## 5 Result and Discussion
When the number of cycles required by the design decreases, the maximum tolerable initial defect area increases rapidly as expected. Nevertheless, our laboratory's non-destructive testing capability (0.5 mm\({}^{2}\)) can meet the requirements for detecting initial defects in Nb\({}_{3}\)Sn jackets undergoing up to 60,000 loading cycles. \[b=\frac{n\Sigma_{i=1}^{n}\ x_{i}y_{i}-\Sigma_{i=1}^{n}\ x_{i}\Sigma_{i=1}^{n}y _{i}}{n\Sigma_{i=1}^{n}\ x_{i}^{2}-\sum_{i=1}^{n}x_{i}\Sigma_{i=1}^{n}\ x_{i}}\]1 Fatigue crack growth rate \(da/dN\) vs. stress intensity factor range \(\Delta K\) of the CHSN01 jacket with a probability of 99% obtained using the MLEM. \[b=\frac{n\Sigma_{i=1}^{n}\ x_{i}y_{i}-\Sigma_{i=1}^{n}\ x_{i}\Sigma_{i=1}^{n}y _{i}}{n\Sigma_{i=1}^{n}\ x_{i}^{2}-\sum_{i=1}^{n}x_{i}\Sigma_{i=1}^{n}\ x_{i}}\]2 The number of cycles as a function of the maximum tolerable initial defect area. The REBCO jacket exhibits better FCGR performance. A comparison has been made between CHSN01 and other materials used in fusion projects. The mechanical test results of stainless steel materials used in fusion projects at 4.2 K are listed in \[b=\frac{n\Sigma_{i=1}^{n}\ x_{i}y_{i}-\Sigma_{i=1}^{n}\ x_{i}\Sigma_{i=1}^{n}y _{i}}{n\Sigma_{i=1}^{n}\ x_{i}^{2}-\sum_{i=1}^{n}x_{i}\Sigma_{i=1}^{n}\ x_{i}}\]3 Due to its higher yield strength compared to other stainless steel materials used in fusion projects, CHSN01 can withstand greater stress, thereby reducing the number of jackets required. This contributes to the economic feasibility of compact fusion devices. Additionally, the FCGR properties of this material are superior to those of existing materials. Considering design margin, the stress ratio \(R\) is assumed to exhibit an allowable variation of \(\pm\)10% relative to the design value during service. The maximum tolerated crack areas under different \(R\) values at 60,000 cycles are calculated, as shown in \[b=\frac{n\Sigma_{i=1}^{n}\ x_{i}y_{i}-\Sigma_{i=1}^{n}\ x_{i}\Sigma_{i=1}^{n}y _{i}}{n\Sigma_{i=1}^{n}\ x_{i}^{2}-\sum_{i=1}^{n}x_{i}\Sigma_{i=1}^{n}\ x_{i}}\]4 The quantitative analysis reveals an inverse relationship between the maximum allowable crack area and the stress ratio \(R\). Meanwhile, it can be seen that in the extreme case, the maximum tolerated crack area is still greater than our detection capability. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Cycles** & **30,000** & **50,000** & **60,000** \\ \hline \multirow{4}{*}{1.1R ratio} & REBCO & 19.50 mm\({}^{2}\) & 8.46 mm\({}^{2}\) & 5.95 mm\({}^{2}\) \\  & & (\(-\)1.8\%) & (\(-\)3.1\%) & (\(-\)3.7\%) \\ \cline{1-1}  & Nb\({}_{3}\)Sn & 17.86 mm\({}^{2}\) & 5.95 mm\({}^{2}\) & 3.89 mm\({}^{2}\) \\  & & (\(-\)2.0\%) & (\(-\)3.9\%) & (\(-\)4.4\%) \\ \hline \multirow{4}{*}{0.9R ratio} & REBCO & 20.19 mm\({}^{2}\) & 9.01 mm\({}^{2}\) & 6.42 mm\({}^{2}\) \\  & & (+1.7\%) & (+3.2\%) & (+3.9\%) \\ \cline{1-1}  & Nb\({}_{3}\)Sn & 18.59 mm\({}^{2}\) & 6.41 mm\({}^{2}\) & 4.25 mm\({}^{2}\) \\ \cline{1-1}  & & (+2.0\%) & (+3.6\%) & (+4.4\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The maximum acceptable defects for different R ratios. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cycles** & **30,000** & **50,000** & **60,000** \\ \hline REBCO & 19.85 mm\({}^{2}\) & 8.73 mm\({}^{2}\) & 6.18 mm\({}^{2}\) \\ Nb\({}_{3}\)Sn & 18.22 mm\({}^{2}\) & 6.19 mm\({}^{2}\) & 4.07 mm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The maximum acceptable defects for different cycles.