## 5 Effect of Width of Semi-Ellipsoidal Notch on Wire Life  
Semi-ellipsoidal notches with different widths are used to investigate the influence of width of machine-cut notches on the corrosion fatigue performance of steel wire. The widths are taken as 3 mm, 4 mm, 5 mm, 6 mm and 7 mm, respectively. The depths of semi-ellipsoidal notches are all 1 mm. The schematic diagram of steel wire and corresponding wire specimen with different notches are shown in Figure 17.  
Figure 16: Logarithmic S-N curve of steel wire with semi-ellipsoidal notch of different depth.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Stress Range** & \multicolumn{5}{c}{**Cyclic Numbers**} \\ \cline{2-6} /**MPa** & **0.6 mm** & **0.8 mm** & **1.0 mm** & **1.1 mm** & **1.2 mm** \\ \hline
720 & 5123 & 3828 & 3531 & 3016 & 2606 \\
600 & 17,954 & 5942 & 5769 & 4887 & 3805 \\
480 & 30,310 & 14,296 & 10,881 & 9018 & 6856 \\
360 & 76,302 & 37,580 & 34,835 & 30,393 & 27,709 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The life of steel wire with semi-ellipsoidal notches of different depths.  
Figure 17: Wire specimens and schematic diagram of steel wire with semi-ellipsoidal notches of different widths.  
Table 6 shows the cyclic numbers of steel wire with semi-ellipsoidal notches of different widths. It can be seen that the life of steel wire increases with the reduction of stress range. At the same time, with the increase of notch width, the life of steel wire increases obviously. When the depth of the notch is constant, the width determines the stress concentration at the bottom of the notch. The smaller the width, the higher the stress concentration at the bottom of notch, the smaller the fatigue life of wire.  
Figure 18 shows the S-N curves of wire life with a machine-cut notch, which are the power exponential curves obtained by MATLAB fitting toolbox. It can be seen that the life of steel wire increases gradually with the increase of notch width. When the stress range is 720 MPa and the width of semi-ellipsoidal notch increases from 3 mm to 7 mm every 1 mm, the life of steel wire increases by 56%, 10%, 14% and 12% respectively. When the stress range is 600 MPa and the width of semi-ellipsoidal notch increases from 3 mm to 7 mm every 1 mm, the life of steel wire increases by 37%, 17%, 11% and 18%, respectively. When the stress range is 480 MPa and the width of the semi-ellipsoidal notch increases from 3 mm to 7 mm every 1 mm, the life of the steel wire increases by 19%, 4%, 11% and 23%, respectively. When the stress range is 360 MPa and the width of the semi-ellipsoidal notch increases from 3 mm to 7 mm every 1 mm, the life of the steel wire increases by 56%, 6%, 1% and 8%, respectively. It can be seen that when the stress range is higher, the life of the steel wire is lower, and the change rate of life is lower when the notch width is 4-6 mm. The growth rate of wire life is highest and by more than 20% when the width of the defect increases from 3 mm to 4 mm.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Stress range** & & & **Cyclic Number** & & \\ /**MPa** & **3 mm** & **4 mm** & **5 mm** & **6 mm** & **7 mm** \\ \hline
720 & 2259 & 3531 & 3887 & 4449 & 4999 \\
600 & 4210 & 5769 & 6746 & 7504 & 8837 \\
480 & 9145 & 10,881 & 11,241 & 12,484 & 15,374 \\
360 & 22,345 & 34,835 & 36,771 & 37,183 & 40,011 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The life of steel wire with semi-ellipsoidal notches of different widths.  
Figure 18: Logarithmic S-N curve of steel wire with notch of different width.