## 3 Examples
### Fatigue Life of Pre-Corroded Steel Wire  
After a fatigue crack in a high-strength steel wire is formed, it will continue to propagate under alternating loads. When the stress intensity factor \(K_{I}\) of the crack reaches the fracture toughness \(K_{IC}\), a fracture occurs, which can be expressed as Equation (17) given in [37]:  
\[K_{I}\ =\ Y\sigma\sqrt{\pi x}<K_{IC} \tag{17}\]  
where \(\sigma\) is the stress in the specimen; \(Y\) is the crack shape factor, and for the hemi-elliptic surface crack under tension on the cylinder, \(Y\) can be expressed as [25]:  
\[Y\ =\ \frac{\frac{1.84}{\pi}\left[tan\left(\frac{\pi x}{2D}\right)/\frac{\pi x} {2D}\right]^{\frac{1}{2}}}{\cos\left(\frac{\pi x}{2D}\right)}\times\left[0.75 2+2.02\frac{x}{D}+0.37\left(1-sin\left(\frac{\pi x}{2D}\right)^{3}\right)\right] \tag{18}\]  
where \(x\) is the depth of the pit and \(D\) is the diameter of the wire. In this paper, in order to unify the damage assessment system, the stress intensity factor is used to quantify the overall damage degree of high strength steel wire. Therefore, the irregular corrosion pit is equivalent to a hemi-elliptic surface crack and does not make too much distinction between the corrosion pit and the crack. Based on the above assumption, the stress intensity factor can be calculated easily by using Equation (17) and Equation (18). According to [6], the fracture toughness of a high-strength steel wire with a diameter of 7 mm is 65.7 MPa\(\cdot\sqrt{m}\). Based on the simulation strategy proposed, the fatigue life of pre-corroded steel wires with different mass loss rates is obtained, as shown in Table 1. Notably, as mentioned above, the accuracy in Table 1 is the ratio of the number of real load cycle to the cycle block. In Table 1, compared with the test results, the fatigue life of the pre-corroded steel wire obtained by this strategy is generally conservative. Specifically, when the corrosion degree and the stress range are large, the gap between these two is wide. This effect is mainly caused by two reasons: (1) the experimental data given in [36] originate from a uniform corrosion test. The number and distribution of corrosion pits in this experiment are random, which is not totally consistent with the model established in Figure 9, especially when the corrosion  
Figure 8: Model of steel wire with a pre-corroded defect at each mass loss rate: (a) \(\eta=0.25\%\); (b) \(\eta=1.85\%\); (c) \(\eta=2.5\%\); (d) \(\eta=3.33\%\). degree is large. (2) The initial pitting morphology generated by CA is also random. The randomness of the simulation and test results leads to the gap between them, but the results of both are on the same order of magnitude. Furthermore, the average deviation is approximately 20.24%, which shows the reliability and practicability of this method in predicting the fatigue life of pre-corroded steel wire. Figure 9 shows the S-N curves of steel wires with different degrees of pre-corrosion. From Figure 9, the fatigue performance of steel wires decreases with increasing corrosion degree, which is consistent with other conclusions in the literature [7; 35; 38]. Hence, it could be found that the influence of pitting corrosion on the fatigue life is far greater than the mass loss. In addition, according to the Chinese standard [39], when stress range equals 360 MPa, it is required that the fatigue life of hot-dip galvanized high-strength steel wire for bridge cables is more than 2,000,000 cycles. Hence, from Figure 9, the corroded steel wire with a mass loss rate of 0.25% still satisfies the requirement but if the mass loss rate is equal or greater than 1.85%, the fatigue life of steel wire reduces to less than 2,000,000 cycles, which no longer meets the requirement and cannot be used.