## 1 Introduction  
Due to the complex geographical locations and climatic conditions of cable-stayed bridges, these structures are likely to be continuously affected by the corrosive environment of the surrounding area throughout their construction and operational phases [1]. Furthermore, owing to the lightweight nature and low rigidity of the cable materials used in these structures, they exhibit heightened sensitivity to wind loads, often leading to pronounced vibrations when subjected to wind excitations. Consequently, the cable systems within suspension bridges frequently contend with the synergistic impact of alternating loads and environmental corrosion, potentially culminating in corrosion fatigue damage, thereby precipitating economic losses and safety hazards [2]. Therefore, it is necessary to study the mechanism of corrosion fatigue-damage evolution in suspension bridge cables. The presence of corrosion pits in high-strength steel wires gives rise to stress concentration, resulting in the formation of high-stress regions at the pit, thereby posing a substantial threat to the structural fatigue life [3]. Addressing the inherent vulnerability of high-strength steel wires to corrosion, various scholars have conducted comprehensive investigations into the intricacies of the fatigue performance of corroded wires. [PERSON] et al. [4] conducted meticulous fatigue-crack propagation-rate tests on high-strength steel wires under diverse stress ratios, concurrently developing a sophisticated numerical model for fatigue-crack propagation using finite element software. [PERSON] et al. [5] unearthea potential correlation between the impact of pitting corrosion on fatigue life and the influence exerted by the equivalent stress concentration factor. [PERSON] et al. [6] conducted comprehensive experimental analyses of the fatigue performance of notched steel wire specimens, extracting the corrosion fatigue life of wires under the coupled influence of the corrosion medium and fatigue load, alongside the fatigue life unaffected by the corrosion medium. [PERSON] et al. [7] seamlessly integrated a fatigue damage evolution model into high-cycle fatigue studies, subsequently validating its applicability through meticulous experimentation. Notably, the model neglects to account for plastic deformation proximate to the corrosion pits. [PERSON] et al. [8] propounded a continuum damage mechanics (CDM) model to explore the realms of pre-corrosion and corrosion fatigue in aluminum alloys. [PERSON] et al. [9], with a grounding in accelerated corrosion trials and traffic load data from a specific bridge, scrutinized the corrosion-fatigue degradation of wires under traffic loads, accentuating the pivotal, influential role of corrosion characteristics in service life, particularly under conditions of low traffic flow intensity. Importantly, the morphological alterations near the corrosion pits and the concomitant plastic fatigue damage during corrosion fatigue, factors often overlooked in prior numerical models, could significantly impact fatigue life. [PERSON] et al. [10] meticulously probed into the corrosion fatigue-crack initiation and propagation dynamics of U75V rail steel, elucidating that crack initiation is contingent not only upon pit size but also markedly influenced by the local pit shape, underscoring the substantial impact of morphological changes in the pit vicinity on the fatigue-damage evolution process. To comprehensively assess the impact of fatigue loads and morphological changes in corrosion pits on the mechanical performance and fatigue life of steel structures, scholars have proposed the application of continuous damage mechanics to establish a fatigue damage model for predicting fatigue life [11]. This method considers corrosion pits on the surface of steel wires as notches rather than cracks. Through iterative computations of the cumulative damage incurred by the wire, the corrosion pit model state is updated, thereby achieving the objective of accounting for morphological changes in corrosion pits.