# Corrosion Fatigue Assessment of Bridge Cables Based on Equivalent Initial Flaw Size Model
## 1 Introduction  
As the primary load-bearing component of bridges, cable systems have a significant impact on its safety and usability [1, 2]. During the service life, the cable components experience high-stress conditions and frequent stress variations while undergoing environmental corrosion [3, 4, 5]. The effect of corrosion is particularly relevant for cable-supported bridges located in harsh marine environments [6]. Corrosion fatigue is a degradation form of metallic materials resulting from the combined effect of corrosion and fatigue. The effect of corrosion fatigue is more severe than the sum of individual corrosion and fatigue damages, which is closely related to the electrochemical corrosion of metals [7, 8, 9]. Extensive studies have been conducted on the development mechanisms, quantitative methods, and influencing factors of corrosion fatigue [10, 11, 12]. The existing research generally divides the process of corrosion fatigue damage development into the pitting corrosion stage and the corrosion fatigue cracking stage [13, 14]. During the development stage of pitting corrosion, the depth and shape of the pits are primarily controlled by corrosion [15]. [PERSON] [16] observed the evolution of pit depths in metallic plates submerged in water and derived an equation describing the evolution of pit depths under corrosion fatigue. The results indicated that the pits would gradually expand into semi-circular shapes under corrosion fatigue. [PERSON] et al. [17] studied the influence of different types of intermetallic compound particles on pittingcorrosion and its morphology development in seawater for aluminum alloys through electrochemical corrosion tests. When the pitting corrosion reaches a certain stage, the bottom of the pit meets the critical conditions for crack extension, and the corrosion fatigue process enters the crack growth stage dominated by fatigue [18]. This critical condition is known as pit nucleation. [PERSON] et al. [19] considered the accumulating effect of local plastic deformation of pits under cyclic loading and further improved the crack nucleation model. During the crack propagation stage dominated by fatigue stresses, the corrosion accelerates crack propagation, making the crack propagation process highly complex [20]. [PERSON] et al. [21] conducted corrosion fatigue tests on steel and concluded that load factors, geometric characteristics, and environmental factors play dominant roles in corrosion fatigue. [PERSON] et al. [22] studied the hydrogen ion migration during the crack propagation of steel wires in magnesium chloride solution through corrosion fatigue tests, while [PERSON] [23] believed that the crack propagation rate in a corrosive fatigue environment is related to the hydrogen ions released during crack tip extension. Based on the concept of a fracture process zone, crack propagation rate models have been established and validated. Currently, there is no universally accepted and comprehensive analysis method for the development of pitting corrosion during corrosion fatigue, despite the existing research progress. Corrosion leads to the formation of pits and weakens the cross-sectional area, thereby increasing the average stress level and local stress concentration on the bridge cables. Under the combined action of corrosion and stress range variation, local pits gradually develop into crack nucleation and eventually propagate until failure. [PERSON] et al. [24] analyzed the crack propagation rate of the bridge wire in artificial seawater and found that the crack propagation rate of microcracks was significantly higher than that of long cracks with the behavior of long crack propagation following the Paris equation. [PERSON] et al. [25] conducted mechanical tests and fatigue loading on service-exposed cables and found that the ultimate strength of the wire was minimally affected by corrosion, but the ductility of the corroded wire significantly decreased. [PERSON] et al.