which have greatly improved the original manuscript. We have tried to do our best to address the comments and respond to the points raised. Changes in the revised manuscript are marked in red.
Response to reviewer #3:
Comment 1: “Any particular reasons/grounds how the years are segmented in section 2? Why 2002? 2009? 2015?”
Response: These segments were chosen based on the relevant milestones in the research and development of FGMs. The classification is based on the idea of FGMs initially proposed, thermal load in addition to thermal load, start of 2D and 3D material distribution, start of material distribution optimization, multi-objective optimization of FGMs, etc.
Comment 2: “The finite element model was first introduced in section 3.6, then section 5 specifically and more comprehensively introduces the finite element analysis approaches. Actually section 3.6 covers more about the application of RVE in Finite element model, while section 4 more specifically and comprehensively introduces the Representation techniques. I think section 3.6 should be reorganized into section 4 and section 5.”
Response: We admit that it was somewhat difficult to organize FEA in the paper as it has been used for homogenization, representation, and analysis of FGMs. The representative volume element (RVE) model is the most popular homogenization-based multi-scale constitutive method used in the finite element method to investigate the effect of microstructures on mechanical and thermal properties of composites. Therefore, we wanted to make sure it is mentioned along other homogenization approaches and included RVE model in homogenization approaches (Section 3).
Comment 3: “Please include a bit more relevant literature about using Finite element analysis approaches for the simulation of FGMs, such as in the aerospace industry: Preparation and thermodynamic analysis of the porous ZrO2/(ZrO2+Ni) functionally graded bolted joint; Load distribution in threads of porous metal–ceramic functionally graded composite joints subjected to thermomechanical loading.”
Response: We added some papers, including the above articles, on using finite element analysis approaches for the simulation of FGMs in Section 5.
Comment 4: “Table 1 is a bit wordy. Perhaps using simple symbols to replace “Yes’ or ‘No’.”
Response: We replaced ‘Yes’ or ‘No’ with ‘√’ and ‘X’ in the table according to your suggestion.
Comment 5: “Fig. 13 has a rather low quality, please try to improve it. Also, there two ‘(a) and ‘(b)’, replace with (c) and (d) and add figure captions.”
Response: We agree with you on the quality of this figure, but it had the same quality in the original paper. So, we could not have a higher quality image. Also, the first two pictures belong to figure 12(a) and 12(b). We added more space between the two figures to avoid confusion.
Comment 6: “There should be a comparison of different models, either in the format of Table or Text, about their advantages, disadvantages and applications. This is like a summary and will provide important reference value for this review paper.”
Response: We added another table in section 4 that outlines different models and their properties for functionally graded materials. We cannot have all the methods because there would be too many of them. We selected some of the important models.
Once again, we would like to express our sincere gratitude to you for your careful review of our manuscript and thoughtful comments, questions, and suggestions.
Round 2
Reviewer 3 Report
The authors have well addressed all my previous comments, as such, I would like to recommend it for publication. Good luck for your future research!
Author Response
We would like to express our sincere gratitude to the reviewer for recommending our paper for publication. Thank You Very much.
