Experimental and Simulation Analysis of the Evolution of Residual Stress Due to Expansion via CMAS Infiltration in Thermal Barrier Coatings

Round 1

Reviewer 1

In my general view, the topic and the scientific content sound interesting and new. My major criticism is about describing the experiment and numerical solution. They are needed to be explained further

Thanks for your comments and suggestions. The experiment and numerical solutions have been discussed in detail in the revised manuscript.

Reviewer 2

The manuscript could be shortened. Various graphs (indicated directly in the manuscript) could be joined into smaller quantity of figures, withos serious loss of clarity.

Thanks for your comments and suggestions.

• The figures 9 and 10 have been joined in the revised manuscript.
• The figure 6 has been ignored since the experimental and numerical data are as the same as in the figure 5.
• The letter of material properties has been added in Table 1 in the revised manuscript.
• All of mistake in the PDF manuscript have been corrected in the revised manuscript.

Reviewer 3

The authors studied experimentally and numerically a double cantilever beam model to investigate thermal buckling induced via CMAS. They show via finite element simulations that the phase transformation leads to damage in the coating system. The study is certainly very interesting to the community and the results are provided in a reasonable way. The reviewer has the following points to be addressed before the final publication of the work: 

1: since the work covers the experimental and numerical approaches to study fracture in coating systems, the introduction part should be enriched via relative literature on these topics, just to name a few (not complete): simulation of fracture in coating systems and influence of the residual stress https://www.sciencedirect.com/science/article/pii/S0020768317302251 https://www.sciencedirect.com/science/article/abs/pii/S0167663617305343 10.1016/j.jeurceramsoc.2016.01.002 10.1016/j.jmatprotec.2008.02.024

simulation setup for phase-transition and fracture in solids: https://www.sciencedirect.com/science/article/abs/pii/S002076832100189X  

Thanks for your comments and suggestions. The literature related to simulation of fracture in coating systems have been added at the introduction section in the revised manuscript.

2:  Not so necessary but can the authors provide more detailed explanations on Eq.1 ? is this purely based on experimental measurements? any other similar studies or relations reported for such behavior?

“Note that the depth of CMAS-rich layer follows parabolic law by Wu et al. [25]. This study [26] also indicated that infiltration behavior was initially faster and became slower as the holding time still operated.” have been added following the Eq. 1 in the revised manuscript.

3: Fig2: interesting! maybe add some short text into the fig to emphasize on the highlighted red box  

The indicator of CMAS-rich layer, Non-infiltration layer, and depth of ten random reaction regions have been added in the Figure 2 in the revised manuscript.

4: Fig3: please increase the size of the fig as well as the numbers and the legend.

All the figures have been modified with higher quality and suitable size in the revised manuscript.

5: Fig4: the quality of the picture is really bad! what is the thickness of the red region?  

The detail thickness of all models has been addressed in the revised manuscript.

6: Fig.4: are the values "w" and "H_2" chosen large enough to avoid the effect of boundary conditions on the obtained results? any studies to prove this point?  

“Actually, the simulation result of interfacial stress shows the same value for different width of coating system w (3.5mm,5mm,6.5mm) which means that the width of coating system will not generate the boundary effect. Hence, the width of the coating system w is set at 3.5 mm owing to saving computational efficiency.” have been added at the Section. 3 in the revised manuscript. In addition, based on the previous study [27], depth of the substrate is assumed as 2 mm.

7: Fig4: it would be great if the authors provide information on the chosen mesh for the simulation.  

“The finite element models are constructed using the mesh with almost 45,000 elements and 414,000 elements for type I and type II model. All of mesh are four-node quadrilateral elements (DC2D4 in the heat transfer analysis and CPE4T in the thermal structure analysis) for the topcoat, bond coat, and substrate.” has been added at the Section. 3 in the revised manuscript.

8: Section 3: no details are provided for the type of material models for the mechanical and thermal problems. The equations for the model should be addressed and explained to the readers  

 “It should be noted that expansion via CMAS infiltration provides the material behavior during the holding time for the both the type I and type II model in the thermal structure analysis.” has been added at the section. 3.2 in the revised manuscript. “It should be noted that the expansion via phase transformation provides the material behavior during the cooling time the both the type I and type II model in the thermal structure analysis.” has been added at the section. 3.3 in the revised manuscript.

9: Table2: very interesting! suggestion for future studies: it would be great if authors can address similar cracking patterns using

Thanks for your suggestions. Actually, the interfacial delamination induced by CMAS infiltration in the thermal barrier coating is under study in our research group. Based on the cohesive element method, the interfacial crack evaluation and propagation can be investigated.

Round 2

Reviewer 3

Thank you for the effort and extra comments. The paper is now ready for being published. The reviewer is also interested in future works considering cracking. Great job.