## 6 Thermal Cracking Simulation in FGMs  
Microcracks are generated during the thermal cracking of FGMs under temperature load, affecting the stress distribution and crack propagation inside the material. Cracks in FGMs are easily affected by temperature, leading to the re-extending of cracks and damage to the material structure. In addition, the spatial distribution characteristics of these cracks, such as the inclination angle and spacing of the cracks, could not be ignored (Figure 18). The thermal cracking of FGMs under temperature load and the influence of crack spacing and the inclination on crack propagation is investigated in this section. For this purpose, we establish an FGM model with double-edge cracks to study its crack propagation under temperature load, as shown in Figure 18. Assuming that the initial temperature of FGMs is high, the surface suddenly cools. Then, the existing cracks will further propagate and affect each other under thermal stress due to a large temperature difference. This section mainly uses the thermo-mechanical coupling model to study the influence of the inclination and spacing of the double-edge cracks on the crack propagation angle. The numerical model has a length of 0.4 m and a width of 0.2 m. The double-edge cracks are symmetrically distributed on both sides of the model. The geometric boundary conditions of the model are shown in Figure 19. The initial crack length of the model \(a=0.04\) m, and the crack spacing is assumed to be a multiple of the crack length  
Figure 17: Residual maximum principal stress along the monitoring line in composite material and FGMs. Figure 18: Schematic diagram of two edges of crack forms (\(\beta\) is the crack inclination angle, \(\varphi\) is the crack propagation angle, \(d\) is the crack spacing, \(L\) is the crack length, and the red arrow is the direction of the propagation crack). (\(d=a\), \(2a\) and \(4a\)). The crack inclination angles are 60\({}^{\circ}\), 70\({}^{\circ}\), 80\({}^{\circ}\), and 90\({}^{\circ}\), respectively. The initial temperature of the model is 100 \({}^{\circ}\)C, the top surface temperature is 0 \({}^{\circ}\)C, and the left and right boundaries are adiabatic. Here, a combination of ceramic and metal are used in FGMs. The top layer of the material has the corrosion resistance and high-temperature resistance of ceramics, and the bottom material has the high strength characteristics of the metal. The input parameters in FDEM are shown in Table 1. The model considers the effects of elastic modulus, Poisson's ratio, thermal conductivity, thermal expansion coefficient, and specific heat capacity, which obey an exponential function distribution, and the distribution functions are as follows:  
\[E=66.2\times 10^{9}*e^{(y*In(117/66.2)/0.2)} \tag{29}\]  
\[k=18.1*e^{(y*In(2.036/18.1)/0.2)} \tag{30}\]  
\[\alpha=10.3\times 10^{-6}*e^{(y*In(7.11/10.3)/0.2)} \tag{31}\]  
\[v=0.321*e^{(y*In(0.333/0.321)*y/0.2)} \tag{32}\]  
\[C_{p}=808.3*e^{(y*In(616.5/808.3)*y/0.2)} \tag{33}\]  
The model is divided into 24,162 triangular elements. The mechanical time step used in the simulation is 1 \(\times\) 10\({}^{-10}\) s. Figure 20 shows the relationship between the crack inclination angle and the crack propagation angle with different crack spacing. Firstly, the effect of the crack inclination angle on the crack propagation angle with different spacings is analyzed. It can be seen that the crack inclination and crack spacing have a significant effect on crack propagation. When the crack spacing is small, the cracks propagate in the opposite direction. As the crack spacing increases, the tendency of the crack propagation in the opposite direction decreases.