# Fretting Fatigue Behavior under Tension-Bending Mixed-Mode Loading
## 5 Conclusions  
This paper presents and numerically analyzes the tension-bending mixed-mode fretting fatigue behavior of a cylindrical pad-on-flat model. The effects of oblique loading, stiffness ratio, and mode angle on the contact width, maximum equivalent stress in the specimen, surface stress, fretting damage initiation location, and extent of damage initiation are analyzed. The finite element method, in combination with the critical plane parameter approach, has been employed to assess fretting damage initiation. Our findings can inform the design and manufacturing processes of fretting-resistant components, enabling engineers to better understand fatigue behavior under mixed-mode fretting loading conditions. By identifying critical stress locations and dominant modes of fatigue loading, these insights facilitate targeted design improvements to enhance the structural integrity and durability of aerospace and mechanical components. The key results can be summarized as follows:  
1. As the dimensionless oblique load increases, the stick-slip ratio decreases, and the contact center and the location of the damage initiation move toward the contact trailing edge. Both the maximum equivalent stress and the extent of fretting damage are positively related to the oblique load.
2. The contact width, the peak surface stress, and the extent of fretting damage increase with the increase in the stiffness ratio. The position of the maximum shear stress will be transformed from the leading edge to the trailing edge when the stiffness ratio is greater than unity.
3. When \(0^{\circ}\leq\theta\leq 45^{\circ}\), the stick-slip ratio, surface stress, maximum equivalent stress, and the extent of damage are very sensitive to the mode angle. However, when \(45^{\circ}\leq\theta\leq 90^{\circ}\), the parameter gradient is not obvious.
4. The damage parameters are concentrated at the contact edge, but the leading edge is more severe. When bending-dominant (\(45^{\circ}\leq\theta\leq 90^{\circ}\)), the maximum value of the damage parameters is similar, and the damage extent for the pure bending mode (\(\theta=90^{\circ}\)) is lower than that of \(\theta=75^{\circ}\).  
Figure 14: Variations in normalized maximum damage parameters with different control variables: (**a**) dimensionless oblique load \(\lambda\), (**b**) stiffness ratio \(\gamma\), and (**c**) mode angle \(\theta\).  
**Author Contributions:** X.Z.: Conceptualization; data curation; formal analysis; investigation; methodology; resources; software; validation; visualization; and writing--original draft. X.C.: Conceptualization; funding acquisition; project administration; supervision; and writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data generated and analyzed in this research are included in this published article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.