## 3 Methodology
### Temperature-Stress Field Coupling Finite Element Model  
Taking the Q235 material as an example, a coupled temperature-stress field finite element model was established, as shown in Figure 4. A size \(H\times L\) thin plate, where \(H=120\) mm and \(L=60\) mm, was placed on the bottom edge and at the center of the location of a circular hole representing a microdefect with a diameter of \(2r=50\) um. On both sides of the thin plate, a line pressure of P = 300 N/mm was applied, respectively, and a temperature load of size T was applied on both sides of the thin plate, which lasted for 100 s. The ambient temperature was 22 \({}^{\circ}\)C and the convective medium was air. The surface of the thin plate was a convective surface, and the convective coefficient was 0.000056 w/mm\({}^{2}\). The submodeling technique was used to perform finite element simulation on the microscopic defects. A submodel with a size of \(h\times l\) was cut from the thin plate, where \(h=0.25\) mm and \(l=0.5\) mm. The temperature obtained from the main \begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline \multirow{2}{*}{**Model**} & **Standard** & **Average** & **Correlation** & **Adjustment Coefficient** & **Variation** & **Signal-To-Noise Ratio** \\  & **Deviation** & **Average Value** & **Correlation Coefficient** & **(\(R_{a}^{2}\))** & **Coefficient (\%)** & **Ratio** \\ \hline \(E(T,R,V)\) & 0.7237 & 132.83 & 0.9999 & 0.9998 & 0.5448 & 434.001 \\ \hline \(Q(T,R,V)\) & 0.1063 & 10.92 & 0.99448 & 0.9921 & 0.9734 & 59.977 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Reliability test and analysis of the model. \begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline  & **Sum of Squares** & **Degrees of Freedom** & **Mean Variance** & **F-Value** & **\(p\)-Value** & **Significance** \\ \hline \(T^{2}V\) & 0.1599 & 1 & 0.1599 & 14.16 & 0.0006 & Significant \\ \hline \(TR^{2}\) & 0.0079 & 1 & 0.0079 & 0.6966 & 0.4093 & \\ \hline \(TV^{2}\) & 0.0006 & 1 & 0.0006 & 0.0519 & 0.8211 & \\ \hline \(R^{2}V\) & 0 & 1 & 0 & 0.0032 & 0.9552 & \\ \hline \(RV^{2}\) & 0.0003 & 1 & 0.0003 & 0.0229 & 0.8805 & \\ \hline \(T^{3}\) & 0.0725 & 1 & 0.0725 & 6.42 & 0.01 model calculation at the location was used as the ambient temperature for the submodel. The displacement and rotation calculated by the main model were mapped to the boundary elements of the submodel. The parameters of the material in question are given in Table 7.  
The boundary temperatures T of the thin plate were 300 K, 573 K, 623 K, 673 K, 723 K, 773 K, 823 K, and 873 K, respectively, and their corresponding stress cloud maps are shown in the Figure 5.  
It can be seen from the stress distribution cloud map that the temperature distribution of the material is uniform at room temperature, the material properties are consistent, and the stress of the entire thin plate is 600 MPa. As the temperature load is applied, due to the uneven temperature of the thin plate and the inconsistent material properties, the stress at the upper and lower boundaries is lower, and the stress in the center is higher. Moreover, the stress gradually increases with the increase in temperature. As the temperature load increases to 823 K, the thin plate gradually becomes unstable, and the stress distribution gradually changes. Until the temperature rises to 873 K, the maximum stress value shifts from the center of the thin plate to both sides of the lower boundary of the thin plate. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature** & **Density (g/cm\({}^{3}\))** & **Elastic Modulus (GPa)** & **Poisson Ratio** & **Thermal Conductivity (w/mm\({}^{2}\))** \\ \hline
300 & 7.8 & 203 & 0.3 & 0.000056 \\ \hline
573 & 7.8 & 195 & — & 0.000048 \\ \hline
673 & 7.7 & 183 & — & — \\ \hline
773 & 7.7 & 169 & — & — \\ \hline
873 & 7.6 & 126 & — & 0.000040 \\ \hline
973 & 7.6 & 35 & — & — \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Q235 material parameters.