## 3 Results and Discussion
### Comparison of the Numerical and Analytical Methods  
For the validation of the FE model, analytical calculations were performed according to the plan in Table 2, and they were compared with the FE simulation results. Table 9 shows the safety factors numerically and analytically calculated for the autofrettaged cylinder without machining at the operating pressure according to the plan in the experiment matrix. Upon examining the results, it is observed that there is a maximum deviation of 4.37% between the numerical and analytical predictions. Table 10 presents the safety factors calculated numerically and analytically for the autofrettaged cylinder subjected to only internal machining, following the experimental matrix plan. Upon review, we find a maximum deviation of 4.75% between the numerical and analytical estimations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **DF** & **Adj SS** & **Adj MS** & **F-Value** & \(p\)**-Value** \\ \hline Regression & 3 & 0.553602 & 0.184534 & 1188.37 & 0.000 \\ \hline \(S_{y}\) & 1 & 0.544380 & 0.544380 & 3505.73 & 0.000 \\ \hline \(E\) & 1 & 0.002220 & 0.002220 & 14.30 & 0.013 \\ \hline \(T\) & 1 & 0.007001 & 0.007001 & 45.09 & 0.001 \\ \hline Error & 5 & 0.000776 & 0.000155 & & \\ \hline Total & 8 & 0.554378 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of ANOVA for the safety factor of the autofrettaged cylinder with only internal machining under working pressure of 400 MPa. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **DF** & **Adj SS** & **Adj MS** & **F-Value** & \(p\)**-Value** \\ \hline Regression & 2 & 0.505400 & 0.252700 & 710.18 & 0.000 \\ \hline \(S_{y}\) & 1 & 0.498357 & 0.498357 & 1400.57 & 0.000 \\ \hline \(T\) & 1 & 0.007043 & 0.007043 & 19.79 & 0.004 \\ \hline Error & 6 & 0.002135 & 0.000356 & & \\ \hline Total & 8 & 0.507535 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of ANOVA for the safety factor of the autofrettaged cylinder with only external machining under working pressure of 400 MPa. Table 11 displays the safety factors calculated numerically and analytically for the autofrettaged cylinder subjected to only external machining, following the experimental matrix plan. Upon examination of the results, we observe a maximum deviation of 5.20% between the numerical and analytical predictions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Order**} & \multicolumn{2}{c}{**Young’s**} & \multicolumn{1}{c}{**Tangent**} & \multirow{2}{*}{**Yield Strength**} & \multirow{2}{*}{**Factor of Safety**} & \multirow{2}{*}{**Factor of Safety**} & \multirow{2}{*}{**Deviation**} \\  & \multicolumn{1}{c}{**Modulus (GPa)**} & & & & & \\ \hline
1 & 100 & 0 & 0.7 & 1.01 & 0.96 & 4.53 \\ \hline
2 & 200 & 20 & 0.7 & 1.04 & 0.99 & 4.75 \\ \hline
3 & 300 & 10 & 0.7 & 1.02 & 0.97 & 4.28 \\ \hline
4 & 100 & 10 & 1 & 1.29 & 1.24 & 3.91 \\ \hline
5 & 200 & 0 & 1 & 1.26 & 1.22 & 3.81 \\ \hline
6 & 300 & 20 & 1 & 1.28 & 1.23 & 3.93 \\ \hline
7 & 100 & 20 & 1.3 & 1.56 & 1.50 & 3.52 \\ \hline
8 & 200 & 10 & 1.3 & 1.52 & 1.48 & 3.22 \\ \hline
9 & 300 & 0 & 1.3 & 1.51 & 1.47 & 2.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of the numerical and analytical results for the safety factor of the autofrettaged cylinder with only internal machining under working pressure of 400 MPa.