## 1 Introduction
The studies listed above establish a connection between the mass loss rate of the steel wire and its lifespan under specific stress amplitudes. Meanwhile, the recorded lifespan of the steel wire exhibits noticeable variability. In order to provide a more comprehensive explanation for the fatigue life degradation and fracture of the steel wire, attention has gradually shifted toward the initiation of fatigue cracks and the process of damage evolution. [PERSON], using a combined experimental and simulation approach, studied the damage evolution process of pre-existing notches in steel wires under the coupling action of fatigue loads and corrosion factors and predicted the service life of steel wires [19]. [PERSON], by preparing pre-existing notches on steel wires, revealed the influence of pits and stress amplitude on the fatigue life of steel wires under simultaneous mechanical and electrochemical corrosion [20]. [PERSON] considered the stochastic and discrete nature of corrosion damage to steel wires and quantitatively studied the effect of corrosion on the fatigue life of high-strength steel wires using a multi-parameter Weibull model. The proposed model enables a quantitative assessment of the life expectancy of steel wires at specific survival rates under a wide range of corrosion conditions [21]. [PERSON] investigated the development process of corrosion damage in steel wires from both microscopic and macroscopic perspectives. By conducting experiments, they determined the fatigue crack growth rate and identified the primary factors influencing the life expectancy of steel wires during the initial microscopic damage phase [22]. [PERSON] et al. quantitatively investigated the effect of corrosion on the residual fatigue life of suspension bridge cables. They proposed a rusted steel wire fatigue life prediction model that simultaneously considers both the corrosion propagation stage and the fatigue crack propagation stage based on the equivalent initial crack size method. Stress concentration induced by pitting corrosion was incorporated into the stress intensity factor model. The fracture morphology of the steel wire was observed using scanning electron microscopy, providing insights into the relationship between corrosion severity and wire life [23]. [PERSON] utilized three-dimensional scanning to measure the surface morphology of rusted steel wires, statistically analyzing corrosion features. By integratingfatigue experiments, they established a predictive method for the fatigue life of rusted steel wires [24]. [PERSON] et al. used artificially created notches to simulate rust-damaged steel wire components and studied the fracture characteristics of the rusted steel wire under different tensile stress conditions [25]. Hydrogen can diffuse through corrosion in acidic environments into the microstructural defects, grain boundaries, or crack tips of steel and accumulate in these areas, leading to stress concentration. [PERSON] et al. 's research indicates that the formation of corrosion product films (CPFs) at the crack tip significantly impacts the stress state and hydrogen diffusion. The CPFs, through hygroscopic expansion-induced stress, reduce the tensile stress at the crack tip and significantly inhibit hydrogen permeation into the crack tip, thereby exerting an important influence on the material's fatigue performance [26]. In the study of hydrogen embrittlement in parallel steel wires within bridge suspender components, [PERSON] conducted tensile tests on galvanized steel wires and found that the decisive factors affecting the ductility of the wires were surface irregularities and damage. By measuring the hydrogen content in wires under different conditions using inert gas methods, it was determined that the hydrogen concentration was insufficient to cause brittle fracture [9]. Similarly, [PERSON] et al.