Previous researches [25, 26] demonstrate that DZ2 steel of axle material and D2 steel of wheel material belong to facecentered cubic lattice (FCC), and their lattice constants are a = b = c = 3.43 mm and α = β = γ = 90°. Therefore, Fe matrix is extended based on the facecentered lattice under this parameter. Fe atoms have been randomly replaced in the matrix according to the material composition in Table 1 to complete the doping in DZ2 and D2 steel alloys. The final molecular dynamics model is shown in Fig. 1.
Table 1
Material

DZ2

D2

C
Si
Mn
P
S
Cr
Mo
Ni

0.24 ~ 0.32
0.20 ~ 0.40
0.60 ~ 0.90
≤ 0.01
≤ 0.01
0.90 ~ 1.20
0.20 ~ 0.30
0.50 ~ 1.50

0.48 ~ 0.58
0.65 ~ 0.80
≤ 0.015
≤ 0.015
≤ 0.030
≤ 0.08
≤ 0.030
≤ 0.016

The whole model is divided into three parts: fixed layer, thermostat and free layer, as demonstrated in Fig. 1. In the present model, the boundary layer fixed model does not move in the y direction. Therefore, the y direction is an aperiodic boundary, and the x and z directions are periodic boundaries. The thermostat is used to adjust the ambient temperature of the system, whereas the initial temperature is set at 300 K. The free layer moves in accordance with Newton's law of motion, and the data needed for the microfriction of wheel and axle are then obtained. A rough peak with height of 20.58 Å was established in the free layer to simulate the fretting wear process. The microcanonical ensemble, also known as NVE ensemble, is selected for the simulation of the working condition between the wheel and axle. This way, the whole system has no energy and particle exchange with the outside world.
EAM is suitable for intermetallic molecular dynamics simulation [27]. In this paper, EAM is used for relaxation processing to accurately characterize the interactions between atoms in the alloy under stable state. The EAM potential function is shown in Eq. (1) [14]:
$$E=\frac{1}{2}\sum\nolimits_{{i=1}}^{N} {\sum\nolimits_{{j=1 \ne i}} {{\varphi _{ij}}({r_{ij}})+} } \sum\nolimits_{{i=1}}^{N} {{F_i}({\rho _i})}$$
1
Where E represents the sum of potential energy between atoms, φij represents the pair potential of interatomic interaction, rij represents the distance between atoms, Fi is the energy required when atom i is embedded into the position of electron density unit 1, and ρi shows the local electron density generated by all atoms in the system at the position of atom i.
LennardJones (LJ) potential consists of a simple structure with high calculation efficiency. It can simultaneously calculate the interaction force between the two interfaces with high calculation efficiency[28]. Hence, LJ potential has been used in this paper to represent the interaction force between wheel and axle. The potential function form of LJ method is shown in Eq. (2) [28]:
$${U_{LJ}}(r)=4\varepsilon [{(\frac{\sigma }{r})^{12}}  {(\frac{\sigma }{r})^6}]$$
2
where, ULJ represents the sum of potential energy between atoms, ε is the potential well depth that reflects the strength of the interaction between two atoms, σ is the fixed distance between atoms when the interaction potential is equal to zero, and r is the distance between two atoms at any instance.
According to the addition and subtraction properties of Eq. (2) regarding r, an increase in r to a certain value leads the potential energy of LJ to zero. The distance at this point is known as truncation radius rc. This phenomenon occurs when the distance between the analyzed atom and the observed atom is greater than rc. Due to the relatively greater spacing between atoms as compared to the truncation radius, the interaction force becomes insignificant [29]. Hence, the force between the two atoms is not calculated. The truncation radius rc is calculated to be 11 Å, according to the atomic parameters of wheel and axle material [29].