## 6 Conclusions  
Through microscopic observation of the corroded steel wire surface and fatigue fracture surfaces, a reasonable summary of the surface cracks, corrosion pits, and fatigue fracture morphology was made. Finite element numerical simulations were used to analyze the propagation behavior of tiny initial cracks under fatigue loading in different scenarios. The conclusions of this study are as follows:  
(1) Microscopic observations have revealed that under mild corrosion, small cracks can initiate on the surface of the steel wire substrate. As the degree of corrosion intensifies, both corrosion pits and cracks appear simultaneously on the surface, resulting in composite damage. These pitting and cracking damages lead to a loss of effective cross-section and alter the local stress field, thereby affecting the stress intensity factor of the cracks, accelerating their propagation, and significantly reducing the service life of the steel wire. (2) The analysis of crack propagation processes reveals that the crack shape significantly influences the initial stress intensity factor. The stress intensity factor at the crack tip in the absence of corrosion pits is higher than that at the base of the corrosion pit, while the stress intensity factor at the center of the crack front is comparatively lower. At the critical fracture stage, the variation trend of the stress intensity factor remains consistent, with values converging to a similar range. This indicates that under the same load, cracks can propagate to the same position, leading to failure. Additionally, crack shape has a notable impact on fatigue life, with variations between 0.5 and 2 times, which accounts for the significant dispersion in the fatigue life of damaged steel wires. (3) In the parameter analysis, the interaction between double cracks was evaluated based on parameters such as initial crack size and crack spacing. The results indicate that multiple-crack propagation is particularly sensitive to crack spacing. Within the range of crack depth, the interaction between adjacent cracks should be carefully considered. When the relative spacing between cracks exceeds the crack depth, the development of double cracks tends to be independent, with minimal interaction effects. Conversely, when the relative spacing is within the range of crack depth, the stress intensity factor between the cracks exhibits significant amplification. The stages of crack merging and post-merging rapidly consume a substantial number of fatigue cycles. (4) Based on the amplification effect of the stress intensity factors at the tips of adjacent cracks, a comparison of the lifetimes of the double-crack system and the equivalent single crack reveals that the results under equivalent single-crack conditions are more conservative. This is because, compared to double cracks, the equivalent single crack lacks the independent development stage of the cracks. Using the equivalent crack instead of double cracks in practical applications tends to be safer and offers higher feasibility. Figure 17: Comparison of fatigue life predicted by multiple-crack FEM simulation and the effective crack. (**a**) Double cracks without corrosion pits. (**b**) Double cracks with corrosion pits. **Author Contributions:** L.D. : methodology, formal analysis, writing--original draft, and writing--review and editing; Y.D. : investigation, supervision. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the National Nature Science Foundation of China (Grant Nos. 51678459 and 51378406) and the Technology Project of Shanxi Transportation Holdings Group Co., Ltd. (Grant Nos. 19-JKKJ-8). Any opinions, findings, and conclusions expressed herein are those of the authors and do not necessarily reflect the views of the sponsors. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.