## 3 Results and Discussion
### Effects of Fretting and Torsional Parameters on Dissipation Energy Characteristics  
#### 3.2.1 Hysteresis Loops of Tangential Force versus Displacement Amplitude  
(1) Effects of loading cycles  
Figure 5a shows that increases of loading cycles cause the transition of hysteresis loop from parallelogram to ellipse and finally stabilized ellipse. That indicates the contact state between steel wires change from a gross slip to a partial slip, which induces a decrease in relative slip (Figure 5b) and an increase in adhesion zone. Figure 5b shows that the dissipation energy (area of hysteresis loop) created by cyclic tensile loading with fretting contact presents an increase at first, then a decrease and the final stabilization. At the initial stage, the protective film is removed from the fretting contact surface of cyclic loaded wire attributed to the fretting wear and corrosion, which causes the friction between steel matrix of wires and thus induces a rapid increase in the tangential force between contact surfaces. Therefore, the dissipation energy increases at first. Afterwards, the regulation and load-bearing of wear debris and corrosion products as the third body cause the decreased tangential force and dissipation  
Figure 4: Fitting of wear depth profiles of cyclic loaded wires in cases of distinct environmental media. **(a)** Air. **(b)** Acid solution. **(c)** Neutral solution. **(d)** Alkaline solution. **(e)** Deionized water. Figure 5: Effects of cycles of loading on hysteresis loops of tangential force versus displacement amplitude and the relative slip. **(a)** Hysteresis loops. **(b)** Relative slip and hysteresis loop area. energy. At the stabilized stage, dynamic equilibriums between formations and dissolutions of wear debris and corrosion products cause the stabilized tangential force. The relative slip between steel wires decreases at first and then stabilizes with increasing loading cycles. Therefore, combined roles of tangential force and relative slip induces the change trend of increase-decrease-stabilization of dissipation energy. Effect of contact load  
Figure 6a shows parallelogram \(F_{t}\)-\(D\) loops at contact load of 30 N, which indicates the gross slip state. Figure 6b-d show that the hysteresis loop changes from the parallelogram to ellipse with increasing loading cycles at contact loads of 40 N, 50 N and 60 N, which indicates that the fretting contact state varies from the gross slip to the partial slip, i.e., a decrease in the relative slip and an increase in the adhesion zone. An increase of contact load induces decreased loading cycles required for the hysteresis loop transition from parallelogram to ellipse, which indicates more difficult relative slip due to larger elastic deformation between contacting surfaces. An increase of contact load from 30 N to 60 N causes an increase in the maximum tangential force from 14.4 N to 20.0 N and a decrease in the relative slip from 78.4 \(\upmu\)m to 23.4 \(\upmu\)m at loading cycles 20,000 (Table 5). In cases of contact loads of 30 N, 40 N, 50 N and 60 N, dissipation energies are \(1.728\times 10^{-3}\) J, \(1.456\times 10^{-3}\) J, \(0.732\times 10^{-3}\) J and \(0.743\times 10^{-3}\) J, respectively. Therefore, the dissipation energy decreases firstly and then changes in a subtle manner with increasing contact load due to cyclic tensile loading with fretting contact. As the contact load increases from 50 N to 60 N, the unobvious change of dissipation energy is mainly attributed to an increase in the maximum tangential force and a decrease in the relative slip. Figure 6: \(F_{t}\)-\(D\) loops during tension–torsion cyclic loading of steel wires with fretting contact in cases of distinct contact loads. (**a**) \(F_{n}\) = 30 N. (**b**) \(F_{n}\) = 40 N. (**c**) \(F_{n}\) = 50 N. (**d**) \(F_{n}\) = 60 N.