Stick-slip boundary friction mode as a second-order phase transition with an inhomogeneous distribution of elastic stress in the contact area

Abstract

This article presents an investigation of the dynamical contact between two atomically flat surfaces separated by an ultrathin lubricant film. Using a thermodynamic approach we describe the second-order phase transition between two structural states of the lubricant which leads to the stick-slip mode of boundary friction. An analytical description and numerical simulation with radial distributions of the order parameter, stress and strain were performed to investigate the spatial inhomogeneity. It is shown that in the case when the driving device is connected to the upper part of the friction block through an elastic spring, the frequency of the melting/solidification phase transitions increases with time.

Keywords: boundary friction; dimensionality reduction; numerical simulation; shear stress and strain; stick–slip motion; tribology.

Figure 1

Geometrical scheme of the system under investigation. Stamp of a cylindrical shape with radius a₀, made of material with shear modulus of G₂ and Poisson ratio v₂, placed over the material with elastic parameters G₁,v₁. Upper and lower friction blocks are separated by a layer of lubricant with thickness h₀.

Figure 2

(a) Kinetic dependence of the friction force F_x(t), calculated at parameters τ^max = 10⁶ Pa, = 1.0, a = 10⁶ Pa, h₀ = 10⁻⁷ m, γ = 10 (Pa·s)⁻¹, a₀ = 2·10⁻⁵ m, G* = 10⁹ Pa, K = 500 N/m, m = 0.1 kg, V₀ = 1 m/s. (b) Spatial distribution of the order parameter φ(r) in the moment of time t = 1.3 ms, related to final point of the dependence shown in Figure 2a. (c) Time dependence of the mean values of the order parameter <φ> (solid line) and elastic strain <ε_el> (dashed line). (d) Spatial distribution of the elastic strain ε_el(r) at t = 1.3 ms.

Figure 3

(a) Time dependence of the order parameter φ(t), calculated using the same parameters as in Figure 2 and corresponding to the melting process (arrow 1) before the first dashed line and to the recrystallization process (arrow 2) after the first dashed line for different values of the radial coordinate r. Arrows show the increment of a radial coordinate r from 2 to 18 μm, with a step of 2 μm. Inset shows the time interval between two dashed lines.

Figure 4

(a) Time dependence of the friction force F_x (Equation 16) using the parameters of Figure 2 and an increasing temperature according to Equation 18 using the parameters A₀ = 1.5·10⁶ Pa and s. (b) Mean values of the order parameter <φ> and elastic strain <ε_el> are according to the parameters of Figure 4a.

Figure 5

(a) Dependence of the friction force F_x on the stamp coordinate X (upper friction surface), corresponding to Figure 2a. (b) Dependence of the friction force F_x on the stamp coordinate X, corresponding to Figure 4a.