## 5 Parametric Analysis of Coplanar Dual Cracks  
### Interaction Between Coplanar Cracks  
The stress intensity factor at the crack tip is a key parameter for predicting crack propagation rates and estimating material fatigue life. It is commonly regarded as the driving force for cracks. To evaluate the effect of mutual interaction between coplanar double cracks, the interaction factor \(\gamma\) can be defined by comparing the stress intensity factors of double cracks with those of single cracks [33], as shown in Equation (5), as follows:  
\[\gamma=\frac{k_{\text{int}}}{k_{s}} \tag{5}\]  
where \(k_{\text{int}}\) represents the stress intensity factor at the crack front of a single crack in a pair of interacting cracks with identical geometries, and \(k_{s}\) represents the stress intensity factor at the crack tip of a single crack with the same geometric shape as in the double-crack system, under identical stress conditions.  
In order to obtain a more comprehensive analysis result, the influence of interaction factors was examined by setting different geometrically shaped initial cracks and crack  
Figure 13: Coplanar dual crack propagation curve. (**a**) Relative spacing. (**b**) Relative spacing. (**c**) Initial crack size. (**d**) Initial crack size.  
tip distances. With the crack depth set to \(a=0.3\) mm, Figure 14a,b illustrates the variation trend of the interaction factor \(\gamma\) for different relative positions of crack fronts under two scenarios. It can be observed that the interaction factor \(\gamma\) for both the combination of cracks with and without corrosion pits exhibits a similar variation trend. Due to the interaction between adjacent crack tips, the cracks tend to coalesce, resulting in the interaction factor \(\gamma\) reaching a peak near the inner crack tip \(C\) and gradually decreasing after moving away from the interaction region. Meanwhile, corrosion pits have a certain amplifying effect on the interaction factor at the crack tips.  
Comparing the interaction factors at the three key points, \(A\), \(C\), and \(C^{\prime}\), in Figure 14c,d, it is found that the interaction factors at points \(A\) and \(C^{\prime}\) are less than 1.05. Therefore, the amplification effect of the stress intensity factor at points \(A\) and \(C^{\prime}\) under the influence of dual cracks can be neglected. The presented case study indicates that as the distance  
Figure 14: Analysis of interaction factor. (**a**) Variation of \(\gamma\) at the crack front. (**b**) Variation of \(\gamma\) at the crack front. (**c**) Relative spacing relative spacing. (**d**) Relative spacing relative spacing. (**e**) Initial crack shape. (**f**) Initial crack shape.  
between crack tips exceeds the crack depth \(a\), the interaction effect gradually converges toward 1.  
Figure 14e,f compares the influence of the initial crack shape on the interaction factor \(\gamma\), showing a similar trend and indicating that the pattern defined by the crack depth \(a\) serves as a boundary and is largely independent of the initial crack shape.  
Figure 15 illustrates the effect of dual crack interaction on the fatigue life of the steel wire. The results indicate that when the distance between adjacent cracks is less than the crack depth, the fatigue life of the dual-crack steel wire is less than 90% of that of the single-crack wire. As the distance between adjacent cracks increases, the fatigue life of the dual-crack steel wire gradually approaches that of the single-crack wire. This also demonstrates the applicability of using the crack depth as a boundary.