**1. Introduction**

Gas turbines form the heart of the electric power and aerospace industries, which has prompted a large amount of research into the use of material, mechanical el, and electrical engineering for increasing their efficiency [1–3]. Significant technological advances have led to increasing operating temperatures and pressures in recent decades, enhancing the efficiency of gas turbines to over 40%. These technological advances include coatings, heat treatments, a new superalloy permitting high operating temperatures, and a new cooling system [4–11]. Specifically, an F-class gas turbine, which operates at approximately 1300 ◦C and a pressure ratio of 16 during full-load conditions, was developed in the late 1990s and deployed to many thermal power plants. Gas turbines of the G and J classes, which operate at approximately 1500 and 1600 ◦C and a pressure ratio of 21 and 23, respectively, during full-load conditions, were also developed in the early 2000s and deployed to newly constructed thermal power plants. Power plants that deploy these high-efficiency gas turbines are currently operational and under construction.

As the operating temperature of gas turbines increases, the thermal barrier coating (TBC) laminated on the hot gas pass components (HGPCs) at the first and second stages of gas turbines [12] has received increased research attention. The blades and vanes of the third and fourth turbine stages of gas turbines are not coated because the metal superalloys used for these components can withstand the more moderate operating temperatures of the third and fourth stages without the TBC. The TBC not only permits increased gas temperatures and reduced cooling requirements but also improves fuel efficiency and reliability. It plays a critical role in protecting the substrate of the HGPCs at the first and second stages of gas turbines because the superalloy, which can withstand high temperatures of over 1500 ◦C, is still developing at this time. Hence, the TBC mitigates heat transfer from the coating surface of the HGPCs to the substrate of the HGPCs; the thermal gradient between the two is approximately 200 ◦C. Therefore, the role of the TBC suggests that the failure modes of HGPCs are different from those of the other components.

If the TBC on the HGPCs becomes damaged or cracked, the substrate starts to degrade because of creep and fatigue. In contrast to HGPCs, other components such as the third- and fourth-stage blades and vanes are affected by creep and fatigue during the entire operation, owing to lack of surface coating. Thus, coating failure accelerates HGPC degradation because the metal is directly exposed to high operating temperatures, suggesting that HGPC coatings should be carefully examined and promptly repaired.

To this end, power utility companies schedule periodic maintenance known as overhaul, during which all HGPCs are disassembled and examined by an expert system following standard maintenance guidelines for gas turbines [13–18]. The expert system evaluates the coating failure and damage of HGPCs according to three categories: normal, repair, or replace. Coating failure is one of the most important features of an overhaul because it results in a fatigue failure of the substrate. Note that creep effects on the substrate can be rejuvenated using heat treatment [19,20]; thus, fatigue damage to the metal after TBC failure is more important than creep. The overhaul procedure and failure mechanism of HGPCs clearly sugges<sup>t</sup> that scheduling prompt operations and maintenances (O&M) can mitigate concerns regarding coating failure due to fatigue. Moreover, the proactive maintenance of and the accurate estimation of an HGPC lifetime is an effective way to secure the safety and reliability of HGPCs as well as decrease O&M costs. Note that power utility companies typically aim to reuse HGPCs after overhaul repairs as replacing them is more expensive.

A coating failure is mainly caused by fatigue resulting from two phenomena on the coating layers. One is rumpling caused by cyclic local volume changes [21,22] due to chemical reactions in the coating layer surfaces. Local volume changes are caused by aluminum depletion and the subsequent decomposition of the β-(Ni, Pt)Al phase in a bond coat. The other phenomenon is ratcheting [23] caused by significant variations in the operating temperature, which results in periodic thermal stress on the coating layers. This phenomenon leads to undulating interfaces between the TBC and the bond coat due to thermally grown oxide that produces undesirable cyclic failure modes when it is larger than a critical undulation amplitude [24]. In addition, creep causes the growth of an interdiffusion zone and aluminum depletion layer when coatings are exposed to constant and uniform high temperature [25–27]. However, these effects do not result in coating failures (i.e., the metal is not directly exposed to high operating temperatures owing to creep).

The effects of fatigue on gas turbine lifetime have been comprehensively studied to understand the degradation mechanisms and failure modes of HGPCs [28–31] and to assess their remaining useful lifetime (RUL) [32–34]. These studies enable one to accurately estimate the operational lifetime of HGPCs and their coating layers in a gas turbine. Hence, fatigue is nowadays considered together with creep to predict the RUL of HGPCs. Specifically, low-cycle fatigue during start, stop, and trip operations and creep during steady-state operations are accounted for by calculating the equivalent operating hours (EOHs) that determine the maintenance interval of a gas turbine. This approach assumes that creep only affects the gas turbine lifetime during a steady-state operation, owing to the constant and uniform temperature [13–18]. However, EOHs cannot fully explain the degradation of actual service-exposed blades and vanes during an overhaul. The gap between EOHs and the scrap rate that represents the RUL of a gas turbine suggests the need to elucidate the effect of both creep and fatigue on gas turbine degradation by evaluating service-exposed blades and vanes and the operating temperature.

This is the first study to characterize the contribution of fatigue to coating degradation using laboratory experiments and an analysis of service-exposed blades and vanes. In the laboratory experiments, the effect of creep on coating failure was quantified by analyzing the roughness changes in coupon specimens, which replicate the actual coatings of blades and vanes, exposed to 8000 h of operation in a range of high, constant temperatures. In the analysis of service-exposed blades and vanes, scrapped F-class service-exposed blades and vanes were analyzed using the evolution of roughness and operational data obtained from a supervisory control and data acquisition (SCADA) system. Several factors were considered to accurately predict the RUL of a gas turbine based on the aforementioned analyses.
