## 5 Thermal Stress Analysis of FGMs and Composite Materials  
The composition and properties of FGMs exhibit spatial gradients without obvious interfaces by controlling the distribution of trace elements during production. Since the elastic modulus, Poisson's ratio, thermal conductivity, and other parameters show continuous changes in space, the thermal stress inside the material can be alleviated to meet specific needs. In addition, the composite is divided into multiple layers from a macro perspective and the internal parameters of each layer are the same, which can also alleviate thermal stress by decreasing or increasing the parameters layer by layer. This reflects the advantages of FGMs in relieving thermal stress and preventing thermal damage; the thermal stresses of FGMs and composite materials are compared under the same boundary conditions in this section. As shown in Figure 14, the initial temperature of the model is 500 \({}^{\circ}\)C, the environment temperature \(T_{\rm c}=25\,^{\circ}\)C, and the left and right boundaries are adiabatic. The heat conduction coefficient between the model and the environment is 2000 W/(m\({}^{2}\).K). The model is divided into 4054 triangular elements. The composites are divided into two and four layers to study the effect of the different layers' parameter distribution on the model's residual thermal stress. The parameters distribution of the models (\(E\)-elastic modulus, \(k\)-thermal conductivity coefficient, \(\alpha\)-thermal expansion coefficient, and \(v\)-[PERSON]'s ratio) are shown in Figure 15.  
The exponential function distribution is used here as an example in FGMs, which is as follows:  
\[E=100\times 10^{9}*e^{(ln(4)*y/0.03)} \tag{25}\]  
Figure 14: Model setup and boundary conditions. Figure 15: Composite material parameters distribution. (**a**) double-layer material; (**b**) Four-layer material (\(l\) is 1/4 of the model’s width). \[k=20*\mathrm{e}^{(In(8.5)*y/0.03)} \tag{26}\] \[\alpha=9\times 10^{-6}*e^{(In(4.2/9)*y/0.03)}\] (27) \[v=0.03*e^{(In(28/31)*y/0.03)} \tag{28}\]  
The residual maximum principal stress distributions for the three different parameter distribution models are shown in Figure 16. For composite materials, there are still obvious stress concentrations and stress sudden-change phenomena at the interface of the composite material. The more layers of the composite material, the better the stress at the interface can be relieved. For FGMs, only smaller tensile stress concentrations are generated on the upper surface of the model. Next, we set a monitoring line at the model coordinates (0.025 m, 0) and (0.025 m, 0.03 m) to compare the maximum principal stress distribution of the three models. The maximum principal stress distributed along the \(y\)-direction for three different parameter distribution models is shown in Figure 17. Under the same thickness condition, the maximum principal stress of the four-layer composite material is smaller than that of the double-layer material, indicating that increasing the number of material layers can improve the thermal stress distribution inside the material. On the monitoring line, the maximum principal stress of the double-layer and four-layer composite materials can reach 1.2 \(\times\) 10\({}^{8}\) Pa and 5 \(\times\) 10\({}^{7}\) Pa, respectively, while only 1.5 \(\times\) 10\({}^{7}\) Pa for FGMs. The thermal stress inside the FGMs is significantly reduced. The maximum principal stress peak of the composite material is at the interface, and the maximum principal stress peaks decrease with the increase in layer numbers. The maximum principal stress distribution curve of FGM shows that stress in the FGM material is continuously distributed inside. It should be pointed out that FGMs can be regarded as special cases of composite materials when the number of layers tends to be infinite. Figure 16: Residual maximum principal stress distribution in composite material and FGMs: (**a**) Double layer composite, (**b**) Four layer composite, (**c**) FGMs.