**5. Discussion**

## *5.1. Crack Initiation Behavior*

Typical microstructures of YSZ-based APS-TBCs were observed on both the surface and cross section with some defects, such as pores, splat boundaries, and cracks, as shown in Figures 1 and 2. The cracks connected with the rhombus-shaped imprints sugges<sup>t</sup> that the induced crack formation was initiated from the angular points as well as the edge of the imprints during the indentation loading procedure. Moreover, the embedded defects, such as pores, can obstruct the formation of the cracks, but cracks beyond the defects were occasionally observed in both cases. However, the cracks on the surface and cross section are induced by di fferent mechanisms, as it can be seen from microstructural images. On the surface, the imprint size and crack length were determined by the loading level regardless of the direction. However, the direction of the crack is a crucial factor in determining the crack length in the cross section. The vertical crack length was less than half of the horizontal crack length, indicating that the vertical crack is more di fficult to form than the horizontal crack in cross section. This is because of the intrinsic characteristics of the APS deposition method. During APS deposition, the instantaneously-melted feedstock powder is sprayed onto the substrate from the perpendicular direction of the interface, resulting in horizontal splat boundaries, which are an obstacle to the formation of the vertical cracks. Meanwhile, the horizontal cracks are formed more easily along the horizontal splat boundaries as intergranular cracks. Consequently, three-times-longer crack length and undulating shape were observed in the horizontal direction on the cross section, as shown in Figure 3.

Basically, typical APS-TBCs contain some defects randomly, so a broad deviation of the initial crack length is observed in just one imprint. Moreover, a larger variation is obtained depending on the indented area, even when the same loading is imposed. However, on the cross section the crack lengths are almost identical regardless of the direction. In the case of surface cracks, the indentation load was imposed perpendicularly to the splat boundary surface. By contrast, the indentation load was parallel to the splat boundary surface on the cross section where in-plane tensile stress is included when the feedstock is cooled after splat [36]. This leads to a detachment of coatings through relatively easy crack growth in the horizontal direction during CTF tests.

## *5.2. Crack-Growth Behavior*

In the APS-TBC system, the crack propagation is continued through linkage and coalescence of microcracks and discontinuities due to damage evolution during temperature change [9,37]. The surface crack-growth behavior was found to be similar regardless of the loading level. As shown in Figure 4, the surface cracks were coalesced because of thermal stresses and propagated through existing defects, such as pores, splat boundaries, and small cracks. Macroscopically, the crack thickness was enlarged because of repeating thermal expansion and contraction, resulting in partial spalling on the surface with the lengthened and thickened cracks. On the other hand, the crack-growth behavior on the cross section depended on the direction to the interface, as shown in Figure 6. Vertical cracks were almost never generated and grown up in the perpendicular direction to most of the splat boundaries, showing a slight increase in thickness. However, horizontal cracks grew through the linkage among existing splat boundaries and pores, which have stresses and low bonding energy, observed in the shape of undulations; this can be evidence of intergranular fracture [38]. In this study, the descriptive crack-growth behavior of conventional APS-TBCs was mainly investigated through thermal cycling tests. The crack-growth behavior based on the porosity and mechanical properties will be further studied as a future work.

## *5.3. Threshold Crack Length for Failure*

The crack-growth behavior on the surface with the number of cycles in CTF tests was similar with loading level and direction, showing similar linear slope and calculated crack length ranges of 189–392 and 244–381 μm for 30 and 50 N at the failure point, respectively. On the other hand, the crack-growth behavior on the cross section was considerably di fferent from that on the surface. As explained previously, the formation of vertical cracks was inhibited by the splat boundaries, while horizontal cracks were formed with relative ease. During CTF tests, the nominal di fference of crack length starting at about 100 μm increased to about 180 μm after 320 cycles on the cross section, expecting calculated

crack lengths of 70–141 and 217–419 μm for the vertical and horizontal cracks at the failure point, respectively. This is because of the originally imposed stresses during coating formation, paving a path along which cracks can grow more easily. Eventually, the threshold crack length can be considered as suggested above in cyclic thermal exposure conditions, especially in typical YSZ-based TBC systems. Thus, the probability of coating failure will be higher and coating reliability is reduced when cracks increase larger than the threshold crack length.

Even when the same load of 30 N was imposed on the surface and cross section, more rapid crack growth was observed in the horizontal crack on the cross section. This can be explained by the following argument. First, the inherent microstructure affects the crack propagation behavior, showing a kind of lamellar structure of splats. The other is thermal stresses during the CTF tests. During the CTF test, the stress is caused by CTE mismatch between the top and bond coats (CTEs of 8YSZ: 10.7 × 17.5 × 10−<sup>6</sup> <sup>K</sup>−1, bond coat: 17.5 × 10−<sup>6</sup> <sup>K</sup>−1) [7,39]. The surface cracks are positioned above the top coat with a thickness of 600 μm, while the cross-section cracks are located just above the interface between top and bond coats. Greater stresses are imposed on the horizontal crack of the cross section in the repeated heating and cooling, and the cracks on the surface suffer comparatively weak stresses.

#### *5.4. Modeling of Residual Stress Distribution and Fatigue Crack-Growth Behavior*

As shown in Figure 9, higher residual tensile stress existed on the surface of the 8YSZ top coat than in the middle of the coating. This stress distribution explains the experimentally-observed crack length sequence in Figures 7 and 8 (i.e., 50 N on surface > 30 N on surface > 30 N in the vertical direction of the cross section). The crack length of 30 N in the horizontal direction of the cross-section case is higher than the above three cases; this is due to the unique splat microstructure formed in the APS process, which is not accounted for in the residual stress model. The residual stress model is isotropic and does not capture the anisotropic feature of TBCs. Tracking the crack-growth behavior within the isotropic dense microstructure shows clear observation rather than the anisotropic porous microstructure, due to the limited contents of defects in dense TBC, such as pores and splat boundaries [22]. TBCs can be reasonably approximated as transversely isotropic materials, where the properties are the same for all directions in the plane, such as along the coating surface, but different from the deposition direction. The horizontal direction in TBCs is the weakest because of splat and void formation during the APS process. This explains why the 30 N in the horizontal direction of the cross-section case has the highest crack-growth length among the four cases.
