Analytical Model of Deformation of a Functionally Graded Ceramic Coating under Local Load

Round 1

Reviewer 1 Report

1.The authors emphasize that the study is specific to FGM coatings, but the basic characteristics of the metal-ceramic phase without a clear interface are not considered completely. In Fig. 1, Table 1 and Table 2, the mutation at the coating interface can be clearly observed. This should have a direct impact on the stress distribution.

 

2. In the analysis of Example 1, the coating structure shown in Figure 1 is set to consist of a 50 μm Al2O3 and a 250 μm gradient layer. However, in actual aluminum diffusion, because the dense α-Al2O3 structure will rapidly form and hinder the deep diffusion of oxygen, the thickness of the gradient layer will be much smaller than the thickness of the α-Al2O3 ceramic layer. I wonder if the coating structure deviates from Example 1 (e.g., 250μmAl2O3 composite 50μm gradient layer), will the same result be given due to differences in stress distribution?

Author Response

1.The authors emphasize that the study is specific to FGM coatings, but the basic characteristics of the metal-ceramic phase without a clear interface are not considered completely. In Fig. 1, Table 1 and Table 2, the mutation at the coating interface can be clearly observed. This should have a direct impact on the stress distribution.

answer

1. In order to achieve analytical results, we approximated the coating properties by piecewise linear functions. It also makes it possible to operate with a minimal set of input data. Of course, taking the blurred interface into account would smooth out the discontinuities of the equivalent stresses a bit.

 

2. In the analysis of Example 1, the coating structure shown in Figure 1 is set to consist of a 50 μm Al2O3 and a 250 μm gradient layer. However, in actual aluminum diffusion, because the dense α-Al2O3 structure will rapidly form and hinder the deep diffusion of oxygen, the thickness of the gradient layer will be much smaller than the thickness of the α-Al2O3 ceramic layer. I wonder if the coating structure deviates from Example 1 (e.g., 250μmAl2O3 composite 50μm gradient layer), will the same result be given due to differences in stress distribution?

answer

2. In the new version of the manuscript, we added calculation examples for a coating with a developed ceramic and thin gradient layer (THE NEW RESULTS ARE PRESENTED IN THE ADDED FIG. 4, 5 AND 8, 9).

Author Response File: Author Response.docx

Reviewer 2 Report

In the present research, the authors try to investigate the deformation of the functionally graded ceramic coating by a analytical model. The paper exhibits some result but there are some questions.

1. The authors titled the paper as “Analytical model of deformation of a functionally graded ceramic coating under local load”. It is some confusing. It wonders why they investigate the deformation not the stress?

2. In the content, the full description should be given for the abbreviations, such FGM.

3. In the abstract and introduction, the authors describe that they aim to study the aluminium oxide coating by PEO. However, they design the model with soft FGM and hard FGM layers. It wonders what is the meaning of soft FGM?

4. In the content, what is the definition of functionally gradient layer? Does it mean the hardness or chemical composition have gradient evolution?

5. The authors have concluded that the coating formed by PEO of the D16T alloy cracks due to bending on a compliant substrate. It wonders whether the authors have performed the experimental test? If they have don, the results should be provided correspondingly.

6. In the content, the authors have simulated the stress in the alumina coating grown on aluminum sprayed on a steel. It wonder whether the authors use the same model with the alumina coating formed on aluminum alloy. In fact, these two kinds coatings would have different interface. Whether the authors have considered these factors?

7.  The authors should performed the experimental to verify their simulation results, which increases the persuasion. 

Author Response

1. The authors titled the paper as “Analytical model of deformation of a functionally graded ceramic coating under local load”. It is some confusing. It wonders why they investigate the deformation not the stress?

The term "deformation" in the title of the article " is used in the sense of "behavior".

2. In the content, the full description should be given for the abbreviations, such FGM.

Thank you! Corrected.

3. In the abstract and introduction, the authors describe that they aim to study the aluminium oxide coating by PEO. However, they design the model with soft FGM and hard FGM layers. It wonders what is the meaning of soft FGM?

Formulation (4) is suitable for calculating the coefficient of integral stiffness of a soft substrate with any FG structure. Although in the examples with sputtered and annealed aluminum, the spatial changes in the properties of the thin aluminum layer are not considered.

4. In the content, what is the definition of functionally gradient layer? Does it mean the hardness or chemical composition have gradient evolution?

That's right. The mechanical properties of coatings generally vary by thickness.

5. The authors have concluded that the coating formed by PEO of the D16T alloy cracks due to bending on a compliant substrate. It wonders whether the authors have performed the experimental test? If they have don, the results should be provided correspondingly.

No experiments were conducted. Our article is theoretical, experiments are planned to be carried out in the future.

6. In the content, the authors have simulated the stress in the alumina coating grown on aluminum sprayed on a steel. It wonder whether the authors use the same model with the alumina coating formed on aluminum alloy. In fact, these two kinds coatings would have different interface. Whether the authors have considered these factors?

In fact, the interfaces are similar. In the first case, it is a non-oxidized layer of sprayed aluminium. In the second case, it is a thin layer of annealed aluminum formed from an alloy.

7. The authors should performed the experimental to verify their simulation results, which increases the persuasion. 

The method of experimental determination of stresses in FGM ceramic coatings requires separate research.

 

Author Response File: Author Response.docx

Reviewer 3 Report

The article by Ivan Shatskyi et al. presents an analytical approach to studying the behavior of FGM coatings under local load. The developed method is suitable for analyzing the mechanics of a functionally gradient coating, but only one that can be conditionally divided into two zones: external relatively hard and internal relatively soft. The solution is presented in an analytical form, which is undoubtedly an advantage of this article. The introduction briefly presents the relevance of the study, describes the need for analytical methods for calculating the parameters of gradient coatings. The main part contains the calculation equations and positions of the model, as well as several examples of the application of calculations to determine the parameters of the coating. The conclusion is made on the basis of the presented results. The main comments to the article are as follows: 1) Figures 2 and 4 should be presented on the same scale. 2) It is necessary to justify why exactly such values of the thickness of the layer H, the thickness of the substrate h are chosen for calculations. 3) Why does it depend that the location of the maximum of the equivalent voltage does not coincide with the location of the minimum safety margin?

Author Response

The article by Ivan Shatskyi et al. presents an analytical approach to studying the behavior of FGM coatings under local load. The developed method is suitable for analyzing the mechanics of a functionally gradient coating, but only one that can be conditionally divided into two zones: external relatively hard and internal relatively soft. The solution is presented in an analytical form, which is undoubtedly an advantage of this article. The introduction briefly presents the relevance of the study, describes the need for analytical methods for calculating the parameters of gradient coatings. The main part contains the calculation equations and positions of the model, as well as several examples of the application of calculations to determine the parameters of the coating. The conclusion is made on the basis of the presented results. The main comments to the article are as follows: 1) Figures 2 and 4 should be presented on the same scale. 2) It is necessary to justify why exactly such values of the thickness of the layer H, the thickness of the substrate h are chosen for calculations. 3) Why does it depend that the location of the maximum of the equivalent voltage does not coincide with the location of the minimum safety margin?

Answers

1. This action will make fig. 4 (in the new version, fig. 6, 8) is very disproportionate. We’d like to ask to leave our

 

2. The chosen thicknesses correspond to the parameters and results of oxidation of aluminum and alloy. In the new version, other thickness ratios are also considered (THE NEW RESULTS ARE PRESENTED IN THE ADDED FIG. 4, 5 AND 8, 9).

 

3. In an inhomogeneous body, the location of the minimal safety factor may or may not coincide with the location of the maximum of the equivalent stress. Confirmation of this thesis is the key result of the article. In FGM, the yield strength depends on the coordinates, therefore, in general, the most dangerous place of the structure is the point where inequality (7) is violated for the first time.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors have revised the manuscript and answered the questions. It is improved and could be accepted.