Simulations of Effects of Geometric and Material Parameters on the Interfacial Stress of the Thermal Barrier Coatings with Free Edges

Round 1

Reviewer 1 Report

I thank the authors for this excellent research. The purpose of the research is clear and the study's path taken is completely correct. The title is cleverly written. In addition, the written language of the manuscript is fluent and understandable for the reader. One of the most important advantages of this manuscript was the interpretation of the results, which was done correctly and the logical reasons for them were mentioned. Even in the section "effects of material properties", the explanations were accompanied by physical phenomena, which shows the high expertise of the authors in this field. In summary, this manuscript contains a lot of valuable results, and therefore I highly recommend it for publication, because the industrialists in the field of turbines, whose biggest challenge is blade failure, can use these results practically. However, in my opinion, it is better for authors to pay attention to the following points and improve the quality of their article before publishing.

1- In an academic and scientific paper, it is better to refer not more than 3 references for one sentence, for example [1-6]. 

2- Finite element simulation should be describe more and in details such as type of element, boundary condition, loading, and analysis type, etc.

3- In this manuscript, the normal stress was shown by P symbol, but it is not general. It is better to change it with Sigma. 

4- Related to all equations that is not presented for the first time by the authors, should be referred to the appropriate references.

5- Related to Table 3,  please refer to an appropriate reference. 

6- Related to Figure 4, the numbers and contours are not clear and should use the image with large. please replace it with new one. 

7- In this research, the authors checked both geometric such as thickness of different layers like TC & BC, and material properties such as elastic modulus and Poisson's ratio of TC. So, which one is more effective than the others? Which one has less effect? Can you specify quantitatively.

8- Between the thickness of TC and BC, which one is more important than others and why?

9-  Related to section 3.3 "Effects of material properties", why the temperature difference is set to 100? It may be better to consider the temperature difference between the turbine off state and the operating temperature.

10- The place of section 4.2 "Experiments and validation" is not okay and it is normally should be located after presenting finite element simulation to show the model validation and after that, perform different analysis and output results. 

11- Related to conclusion section, point 1, it is better to show which parameter is more effective and important than others. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Review Letter

Simulations of Effects of Geometric and Material Parameters on the Interfacial Stress of the Thermal Barrier Coatings with Free Edges

Review of the manuscript with the paper ID of Coatings-2519691

This work models the stress state in disks with ordinary bilayer thermal barrier coatings considering both analytical and FEM approaches. A mathematical model is developed to determine the parameters affecting the interfacial stress of the system with thick coatings. The publication of this article needs to consider the following comments, completely:

 Compared to analytical strategies, what is the main advantage of FEM in this problems?

 Based on the configuration of Fig.3, what strategy is applied to balance the equilibrium moment at point ?1 ?

 According to the results of laboratory measurements, what subject can be concluded?

 Please explore that why when the distance from one point on the interface to the edge exceeds the distance from point A2 to the edge, the interfacial stress and radial stress do not change along the radial direction.

 The numbers of the offered configurations are too much. Please reduce them focusing on important ones which are essential. Offering a large number of configurations reduces the quality of the manuscript.

 In this regard, the following studies https://doi.org/10.1016/j.compstruct.2021.114557, https://doi.org/10.1016/j.ast.2017.06.008 on thermal environment can be investigated.

 Please support the following comment ‘’ the maximum absolute values of the interfacial shear and normal stresses increase with increasing TGO thickness, while the maximum absolute value of the second peak decreases with increasing TGO thickness’’ in the revised version. What is the reason of this trend?

 Based on the results, it is found that the existence of TGO does not have a significant effect on the parameter dA2/HTC. Please explain.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Manuscript Title: Simulations of Effects of Geometric and Material Parameters on the Interfacial Stress of the Thermal Barrier Coatings with Free Edges

About the manuscript:

This paper investigates interfacial stress in thermal barrier coatings near free edges, which can lead to turbine blade failure. The study uses simulation methods to analyze the effects of geometric and material variations on stress. Analytical and finite element methods are employed to calculate stress distributions in a coating-substrate system under thermal mismatch.

Strengths of the manuscript

Upon thorough evaluation of the manuscript, I find that it demonstrates a commendable level of research and presents an in-depth analysis of the interfacial stress between layers of thermal barrier coatings near free edges. The authors have utilized simulation methods to investigate the impact of variations in geometric and material parameters on the stress distribution of the thermal barrier coatings, particularly in the context of turbine blade failure.

One notable strength of the manuscript lies in its methodological approach. The use of both analytical methods and finite element simulations to calculate stress distributions in a disk-shaped coating-substrate system undergoing thermal mismatch adds robustness to the findings. By employing these complementary techniques, the authors have ensured a comprehensive exploration of the interfacial stress behavior, enhancing the reliability of the results.

Furthermore, the paper presents a comprehensive parametric analysis, systematically investigating the influence of important factors such as the coefficient of thermal expansion, elasticity modulus, Poisson's ratio, and thickness of each layer on the interfacial stress between coatings and substrate. The authors effectively demonstrate how variations in these parameters can significantly impact the stress distribution, thereby contributing to the understanding of the mechanisms that may lead to coating system failure near free edges.

The simulation results revealing notable concentrations of normal and shear stresses, which render the coating system susceptible to cracking and spalling from the free edge, are a significant contribution to the field. The observations shed light on critical failure points and potential weak spots in the thermal barrier coatings, alerting researchers and engineers to key areas that require attention during turbine blade design and operation. In addition, the manuscript proposes two integral parameters as novel indicators of the stress state near the free edge, related to mode I and II fracture, respectively. This proposal represents a noteworthy advancement in the field, providing valuable tools for characterizing and quantifying stress-related fracture risks. The validation of these parameters through experiments further adds to the paper's credibility and practical relevance.

One particular aspect worth highlighting is the manuscript's clarity and concise presentation of the research findings. The authors have effectively communicated their methodologies, results, and conclusions, making the paper accessible to a broad readership, including researchers and professionals working in the field of thermal barrier coatings and turbine blade design.

In conclusion, I am pleased to report that no weaknesses have been identified in the manuscript. The study is well-executed, offering valuable insights into the interfacial stress behavior of thermal barrier coatings and its implications for turbine blade performance. I also suggest considering the potential for further practical applications and discussing any limitations or potential future research directions to enrich the discussion further. Overall, the manuscript is a well-written and compelling piece of research deserving of consideration for publication.

Weakness of the manuscript

No weaknesses are identified in the manuscript.

General Comments

The reviewer has no general comments to make.

Minor Comments

1)     The reviewer feels that figure 6 can be improved by making the size of the points smaller. Additionally, the fonts of the numbers on the axis in the internal plots can be also smaller. Same for figure 7, 10b, 11b.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Accept. 

The authors tried to edit the manuscript according to the reviewers' comments and of course they did it well. In addition, they responded to comments one by one. In my opinion, the manuscript can be published in the present form.