# Fretting Fatigue Behavior under Tension-Bending Mixed-Mode Loading
## 1 Introduction  
Fretting can be defined as a small amplitude slip caused by cyclic loading. It generally occurs between two nominally fastened bodies, causing surface damage initiation as well as material fatigue fracture [1]. Fretting fatigue is a major source of failure in many engineering components such as bolted joints [2; 3; 4], riveted joints [5; 6], wire ropes [7; 8; 9], and dovetail joints [1; 9]. It is generally accepted that a slip band is produced at the edge of the contact surface in the fretting fatigue process. The crack can be initiated and grow due to the high gradient of cyclic stress there, which can severely reduce the fatigue life of the structure [10; 11; 12]. Researchers have adopted three single-mode models according to the loading conditions of the structure to simulate fretting fatigue phenomena, i.e., tension fretting fatigue [13; 14; 15], torsional fretting fatigue [16], and bending fretting fatigue [17; 18; 19]. These three single modes of fretting were set up in a series of experiments to study the effects of multiple variables (such as loading [20; 21], material properties [22; 23], and environmental conditions [24; 25]) on refetting damage. The results of the experiment provide guidance for enhancing the fretting fatigue resistance of materials. With an in-depth understanding of the damage evolution of fretting fatigue, numerical analysis has also been developed. The finite element method with multiaxial fatigue theory and fracture mechanics is combined to analyze and predict the initiation and propagation of cracks and fatigue life in fretting fatigue [26; 27; 28; 29], and the results show a good correlation with experimental data. However, due to the complex geometry and combinations of the boundary conditions of the components, the mixed-mode fretting fatigue that is subjected to mixed loadingconditions is more common in engineering applications. Few studies have been found regarding mixed-mode loading conditions in fretting damage. [PERSON] et al. [27] developed a novel experimental apparatus to simulate combined fretting conditions. The apparatus integrated tangential fretting and radial fretting loading modes, allowing the investigation of dynamic behavior, contact conditions, and damage processes under combined loads by varying the maximum load and inclination angles. The results revealed that material damage was governed by the competition between the two fretting loading modes, closely related to experimental parameters such as normal force, inclination angle, and material properties. Contact surface observations showed asymmetric fretting scars, with some tests exhibiting eccentricity between the center of the adhered region and the overall scar pattern. [PERSON] et al. [26] explored the influence of the torsion angle on the multiaxial fretting fatigue behavior of steel wires using a custom-built tension-torsion combined multiaxial fretting fatigue test rig. They found that increasing the torsion angle led to an increase in wire deflection angle, wear scar size, friction coefficient, and maximum crack depth, indicating that larger torsional loads would exacerbate fretting damage in wires. [PERSON] et al. [30] conducted tests on steel wires using a custom-built tension-torsion fretting corrosion fatigue test apparatus to investigate the effects of tensile stress ratio and amplitude on fretting fatigue behavior. The results demonstrated that increasing the tensile stress ratio and amplitude led to an overall increase in dissipated energy, friction coefficient, maximum wear depth, crack propagation rate, lifetime impact, fractal dimension, and surface complexity of the wires, suggesting that higher tensile stresses accelerate combined fretting fatigue damage. [PERSON] et al. [31] studied the bi-directional composite fretting wear behavior of Zr-4 alloy tubes under different phase differences, simulating the normal and radial composite loading conditions experienced by fuel assemblies in pressurized water reactors.