## 3 Examples
### Influence of the Initial Pitting Morphology on the Fatigue Life
Obviously, this kind of irregular sharp angle cannot be avoided in natural corrosion or artificial accelerated corrosion tests, so the random pits generated based on CA technology proposed in this paper are more in line with reality. Figure 16 is the time-varying curves of the stress intensity factor of steel wires with different pit morphologies. From the point of view of damage accumulation, the initial damage of the regular pit model with a shape factor of 0.25 is the greatest, but the random pit model has the fastest damage accumulation rate, which leads to it being that at the 40 th step, the damage degree in the latter is greater than that in the former. In addition, the initial damage of regular pit model with a shape factor of 0.25 is almost three times that of regular pit model with a shape factor of 2.0, indicating that the initial pit depth (corresponding to the initial damage degree) is the main reason for the difference in fatigue life between regular pit models. Figure 14: S-N curves of pre-corroded steel wire with mass loss rate of 0.25%. Figure 15: Stress contours of random pit model and two semi-ellipsoidal pit models with mass loss rate of 0.25%. (**a**) Random corrosion pit; (**b**) Hemi-ellipsoidal corrosion pit (\(\lambda=0.25\)). The hemi-ellipsoidal pit models with a mass rate of 2.5% are established, which is consistent with the mass loss rate of the random pit model generated by CA technology in Figure 8c. The simulative results are shown in Table 3. By comparing Table 2 with Table 3, in the steel wire model, the increasing rate of fatigue life at a mass loss rate of 2.5% is significantly higher than that at a mass loss rate of 0.25%. Figure 17 shows the S-N curves of the pre-corroded steel wires with a hemi-ellipsoidal pit and they are compared with that of steel wire with a random corrosion pit. When the mass loss rate is 2.5%, the fatigue life of random pit model is less than that of regular pit models, even if the maximum depth of the random pit model is less than that of regular pit model with a shape factor of 0.5. Figure 18a,b are the stress contours of the random pit and hemi-ellipsoidal pit model with shape factors of 0.5. In contrast to the model with a mass loss rate of 0.25%, the random pit model with a mass loss rate of 2.5% has more irregular shape angles, which lead to a larger stress in the random pit model and a larger gap with the regular pit model. Figure 16: Time-varying curves of the stress intensity factor for steel wire with different pit morphologies. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(S\)/MPa & \(n\) & \(A\) & \(x\)/mm & \(N_{e}\) \\ \hline \multirow{4}{*}{335} & & 0.25 & 1.9443 & 2,100,000 \\  & & 0.5 & 1.2248 & 3,180,000 \\  & & 1.0 & 0.7716 & 3,560,000 \\  & & 1.5 & 0.589 & 3,640,000 \\  & & 2.0 & 0.486 & 3,720,000 \\ \hline \multirow{4}{*}{418} & & 0.25 & 1.9443 & - \\  & & 0.5 & 1.2248 & 600,000 \\  & & 1.0 & 0.7716 & 730,000 \\  & & 1.5 & 0.589 & 790,000 \\  & & 2.0 & 0.486 & 800,000 \\ \hline \multirow{4}{*}{520} & & 0.25 & 1.9443 & - \\  & & 0.5 & 1.2248 & 78,000 \\ \cline{1-1}  & & 1.0 & 0.7716 & 141,000 \\ \cline{1-1}  & & 1.5 & 0.589 & 158,000 \\ \cline{1-1}  & & 2.0 & 0.486 & 168,000 \\ \hline \hline \end{tabular} Note: The stress intensity factor \(K_{\rm f}\) for steel wire crack has reached the critical value \(K_{\rm IC}\) under the cyclic stress with stress range of 418 MPa or 520 MPa when \(\lambda\) is 0.25. Failure of the steel wire will occur, so the fatigue life in this case is not discussed.  
\end{table} 
Table 3: Fatigue life of pre-corroded steel wire with a regular corrosion pit (\(\eta~{}=~{}2.5\%\)). Figure 19 represents the time-varying curves of the stress intensity factor for steel wire with different pit morphologies.