## 4 Results and Discussion
### Evaluation of SIF
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Machining Conditions**} & \multirow{2}{*}{**No.**} & **Facet Area** & \multicolumn{3}{c}{**Moussaoui’s Model**[16; 17]} & \multicolumn{3}{c}{**The Proposed Model**} \\ \cline{3-8}  & & **(mm\({}^{2}\))** & \(\sigma_{local,\text{max}}\) & \(\sigma_{local,\text{min}}\) & \(\Delta\sigma_{\text{eff}}\) & \(\sigma_{\text{u,max}}\) & \(\sigma_{\text{v,min}}\) & \(\Delta\sigma^{\prime}\)_eff_ \\ \hline \multirow{2}{*}{\(Vc=50\) m/min} & 1 & 0.05854 & 1406 & 388.1 & 1017.9 & 1304 & 523.6 & 780.4 \\ \cline{2-8}  & 3 & 0.05526 & 1406 & 388.1 & 1017.9 & 1304 & 523.6 & 780.4 \\ \cline{2-8}  & 4 & 0.05148 & 1406 & 388.1 & 1017.9 & 1304 & 523.6 & 780.4 \\ \hline \multirow{2}{*}{\(Vc=60\) m/min} & 7 & 0.03014 & 1374 & 356.1 & 1017.9 & 1317 & 579.9 & 737.1 \\ \cline{2-8}  & 9 & 0.04876 & 1374 & 356.1 & 1017.9 & 1317 & 579.9 & 737.1 \\ \cline{2-8}  & 12 & 0.04198 & 1374 & 356.1 & 1017.9 & 1317 & 579.9 & 737.1 \\ \hline \multirow{2}{*}{\(Vc=70\) m/min} & 13 & 0.07619 & 1374 & 342.1 & 1017.9 & 1248 & 485 & 763 \\ \cline{2-8}  & 14 & 0.07061 & 1360 & 342.1 & 1017.9 & 1248 & 485 & 763 \\ \cline{2-8}  & 17 & 0.08001 & 1360 & 342.1 & 1017.9 & 1248 & 485 & 763 \\ \hline \multirow{2}{*}{\(Vc=80\) m/min} & 19 & 0.06538 & 1330 & 312.1 & 1017.9 & 1264 & 521 & 743 \\ \cline{2-8}  & 21 & 0.06297 & 1330 & 312.1 & 1017.9 & 1264 & 521 & 743 \\ \cline{2-8}  & 24 & 0.05689 & 1330 & 312.1 & 1017.9 & 1264 & 521 & 743 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The facet area of specimen fracture surfaces under different machining conditions. 13.25 MPa \(\sqrt{\text{m}}\) which coincides with the threshold value in the range of 13.21\(\sim\)13.89 MPa \(\sqrt{\text{m}}\) obtained by [PERSON] et al. [30]. Nevertheless, the value of \(\Delta K_{th}\) obtained by [PERSON] et al. [31] was approximately 21.39 MPa \(\sqrt{\text{m}}\) which is higher than that obtained by [PERSON] [29] and [PERSON] [30]. This could be explained by the fact that the experiments were performed in vacuum and under the lower stress ratio \(R=0.05\). [PERSON] and [PERSON] [32; 33] reported a threshold value \(\Delta K_{th}\) that was approximately within the range of 11-12 MPa \(\sqrt{\text{m}}\) at the stress ration \(R=0.1\) for Inconel 718. It can be noted that the yield stress \(\sigma_{0.2}\) of Inconel 718 employed in References [32; 33] was 1060 MPa which is much lower than the Inconel 718 used in this paper (\(\sigma_{0.2}=1360.5\) MPa). Thus, the threshold value \(\Delta K_{th}\) obtained by [PERSON] [32; 33] is a little conservative. In the present work, the mean value of \(\Delta K_{th}\) (13.45 MPa \(\sqrt{\text{m}}\)), calculated by the proposed model agreed well with the threshold value that was demonstrated by [PERSON] [29] and [PERSON] [30]. The calculated results showed that the mean value of \(\Delta K_{th}\) was much higher than the experimental results when the residual shear stress was not considered. However, the mean value of \(\Delta K_{th}\) had good agreement with the experimental data when the residual shear stress was taken into account. This phenomenon supported the previous analysis that the residual shear stress was not negligible and should be considered in analyzing the effect of residual stress on fatigue behavior. Therefore, it can be concluded that the effect of residual shear stress on the threshold stress intensity factor is significant and ignoring it can cause considerable deviation from the experimental results.