Role of interfacial adhesion on minimum wear particle size and roughness evolution

Adhesion between two bodies is a key parameter in wear processes. At the macroscale, strong adhesive bonds are known to lead to high wear rates, as observed in clean metal-on-metal contact. Reducing the strength of the interfacial adhesion is then desirable, and techniques such as lubrication and surface passivation are employed to this end. Still, little is known about the influence of adhesion on the microscopic processes of wear. In particular, the effects of interfacial adhesion on the wear particle size and on the surface roughness evolution are not clear and are therefore addressed here by means of molecular dynamics simulations. We show that, at short timescales, the surface morphology and not the interfacial adhesion strength dictates the minimum size of wear particles. However, at longer timescales, adhesion alters the particle motion and thus the wear rate and the surface morphology.

Figure 1

Short timescale evolution. Starting from the same geometry (a), two different scenarios can develop. Either a well-defined debris particle is formed [Scenario 1, (b), full-adhesion simulation], or the effective contact spreads throughout the interface. In the latter case (Scenario 2), the system attempts to create a debris particle comparable in size with $l_x$ [(c), simulation with $\tilde{\gamma }=0.8$], or even larger, which results in welding of the interface within the simulated box size and damage initiating near the boundaries [(d), simulation with $\tilde{\gamma }=0.6$]. In all panels colors distinguish atoms originally belonging to the top (light blue) and bottom (dark blue) surfaces. Atoms that at some previous instant were detected as surface atoms and reassigned to the interfacial potential are depicted in yellow. Black lines represent simulation box boundaries and $s$ is the sliding distance in units of $r_0$. Frame (b) is from simulation S-100-01 (see Supplemental Material Table S.I), frame (c) is from simulation S-080-01 (see Supplemental Material Table S.II), and frame (d) is from simulation S-060-01 (see Supplemental Material Table S.III).

Figure 2

Scenario 1: debris particle formation and initial volume $V_0$. (a–c) The surfaces, initially self-affine (a), come into contact at multiple points (b) and a peak in the tangential force $F_{\mathrm{t}}$ is recorded (d). Upon further sliding, the contact junction is large enough to generate a debris particle, whose formation is over (c) when the first local minimum of the tangential force $F_{\mathrm{t}}$ is reached (d). At this moment the initial debris particle volume $V_0$ is measured (d). (d) Recorded tangential force $F_{\mathrm{t}}$ (black triangles), measured debris particle volume $V$ (blue circles) and measured initial debris particle volume $V_0$ (large orange circle) during a simulation that exhibits Scenario 1. In panels (a–c) colors distinguish atoms originally belonging to the top (light blue) and bottom (dark blue) bodies; in panels (b, c) colors further identify atoms that at some previous instant were detected as surface atoms and reassigned to the interfacial potential (yellow) and atoms detected as belonging to the debris particle (red); in panels (a–c) black lines represent simulation box boundaries. In all panels $s$ is the sliding distance expressed in units of $r_0$. In panel (d), the volume $V$ and the tangential force $F_{\mathrm{t}}$ are expressed in units of $r_0^2$ and $\varepsilon r_0^{-1}$, respectively. Snapshots in panels (a–c) and data in panel (d) are from the reduced-adhesion simulation S-060-32 (see Supplemental Material Table S.III [28]).

Figure 3

Effect of interfacial adhesion $\tilde{\gamma }$ and surface morphology on the initial debris particle volume $V_0$. In all cases $V_0$ is larger than the minimum size $V_{0,\min }^{*}$ determined by the material critical length scale (solid purple line). The actual value $V_0\ge V_{0,\min }^{*}$ is controlled by the random morphology. No statistically significant increase in the minimum $V_0$ is observed when the interfacial adhesion decreases, as would be expected by a corresponding reduction in the junction shear strength (green shaded area). The green dotted line corresponds to $V_0^{*}({\mathrm{\Lambda }}_{\min },\tilde{\gamma })$ and the green dashed line to $V_0^{*}({\mathrm{\Lambda }}_{\max },\tilde{\gamma })$. Each symbol identifies a unique initial surface roughness in terms of root-mean square of heights $\sigma$: $\sigma =5r_0$ (black circles), $\sigma =10r_0$ (light blue squares), and $\sigma =20r_0$ (orange triangles). One data point ($\tilde{\gamma }=1.0, V_0=40339r_0^2, \sigma =5r_0$) is not represented for readability. The root-mean square of heights $\sigma$ and the volume $V_0$ are expressed in units of $r_0$ and $r_0^2$, respectively.

Figure 4

Long timescale evolution and effect of adhesion on debris particle motion. (a, b) Full adhesion, $\tilde{\gamma }=1.0$ (frames from simulation L-100-A, see Supplemental Material Table S.IV [28]). Upon sliding, contacts develop at multiple spots and grow, until cracks develop and a debris particle is formed (a). The particle then rolls between the two surfaces, wearing them and growing significantly in size (b). (c–f) Low adhesion, $\tilde{\gamma }=0.6$ (frames from simulation L-060-A, see Supplemental Material Table S.IV [28]). Starting from the same geometry of the full-adhesion simulation of panels (a, b), upon sliding a debris particle is formed (c). This is constrained between the two surfaces and, because of the reduced interfacial adhesion and perhaps counterintuitively, it can stick for long times to one of the surfaces [e.g., the bottom one in (d)], the opposing surface sliding against the particle. The particle is gradually pushed into a valley (e) and, after a sticking time [where $\mathrm{\Delta }{s}_{\mathrm{t}}/\mathrm{\Delta }s\approx 0.0$, see arrow and (g)], it detaches again with a fracture event in a two-body like configuration (f). (g) Distance $s_{\mathrm{t}}$ traveled by the debris particle as a function of the sliding distance. For full and intermediate adhesion simulations (i.e., $\tilde{\gamma }=1.0$ and $\tilde{\gamma }=0.8$), the particle rolls most of the time. For low adhesion cases ($\tilde{\gamma }=0.6$), the particle undergoes long times of sticking to one surface (and sliding against the other). These periods are characterized by $\mathrm{\Delta }{s}_{\mathrm{t}}/\mathrm{\Delta }s\approx 0.0$ and $\mathrm{\Delta }{s}_{\mathrm{t}}/\mathrm{\Delta }s\approx 1.0$ (see arrows). In panels (a–f) colors distinguish atoms originally belonging to the top (light blue) and bottom (dark blue) surfaces. Atoms that at some previous instant were detected as surface atoms and reassigned to the interfacial potential are depicted in yellow. In panels (a–f), black lines represent the boundaries of the simulation box. Both the sliding distance $s$ (panels a–g) and the traveled distance $s_{\mathrm{t}}$ (panel g) are expressed in units of $r_0$. See Supplemental Material Fig. S.3 [28] for data of $s_{\mathrm{t}}$ for further simulations.

Figure 5

Surface morphology analysis. (a) PSD per unit length $\mathrm{\Phi }$ as a function of the wave vector $q$ and the wavelength $\lambda$, where $q=2\pi /\lambda$. (b) Height-height correlation function $\mathrm{\Delta }h\left(\delta x\right)={\langle {\left[h(x+\delta x)-h\left(x\right)\right]}^2\rangle }^{1/2}$. The surfaces are taken from the top (“T”) bodies of different simulations with different values of interfacial adhesion $\tilde{\gamma }$ and system sizes (see Supplemental Material Table S.IV for details [28]). While top surfaces of the full-adhesion simulation (L-100-X, see Supplemental Material Table S.IV [28]) and of the simulation with $\tilde{\gamma }=0.8$ (L-080-X, see Supplemental Material Table S.IV [28]) display a self-affine morphology, this is not observed for the top surface of the simulation with $\tilde{\gamma }=0.6$ (simulation L-060-C, see Supplemental Material Table S.IV [28]). In this case the particle traveled a longer distance $s_{\mathrm{t}}$ but did not roll for most of the simulation [see Fig. 4]. In both panels the solid black straight guide-line corresponds to a Hurst exponent $H=0.7$. Dotted black straight guide-lines show the hypothetical slope for distributions of $H=0.5$ and $H=1.0$. Data for all the other surfaces are reported in Supplemental Material Fig. S.2 [28]. In panel (a), the PSD per unit length $\mathrm{\Phi }$, the wave vector $q$ and the wavelength $\lambda$ are expressed in units of $r_0^3, r_0^{-1}$ and $r_0$, respectively. In panel (b), both the height-height correlation function $\mathrm{\Delta }h$ and the horizontal distance $\delta x$ are expressed in units of $r_0$.

Figure 6

Evolution of the equivalent roughness ${\sigma }_{\mathrm{eq}}$ and of the wear volume $V$. (a) Evolution of ${\sigma }_{\mathrm{eq}}$ for the simulations in set L (see Supplemental Material Table S.IV [28]). For simulations with $\tilde{\gamma }=1.0$ and $\tilde{\gamma }=0.8, {\sigma }_{\mathrm{eq}}$ decreases until a steady-state is reached, where possible fluctuations due to local events can take place. For simulations with $\tilde{\gamma }=0.6$, the steady-state is not always reached, e.g., simulation with $\tilde{\gamma }=0.6$ (simulation L-060-D, see Supplemental Material Table S.IV [28]), because of the long sticking times (see also Fig. 4). (b) Evolution of the wear volume $V$ of the rolling debris particle, as defined only after its formation. The simulations with $\tilde{\gamma }=1.0$ display steady growth of the particle volume, while simulations with $\tilde{\gamma }=0.6$ are characterized by a negligible wear rate for most of the sliding distance, and the wear volume significantly increases only through fracturelike brittle events (see Fig. 4). Simulations with $\tilde{\gamma }=0.8$ show an intermediate behavior. In both panels, the sliding distance $s$ is expressed in units of $r_0$. The equivalent roughness ${\sigma }_{\mathrm{eq}}$ (panel a) and the volume $V$ (panel b) are expressed in units of $r_0$ and $r_0^2$, respectively. Further simulations are shown in Supplemental Material Fig. S.4 [28].