**1. Introduction**

Thermal barrier coatings (TBCs) are employed for the accommodation of the turbine-inlet temperature increase as well as protection of the hot components from severe operating conditions in gas turbine and jet engine systems [1–4]. A typical TBC system includes a thermal insulating ceramic top coat, metallic bond coat, and thermally-grown oxide (TGO), which results from oxidation of metallic elements diffused from the bond coat [5]. Yttria-stabilized zirconia (YSZ) with 7–8 wt.% yttria is commonly used for top-coat material because of its excellent thermomechanical properties, such as low thermal conductivity, relatively high coefficient of thermal expansion (CTE), and mechanical properties of fracture toughness and hardness [6,7]. In some cases, however, a bare metal substrate or metallic bond coat of rotational components is directly exposed to a flame when TBCs are delaminated or spalled because of crack propagation and coalescence during operation. This exposure can cause the fracture of rotational components as well as the other parts, which results in fatal problems. Some researchers have shown that the delamination of TBCs occurs just above the interface between the top coat and TGO layer [5,8–10]. Khan et al. [10] evaluated the thermal durability of an air-plasma-sprayed (APS) TBC through a thermal cyclic exposure test, indicating that the 8YSZ-based TBC is delaminated within the top coat around the interface between the top coat and the TGO layer. Accordingly, the investigation of crack propagation and its coalescence is essential for understanding the failure mechanism of TBCs, predicting the lifetime performance of TBCs, and designing reliable TBCs.

During actual operation, the TBC system is placed in severe circumstances [11,12]: (i) thermal stress from hot-gas exposure; (ii) mechanical stress caused by high-speed rotation; (iii) corrosive environment with Calcia–Magnesia–Alumina–Silica; (iv) erosion caused by direct flame and/or particles from outside; and (v) interaction through the di ffusion between top and bond coats. Under these conditions, the failure of TBCs, especially plasma-sprayed TBCs, is explained by a complex mechanism with one or more combined phenomena [5,11,13–21]. (i) At the initial operation stage, the TGO layer is grown by oxidation of the bond coat. Further oxidation of the bond coat can be avoided owing to the uniformly grown TGO layer, which functions as a di ffusion barrier. During thermal exposure, the TGO thickness increases with the undulating interface. As heating and cooling procedures continue; however, the TGO layer is cracked by interfacial stress resulting from CTE mismatch between the top and bond coats. Cracks can play a role in the oxygen path, so the bond coat su ffers from further oxidation. (ii) As oxidation continues, Al is depleted and some other brittle oxides, such as chromia and spinel, can be formed by oxidation of Co, Ni, and Cr components around the TGO layer with volume change, which can cause crack nucleation and further oxidation, finally leading to TBC failure. On the other hand, (iii) high thermal stress, especially compressive stress in a hot area, is imposed on the surface of the coating during engine operation, and the surface area su ffers deformation with stress relaxation. Then, a surface crack is initiated because of the tensile stress during cooling, resulting in delamination along the TBC to the bond coat interface.

Donohue et al. [22] suggested converting the energy release rate into toughness within dense vertically-cracked TBCs, indicating the positive impact of the segmented microstructure on long-crack toughness. The fracture toughness of plasma-sprayed TBC was investigated according to the aspects of processing, microstructure, and thermal aging [23]. Recently, there are extensive experimental work and analytical calculations on more complicated TBCs, such as multilayered structure [24–26], solution precursor plasma spray coating [27], and suspension plasma spray coating [28,29]. Their crack initiation and propagation under a thermal cyclic environment were investigated with analysis of mechanical and thermal properties.

In this study, crack-growth behavior just above the TGO layer was observed to understand the failure mechanism of TBCs. An initial crack was formed (i) on the TBC surface to simulate damage due to extrinsic factors (e.g., erosion or foreign object debris (FOD)) and (ii) within the top coat just above the interface between the top and bond coats in the cross section, which simulates the cracking initiation site due to bond coat oxidation and TGO growth in a typical APS coating. The crack growth behavior was investigated and described in detail through cyclic thermal fatigue (CTF) tests. An analytical model was employed to predict the residual stress distribution and fatigue crack-growth behavior. The results and analysis of this study can be helpful for further understanding of the TBC failure mechanism, resulting in the development of reliable TBC systems.

## **2. Experimental Procedure**

## *2.1. Sample Preparation*

In this study, typical 8YSZ TBC systems were prepared using commercial feedstock powders. The Ni-based superalloy (Nimonic 263, ThyssenKrupp VDM, Essen, Germany; nominal composition of Ni–20Cr–20Co–5.9Mo–0.5Al–2.1Ti–0.4Mn–0.3Si–0.06C, in wt.%) was used as a substrate in the shape of a disk and dimensions of 25 mm in diameter and 5 mm in thickness. Sandblasting using Al2O3 powder (particle size ≈ 420 μm) was performed before the deposition of the bond coat. A bond coat with a thickness of about 300 μm was formed on the substrate by the APS method, using AMDRY 9625 (Sulzer Metco Holding AG, Winterthur, Switzerland, the nominal composition of Ni–22Cr–10Al–1.0Y in wt.% and particle size 45–75 μm). After creating the bond coat, the top coat was deposited by the APS method with a thickness of about 600 μm, using METCO 204 C-NS (Sulzer Metco Holding AG, Switzerland, 8Y2O3–ZrO2) and particle size of 45–125 μm. The fabrication parameters employed for the bond and top coats were recommended by the manufacturer; see Table 1.


**Table 1.** Parameters of air plasma spraying.

## *2.2. Crack Formation and Observation*

To create the initial cracks on the surface, the selected TBC samples before crack formation were polished using silicon carbide paper and fine polished with a 1 μm diamond paste. On the other hand, the selected TBC samples for the cross-sectional cracks were sectioned and given a final polish with a 1 μm diamond paste. The initial surface crack was generated in the center of the polished top coat surface, while the cross-sectional crack was generated above the interface of top and bond coats within 100 μm. A micro-indenter (HM-114, Mitutoyo Corp., Kawasaki City, Japan) with a Vickers tip was used for the formation of cracks through the indentation load with loading levels of 30 and 50 N for the surface, but only 30 N of load was employed on the cross section because of the formation of large imprints (>100 μm).

CTF tests were performed for both the surface and cross-sectional-cracked TBCs to impose thermal fatigue conditions and observe the growth behavior of the induced cracks. The TBC samples were held in the furnace with a dwell time of 40 min at a temperature of 1121 ◦C and then naturally cooled for 20 min in air. The CTF tests were performed up to 640 cycles and the criterion of delamination was defined as about 25% spallation of the top coat. At least five specimens were tested for each crack formation condition, and each specimen had only one imprint to avoid interrelation of stresses and/or cracks between the imprints in di fferent locations. The microstructure was observed by scanning electron microscope (SEM, JEOL Model JSM-5610, Tokyo, Japan) to investigate the crack-growth behavior. The samples after 10, 20, 40, 80, 160, and 320 cycles in the CTF tests were cleaned to observe the microstructure around the induced cracks and to measure the crack length grown after the CTF tests. The crack length was measured from the center of the indentation imprints. The surface crack length was measured regardless of the direction, while vertical and horizontal cracks were measured on the cross section.

#### **3. Modeling of Residual Stress and Crack-Growth Behavior in TBC Samples**

In cyclic thermal exposure environments, thermally-induced residual stress forms in the TBC multilayers because of di fferential coe fficients of thermal expansion in each layer [30,31]. In this work, a linear elastic analytical model was employed to understand the residual stress distribution and resultant cracking phenomena, as in [30–33]. In the model, the interface between the substrate and the bond coat was defined as the origin line, where *z* = 0. The distance from layer *i* to the substrate was defined as *hi* [32,34,35]. The thermal residual stress in the substrate and the *i*th coating layer, which is related to the misfit strain ε*i*and bending curvature *K*, can be expressed as [32,33]:

$$
\sigma\_8 = E\_5 \left[ \varepsilon\_6 + K(z + \delta) \right] \left( -t\_\kappa \le z \le 0 \right) \tag{1}
$$

$$
\sigma\_i = E\_i[\varepsilon\_i + K(z + \delta)] \text{ (1 } \le i \le n \text{, } h\_{i-1} \le z < h\_i) \tag{2}
$$

where *Es* and *Ei* are Young's moduli of the substrate and *i*th coating layer, respectively. δ is the distance from the bending axis, where the bending strain is zero. ε*i*, ε*s*, δ, and *K* can be individually expressed as [33]:

$$
\varepsilon\_i = \Delta \alpha \Delta T + \sum\_{k=1}^{n} \frac{E\_k t\_k}{E\_s t\_s} (\alpha\_k - \alpha\_i) \Delta T \tag{3}
$$

$$\varepsilon\_{\rm s} = -\sum\_{i=1}^{n} \frac{E\_i t\_i}{E\_s t\_s} \Delta \alpha \Delta T \tag{4}$$

$$\delta = \frac{t\_s}{2} - \sum\_{i=1}^{n} \frac{E\_i t\_i}{E\_s t\_s} (2l\_{i-1} + t\_i) \tag{5}$$

$$K = -\sum\_{i=1}^{n} \frac{6E\_i t\_i \Delta \alpha \Delta T}{E\_s t\_s^2} \tag{6}$$

where α is the CTE, *k* is the coating layers range from 1 to *n*, and *ti* is the thickness of the *i*th layer.
