Tribo-corrosion interaction of the parallel steel wires in the suspension bridges

The effect of contact load and relative displacement on tribo-corrosion interaction of parallel steel wires of main cable in the suspension bridge was investigated in this study. A self-made tribo-corrosion test bench was employed to conduct tribo-corrosion tests of parallel steel wires in 3.5% (wt%) NaCl solution and deionized water under different contact loads and different relative displacements. The friction coefficient and wear coefficient of wires were presented. Electrochemical corrosion behavior (Tafel polarization curves, Nyquist diagram, and equivalent circuit diagram) was characterized by electrochemical analyzer. Wear morphology was observed by scanning electron microscope. Wear volume loss and corrosion-wear interaction were quantitatively demonstrated by high-precision weighing balance. The results show that the electrochemical corrosion ability of the steel wires increases with the increase of the contact load or relative displacement. The increased contact load or relative displacement increases the volume loss of corrosion-wear and pure wear, but decreases the wear coefficient. The wear mechanisms in 3.5% NaCl solution are adhesive wear, abrasive wear, and corrosive wear as compared to adhesive wear and abrasive wear in deionized water under different contact loads. The wear mechanisms of parallel steel wires are slightly different under different relative displacements. But the main wear mechanisms are similar to that under different contact loads. The interaction effects of corrosion and wear produced by the contact load and relative displacement are all the synergistic effects.


Introduction
The long-span multi-tower suspension bridges are widely used in the construction of river and sea crossing bridges [1]. The main cable with the characteristics of high cost and difficult replacement is a flexible load-bearing component, which is the "lifeline" of the suspension bridge [1,2]. The bearing safety and anti-sliding safety of the main cable are directly related to the structural safety of the suspension bridge [2][3][4]. Once it fails, it will seriously cause huge economic losses and endanger people's lives. The main cables are subjected to wind loads in different directions due to strong wind [5]. The effects of ambient temperature changes and sunlight radiation lead to significant temperature gradients in the temperature field inside and on the main cable (due to the hysteresis of the temperature change inside the main cable), which causes changes in the internal force and the shape of the main cable [1,3]. In addition, the main cables shared by road and railway are subjected to dead loads (deck systems, stiffening beams, main cables, hangers) and live loads (cars, railway trains) through hangers and cable clamps. At the same time, the atmospheric environment of the river and the sea is characterized by high humidity and high salt fog [6], which is easy to form electrolyte corrosion solutions with different salt concentrations and pH values. Due to the lack of winding protection, the poor sealing of the cable inlet and outlet, and the wind effect at the main cable saddle, the electrolyte corrosion solution easily invades and accumulates in the main cable gap [7]. Therefore, the main cable is always subject to the electrolyte corrosive solution. In summary, the coupling effects of corrosion solution, wind load, temperature, dead load, and live load cause the corrosion of main cables and the coupling vibration of the wind-vehicle-bridge system [8], thereby inducing the acceleration of the failure of the main cable.
Many researchers have studied the corrosion and wear behavior of steel wire and wire rope. The straddle suspender of a suspension bridge is made up of wire ropes. The suspension bridge of the sea-crossing bridge is located in the marine atmosphere environment with an important component of sulfur dioxide, which can increase the corrosion rate and result in suspender break. Li et al. [9] gave macroscopic and microscopic explanations of the corrosion of steel wire. Karanci and Betti [10,11] presented a method based on monitored environmental condition for estimating the remaining capacity of cables, which can explore the effect of corrosion of the steel wires on the decrease in strength. Lan et al. [12] found out the quantitative effect of corrosion on the fatigue life of parallel stay cables using accelerated corrosion testing with acetic acid salt spray. The fatigue life of stay cable decreases significantly with the increased corrosion degree of the steel wire, especially, in the lower stress ranges. Sun et al. [13] reported a study on distribution model of steel wire corrosion, corrosion rate, and mechanical model of corroded cables, proving governing equations for static arrangement and in-plane free vibration of corroded cables. Chang et al. [14] investigated the friction and wear properties of wire ropes with different corrosion types, and analyzed the interaction of corrosion and wear on the residual strength of rope samples. The corrosion solutions degenerate the anti-friction and anti-wear properties of the lubricating grease and oil [15]. Lin et al. [16] evaluated the failure behaviors of wire ropes under different surface conditions by using salt spray, wear, and tensile testing. The result showed that the naked wire was more easily corroded in 3.5 wt% NaCl solution as compared to the case of 5 wt% NaCl solution. Kim et al. [17] performed repeated bending tests using a bending fatigue test rig and concluded that corrosion-fatigue is an important reason for reducing the life of the wire rope. Aiming at the interaction law of friction, wear, and corrosion of steel wire and wire rope, predecessors mainly studied the effect of corrosion on wire rope damage and proposed a theoretical model of fretting corrosion. However, researches on the tribo-corrosion behavior of parallel steel wires of main cables are rarely reported, and there is a lack of qualitative analysis and quantitative characterization of the interaction between wear and corrosion. The tribo-corrosion behavior (friction coefficient, wear volume loss, wear coefficient, wear mechanism, electrochemical corrosion damage, and corrosion-wear interaction) of main cable parallel wires under different contact loads and relative displacements will be revealed in this study.

Materials and parameters
The main cable galvanized steel wires with a diameter of 5.3 mm, tensile strength of 2,050 MPa, yield strength of 1,350 MPa, elastic modulus of 2.1×10 5 MPa, and Poisson's ratios of 0.31 were selected for the test. The steel wire is hot-dip galvanized for bridge cables in accordance with the national standard GB/T 17101-2019. Steel wire rod for bridge cable wire conforms to the industry standard YB/T 4264-2020. The grade of steel used is QS82. The corrosion medium is a self-prepared 3.5% NaCl solution (NS). The friction and wear in deionized water (DW) were used as the control group. The effect of different contact loads and different relative displacements on the tribo-corrosion interaction behavior of parallel steel wires were explored. When the contact load effect was explored, the relative displacement was selected as 1,000 μm, and when the relative displacement effect was explored, the contact load was selected as 100 N. Considering the volatilization of NS at 40 °C, when we explored the effect of different relative displacements  www.Springer.com/journal/40544 | Friction on the tribo-corrosion of parallel steel wires, the number of cycles was increased to 1×10 5 and the temperature was reduced to 30 °C. According to Refs. [3,4], the specific experimental parameters are shown in Table 1.

Tribo-corrosion test
The tribo-corrosion test rig of parallel steel wires is shown in Fig. 1. Before the test, the experimental steel wire samples were lightly sanded with fine sandpaper and wiped with alcohol to remove contaminants such as oil stains and oxides on the surface. After the wires was dried, a high-precision weighing balance was used to measure the mass m 1 (average of three times). First, the upper and lower steel wire samples were fixed on the clamps, the lower clamp was placed in the temperature-controlled corrosion tank, with which the NS or DW was filled to adjust the test temperature. The upper clamp was fixed on the upper sliding platform, which can apply a constant contact load F N between the wires. Then, the relative displacement parameter of the lower sliding platform was set to apply cyclic displacement, the tribocorrosion test was carried out. After the test, the steel wire samples were washed, dried and weighed their mass m 2 , and the average value was taken three times. The electrochemical workstation was set with electrochemical parameters and was connected with electrodes and lower steel wires. The tangential force Q between the wires was obtained in real time by the tangential force sensor. The friction coefficient between the wires μ is the ratio of Q and F N . The surface morphology of the worn area of the steel wire samples was observed by scanning electron microscope (SEM).

Calculation of wear volume loss
The pure wear volume (V w ) and corrosion-wear volume (V) of the steel wire samples are calculated by Eq. (1). The wear coefficient is calculated as Eq. (2). That is, the wear volume of the main cable wires under the unit contact load and unit relative displacement [18].
where Δm is the mass difference of the steel wire samples before and after the test (m 1 -m 2 ),  is the density of parallel steel wires.  where Δx is the relative displacement, N is the number of cycles, F N is the contact load, and V cof is the wear volume. The volume loss of pure corrosion (V C ) and the volume loss promoted by wear to corrosion (V WC ) are determined by electrochemical method. According to the corrosion-wear interaction standard ASTM G119-09 [19], the corrosion current values of the steel wire samples under static corrosion conditions and in the process of friction and wear are obtained. The calculation equations are as Eqs. (3) and (4) [20]: where t is the duration of corrosion-wear, F is the Faraday constant (96,500 C·mol -1 ), I W is the current of corrosion-wear, I a is the current of pure corrosion, ρ is the density of the steel wire, W is the relative atomic mass of the steel wire, and n is its valence.

Tafel polarization curve
The damage caused by the electrochemical multiphase reaction between the metal surface and the corrosive solution is called electrochemical corrosion, the essence of which is the short-circuiting effect of the corrosion galvanic cell [21]. The self-corrosion potential indicates how easy it is to lose electrons and reveals the corrosion trend. As shown in Fig. 2, with the increase of contact load and relative displacement, the polarization curve shifts negatively, the self-corrosion potential decreases, and the self-corrosion current increases. The steel wire is more likely to lose electrons and be more easily corroded. The decrease rates of self-corrosion potentials under different contact loads are 6.55% and 1.46%, respectively. The increase rates of self-corrosion currents are 98.48% and 59.55%, respectively. They all decrease with the increase of contact load. The decrease rates of self-corrosion potentials under different relative displacements are 2.91% and 6.67%, respectively. The increase rates of self-corrosion currents are 76.65% and 168.14%, respectively. They all increase with the increased relative displacement. The effect of increasing contact load on corrosion is slowed, while the effect of increasing relative displacement on corrosion is accelerated. Due to its smaller ionic radius, Clhas a strong adsorption capacity, adheres to the surface of the passivation film, and continuously penetrates into the interior of it, accelerating the destruction of the passivation film [22]. In NS, the potential of the Fe substrate is lower than that of the passivation film, so that a corrosion galvanic cell is formed between the two. An electrochemical reaction occurs. With the increase of contact load, the passivation film between the main cable steel wires is aggravated and destroyed. Meanwhile, high temperature enhances the activity of ions in solution and metal on steel wire surface. The fresh Fe substrate is continuously exposed to the corrosion solution, loses electrons easily as the negative electrode of the corroded galvanic cell and generates Fe 2+ . On the surface of the passivation film, O 2 from the air and H 2 O in NS gets electrons to form OH¯. Part of the Fe 2+ combines with OHto form Fe(OH) 2 , and part of them combine with Cland H 2 O to form FeCl 2 ·4H 2 O, which will decompose to form Fe(OH) 2 because of its instability. Corrosion products are more likely to be peeled off and removed under the increased contact load. Therefore, the corrosion resistance of steel wire samples is reduced and more easily corroded. However, the larger contact load does not increase the increase rate of corrosion current and the decrease rate of corrosion potential. This can be attributed to the fact that the larger contact load increases the wear between the contact surfaces, but at the same time, the ions are discharged in a small amount, the corrosion growth rate is slowed down. The corrosion rate is related to the size of the wear area on the contact surface of the steel wires. The larger the wear area, the greater the corrosion rate [23]. Under the same cycle period, the larger the relative displacement, the longer the sliding distance between the steel wires. Therefore, the contact and wear area increase, and the damage to the passivation film is more serious. Serious damage to the passivation film leads to the aggravation of the electrochemical reaction of steel wire substrate. Compared with the displacement of 500 μm, the relative displacement of 1,000 μm is doubled, the contact area between the steel wires is significantly increased, so the corrosion current growth rate and corrosion potential reduction rate are both increased.

Electrochemical AC impedance spectra
As shown in Figs. 3(a) and 3(b), the Nyquist diagrams  show the capacitive arc of different radii under different loads and different relative displacements. Both the increased contact load and the relative displacement result in smaller capacitive arc radii. The size of the capacitive arc radius reflects the corrosion resistance of the samples. The better the corrosion resistance of the parallel steel wires corresponds to the larger the capacitive arc radius. On the contrary, the smaller the capacitive arc radius, the worse the corrosion resistance [24,25].
That is, the greater the contact load and the relative displacement between parallel steel wires, the worse the corrosion resistance and the easier it is to be corroded. The electrochemical impedance spectra (EIS) between parallel steel wires show the same corrosion trend as the polarization curve. The main reason is consistent with the cause of the negative shift of the Tafel polarization curves, the gradually severe wear leads to aggravated corrosion. The Nyquist diagram data were inputted into the Zsimpwin software for fitting and analysis through the equivalent circuit R(Q(R(QR))), obtaining the equivalent circuit diagram (Fig. 3(c)) and AC impedance fitting data (Table 3). Since the corrosion solution and the steel wires remain unchanged, the equivalent circuits under different contact loads and relative displacements are also the same. In the whole equivalent circuit, the dielectric resistance of NS is represented by R s , C 1 and R t are the capacitance and resistance of the passivation film, respectively. The value of n 1 represents the dispersion coefficient of the non-ideal capacitance of the passivation film. The capacitance between the parallel steel wire and the passivation film is represented by C 2 . The charge transfer resistance is expressed as R f . The n 2 value is the dispersion coefficient of the non-ideal capacitance between the parallel steel wire and the passivation film. Usually, the number of semicircles in the impedance complex plane is the same as the number of time constants [23]. The dispersion effect is caused by the difference in the roughness of the wear surface during the tribo-corrosion process. In the test, the reaction on the cathode and anode surfaces of the corrosion galvanic cell results in an increase in rough pores and dissipated energy, causing a capacitive shift, which makes it impossible to fit the data through the pure capacitor. Therefore, the equivalent circuit element of CPE constant phase angle is used to replace the pure capacitor for the equivalent circuit fitting.
In order to ensure the accuracy and reliability of the test, we replaced the NS after each test. However, due to the influence of constant corrosion products, the R s fluctuates in a small range under different contact loads and different relative displacements. C 1 increases with the increase of the contact load, but C 2 first decreases and then increases. R t changes in the same trend as C 2 , while R f gradually decreases with the increasing contact load. The fluctuation of R t is mainly caused by the influence of corrosion products. The increase of the contact load causes the aggravated damage to the passivation film of the parallel steel wires. The wear rate exceeds the new formation rate of the passivation film. Therefore, Fe substrate of parallel steel wire is more exposed to NS, leading to corrosion reaction. The corrosion of the parallel steel wire is intensified, which is consistent with the trend shown by the Tafel polarization curves (Fig. 2). Under different relative displacements, C 1 and C 2 show an overall increasing trend with the increasing relative displacement, while R t and R f have different trends.  The fluctuation of R t is mainly attributed to the formation and dissolution of corrosion products, but the overall trend is still decreasing. The dispersion coefficient n values of the CPE element are always kept between 0.3-1. Their fluctuations are mainly due to the change of the surface roughness of the parallel steel wires, which is induced by the corrosion pits caused by corrosion on the one hand, and the surface wear caused by friction on the other hand. These will be explained further in the wear mechanism section (Section 3.2.2). The greater the polarization resistance R f , the better the corrosion resistance of the material [25,26]. As shown in Table 3, R f decreases with the increasing contact load and increasing relative displacement, which means that the charge transfer between the substrate and the passivation film increases, the electrochemical corrosion effect is continuously enhanced. In addition, the decreasing rate of R f becomes slower with the increase of the contact load and becomes faster with the increasing relative displacement, indicating that the increase rate of corrosion slows down with the increasing contact load as compared to acceleration with the increase of relative displacement. It is consistent with the results indicated by the Tafel polarization curves (Section 3.1.1). The corrosion resistance of the main cable steel wires is gradually decreasing, and the surface of the steel wires is more likely to be corroded.

Friction coefficient
As shown in Figs. 4(a) and 4(b), whether in NS or DW, the friction coefficient between the contact surfaces of the steel wires shows a trend of rapid increase -slight decrease -increase -rapid decrease -stabilization. Finally, the friction coefficients vary in the range of 0.3 to 0.4 in the later stage and decrease with the increasing contact load. Meanwhile, the steel wires show higher friction coefficient values in NS than that in DW. At the beginning of the test, due to the large surface roughness of the steel wire, the actual contact area is small. The number of contact points is small, the area of most contact points is large and the contact points are seriously adhered. The asperities and attachments on the surface are quickly worn away, so the friction coefficient increases sharply. Subsequently, the peaks of the surface micro-peaks are gradually ground off, leading to the decrease of the surface roughness. That is, the actual contact area and the number of contact points increase, the surface tends to be smooth, so the friction coefficient shows a downward trend. The corrosion effect of NS on the friction surface makes the surface loose and porous. The surface metal corrodes and flakes off during wear, resulting in increasing roughness. Part of the exfoliated material overflows from the friction surface, and the other part exists between the two friction surfaces as abrasive particles, which makes the wear change from two-body abrasion to three-body abrasion. Therefore, the friction coefficients are in the stage of small increase. With the increase of the number of cycles, the Zn coating of the galvanized steel wires is gradually depleted and the friction pair becomes Fe-Fe substrates. Due to the nature of the metal itself, the friction coefficient between the Zn-Zn contact surfaces is greater than that between the Fe-Fe contact surfaces [27]. At the same time, the generation and escape of wear debris on the contact surfaces also reach a dynamic balance, so the friction coefficients decrease and gradually stabilize [28,29]. In the corrosion solution, the passivation film is continuously destroyed and reformed, the corrosion reaction continues, leading to the fluctuation of friction coefficient. Meanwhile, the effect of corrosion makes corrosion-wear more serious than pure wear to damage the steel wire, so that the friction coefficient in NS is slightly larger than that in DW. As the contact load increases, the contact between the steel wires is tighter, the corrosion effect of NS on the wear debris between the contact surfaces is weakened. The wear debris is difficult to discharge, and the direct contact surface between the steel wires becomes smaller, resulting in a decrease in the friction coefficient. The increase of the contact load increases the actual contact area, and the magnitude of the friction force mainly depends on the size of the actual contact area. In general, the increase of the actual contact area is not proportional to the contact load, but is slower than the increase of the contact load, so the increase of the contact load actually decreases the friction coefficient [29]. Under different relative displacements (Figs. 4(c) and 4(d)), the friction coefficients show a trend of rapid increase -slight decrease -slight increaserapid decrease -stabilization at the displacements of 500 μm and 1,000 μm. However, the friction coefficient at the displacement of 100 μm shows a different trend from them, it first increases rapidly, then slightly increases, and finally stabilizes. Due to the fretting between the steel wires at the displacement of 100 μm, the contact surfaces are partially slipped, the adhesion between the surfaces is relatively strong, resulting in little change in the friction coefficient. In addition, the amount of material removed under fretting conditions is small, coupled with material adhesion and increasing transverse shear force, leading to the largest friction coefficient among the three working conditions. The friction coefficient at the displacement of 1,000 μm decreases before that at the displacement of 500 μm to stabilize, mainly because the long sliding distance is conducive to the dynamic balance of wear debris generation and overflow. Under the same cycle, the wear area is larger under the long relative displacement, that is, the actual contact area of the steel wire samples is larger, resulting in increasing friction between the contact surfaces. Therefore, the friction coefficient at the displacement of 1,000 μm is greater than that of the displacement of 500 μm after the friction coefficient is stabilized.

Wear mechanisms
As shown in Figs. 5 and 6, corrosion pits of different sizes appear on the surface of the steel wires in NS, which is characteristic of corrosion wear. Corrosion pits in unworn areas are more pronounced because friction erases some of the pits. However, there is no corrosion on the wire surface in DW. Under the contact load of 80 N in NS, the wear scars in the contact area are wide and shallow, with asperities and obvious ploughings appearing on the surface, which are typical abrasive wear characteristics. In addition, there is plastic deformation and tiny flake-like peeling on the surface, which is the phenomenon of adhesive wear. Therefore, the wear mechanisms of the parallel steel wires under the contact load of 80 N in NS are abrasive wear, adhesive wear, and corrosive wear. With the increase of the contact load, the adhesion and extrusion of the material are more obvious, the surface shows a large number of flake-spalling www.Springer.com/journal/40544 | Friction pits and shallow spalling, the adhesion and tearing area increases. Therefore, the wear mechanisms under the contact load of 100 N and 120 N are also abrasive wear, adhesive wear, and corrosive wear. From Figs. 5(b1)-5(b3), the normal force induces hard protrusions or rough peaks on the surface of the main cable wires to extrude the surface out of layered or scaly flaking debris. Then, under the action of tangential force, the surface is sheared, ploughed, and cut, causing the surface material to fall off, which is a typical abrasive wear feature. Meanwhile, under a certain normal load, when the local pressure exceeds the yield pressure of the material, plastic deformation of the friction surface occurs, and then adhesion is formed. Both in NS and DW, the contact pressures increase with the increase of contact load, and the contact pressures in NS are greater than that in DW ( Fig. S1 and Table S1 in the Electronic Supplementary Material (ESM)). When the wires slide relative to each other, shear fracture occurs at the nodes formed by the adhesive effect, and the sheared material falls off into wear debris, or migrates from one surface to another surface, which is adhesive wear. Therefore, the adhesion becomes more significant with the increase of contact load. Moreover, the adhesion in NS is more significant than that in DW under the same contact load. As the contact load increases, the ploughing phenomenon and other characteristics of abrasive wear are more obvious. Therefore, the wear mechanisms in DW under different contact loads are all abrasive wear and adhesive wear.
At the displacement of 1,000 μm in NS, there is obvious plastic deformation and material extrusion and adhesion on the surface of the steel wires. There  are small hard particles, flaky wear debris, and many obvious fatigue cracks on the surface. A slight ploughing parallel to the sliding direction can be seen in the wear area, but the ploughing has less damage to the surface. Therefore, the wear mechanisms under the relative displacement of 1,000 μm in NS are abrasive wear, adhesive wear, corrosive wear, and fatigue wear. When the relative displacement is 500 μm, the wear scars show more grooves parallel to the sliding direction, and the wear scars gradually become deeper and more numerous. This is the result of the ploughing action of granular abrasive debris on the friction surface, which is a typical abrasive wear characteristic. Obvious material adhesion, extrusion tearing, and flake-like spalling are distributed on the worn surface. Therefore, the wear mechanisms at the displacement of 500 μm in NS are abrasive wear, adhesive wear, and corrosive wear. At the displacement of 100 μm in NS, no ploughing phenomenon is observed, so the wear mechanisms are adhesive wear and corrosive wear. As shown in Fig. 5(d1), there are a large number of river-like ploughings parallel to the sliding direction in the wear area, and small wear debris is distributed on the surface. Therefore, the wear mechanism of the displacement of 1,000 μm in DW is abrasive wear. Obvious adhesion and flakespalling appear on the surface, with small hard particles attaching to, and ploughings are visible (Fig. 5(d2)), indicating that the wear mechanisms of the displacement of 500 μm in DW are abrasive wear and adhesive wear. The surface has obvious plastic deformation and adhesion, so the wear mechanism of the displacement of 100 μm in DW is adhesive wear. It is worth noting that with the increase of relative displacement, adhesion and other phenomena are not more obvious, mainly due to the decrease of contact pressure (Table S1 in the ESM).

Wear loss and wear coefficient
The interaction between different wear volume losses www.Springer.com/journal/40544 | Friction and corrosion will be analyzed in Section 3.3. Here, the focus is on the relationship between the wear coefficient and the contact load and relative displacement. As shown in Figs. 7(a) and 7(b), the volume losses of corrosion-wear all increase with the increase of contact load and relative displacement in NS and DW. The corrosion-wear volume loss has an almost linear relationship with the above two parameters. Figures 7(c) and 7(d) show the wear coefficients in NS and DW decrease with the increasing contact load and relative displacement, indicating that the effect of contact load and relative displacement is greater than that of volume loss according to Eq. (2). The wear coefficient in NS is an order of magnitude higher than that in DW, which shows that corrosion does have a significant promoting effect on wear. The wear coefficient of corrosion-wear in NS almost decreases linearly. The corrosion-wear coefficient is 1.37147×10 -6 mm 3 /(N·mm) in NS under the contact load of 80 N as compared to 1.04648×10 -6 mm 3 /(N·mm) under the contact load of 120 N, which decreases by 23.70%. Under the same conditions, the pure wear coefficient is only decreased by 8.97%. When the contact load increases from 100 to 120 N, the pure wear coefficient remains basically unchanged, only decreases by 0.36%. The passivation film on the contact surface of the main cable steel wire is broken due to shear force, so the anti-wear and anti-corrosion abilities of wires decrease, resulting in layered or blocky peeling of surface corrosion products and increasing material loss [15,30]. The steel wires keep sliding relative to each other, so that part of the peeled metal flows out with the solution, and the other part exists in the contact surface of the samples, acting as a third body to participate in wear. Due to the continuous increase of the contact load, the discharge of the wear debris from the contact part is also more and more difficult, so the wear coefficient is gradually decreased. The contact loads range from 100 to 120 N, since the ratio of contact load to wear volume is basically unchanged, the wear coefficient in DW does not change significantly.
The corrosion-wear coefficient is 2.13503×10 -6 mm 3 / (N·mm) in NS at the displacement of 100 μm as compared to 6.4379×10 -7 mm 3 /(N·mm) at the displacement of 1,000 μm, which decreases by 69.85%. Under the same relative displacement, the pure wear coefficient is decreased by 66.39%. However, the wear volume losses increase by 201.54% in NS and 236.13% in DW, respectively ( Fig. 7(b)). Therefore, the  | https://mc03.manuscriptcentral.com/friction decreasing wear coefficient with increasing relative displacement thanks to the cushioning of the wear debris. The relative displacement dominates as compared to wear volume loss. The increase of the relative displacement has a greater effect on the wear loss and wear coefficient than the increasing contact load, mainly due to the prolongation of the test cycles. If the wear coefficient and wear loss in NS are compared with those in DW, the wear and corrosion show a "positive" interaction, which is consistent with the analysis in Section 3.3.

Corrosion-wear interaction
Corrosion-wear between materials is not a simple algebraic accumulation of single corrosion and wear, but a loss caused by the combined action of mechanical factors, electrochemical factors, and environmental factors. There is a clear interaction between corrosion and wear on material loss. Corrosion can accelerate wear, in turn, wear can also accelerate corrosion [31]. According to Ref. [32] and the ASTM G119-09, the total volume loss of corrosion-wear (V) is the sum of V C , the volume loss of pure wear (V W ) and the volume loss of the interaction between corrosion and wear (ΔV). ΔV consists of two components, V WC and the volume loss promoted by corrosion to wear (V CW ) [33]. The total volume loss of wear (ΔV W ) is composed of V W and V CW , and the total volume loss of corrosion (ΔV C ) consists of V C and V WC . The volume loss of corrosion-wear and each component under different contact loads and different relative displacements are shown in Table 4. As shown in Fig. 8(a), the high temperature enhances the ionic activity, the friction destroys the passivation film and exposes the fresh Fe substrate to NS. Therefore, the corrosion galvanic cell forms and reacts rapidly. At the same time, corrosion makes the contact surface rough and porous, making it more susceptible to wear. Corrosion products are peeled off from the surface under the action of friction. The wear particles and debris become loose and are peeled off under the action of corrosion. They are corrosion-wear particles floating in NS or trapped between the contact surfaces, which will participate in friction as third bodies. It can be seen from Figs. 8(b) and 8(c), the volume loss of the parallel steel wires is mainly the sum of V W and V CW , V W and V WC account for a very small part, indicating that the volume loss of the parallel wires is determined by their wear resistance.
As shown in Figs. 9(a) and 9(c), the total volume loss of wear is close to the total volume loss of corrosion-wear, accounting for about 98.8%-99.5% of V under different contact loads and 97.6%-98.1% under different relative displacements ( Table 4). The sum of V CW and V WC accounts for about 87.7%-89.7% of the total volume loss of corrosion-wear under different contact loads as compared to 92.4%-93.4% under different relative displacements (Figs. 9(b) and 9(d)). These indicate that there is a serious interaction between the corrosion and wear of the parallel steel wires, and the corrosion-wear interaction cannot be ignored in the damage of the main cable steel wires. Table 4 shows that V, ΔV W , and ΔV C increase with the increase of the contact load and relative displacement. However, the proportion of ΔV W and ΔV in V shows a downward trend, which is attributed to the increase of V W and the increasing proportion ( Fig. 10(a)). With the continuous increase of the contact load, the material removal on the surface of the steel wire increases. Meanwhile, the abrasive particles are continuously crushed to form a third body to participate in the wear process. The abrasive particles    continuously destroy the passivation film on the contact surface of the samples, which increases the pure wear. In addition, when the contact load increases, the abrasive wear effect in corrosion-wear is enhanced, leading to the weakened interaction (obtained from the analysis of electrochemical behavior in Section 3.1), so that the proportion of interaction is reduced. In the case of different relative displacements, the proportion of part component is slightly different from that under different contact loads. When the relative displacement is 100 μm, the interaction ratio is the highest, indicating that the corrosion-wear interaction effect under fretting conditions is relatively strong. The main reason is that in the case of fretting, the slip form is mainly partial slip, the contact surface adhesion state lasts for a long time, wear debris is trapped between the contact surfaces and difficult to discharge. Therefore, the volume loss of pure wear is the least. At the displacement of 500 μm, the proportion of pure wear in total corrosion-wear loss increases to 7.4% ( Fig. 9(b)), and the proportion of interaction is the lowest. At this time, the duration of the adhesion state of the contact surface is shortened, the wear debris is discharged under the long relative displacement. The new contact surface continues to wear and generates new wear debris, which are continuously discharged with sliding, so the volume of pure wear and its proportion in V increase. However, the proportions of V CW in V under the relative displacements of 500 μm and 1,000 μm are 90.7% and 90.6%, respectively. They are almost the same, revealing that the promoting effect of corrosion on wear is in a dynamic balance. At the displacement of 1,000 μm, ΔV/V increases slightly. Due to the increase of relative displacement, the fresh Fe substrate is more exposed in NS continuously by friction. The gradually increasing contact area is constantly in contact with the ions and oxygen in the solution to further react. Therefore, the promoting effect of wear on corrosion increases continuously, and the proportion of corrosion-wear interaction in V increases.
The V WC /V CW value is used to measure the degree of interaction between corrosion and wear. When V WC or V CW is a negative value, the corrosion and wear are mutually inhibiting. On the contrary, when they are both positive values, the two are mutually reinforcing relationships [33]. The synergistic V WC /V CW value ranges from 0 to 0.1, the promotion effect of corrosion on wear is dominant [32,34]. As shown in Fig. 11, V WC /V CW values under different contact loads and different relative displacements are always in the range 0 to 0.1, which means that the interaction of corrosion and wear is a synergistic effect. The increasing contact load and relative displacement enhance the synergistic effect, which is attributed to the fact that the larger the contact load and longer relative displacement, the more severe the surface wear of the steel wires. The destruction of the passivation film promotes the exposure of the fresh Fe substrate to NS. Meanwhile, due to the higher temperature of the solution, the ions and metals are more active, so the corrosion is intensified.

Conclusions
In this paper, a self-made tribo-corrosion test bench was employed for corrosion-wear interaction test www.Springer.com/journal/40544 | Friction of the parallel steel wires of the main cable in suspension bridges. The effects of contact load and relative displacement on tribological behaviors and corrosion-wear behavior are revealed. The following conclusions are obtained.
1) With the increase of the contact load or relative displacement, the electrochemical corrosion ability of the steel wires increases, and the corrosion resistance gradually decreases.
2) The volume loss of corrosion-wear and pure wear both increase with the increased contact load or relative displacement, while the wear coefficient gradually decreases.
3) The wear mechanisms in NS are adhesive wear, abrasive wear, and corrosive wear as compared to adhesive wear, and abrasive wear in DW under different contact load. At the displacement of 1,000 μm, the wear mechanisms in NS are adhesive wear, abrasive wear, corrosive wear, and fatigue wear as compared to abrasive wear in DW. When the relative displacement is 500 μm, the wear mechanisms in NS are adhesive wear, abrasive wear, and corrosive wear, and they are abrasive wear as compared to adhesive wear in DW. The wear mechanisms at the displacement of 100 μm in NS are adhesive wear and corrosive wear as compared to adhesive wear in DW.
4) The interaction between corrosion and wear accounting for 87.7%-89.7% decreases with the increased contact load, while the proportion of pure wear loss gradually increases. The interaction between corrosion and wear accounting for 92.4%-93.4% first decreases and then increases slightly with the increasing relative displacement. The proportion of pure wear loss is the largest at the displacement of 500 μm, which proves the smallest interaction effect.

Declaration of competing interest
The authors have no competing interests to declare that are relevant to the content of this article. The author Shirong GE is the Editorial Board Member of this journal.
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