**4. Conclusions**

This study characterized the contribution of three factors relevant to the fatigue coating failure of HGPCs in gas turbines, which plays a critical role in the degradation of gas turbines, with the evolution of the surface roughness between the TBC and the bond coat; the factors are low-cycle fatigue during a transient operation, creep (isothermal heat exposure) during a steady state operation, and high thermomechanical fatigue during a steady state operation.


evaluating the quantitative effect of HMF on coating degradation using additional long-term operational data at various operating conditions and results from laboratory experiments. A detailed phenomenological model of RUL that accounts for the effects of HMF will be developed and validated based on a quantitative analysis.

**Author Contributions:** Methodology, S.Y.C.; Writing—Original Draft Preparation, K.-Y.O.; Writing—Review and Editing, K.-Y.O.; Supervision, S.Y.C.

**Funding:** This research was supported by the National Research Foundation of Korea (NRF) gran<sup>t</sup> funded by the Korea governmen<sup>t</sup> (MEST) (No. 2017R1D1A1B03032746) and the Chung-Ang University Research Grants in 2019.

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