Review Reports - Influence of Thermally Grown Oxide Dynamic Growth Mode and Creep Strength on the Delamination and Failure of Thermal Barrier Coatings in the Furnace Cycle

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Overall Evaluation

This study presents a numerical investigation on the effects of thermally grown oxide (TGO) growth modes and creep strength on the delamination and failure of thermal barrier coatings (TBCs) under furnace cyclic loading. The paper uses finite element modeling (ABAQUS) to simulate three TGO growth modes and explores how stress evolution, interface delamination, and coating failure are influenced by these modes and TGO creep. The work is methodically executed, technically rich, and relevant to current research in high-temperature coatings, yet it could benefit from minor improvements in structure, clarity, and novelty justification.

Comments

Title

Using abbreviations such as “TGO” in the title makes it difficult for readers to immediately understand the research focus. It is recommended that the authors use the full form of the term and refine the title for clarity and precision.

Suggested revision: Influence of Thermally Grown Oxide Dynamic Growth Mode and Creep Strength on the Delamination and Failure of Thermal Barrier Coatings during Furnace Cycling

Keywords

Avoid abbreviations in the keyword.

Novelty and Context Need Clearer Articulation

The introduction cites many prior works (Wei et al., Ranjbar-Far et al., Cen et al., etc.), but the novelty compared to existing TGO growth simulations is not distinctly stated.
Recommendation: Add a paragraph explicitly explaining what gap remains after [32, 36, 41] and how this work extends the understanding beyond previous modeling approaches.

Model Validation

The model validation section (3.1) only checks TGO thickness consistency across modes. This is insufficient to validate mechanical accuracy.

Recommendation: Compare simulated interface stresses or delamination trends with published experimental or numerical data (e.g., from Li et al., 2017; Dong et al., 2014).
Alternatively, include a discussion on why the parabolic-to-linear growth assumption remains acceptable.

Insufficient Justification for Boundary Conditions

The model applies a cosine interface and 2D plane-strain conditions. However, out-of-plane effects and 3D stress components can be significant for furnace cycling.

Suggestion: Discuss limitations of the 2D model and briefly justify the use of generalized plane strain (CPEG4R) instead of full 3D modeling.

Quantitative Results Missing

While qualitative stress evolution is well presented, the study lacks numerical quantification (e.g., maximum σ22, σ12 values, creep rate thresholds).

Recommendation: Provide a summary table comparing stress magnitudes and first-delamination cycle numbers for each mode.

Language and Grammar

The manuscript has frequent grammatical errors and awkward phrasing (e.g., “growth stress brought by TGO growth” → “growth stress induced by TGO thickening”).

Recommendation: A full English editing pass is strongly needed before publication.

Discussion of Practical Implications

The conclusion focuses on numerical outcomes but doesn’t interpret them mechanistically.
Suggestion: Add a discussion on how these findings influence TBC design strategies, such as optimizing bond coat composition or TGO morphology control.

Author Response

Responses to Reviewer #1

Thank you very much for your valuable comments. We have revised the manuscript by taking account of your suggestions. All corrections were highlighted by red color in the revised text. The following are responses and explanations to your comments.

Comments-in-brief: This study presents a numerical investigation on the effects of thermally grown oxide (TGO) growth modes and creep strength on the delamination and failure of thermal barrier coatings (TBCs) under furnace cyclic loading. The paper uses finite element modeling (ABAQUS) to simulate three TGO growth modes and explores how stress evolution, interface delamination, and coating failure are influenced by these modes and TGO creep. The work is methodically executed, technically rich, and relevant to current research in high-temperature coatings, yet it could benefit from minor improvements in structure, clarity, and novelty justification.

Response:

Thank you for your positive evaluation on our work.

Comment-1: Using abbreviations such as “TGO” in the title makes it difficult for readers to immediately understand the research focus. It is recommended that the authors use the full form of the term and refine the title for clarity and precision. Suggested revision: Influence of Thermally Grown Oxide Dynamic Growth Mode and Creep Strength on the Delamination and Failure of Thermal Barrier Coatings during Furnace Cycling

Response:

Thank you very much for your comment. We had modified the title to make this point clear by taking account of your suggestions.

Comment-2: Avoid abbreviations in the keyword.

Response:

Thank you very much for your comment. We had deleted abbreviations in the keyword to make this point clear by taking account of your suggestions.

Comment-3: The introduction cites many prior works (Wei et al., Ranjbar-Far et al., Cen et al., etc.), but the novelty compared to existing TGO growth simulations is not distinctly stated. Recommendation: Add a paragraph explicitly explaining what gap remains after [32, 36, 41] and how this work extends the understanding beyond previous modeling approaches.

Response:

Thank you very much for your comment. We modified the paper to make this point clear and would like to explain herein as follows.

TGO growth between TC and BC causes significant stress accumulation near the interface. Different TGO growth methods lead to differences in stress amplitude and distribution, which may affect the accuracy of coating life prediction.The novelty of this study is to compare the effects of different TGO growth modes on the stress evolution and interface damage of coatings. In addition, the influences of TGO creep on interface damage evolution under different TGO growth modes are systematically studied.

In order to make it clearer, we also modified and added some detailed descriptions explaining what gap remains and how this work extends the understanding beyond previous modeling approaches at paragraph 6 in section 1. All corrections are highlighted by red color.

Comment-4: The model validation section (3.1) only checks TGO thickness consistency across modes. This is insufficient to validate mechanical accuracy. Recommendation: Compare simulated interface stresses or delamination trends with published experimental or numerical data (e.g., from Li et al., 2017; Dong et al., 2014). Alternatively, include a discussion on why the parabolic-to-linear growth assumption remains acceptable.

Response:

Thank you very much for your comment. We modified the paper to make this point clear and would like to explain herein as follows.

The effectiveness of the TGO growth mode was validated in Section 3.1 through TGO thickening simulation ( only considering TGO thickening growth strain). When lateral growth strain of TGO is taken into account in the model, the valleys are in the normal tensile stress state after thermal cycling, while the peaks are in the compressive stress state, and the shear stress is located on both sides of the peaks, which is consistent with previous stress distribution research results. Therefore, the mechanical accuracy of the model is valid.

Although TGO growth follows the parabolic rule, TGO growth can be simplified to linear in a short period of time, which can not change the stress and damage distribution in the coating. The focus of this study is to compare and analyze the effects of TGO growth mode and creep on stress and delamination evolution. So a constant growth strain is used during each thermal cycle.

In order to make it clearer, we also modified and added some detailed descriptions at paragraph 3 in section 2.1 and at paragraph 1 in section 3.2.1. All corrections are highlighted by red color.

Comment-5: The model applies a cosine interface and 2D plane-strain conditions. However, out-of-plane effects and 3D stress components can be significant for furnace cycling. Suggestion: Discuss limitations of the 2D model and briefly justify the use of generalized plane strain (CPEG4R) instead of full 3D modeling.

Response:

Thank you very much for your comment. We modified the paper to make this point clear and would like to explain herein as follows.

Because the representative volume element (RVE) is extracted from the plane sample. The use of plane strain elements will completely limit the deformation in the third direction, which is different from the actual deformation. The generalized plane strain element has been widely used to simulate the stress distribution and failure in thermal barrier coatings. Moreover, the simulation results are consistent with the 3D stress distribution results.

In order to make it clearer, we also modified and added some detailed descriptions at paragraph 2 in section 2.1. All corrections are highlighted by red color.

Comment-6: While qualitative stress evolution is well presented, the study lacks numerical quantification (e.g., maximum σ₂₂, σ₁₂ values, creep rate thresholds). Recommendation: Provide a summary table comparing stress magnitudes and first-delamination cycle numbers for each mode.

Response:

Thank you very much for your comment. We modified the paper to make this point clear and would like to explain herein as follows.

Because the material and geometric parameters of the coating can affect stress amplitude and lifetime. Therefore, The focus of this study is to analyze the influence of TGO growth mode and creep on the evolution of stress and interface damage, and obtain some universally applicable rules, which provide direction for coating optimization and establishing life evaluation model. The stress and damage values at some important locations are also marked for comparison in the figures, such as Fig. 7, Fig. 10, Fig. 12, etc.

Comment-7: The manuscript has frequent grammatical errors and awkward phrasing (e.g., “growth stress brought by TGO growth” → “growth stress induced by TGO thickening”). Recommendation: A full English editing pass is strongly needed before publication.e.

Response:

Thank you very much for your comment. We modified the format and language throughout the manuscript. All corrections are highlighted by red color.

Comment-8: The conclusion focuses on numerical outcomes but doesn’t interpret them mechanistically. Suggestion: Add a discussion on how these findings influence TBC design strategies, such as optimizing bond coat composition or TGO morphology control.

Response:

Thank you very much for your comment. We modified the paper to make this point clear and would like to explain herein as follows.

The results of this study indicate that with the increase of thermal cycling, the growth strain of TGO is accumulated, which leads to a continuous increase in stress near the interface. In addition, although different TGO growth modes result in similar stress distributions, they affect the normal stress distribution and amplitude at the valley. Therefore, TGO growth is an important factor affecting stress distribution and cracking near the interface. To delay premature peeling of the coating, it is reported that the growth rate of TGO can be reduced by grain coarsening. It should be noted that a strong TGO creep rate can significantly reduce the stress amplitude in the coating. The previous results indicate that grain refinement can increase the creep rate of TGO. Therefore, considering the combined effects of TGO growth and creep, appropriate grain refinement can delay the peeling of the coating and improve lifespan.

In order to make it clearer, we also added a discussion at paragraph 4 in section 3.3.2. All corrections are highlighted by red color.

We do appreciate your valuable comments and suggestions. Our paper has been improved a lot following your suggestions. We can also derive nutrition from your suggestions to continue our future work with more powerful supports. Thank you.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

General review:

The authors conducted a study on the growth kinetics and irreversible deformation of thermally grown oxide (TGO), which critically influence delamination and cracking at the interface of thermal barrier coatings (TBCs). In this study, dynamic TGO growth during furnace cycling was simulated using three different approaches. The stress evolution and damage characteristics near the interface were compared under various TGO growth modes. Furthermore, the effects of TGO creep at high temperature on interface delamination and coating failure were investigated. The results reveal that TGO growth achieved through material transformation (growth mode III) leads to earlier interface delamination compared to the elemental swelling methods (growth modes I and II). Although the stress value in growth mode II is higher than that in growth mode I after all thermal cycles, earlier delamination and spallation occur in mode I due to the faster stress accumulation in the initial stage of the thermal cycle. Moreover, rapid TGO creep was found to reduce the accumulated stress within the ceramic layer and delay the onset of interface delamination. These findings provide important theoretical insights for the development and lifetime assessment of advanced thermal barrier coatings. Here’s the revised version of that sentence for clarity and flow:

Minor review:

The first paragraph of the Introduction section is too broad. It would be helpful to refine it to provide a more focused and concise introduction to the study's objectives and contributions.
How do different thermally grown oxide (TGO) dynamic growth modes (I, II, and III) influence the stress evolution and delamination behavior at the top-coat/bond-coat interface in thermal barrier coatings (TBCs)?
What are the primary differences in the stress distribution and cracking characteristics between TGO growth achieved through element swelling (modes I and II) and material transformation (mode III)?
In what way does TGO creep at elevated temperatures modify the local stress field and affect the onset and propagation of interface delamination during furnace cycling?
Why does the growth mode based on material transformation (mode III) lead to earlier interface delamination compared with the element swelling modes?
How does the variation in TGO creep strength influence the magnitude and location of maximum normal tensile stress (σ22) and shear stress (σ12) within the ceramic layer?
What role does early-stage stress accumulation play in determining the differences in delamination and spallation behavior among the three TGO growth modes?
How can controlling TGO creep and growth mode contribute to the development and life-time prediction of advanced thermal barrier coating systems?
In the manuscript, the process and analysis appear to have been conducted thoroughly. However, the explanation of the analysis in terms of processability seems similar to the specific approach described in the following paper. Therefore, you should review and cite the paper: Meta-structure of amorphous-inspired 65.1Co28.2Cr5.3Mo lattices augmented by artificial intelligence.
Some of the references are outdated. Please replace them with more recent ones.

Comments on the Quality of English Language

The English quality is acceptable for academic publication, though moderate editing is recommended to improve grammatical accuracy, sentence flow, and technical clarity.

Author Response

Responses to Reviewer #2

Comments-in-brief: The authors conducted a study on the growth kinetics and irreversible deformation of thermally grown oxide (TGO), which critically influence delamination and cracking at the interface of thermal barrier coatings (TBCs). In this study, dynamic TGO growth during furnace cycling was simulated using three different approaches. The stress evolution and damage characteristics near the interface were compared under various TGO growth modes. Furthermore, the effects of TGO creep at high temperature on interface delamination and coating failure were investigated. The results reveal that TGO growth achieved through material transformation (growth mode III) leads to earlier interface delamination compared to the elemental swelling methods (growth modes I and II). Although the stress value in growth mode II is higher than that in growth mode I after all thermal cycles, earlier delamination and spallation occur in mode I due to the faster stress accumulation in the initial stage of the thermal cycle. Moreover, rapid TGO creep was found to reduce the accumulated stress within the ceramic layer and delay the onset of interface delamination. These findings provide important theoretical insights for the development and lifetime assessment of advanced thermal barrier coatings. Here’s the revised version of that sentence for clarity and flow.

Response:

Thank you for your positive evaluation on our work and revised abstract.

Comment-1: The first paragraph of the Introduction section is too broad. It would be helpful to refine it to provide a more focused and concise introduction to the study's objectives and contributions.

Response:

Thank you very much for your comment. We modified the paper to make this point clear and would like to explain herein as follows.

In the Introduction, the application and structure of TBC are introduced in the first paragraph. The microstructure changes of plasma sprayed TBC before and after thermal service are demonstrated in the second paragraph. The cracking near the interface induced by TGO growth is introduced during the isothermal cycle and gradient cycle tests in the third paragraph. The fourth and fifth paragraphs respectively introduce the current research progress on TGO growth induced coating failure and TGO creep effects. The problems in the research and the content of this study are presented in the sixth paragraph.

Comment-2: How do different thermally grown oxide (TGO) dynamic growth modes (I, II, and III) influence the stress evolution and delamination behavior at the top-coat/bond-coat interface in thermal barrier coatings (TBCs)?

Response:

Thank you for your valuable suggestion. We would like to explain herein as follows.

For TGO growth mode I and II, the maximum normal tensile stress is located near the valley, while it is always located near the valley in growth mode III. Although the maximum normal stress in the final growth mode I is greater than that in growth mode II, the value in the early stage of thermal cycling in growth mode II is greater. Before the first delamination cracking, the damage degree in growth mode III is always the highest. After 45 thermal cycles, the interface delamination degree of growth modes II and III is similar. The delamination cracks in the growth mode I are relatively smaller, which is attributed to the lower stress value at the valley in the early stage of thermal cycling.

Comment-3: What are the primary differences in the stress distribution and cracking characteristics between TGO growth achieved through element swelling (modes I and II) and material transformation (mode III)?

Response:

Thank you very much for your comment. We would like to explain herein as follows.

For TGO growth mode I and II, the maximum normal tensile stress is located near the valley, while it is always located near the valley in growth mode III. In addition, the stress value at the valley in the early stage of thermal cycling in growth mode II is greater than that in the growth mode I. The earliest interface cracking occurred in growth mode III, followed by growth mode II, and finally growth mode I.

Comment-4: In what way does TGO creep at elevated temperatures modify the local stress field and affect the onset and propagation of interface delamination during furnace cycling?

Response:

Thank you very much for your comment. We would like to explain herein as follows.

When materials undergo creep under high temperature and sustained stress, mechanisms such as internal dislocation movement and grain boundary diffusion can lead to irreversible plastic deformation. This deformation will gradually release elastic stress, causing the externally applied stress to decrease over time. TGO creep causes irreversible deformation of materials. The increase in creep strength reduces the stress near the interface, which in turn affects the initiation and propagation of interface cracking.

Comment-5: Why does the growth mode based on material transformation (mode III) lead to earlier interface delamination compared with the element swelling modes?

Response:

Thank you very much for your comment. We would like to explain herein as follows.

In TGO growth mode III, due to the larger downward movement of the interface displacement at the valley during thermal cycling (see Fig. 9), the normal stress value at the valley is higher (see Fig. 7). Therefore, an earlier interface cracking occurs in the growth mode III compared to growth modes I and II.

Comment-6: How does the variation in TGO creep strength influence the magnitude and location of maximum normal tensile stress (σ22) and shear stress (σ12) within the ceramic layer?

Response:

Thank you very much for your comment. We would like to explain herein as follows.

As the creep strength increases, the maximum normal tensile stress begins to shift from the valley to the vicinity of the peak in the three growth modes. At the same time, the tensile stress area at the valley also shifts to the area between the peaks and valleys, and finally to the vicinity of peak position (see Fig. 10 and Fig. 11). The shear stress remains on both sides of the peak. As creep increases, shear stress decreases.

Comment-7: What role does early-stage stress accumulation play in determining the differences in delamination and spallation behavior among the three TGO growth modes?

Response:

Thank you very much for your comment. We would like to explain herein as follows.

In the early stage of thermal cycling, the normal tensile stress at the valley is the highest in growth mode III, followed by growth mode II, and finally growth mode I. Faster stress accumulation will lead to earlier interface damage and cracking. Therefore, the earliest interface cracking and delamination occurred in growth mode III, followed by growth mode II, and finally growth mode I. After 45 thermal cycles, the interface delamination degree of growth modes II and III is similar. The delamination cracks in the growth mode I are relatively smaller (see Fig. 12).

Comment-8: How can controlling TGO creep and growth mode contribute to the development and life-time prediction of advanced thermal barrier coating systems?

Response:

Thank you very much for your comment. We modified the paper to make this point clear and would like to explain herein as follows.

In order to make it clearer, we also added a discussion at paragraph 4 in section 3.3.2. All corrections are highlighted by red color.

Comment-9: In the manuscript, the process and analysis appear to have been conducted thoroughly. However, the explanation of the analysis in terms of processability seems similar to the specific approach described in the following paper. Therefore, you should review and cite the paper: Meta-structure of amorphous-inspired 65.1Co28.2Cr5.3Mo lattices augmented by artificial intelligence.

Response:

Thank you very much for your comment.

We have appropriately cited relevant literature according to your suggestions.

Comment-10: Some of the references are outdated. Please replace them with more recent ones.

Response:

Thank you very much for your comment.

Based on your suggestion, we have replaced some outdated literature. However, due to some references being classic literature on TBC simulations, they are still used in this study. All corrections are highlighted by red color.