# Development of Automatic Crack Growth Simulation Program Based on Finite Element Analysis
## 4 Verification of AI-FEM
### Comparison of SCC Growth with the ASME Method
#### 4.1.4 SCC Growth Calculation Using ASME Code, Sec. XI  
ASME code, Sec. XI, App. C provides cracked pipe evaluation methods and SCC growth rate relation according to the material. The method of calculating the SCC growth is as follows:  
1. Obtain the stress distribution in the pipe thickness direction by performing the thermal-structural coupling analysis of cracked pipe. This stress result is curve-fitted using the stress distribution formula of Equation (3) presented in ASME code, Sec. XI, App. A, A-3000.
2. Calculate the SIF using the SIF formula of Equations (4) and (5) presented in ASME code, Sec. XI, App. A, A-3411 by applying the stress distribution formula.
3. Calculate the crack growth rate for the corresponding SIF using the SCC growth rate calculation formula presented in ASME code, Sec. XI, App. C. When using this formula, if the crack growth cycle is defined largely, the SIF may change rapidly, and the crack growth rate may not be calculated accurately. Therefore, the crack growth cycle should be defined short enough in consideration of accuracy. (In this study, it was set to 100 h.)
4. The crack size is updated by adding the calculated crack growth amount to the crack of the previous cycle.
5. By repeating the above process until the load reaches the final cycle, the final crack size can be calculated.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(K_{LH}\) [MPa\(\sqrt{\overline{m}}\)] & \(Q_{g}\) [kcal/mole] & \(R_{g}\) [kcal/mole-R] & \(T_{abs}\) [\({}^{\circ}\)R] & \(T_{ref}\) [\({}^{\circ}\)R] & \(\sigma\) & \(\eta\) \\ \hline
0 & 31 & \(1.103\times 10^{-3}\) & 1076.7 & 1009.67 & 0 & 1.6 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameters of SCC growth.  
Figure 11: Stress distribution in the thickness direction applied to the pipe.  
The stress distribution formula in the thickness direction is presented in ASME code, Sec. XI, App. A, A-3000 is as follows Equation (3):  
\[\sigma=B_{0}+B_{1}\Big{(}\frac{x}{t}\Big{)}+B_{2}\Big{(}\frac{x}{t}\Big{)}^{2}+B _{3}\Big{(}\frac{x}{t}\Big{)}^{3}+B_{4}\Big{(}\frac{x}{t}\Big{)}^{4} \tag{3}\]  
where, \(B_{0}\)-\(B_{4}\) are the coefficients of a 4 th-order polynomial, and these can be obtained by curve-fitting the stress distribution. By applying these coefficients to the SIF (\(K_{l}\)) formula of Equation (4) presented in ASME code, Sec. XI, App. A, A-3411, the SIF of a surface cracked pipe can be calculated.  
\[K_{l}=\bigg{[}B_{0}G_{0}+B_{1}\Big{(}\frac{x}{t}\Big{)}G_{1}+B_{2}\Big{(}\frac {x}{t}\Big{)}^{2}G_{2}+B_{3}\Big{(}\frac{x}{t}\Big{)}^{3}G_{3}+B_{4}\Big{(} \frac{x}{t}\Big{)}^{4}G_{4}\bigg{]}\sqrt{\pi a/Q} \tag{4}\]  
\[Q=1+4.593\Big{(}\frac{a}{t}\Big{)}^{1.65}-q_{y} \tag{5}\]  
where \(G_{1}\)-\(G_{4}\) are SIF coefficients that vary depending on the crack shape and are presented in the ASME code, Sec. XI as a table form. \(Q\) is the crack shape parameter and is shown in Equation (5). \(I\) is the crack length, \(a/l\) is the crack aspect ratio, \(q_{y}\) is the plastic region correction coefficient. To define crack growth, the SCC growth rate should be determined. From this, it is possible to calculate the final crack size due to SCC growth until the end of the loading period. In this section, the SCC growth rate of Alloy 182 is presented in ASME code, Sec. XI, App. C was used. The final crack size was calculated through the above procedure.