**2. Experiments**

Two experimental approaches were employed to quantify the effects of isothermal heat exposure and fatigue on coating degradation. First, coupon specimens were prepared in the laboratory. These specimens were exposed to a range of uniform high temperatures to characterize the correlation between an isothermal heat treatment and the evolution of fatigue. Second, scrap blades and vanes were analyzed by observing the evolution of the roughness and analyzing the operational data obtained from a SCADA system, including the generated power and the inlet temperature of the gas turbine. Scrapped blades and vanes were deployed in an F-class gas turbine operating at a rotating speed of 3600 rpm and inlet temperature of 1293 ◦C (Figure 1). The specimens were cut from a cross section of the service-exposed blade airfoil 15 mm below the top of the blade tip. The specimens were fabricated with a diameter of 30 mm and thickness of 3 mm. The roughness due to rumpling and ratcheting, which is a sensitive metric for evaluating coating fatigue failure, was measured for a quantitative comparison.

**Figure 1.** Service-exposed hot gas pass components (HGPCs): (**a**) first-stage blade, (**b**) second-stage blade, and (**c**) second-stage vane (unit: mm).

For the matrix of the coupon specimens in the laboratory experiments, a nickel-based directionally solidified IN738LC superalloy (nominal composition: 8.5 wt. % Co, 16 wt. % Cr, 3.4 wt. % Al, 3.4 wt. % Ti, 1.75 wt. % Mo, 2.6 wt. % W, 1.75 wt. % Ta, 0.85 wt. % Nb, 0.12 wt. % Zr, 0.012 wt. % B, 0.13 wt. % C, and the rest is Ni [35]) was cast. The specimens were cut to a diameter of 30 mm and thickness of 3 mm and prepared with the appropriate surface roughness for the adhesion of the bond and top coats by sand blasting; Sa, measured with Keyence VX-X260K (Keyence, Osaka, Japan), was less than 10.49 μm. Atmospheric plasma spray (APS, 9M, Oerlikon Metco, Westbury, NY, USA) and low-vacuum plasma spray (LVPS, Multicoat, Oerlikon Metco, Wohlen, Switzerland), 8 wt. % Y2O3-ZrO3 and NiCoCrAlY, were applied onto the IN738LC coupons as a TBC and a corrosion-resistant bond coat, respectively. The thicknesses of the TBC and bond coat (310 and 230 μm, respectively) were designed to replicate those of actual HGPCs, and these vary in the range of 250–400 and 150–300 μm, respectively depending on the manufacturer, type of components, and location, even for the same component [36].

The heat treatment of the specimens was conducted at 1120 ◦C for 2 h and 840 ◦C for 24 h in sequence. The specimens were annealed for 8000 h in a furnace at a constant temperature of 850, 950, or 1000 ◦C at a heating rate of 5 ◦C/min to quantify the effect of isothermal heat exposure on the evolution of coating fatigue.

Eight of the service-exposed blades and vanes were used to elucidate the effect of high thermomechanical fatigue as well as low-cycle fatigue and isothermal heat exposure on the blades and vanes. The blades and vanes were coated with NiCoCrAlY and stabilized zirconia after being disassembled from a W501F gas turbine at a thermal power plant in Korea, referred to as "power plant A" hereafter because of confidentiality. The blades and vanes were attached to an F-class gas turbine and were determined as fully scrapped during the overhaul by the expert system. The operational history of the blades and vanes obtained from the SCADA system are summarized in Table 1.


**Table 1.** The operational history of the blades and vanes scrapped from power plant A.

The equivalent operating hours (EOH) in Table 1 are calculated as

$$\text{EOH} = 20 \times \text{ES} + \text{OH} \tag{1}$$

where ES and OH denote the equivalent stop and operating hours [13], respectively. The O&M guidelines of the manufacturers sugges<sup>t</sup> that overhaul should be carried out to repair or replace HGPCs when an ES of 8000 h or an EOH of 24,000 h is met [14–18]. Hence, ES and EOH determines the RUL of components including HPGCs, and the period of overhaul considering two effects; ES accounts for the low-cycle fatigue during transient operations including start, stop, and trip operations, and OH accounts for the creep during steady-state operations. Note that Equation (1) is a phenomenological equation proposed by the manufacturers. The approach used by manufacturers to build Equation (1) and the values of ES and EOH that determine the RUL are strictly confidential. Hence, utility companies follow this guideline [14–18] to schedule the overhaul in general.

One important assumption in Equation (1) is that the operating temperature is constant and uniform during a steady-state operation; therefore, a steady-state operation does not contribute to fatigue. However, the failure mechanism of the HGPCs differs from that of other components, which suggests that the same formula cannot be deployed to calculate the EOH of HGPCs. As mentioned earlier, a coating failure from fatigue occurs first in HPGCs laminated using TBC and a bond coat. Once the coating is completely cracked or damaged, the metal underneath is degraded by creep and fatigue. Degradation is particularly significant in the first and second stages because the metal is exposed to high operating temperatures.

All coupon specimens and service-exposed blades/vanes were mounted and then polished with #800–#2000 SiC paper and then a vibratory polisher with alumina solutions to study their cross-sectional microstructures. The roughness of the bond coat was measured for all specimens by using an optical microscope (DM15000M, Leica, Wizlar, Germany) to quantify the fatigue due to a coating failure. Digital cross-sectional images of all the specimens were analyzed at ×100 magnification to calculate the roughness of the bond coat. Each image was vertically divided into 200 sections, each of which had a horizontal length of approximately 6 μm. Then, the standard deviation of the bond coat surface with respect to the mean value was measured, which is defined as the roughness hereafter, using the Leica Material workstation software (V3.6.2). Four digital images were obtained for each specimen at different locations. The standard deviations of the four digital images were averaged for an accurate estimation of the roughness of each specimen.

## **3. Results and Discussion**

## *3.1. Contribution of Isothermal Heat Exposure to Fatigue*

The thicknesses of the TBC and bond coat of the coupon specimens were measured 10 times via a scanning electron microscope (JSM-7001F, JEOL, Akishima, Tokyo; Figure 2) to verify that the coupon specimens were fabricated as designed. The accuracy and resolution of JSM-7001F were 0.1 and 0.01 μm, respectively. The mean thicknesses of the TBC and bond coat for one coupon specimen were 310.8 and 231.1 μm, respectively. Their respective standard deviations were 15.2 and 13.2 μm, respectively. The thicknesses of other specimens were of a similar order. A reference roughness (i.e., initial roughness) was also measured on one specimen without the isothermal heat treatment as 11.2 μm. This reference roughness (i.e., initial roughness) is shown as a green circle in Figure 3a. The initial roughness was in the preferred range of 8.9–11.4 μm for the plasma sprayed TBC performance [37], suggesting that coupon specimens could be employed to represent the coatings of blades and vanes deployed on F-class gas turbines.

**Figure 2.** The scanning electron microscope images of a coated specimen: the measured thickness of (**a**) the thermal barrier coating (TBC) and (**b**) the bond coat.

The roughness of the bond coat on coupon specimens was measured to quantify the contribution of isothermal heat exposure to the evolution of fatigue. The evolution of roughness due to isothermal heat treatment is shown in Figure 3a. The square markers with a dashed line, the triangle markers with a solid line, and the circle markers with a dotted line denote the roughness at 850, 950, and 1000 ◦C (for 8000 h of exposure), respectively.

In Figure 3a, the roughness does not indicate any trends with isothermal heat exposure, suggesting that the isothermal heat treatment does not contribute to the rumpling and ratcheting that result in the fatigue failure of the bond coat. Specifically, an image of the bond coat surface exposed to 8000 h of heat treatment (Figure 3c) is not significantly different from that exposed to 500 h of heat treatment (Figure 3b) at a constant temperature of 1000 ◦C; the roughness values on the surface between TBC and the bond coat are 11.2 and 11.4 μm, respectively. It can be deduced that the isothermal heat exposure of the blades and vanes only contributes to the degradation caused by creep. In particular, the thermally grown oxide, which is caused by the degradation due to isothermal heat exposure, is negligible in Figure 3b because the coupon specimen is only exposed for 500 h. In contrast, the thickness of thermally grown oxide is 55.3 μm when the coupon specimen is exposed for 8000 h, as shown in Figure 3c. The thickness of the thermally grown oxide is averaged 10 times, and its standard deviation is 9.0 μm. Note that fatigue, which mainly causes coating failure, is of interest in this study. Hence, thermally grown oxide representing the evolution of creep is not analyzed in detail in this study. It can be deduced that the EOH calculated by Equation (1) is reasonable if HGPCs operate only under a constant operating temperature during a steady-state operation.

**Figure 3.** (**a**) The evolution of roughness on the surface between a TBC and bond coating for a variety of isothermal heat exposures and the post-processed optical microscope images representing a slight variation in the roughness on the surface between the TBC and bond coating exposed to (**b**) 500 h and (**c**) 8000 h at a constant temperature of 1000 ◦C.

## *3.2. Effects of Steady-State and Transient Operations on Fatigue*

The roughness of service-exposed blades and vanes was analyzed to characterize the effect of steady-state and transient operations on the evolution of fatigue (Figure 4). The square markers with a dashed line, the triangle markers with a solid line, and the circle markers with a dotted line denote the roughness of first-stage blades, second-stage blades, and second-stage vanes, respectively.

Figure 4a shows the relationship between EOH and roughness. The roughness shows a linear dependence on EOH for all blades and vanes. Moreover, the slope of roughness with respect to EOH in the first stage is larger than that of blades and vanes exposed in the second stage, suggesting that the blades in the first stage are affected by a severe operating condition, namely a high operating temperature. These results indicate that an increase in roughness correlates directly with EOH and operating temperature. However, the limit of the result is that the contribution of a steady-state operation cannot be distinguished from that of a transient operation in these data.

**Figure 4.** The controls on blade and vane roughness: The effect of (**a**) the equivalent operating hours (EOHs), (**b**) equivalent stop (ES), and (**c**) operational hours (OH) on the blade and vane roughness.

Figure 4b shows the contribution of transient operations, such as the start, stop, and trip operations, to fatigue. A low-cycle fatigue results in rumpling and ratcheting due to thermal shock loading [21,23]; therefore, the roughness should be proportional to ES. Overall, roughness should be proportional the roughness trends for all blades and vanes increase with ES. Moreover, the slope of roughness with respect to ES in the first stage is larger than that of blades and vanes exposed in the second stage, also suggesting that an increase in roughness is directly related to ES and the operating temperature. However, the roughness of the first-stage blade exposed to an ES of 741 h (sample 1) is larger than that exposed to ES of 755 h (sample 2). Although the ES of sample 1 is smaller than that of sample 2, the OH of sample 1 is larger than that of sample 2. Similarly, the roughness of the second-stage vane exposed to an ES of 232 h (sample 7) is larger than that exposed to an ES of 238 h; however, the OH of sample 7 is over three times larger than that of sample 6. These observations sugges<sup>t</sup> a hypothesis that a steady-state operation can contribute to an increase in roughness: the longer the steady-state operation, the larger the roughness. However, the variation in the roughness of two vanes at the second stage is not significant, suggesting that the contribution of a steady-state operation to fatigue may be smaller than that of a transient operation.

Figure 4c shows the contribution of a steady-state operation duration to the evolution of roughness. Interestingly, the roughness of all blades and vanes increases with the number of operating hours. This result differs from the results of laboratory experiments with coupon specimens, where the roughness does not vary with the duration of the steady-state operation. There are two possibilities to explain the linear dependence of roughness on the steady-state operation. One is that power plants in Korea use a load-following mode and thereby control the power generation depending on the electricity demand. Hence, the effect of the transient response (i.e., the effect of ES) would be stochastically included in Figure 4c. The other possibility is that another reason exists for the increase in roughness during a steady-state operation. An in-depth analysis of the first hypothesis is not possible with service-exposed blades and vanes because the detailed operational history of the roughness evolution during transient and steady-state operations is not available. Regarding the second hypothesis, it is possible that the temperature is not constant during a steady-state operation. It is our view that both hypotheses contribute to the increased roughness in Figure 4c.

Figure 5 clearly shows an increase in the roughness for service-exposed blades and vanes due to fatigue. Figure 5a shows an image of the first-stage blade (sample 1 in Table 1), whereas Figure 5b shows an image of the second-stage blade (sample 4 in Table 1). The surfaces of the bond coats are rougher than those subjected to an isothermal heat treatment (Figure 3b,c) at 21.6 and 19.0 μm, suggesting again that roughness is a sensitive metric for evaluating the evolution of fatigue.

**Figure 5.** Post-processed optical microscope images of the bond coat surface representing a significant increase in the surface roughness compared to the fresh state (Figure 3b): (**a**) First-stage blade (sample 1 in Table 1) and (**b**) second-stage blade (sample 4 in Table 1).

To test the second hypothesis, the operating temperature of a gas turbine, which was measured from a different power plant, was analyzed. Note that the operational data is extremely difficult to obtain as these are confidential. The temperature of the steady-state operation was obtained from the SCADA system of a different power plant, referred to as "power plant B" hereafter because of confidentiality. This power plant deployed an F-class gas turbine manufactured by General Electric (GE). The total period of the obtained operational data was approximately 22 months, from 18 July 2008 to 27 May 2010. The data included the date, the generated power, and the inlet temperature at 1-h intervals. The inlet temperature of the gas turbine was calculated using the exhaust gas measured at an outlet of the gas turbine with an GE in-house code embedded in the SCADA system [19,38]. This code was developed to predict the temperature of HGPCs because the gas temperature around HGPCs is so high that it is difficult to measure. This data was fed into the SCADA system for optimal control of the power plant.

Figure 6a shows the inlet temperature with respect to the generated power. The generated power of over 150 MW is generally in a steady-state operation (inset of Figure 6a). However, the generated power in the other ranges also includes a steady-state operation because power plants in Korea have introduced a load-following mode. Hence, the inlet temperature during a steady-state operation should be separated from that during a transient operation by considering the inlet temperature over the generated power together with the operational trend. The temperature during a steady-state operation is generally in the range of 1250–1340 ◦C, whereas the temperature in the transient state changes over a wider range, from room temperature to 1340 ◦C. The maximum variation of the inlet temperature is approximately 140 ◦C at steady state, suggesting that temperature variations during a steady-state operation can also result in thermal stress, in addition to transient operations.

Figure 6b shows the temperature variations with 1-h intervals. Within this time interval, temperature variations above 140 ◦C generally occurred during transient states including the start, stop, and trip operations, whereas temperature variations below 140 ◦C occurred during the steady-state operation. This figure also demonstrates that the operating temperature varies even during a steady-state operation.

Figure 6c shows the temperature variations during a steady-state operation. The steady-state operation accounted for approximately 4600 h during the entire period of operation. The figure clearly shows that the inlet temperatures of the gas turbine during the steady-state operation are not constant, with a maximum variation of approximately 140 ◦C. Thus, it can be inferred that temperature variations during a steady-state operation contribute to rumpling and ratcheting and can contribute to thermal fatigue caused by thermal stress. Note that the coefficient of thermal expansion at a temperature of 1000 ◦C is 1.5 times greater than that at room temperature [39], suggesting that thermal stress during a steady-state operation also significantly affects coating degradation, although the

steady-state temperature variations are significantly smaller than those during transient operations. This high thermomechanical fatigue (HMF) observed during a steady-state operation is defined as HMF hereafter.

**Figure 6.** The temperature variation during operation: (**a**) The inlet temperature of a gas turbine against the generated power, (**b**) the variations of the inlet temperature during the entire operation, and (**c**) the variations of the inlet temperature during a steady-state operation.

In order to confirm the contribution of HMF to coating failure, additional operational data were analyzed, as presented in Table 2. These datasets were obtained from the first-stage blades in a different gas turbine in power plant B. Blade 1 and blade 2 were similarly serviced, whereas blade 3 and blade 4 were similarly serviced based on EOH. However, the scrap rate of blades 1 and 2 was different as well as that of blades 3 and 4, suggesting that EOH cannot fully account for the degradation mechanism of the HPGCs. Specifically, the scrap rate ratio of blade 4 to blade 3 was 1.10, whereas the EOH ratio of blade 4 to blade 3 was 1.01. The difference in the scrap rate could be explained by the fact that blade 4 experienced a severely transient operation (ES value in Table 2) compared to blade 3.


**Table 2.** The scrap rate and operational information of service-exposed blades in the gas turbines of power plant B.

Similarly, blade 1 and blade 4 were both operated under steady state; blade 1 was used 1.6% more than blade 4. However, blade 4 was affected by long transient operation; hence, the scrap rate of blade 4 was higher than that of blade 1. These comparisons demonstrated that the thermal shock loading during a transient operation increased the coating failure and, hence, the scrap rate.

In contrast, although the EOH of blade 1 had a similar order of magnitude to that of blade 2, the scrap rate of blade 1 was higher than that of blade 2. A notable factor was that blade 1 was exposed to a shorter transient operation and a longer steady-state operation. This observation cannot be explained using the previous approach. The above comparison clearly suggests that thermal stresses

from steady-state temperature fluctuations accumulate in the coatings and contribute to coating failure. Hence, accumulated thermal stress during a steady-state operation should be accounted for when estimating fatigue lifetime to accurately predict the RUL of a gas turbine.

Our analysis of the operational data clearly demonstrates that EOH cannot fully account for the lifetime of HGPCs in a gas turbine because the coatings laminated on the surfaces of the HGPCs have different failure mechanisms compared to other components. Hence, HMF during steady state should be considered to accurately predict coating failures of HGPCs, as proposed in Figure 7. The current approach accounts for only two phenomena: low-cycle fatigue during transient states and creep during steady states. However, HMF during steady states also contributes to coating fatigue. Hence, HMF during steady states should be combined with a low-cycle fatigue to calculate the accumulated fatigue as

$$\text{EOH} = \alpha \times \text{ES} + \beta \times \text{HMP} \tag{2}$$

where α and β denote the contribution factors of each effect.

**Figure 7.** The proposed approach for predicting the remaining useful lifetime (RUL) and coating failure of blades and vanes in a gas turbine.
