**5. Conclusions**

For two kinds of TBCs, experimental microstructure observation, hardness, and modulus measurement by using the nanoindentation tests were performed, and nanoindentation size e ffect was described by using the trans-scale mechanics model. The main conclusions can be summarized as follows:


**Author Contributions:** Data curation, Y.W. (Yingbiao Wang) and Y.L.; Methodology, J.S. and H.L. (Hao Long); Writing—original draft, H.L. (Haiyan Liu); Writing—review and editing, Y.W. (Yueguang Wei) and L.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, Nos.: 11890681, 11672301, 11511202, 11672296, 91860102, 11432014.

**Conflicts of Interest:** The authors declare no conflict of interest.
