# Thermal Fatigue Life Prediction of Thermal Barrier Coat on Nozzle Guide Vane via Master-Slave Model
## 4 Thermal Cycle Analysis and Life Prediction of NGV.
### Thermal Fatigue Life Analysis of Nozzle Guide Vane with TBC  
When the TGO thickness was 2 \(\upmu\)m, the thermal stress simulation results in the TC layer based on the slave model with sinusoidal interface are as shown in Figure 17. Compared to Figure 16, the thermal stress in Figure 17 changed smoothly on the sinusoidal interface, because the shape of the mixed TC/TGO layer was a buffer. Furthermore, we found that the risk moment was at the beginning of the cooling stage. The strain contours of the slave model at 60.6 s are drawn in Figure 18.  
As shown in Figure 18, the peaks of the shear strain and axial strain occurred near the mixed TC/TGO layer, and the maximum strain point was in the valley region. The distributions of the shear and axial strain were basically consistent with those of the ceramic tube in Figure 7b. The reason for  
Figure 17: Stress curves in the slave model. (**a**) TC layer at the leading edge; (**b**) TC layer at the trailing edge. Figure 18: Strain contours of the slave model. (**a**) Leading edge; (**b**) Trailing edge. this is that the thermal stress level of the mixed TC/TGO layer at the trailing edge was affected by the total deformation of the master model. The leading edge and trailing edge can be considered as a series of ceramic tubes with different radii, which is also the reason for why the distribution of the thermal strain was similar to the slave model and ceramic tube model. The stress and strain at the risk point in the mixed TC/TGO layer were almost independent with the radius of the ceramic tube [14]. As a result, the TFL model of ceramic tubes previously established is also applicable to the high-integrity life prediction of a NGV. The grid node at the shear strain concentration points highlighted in Figure 18 was regarded as the crack initiation point (i.e., risk point) as the shear strain was much higher than the axial strain. The stress-strain curves at the risk point are shown in Figure 19.  
As revealed in Figure 19, the integral area (red and black region) and strain range of the stress-strain curve of the trailing edge were larger than that of the leading edge (black region), indicating that the thermal shock attacking at the leading edge has a stronger failure energy under the same thermal cycle. On the other side, the fatigue hysteresis loops at the risk point basically reached a stable state, indicating that the thermal stress of the TC layer reached the plastic stability stage after two thermal cycles (i.e., the axis and shear strain range do not vary by repeating the thermal cycle simulation). Thus, the thermal strain range at the second thermal cycle was inputted into the TFL model. By repeatedly producing the high-integrity TFL analysis of the NGV, the thermal strain ranges of six TGO thicknesses (i.e., 0, 2 \(\upmu\)m, 4 \(\upmu\)m, 6 \(\upmu\)m, 8 \(\upmu\)m, and 10 \(\upmu\)m) were obtained as shown in Figure 20.  
As shown in Figure 20, the strain levels at the sinusoidal interface regions were correlated with TGO thickness. The axial strain ranges were basically smaller than the shear strain range, and the changing trends of the axial strain ranges at both the leading edge and trailing edge were opposite the  
Figure 19: Stress–strain curve at the risk point of the slave model. (a) Leading edge; (b) Trailing edge. Figure 20: Strain ranges and fitted curves. (a) Region A; (b) Region B.  
shear strain ranges. The strain ranges of the TC layer did not change much at the beginning of the thermal cycles, but the shear strain ranged increased obviously with the increase in the TGO thickness, which indicates that shear strain is a key factor inducing the thermal fatigue of the TBC material. The varying trends of strain range at the leading and trailing edge were similar, proving that the corner radius slightly influences the micro-strain. The fitted equations of the TGO thickness and strain range at the risk points are as follows. Strain range of leading edge:  
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