*4.2. Crack Propagation*

Crack coalescence and increase of crack dimension due to the damage accumulation from thermal stress were detected during CTF tests, as shown in Figures 4 and 5, respectively, which were observed after 320 cycles. The crack length formed on the surface was increased through their linkage, and microstructural degradation was observed, including defects such as pores and small cracks. At the same time, the dimension of the surface crack was increased during the CTF tests about 20–100 μm, showing degraded surface microstructure.

**Figure 4.** Surface crack-growth behavior during CTF tests: (**A**) as-prepared crack and (**B**) crack grown after 320 cycles.

**Figure 5.** Surface crack thickening during CTF tests: (**A**) as-prepared crack and (**B**) thickened crack after 320 cycles.

The crack-growth behavior on the cross section during CTF tests is shown in Figure 6. The cracks formed in the direction vertical to the interface did not grow compared with the horizontal crack, while crack coalescence and thickening were observed in the horizontal crack with an undulating shape. Overall, the microstructure was degraded after the CTF tests, showing increased defects, such as pores and small cracks.

**Figure 6.** Crack-growth behavior on the cross section during CTF tests: (**A**) vertical crack and (**B**) horizontal crack. Each number indicates crack images: (**1**) before test and (**2**) after 320 cycles.

## *4.3. Crack Growth to Failure*

The crack-growth behavior on the surface is shown in Figures 7 and 8 with cycle during CTF tests. The crack lengths were measured through SEM images after 10, 20, 40, 80, 160, and 320 cycles. The dotted and solid curves are empirical data fits for each crack length grown during CTF tests for the initial cracks formed by 30 and 50 N, respectively. The vertical dotted and solid lines indicate the average failure cycle number in the CTF tests, respectively, indicating that the nominal numbers of cycles to failure for each TBC with cracks formed by 30 and 50 N were 593 and 460 cycles, respectively. The crack-growth behavior showed a similar trend with the number of cycles, independent of initial crack length. The nominal difference of crack length with applied load was changed from 20 μm in the initial stage to 50 μm after 320 cycles between 30 and 50 N, with linear slopes of 0.37 ± 0.16 and 0.41 ± 0.17, respectively. In the failure point, each of the computed crack lengths were about 189–392 and 244–381 μm for 30 and 50 N, respectively.

**Figure 7.** Variation of crack length on the surface during CTF tests. Dotted and solid curves indicate empirical data fits for 30 and 50 N, respectively. Dotted and solid vertical lines are the failure cycles of TBCs with cracks formed by 30 and 50 N, respectively.

On the other hand, comparable crack-growth behavior for the initial cracks formed by 30 N on the cross section is shown in Figure 8, displaying longer crack lengths in the horizontal direction. The dotted and solid curves are empirical data fits for the horizontal and vertical cracks, respectively, grown during the CTF tests. The dotted vertical line indicates average cycles for TBC failure in CTF tests, with 396 cycles. The nominal difference in the initial lengths between the horizontal and vertical cracks gap was about 100 μm with linear slopes of 0.15 ± 0.08 and 0.52 ± 0.21, respectively, and the gap was increased to about 180 μm after 320 cycles. Each crack length in the failure could be expected to be about 217–419 and 70–141 μm on the cross section for the horizontal and vertical cracks, respectively.

**Figure 8.** Variation of crack length on the cross section during CTF tests. Dotted and solid curves indicate empirical data fits for the horizontal and vertical cracks, respectively. The dotted vertical line is the failure cycles of TBCs with cracks formed by 30 N.

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

The calculated residual stress distribution in the TBC sample is shown in Figure 9. As shown in the figure, in the top coat 8YSZ layer, there was extensive compressive residual stress, with maximum stress on the top coat interface. Similar to the results shown in Figures 7 and 8, the crack lengths in decreasing order were 30 N in the horizontal direction of cross section > 50 N on surface > 30 N on surface > 30 N in the vertical direction of the cross section.

**Figure 9.** Calculated residual stress distribution in the TBC sample.
