## 3 Results and Discussion
### Effects of Environmental Media on Dissipation Energy Characteristics
#### 3.1.3 Wear Coefficient  
Figure 3 shows the irregularly elliptical front profile of wear scar of cyclic loaded wire in the case of acid solution. The long axis of ellipse shows an inclined angle \(\gamma\) with the wire axis attributed to combined roles of cyclic tension and torsion. Meanwhile, \(\gamma\) value coincides with the theoretical torsion angle amplitude, i.e., \(4^{\circ}\). Table 4 shows sizes of wear scars of cyclic loaded wires in different environmental media. It is observed that in cases of different environmental media wear scar sizes decrease in the order: air, acid, alkaline and neutral solutions, and deionized water. Figure 2: Hysteresis loops of torque versus torsion angle during tension–torsion cyclic loading of steel wires with fretting contact in different environmental media. (**a**) Air. (**b**) Acid solution. (**c**) Neutral solution. (**d**) Alkaline solution. (**e**) Deionized water. Based on wear depth profiles (Figures 3 and 4 and Table 4) and polynomial fitting, theoretical equations of wear depth profiles are established as shown in Figure 5. According to theoretical equations of wear depth profiles, the three-dimensional geometric model of wear scar is reconstructed using Pro/Engineer 5.0, PTC, Massachusetts, USA (see Figure 5 in reference [25]). The wear volume between surfaces of \(P\) and \(Q\) can be calculated automatically by Pro/Engineer 5.0. Substitutions of wear volume, relative slip amplitude, loading cycles and contact load into formula (1) derives the cyclic wear coefficient, i.e., the wear volume per unit local relative slip and per unit contact load [25,26]:  
\[k_{cof}=\frac{V}{S_{x}F_{n}}=\frac{V}{2\Delta xNF_{n}} \tag{1}\]  
where \(S_{x}\) is the total stroke, \(F_{n}\) denotes the contact load, and \(\Delta x\) represents the relative slip. In the present study, \(\Delta x\) is equal to relative displacement amplitude for simplicity. Coefficients of cyclic wear can be calculated using Equation (1). In cases of distinct environmental media, the wear coefficient decreases in the order: air, acid, neutral and alkaline solutions, and deionized water, i.e., \(K_{cof}=8.25\times 10^{-3}\)\(\mu\)m\({}^{2}\)/N, \(4.58\times 10^{-3}\)\(\mu\)m\({}^{2}\)/N, \(2.85\times 10^{-3}\)\(\mu\)m\({}^{2}\)/N, \(2.4\times 10^{-3}\)\(\mu\)m\({}^{2}\)/N and \(1.44\times 10^{-3}\)\(\mu\)m\({}^{2}\)/N, respectively. In cases of solutions, wear scars of cyclic loaded wires present the smaller wear depth (Table 4) and wear coefficient, as compared to the air medium, which reveals the negative interaction between wear and electrochemical corrosion. In the case of deionized water, no electrochemical corrosion and better lubrication effect cause a smaller wear coefficient as compared to solutions. In the acid solution, H\({}^{+}\) dissolves the debris and exfoliation products, and thus accelerates fretting wear. Meanwhile, the lubrication and polishing effect may reduce the wear between contacting wires. In the neutral solution, the strong electrochemical effect due to great Cl\({}^{-}\) concentration counteracts the lubrication effect of electrolyte solution [20, 21, 22, 27]. In the alkaline electrolyte solution, the contact surface exhibits corrosion resistant passivation film due to OH\({}^{-}\) concentration, decreased lubricating effect due to great Cl\({}^{-}\) concentration, and weakened electrochemical corrosion of chloride attributed to decreased Mg\({}^{2+}\), Ca\({}^{2+}\), Na\({}^{+}\) contents [20]. Therefore, the acid solution presents the largest wear depth and wear coefficient as compared to cases of neutral and alkaline solutions, while neutral and alkaline solutions exhibit essentially the same wear coefficient attributed to complex interactions of ions.