## 4 Numerical Simulation of Damaged Steel Wire
### Influence of the Initial Crack Shape  
To verify the accuracy of the finite element model, this study conducted a comparative analysis of the fatigue life data of corroded steel wires obtained from existing references [12; 16; 18]. Figure 9 presents a comparison between the numerical simulated lives and experimental lives of 50 samples, with the vertical axis indicating the logarithmic ratio of the numerical simulation values to the fatigue life values reported in the literature. The analysis shows that this ratio fluctuates around one, indicating a relative consistency between the numerical simulations and experimental results. Considering the variability in the fatigue life of corroded steel wires, this result further supports the validity of the established model. Therefore, it can be concluded that the model demonstrates good predictive capability in simulating the fatigue behavior of corroded steel wires.  
Figure 8: Stress contour plot of damaged steel wire. (**a**) Hemispherical pits. (**b**) Groove-shaped pits. (**c**) Cracks without pits. (**d**) Cracks with pits.  
Figure 9: Stress contour plot of damaged steel wire.  
The microscopic observations indicate that micro-cracks can occur in the steel wire matrix under mild corrosion conditions. Some cracks may even develop within the areas affected by corrosion pits. Therefore, prior to analyzing the propagation of multiple cracks, it is essential to examine the behavior of single-crack propagation.  
In the model without corrosion pits, the initial crack depth is set to 0.3 mm, corresponding to the short radius of an ellipse. For the model containing corrosion pits, the depth of these pits is established at 0.2 mm, with the crack located 0.1 mm deep within the deepest portion of the corrosion pit. The ratio of the long radius to the short radius--referred to as the width-to-depth ratio--dictates the shape of the crack and is categorized into five groups: 3, 2, 1, 1/2, and 1/3.  
Figure 10 presents the stress intensity factors at the crack front during both the initial and critical stages preceding fracture. The data illustrate that the shape of the crack significantly influences the stress intensity factor during the initial stage. When comparing the impact of corrosion pits on the initial crack stress intensity factor, it was observed that the stress intensity factor near the ends of the crack without corrosion pits is greater than that of the crack situated within corrosion pits. Conversely, the stress intensity factor at the midpoint of the crack front without corrosion pits is lower than that of the crack with corrosion pits. This indicates that corrosion pits have a significant impact on crack propagation behavior.  
The trends in stress intensity factors at the critical fracture stage are largely consistent, with the values of the stress intensity factors being relatively close. This indicates that under axial tensile loading, the crack advances to a similar position, ultimately leading to the failure and fracture of the steel wire.  
Using a semicircular crack with a radius of 0.3 mm as the benchmark, where \(a=b=0.3\), Figure 11 illustrates the impact of crack geometry on fatigue life under two distinct condi  
Figure 10: Influence of initial crack shape on the stress intensity factor. (**a**) Initial SIF for a single crack. (**b**) Initial SIF for a single crack with a pit. (**c**) Critical SIF for a single crack. (**d**) Critical SIF for a single crack with a pit.  
tions. The results indicate that the fatigue life of double cracks with corrosion pits is lower than that without corrosion pits, and the effect of crack size variation on fatigue life ranges from 0.5 to 2 times.