1 Introduction

Adhesive wear is a common tribological phenomenon and is found in many tribological systems [1]. Typically, adhesive wear occurs when two materials with comparable hardness are rubbed under poor lubrication conditions. In such a situation, local contact junctions are formed between two surfaces, and then they are broken owing to sliding. Consequently, the surfaces gradually wear with the formation of wear particles and material transfer to the counter surface. Adhesive wear causes gradual material loss and shortens the lifetime of the sliding parts. Furthermore, adhesive wear sometimes causes seizures, which immediately leads to serious machine failure. Thus, understanding the adhesive wear mechanism of materials is important in tribology.

The adhesive wear of steel is of particular interest because steel is one of the most important materials in industry and is widely used in various machine systems. Therefore, the wear mechanism has been extensively studied experimentally. Steijn studied the tribological properties of single-crystal iron and found that the width of wear track was larger when the sliding test was conducted in < 100 > direction than that in < 101 > direction on (001) plane [2]. Boas et al. showed that hard particles in the matrix, such as carbides, improve the resistance of steel to severe adhesive wear [3]. A later study by Fontalvo et al. showed that not only the carbide content but also the distance between carbide particles in the matrix significantly affects the adhesive wear behavior of steel [4]. Wang et al. showed that the microstructure of steel strongly affects its wear resistance [5]. A humid atmosphere also affects the wear properties of steels through chemical reactions induced at the sliding interface, that is, tribochemical reactions. Therefore, the understanding of the detailed effects of the humid atmosphere on the wear is crucial in industrial fields (e.g., railroad [6]). It has been widely reported that the wear amount decreases as the relative humidity increases owing to the formation of protective oxide layers on the surfaces [7]. More specifically, Esteves et al. found that Fe3O4 (magnetite), Fe2O3 (hematite), and FeO(OH) (goethite) are formed on the wear scar using Raman spectroscopy [8]. The microscopic phenomena in actual contact junction are also important issue to understand the tribological phenomena of materials. Merkle et al. and Sato et al. used transmission electron microscope technique to investigate the microscale frictional and wear property of metals [9, 10]. However, the detailed adhesive wear mechanism, including the wear protection mechanism of humid atmospheres, is still under debate owing to its complexity. Therefore, atomic-scale insights are required for further improvement of the wear resistance of steel.

Molecular dynamics (MD) simulations are useful for elucidating the tribological properties of materials at the atomic scale. Several MD-based sliding simulations with embedded-atom method (EAM) potential have been reported. Gao et al. performed an MD-based sliding simulation of single-crystal iron with various surface orientations and sliding directions [11]. They found that the atoms on the surface pile up owing to scratching and that the shape of the pile-up patterns depends on the surface orientation and sliding direction. AlMotasem et al. performed a sliding simulation for polycrystalline iron and showed that the pile-up pattern does not depend on the grain size [12]. These sliding simulations provide fundamental insights into the wear mechanism of iron. However, the detailed adhesive wear mechanism is still under debate because the EAM potential used in previous studies cannot address chemical reactions, which play a crucial role in the adhesive wear of iron.

In this work, we performed an MD-based sliding simulation for single crystalline body-centered cubic (BCC) iron, which is a model system of nascent surface of steel, to elucidate the atomic-scale adhesive wear mechanism. The nascent surface is typically generated by removing the native oxide layer due to sliding and plays a crucial role in adhesive wear due to its high activity for chemical reactions. We used a reactive force field (ReaxFF) [13]. ReaxFF is a variable bond-order-based force field that can describe complex interatomic interactions with reasonable accuracy; therefore, it can deal with chemical reactions at sliding interface [14, 15]. The effects of the surface orientation, sliding direction, and tribochemical reaction [16] with water on adhesive wear were analyzed to elucidate the fundamental wear mechanism at the atomic scale.

2 Computational Details

In this study, we performed a reactive MD-based sliding simulation of single-crystalline BCC iron to elucidate the atomic-scale adhesive wear mechanism. Figure 1 shows the sliding simulation model. Here, we focused on the nascent surface, which is typically generated by removing the native oxide layer due to sliding (Fig. 1a), because chemically active nascent surfaces play a crucial role in adhesive wear [17, 18]. To investigate the effect of surface orientation, we performed a sliding simulation for two typical iron surfaces: (110) and (100), which are known to be stable [19]. For each surface, several sliding directions were examined: \([1\overline{1}1]\), \([1\overline{1}0]\), and [001] directions for the (110) surface (denoted as (110)/\([1\overline{1}1]\), (110)/\([1\overline{1}0]\), and (110)/[001]) and [011] and [010] directions for the (100) surface (denoted as (100)/[011] and (100)/[010]) (Fig. 1b). To investigate the effects of a humid atmosphere, we performed sliding simulations without H2O molecules (dry state) and with 1000 H2O molecules (humid atmosphere) at the sliding interface. The simulation box had an orthorhombic structure whose size was Lx = 217–218 Å, Ly = 11–12 Å, and Lz = 600 Å, depending on the surface orientation and sliding direction to be simulated (The detailed values are listed in Table S1). A three-dimensional periodic boundary condition was applied to the simulation box. The height (z-direction) of the lower substrate was 245 Å, whereas that of the upper substrate was 200 Å. A half cylinder shape asperity with a height of 40 Å was introduced on the upper substrate to model the true contact area of the surfaces. The size corresponds to the minimum length scale of the contact junction found in experiments [20]. The lattice parameter of BCC iron was 2.866 Å. In the sliding simulation, the Fe atoms on the lowermost part of the lower substrate were fixed, whereas the Fe atoms on the topmost part of the upper substrate slid at 100 m/s in the x-direction with a normal load of 1 GPa (normal force divided by the area of xy-plane) in the z-direction. We used the normal load of 1 GPa which is rather higher than typical Hertzian contact pressure. The contact pressure is not uniform at the sliding interface due to the surface roughness; contact pressure is high in some regions whereas it is lower in other regions. In this work, we focus on the high contact pressure region, because the adhesive wear severely occurs in the high contact pressure region. The time step of 1.0 and 0.25 fs was used in the MD simulations for dry state and humid atmosphere, respectively. The Langevin thermostat was applied only to atoms with a thickness of 10 Å next to the fixed and slid regions to consider the effects of frictional heat generated at the true contact area. The dumping parameter was 1 ps–1. The temperature of the thermostat was 300 K. For each condition, we performed three sliding simulations with different initial atomic coordinates and velocities to check repeatability. The ReaxFF was used with a parameter set developed by Shin et al. [21] This parameter set can reproduce the interatomic interaction between Fe, O, and H atoms [21], as well as the mechanical properties of iron correctly [22]. To fairly compare the dry and humid state, we employed ReaxFF for both dry and humid state simulations, though EAM which is widely used in the simulation of metals is also applicable for dry state. In the structural analysis, we identified a chemical bond between two atoms when the bond order between the two atoms was greater than 0.45. The shear stress (σxz) was obtained as the xz-component of the stress tensor σab,

$${\sigma }_{\alpha \beta } = \frac{1}{V} \left(\sum_{i}^{N}{m}_{i}{v}_{i}^{\alpha }{v}_{i}^{\beta } + \frac{1}{2}\sum_{i}^{N}\sum_{j>i}^{N}{r}_{ij}^{\alpha }{F}_{ij}^{\beta }\right)\phantom{xx}\mathrm{ \alpha },\upbeta =\mathrm{ x},\mathrm{ y},{\text{z}}$$
Fig. 1
figure 1

a Sliding simulation models. Gray, red, and cyan balls indicate Fe, O, and H atoms respectively. The insets show the enlarged picture of the contact junction. b Sliding surface (yellow plane) and sliding direction (red arrow) analyzed in this work

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All simulations were performed using an in-house MD code. The simulation results were visualized using OVITO [23].

3 Results and Discussion

First, we investigated the atomic-scale adhesive wear mechanism of a nascent iron surface in the dry state. Figure 2 shows snapshots of the sliding simulation of the (110) surface colored by atomic strain [24]. The time evolution of the shear stress is shown in Fig. 3. The shear stress obtained by three independent simulations with different initial conditions are shown in Figure S1. Snapshots of the sliding simulation colored by the crystal structure are also shown in Figure S2. In the (110)/\([1\overline{1}1]\) case (Fig. 2(a)), a deformation band was formed along the {110} plane, as well as along the {112} plane (34 ps). Then, the surface gradually deformed with slip along the {110} plane in the < 111 > direction, which is a typical slip system of BCC crystals. Consequently, the asperity smoothened and severely adhered to the lower surface. The shear stress analysis showed that the asperity yielded with a shear stress of 1.8 GPa at 33 ps (Fig. 3(a)). No crack generation was observed during this process. In the (110)/\([1\overline{1}0]\) case, a similar trend was observed (Fig. 2(b)) as in the (110)/\([1\overline{1}1]\) case. The asperity yielded with a shear stress of 2.3 GPa at 29 ps (Fig. 3b). In contrast, a different behavior was found in the (110)/[001] case. Here, several deformation bands were formed along the {112} plane (28 ps) (Fig. 2(c)). Then, the surface fractured with the formation of cracks along the {112} plane in the lower substrate adjacent to the contact junction and the bottom part of the asperity in the upper substrate (50 ps). Severe deformation of the surface was not observed in this case, in contrast to the (110)/\([1\overline{1}1]\) and (110)/\([1\overline{1}0]\) cases. The crystal structure analysis (Figure S2(c)) showed that the substrate slightly deformed by twinning (28 ps). The shear stress increased up to 2.4 GPa at ~ 24 ps, then slightly dropped due to twinning. Subsequently, the shear stress continuously increased (Fig. 3c). Finally, the surfaces fractured at 40 ps with a maximum shear stress of 3.0 GPa.

Fig. 2
figure 2

Snapshots of the sliding simulation in dry state for a (110)/\([1\overline{1}1]\), b (110)/\([1\overline{1}0]\), and c (110)/[001] cases. Atoms are colored according to the shear strain

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Fig. 3
figure 3

Time evolution of shear stress (σxz) in sliding simulation in dry state for a (110)/\([1\overline{1}1]\), b (110)/\([1\overline{1}0]\), and c (110)/[001] cases

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Figures 4 shows snapshots of the sliding simulation of the (100) surface colored by the atomic strain. The time evolution of the shear stress is shown in Fig. 5. The shear stress obtained by three independent simulations with different initial conditions are shown in Figure S3. Snapshots of the sliding simulation colored by the crystal structure are also shown in Figure S4. In the (100)/[011] case, the surface gradually deformed with slip along the {112} plane in the < 111 > direction, which is a typical slip system of BCC crystals (Fig. 4a). Crystal structure analysis showed that twins were also formed (Figure S4(a)). No notable crack generation was observed. The asperity yielded with a shear stress of 2.3 GPa at ~ 22 ps (Fig. 5a). In contrast, in the (100)/[010] case, both the upper and lower surfaces fractured with crack generation along the {110} plane. The crack propagated to the bulk region and then turned its direction to the surface; as a result, square wear debris was formed. No severe deformation of the surface was observed. Twinning was also not observed in this process (Figure S4(b)). The substrate fractured at 26 ps with a maximum shear stress of 2.8 GPa (Fig. 5(b)). We note that the shear stress transiently has negative value at ~ 60–90 ps. In this duration, the wear particles jumped out of the surface. This jump can cause the force in + x-direction transiently. Thus, shear stress has negative value.

Fig. 4
figure 4

Snapshots of the sliding simulation in dry state for a (100)/[011] and b (100)/[010] cases. Atoms are colored according to the shear strain

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Fig. 5
figure 5

Time evolution of shear stress (σxz) in sliding simulation in dry state for a (100)/[011] and b (100)/[010] cases

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In the sliding simulation for dry state, we observed two adhesive wear types. One is that the wear accompanies the surface deformation found in the (110)/\([1\overline{1}1]\), (110)/\([1\overline{1}0]\), and (100)/[011] cases (Figs. 2(a,b), and 4(a)). In this wear type, the asperities deformed by slip; consequently, the asperities smoothened and adhered severely to the counter surface. Severe adhesion can lead to seizures. The other is that the wear accompanies the surface fracture found in the (110)/[001] and (100)/[010] cases (Figs. 2(c) and 4(b)). In this wear type, surface deformation did not occur, and thus shear stress increased up to ~ 3 GPa; as a result, the surfaces fractured with sudden crack generation. Surface fractures can lead to wear debris formation. This notable difference in wear type is due to the anisotropy of the mechanical properties of BCC iron. Wear with surface deformation occurs when the deformation by slip is favorable (Fig. 2(a), 2(b), and 4(a)), whereas wear with surface fracture occurs when the slip is unfavorable (Fig. 2(c) and 4(b)). These two types of adhesive wear have been previously reported in several friction experiments [9, 10, 25, 26], although the critical condition that determines the adhesive wear type is still under debate. Aghababaei et al. reported that the adhesive wear type is determined by the size of the contact junction; the contact junction which is smaller than critical length scale shows the wear with surface deformation, whereas the contact junction which is larger than critical length scale shows the wear with surface fracture [20]. A later study by Brach et al. reported that the adhesive wear type is determined not only by the ductility but also by the morphological features of the contact surface [27]. In this study, we proposed that the surface orientation and sliding direction are also crucial factors that determine the adhesive wear type. Here, we note that the dependency of the wear type on the surface orientation and sliding direction can be affected by the size of contact junction. If the asperity size is large enough, the wear with surface deformation become unfavorable for any surface orientation and sliding direction because the energy required for the shear deformation increases as the area of the deformation section increases. Therefore, the wear with surface fracture become favorable for any surface orientation and sliding directions in large scale. This idea is consistent with the aforementioned results by Aghababaei et al.; a contact junction which is larger than critical length scale shows the wear with surface fracture [20]. We also note that, in our simulations, upper and lower substrates have same surface orientation and direction, therefore the structure of both substrates match each other at the contact junction. Here, it is worth to discuss about the non-matching case. In the non-matching case, contact junction has smaller shear strength than matching case, thus slip easily occurs at the contact junction. In consequence, both the wear accompanying the surface deformation and surface fracture can be suppressed.

Next, we performed a sliding simulation in a humid atmosphere to investigate the tribochemical reaction process of Fe and water and their effects on adhesive wear. Here, we focus on the (110) surface because it is the most stable [19]. Three sliding directions were considered: \([1\overline{1}1]\), \([1\overline{1}0]\) and [001], as in the sliding simulations for the dry state (Fig.  1 b). The corresponding results for (100) surface are shown in Supporting Information because they are similar to those for (110) surface (Figure S5–S7). Fig. 6 shows snapshots of the sliding simulations. Snapshots of the sliding simulation colored by the crystal structure are also shown in Figure S8. In the (110)/\([1\overline{1}1]\) case (Fig. 6 (a)), at the initial state (0 ps), Fe surfaces were fully covered with 2–3 water layers (The detailed structure are shown in Figure S9). H2O molecules also existed at the contact area of the surface. In the sliding process (150 ps), water molecules were squeezed out from the contact area of the surfaces. Meanwhile, Fe–OH and Fe–O–Fe groups were formed at the contact area of the surfaces. This indicates that the chemical reaction of H2O molecules and Fe surfaces was induced at the contact area. The Fe–OH and Fe–O–Fe groups remained on the scar of the lower surface (150–250 ps). No severe surface deformation or crack generation, which were observed in the sliding simulations in the dry state, were observed. Similar trends were also observed in the (110)/\([1\overline{1}0]\) and (110)/[001] cases. These results show that the water at the sliding interface suppresses adhesive wear regardless of the adhesive wear type.

Figure 7 shows the time evolution of the number of H2O molecules, Fe–OH groups, and Fe–O–Fe groups in the sliding simulation. As the sliding simulation proceeded, the water molecules gradually decreased, whereas the number of Fe–OH groups and Fe–O–Fe groups gradually increased. This result indicates that Fe–OH groups and Fe–O–Fe groups were formed by tribochemical reactions of H2O molecules and the Fe surface.

Fig. 6
figure 6

Snapshots of the sliding simulation in humid state for a (110)/\([1\overline{1}1]\), b (110)/\([1\overline{1}0]\), and c (110)/[001]. Gray dots indicate the Fe atoms. Blue, yellow, and red balls indicate the O atoms in H2O molecules, Fe–OH groups, and Fe–O–Fe groups, respectively

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Fig. 7
figure 7

Time evolution of the number of H2O molecules (blue), Fe–OH groups (green), and Fe–O–Fe groups (red) in the sliding simulation for a (110)/\([1\overline{1}1]\), b (110)/\([1\overline{1}0]\), and c (110)/[001] cases. Error bars indicate the standard deviation evaluated with the simulation data obtained by three independent simulations with different initial conditions

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Previous experiments have shown that the wear amount of iron decreases as the relative humidity increases [7, 17]. The simulation results above can explain this wear protection mechanism in humid atmospheres. Tribochemical reactions with water generate Fe–OH and Fe–O–Fe groups on the scar. They passivate the nascent Fe surfaces and suppress adhesion. Consequently, the wear accompanying surface deformation and wear accompanying surface fracture were suppressed. Therefore, we propose that the humid atmosphere reduces the wear amount of iron because surface passivation formed by the tribochemical reaction with water suppressed the adhesion of the surfaces.

4 Conclusion

In this study, we investigated the atomic-scale adhesive wear mechanism of BCC iron to improve the adhesive wear resistance of steel with an MD-based sliding simulation using ReaxFF. The effects of surface orientation, sliding direction, and chemical reaction with water were analyzed. In the sliding simulation for dry state, we observed two adhesive wear types. One is the wear accompanying surface deformation found in the (110)/\([1\overline{1}1]\), (110)/\([1\overline{1}0]\), and (100)/[011] cases. The other is the wear accompanying the surface fracture found in the (110)/[001] and (100)/[010] cases. In the former type, the surface asperities gradually deform owing to slip and severely adhere, leading to seizure. In the latter type, the surfaces fracture with crack generation, leading to wear debris formation. We propose that the surface orientation and sliding direction alter the atomic-scale adhesive wear type. Wear with surface deformation occurs when deformation by slip is favorable, whereas wear with surface fracture occurs when slip is not favorable. When water molecules were present at the sliding interface, both types of adhesive wear were suppressed. At the sliding interface, Fe–OH and Fe–O–Fe groups are formed on the scars through the tribochemical reaction with water. They passivate the nascent Fe surface and suppresses adhesion to the counter surface, thereby reducing adhesive wear. Therefore, we conclude that the surface orientation and sliding direction determine the atomic-scale adhesive wear type, whereas a humid atmosphere affects the wear amount at the atomic scale.