Effect of wear particles and roughness on nanoscale friction

Tobias Brink, Enrico Milanese, and Jean-François Molinari

Phys. Rev. Materials 6, 013606 – Published 12 January 2022

Abstract

Frictional contacts lead to the formation of a surface layer called the third body, consisting of wear particles and structures resulting from their agglomerates. Its behavior and properties at the nanoscale control the macroscopic tribological performance. It is known that wear particles and surface topography evolve with time and mutually influence one another. However, the formation of the mature third body is largely uncharted territory, and the properties of its early stages are unknown. Here we show how a third body initially consisting of particles acting as roller bearings transitions into a shear-band-like state by forming adhesive bridges between the particles. Using large-scale atomistic simulations on a brittle model material, we find that this transition is controlled by the growth and increasing disorganization of the particles with increasing sliding distance. Sliding resistance and wear rate are, at first, controlled by the surface roughness, but upon agglomeration wear stagnates and friction becomes solely dependent on the real contact area in accordance with the plasticity theory of contact by Bowden and Tabor.

Received 7 September 2021
Revised 14 December 2021
Accepted 21 December 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.6.013606

Physics Subject Headings (PhySH)

Friction Roughness Wear

Surfaces

Molecular dynamics

General PhysicsInterdisciplinary PhysicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Tobias Brink ^*, Enrico Milanese^†, and Jean-François Molinari

Civil Engineering Institute and Institute of Materials Science and Engineering, École polytechnique fédérale de Lausanne (EPFL), Station 18, CH-1015 Lausanne, Switzerland

^*Present address: Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Straße 1, D-40237 Düsseldorf, Germany; t.brink@mpie.de
^†Present address: Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

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Vol. 6, Iss. 1 — January 2022

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Images

Figure 1
Early stages of the third body. (a) Particles were introduced between two surfaces and subjected to sliding motion. (b)–(f) show only the third body as it evolves from spherical particles in (b), to cylindrical rollers in (c) and (d), to a porous, shear-band-like state in (e) and (f). Atoms are colored according to the body they originally belonged to, namely, the top surface (red), bottom surface (yellow), third body (gray), or boundary (blue). The box indicates the periodic boundaries, and atoms are shown outside if that makes the shape of the particle clearer. The sliding direction is indicated in (b).
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Figure 2
Influence of roughness on friction. (a) In Bowden and Tabor's model, friction is due to the real contact area $A_{c} \propto F_{N}$ . The proportionality is a consequence of the fractal nature of the surface roughness, where more asperities come into contact with increasing load. (b) When the system includes wear particles, this simple proportionality is insufficient to explain the friction force, which now also depends on the rolling friction of the particles. Nevertheless, there is still a contact area between the third-body particle and the two first bodies, which can lead to friction due to adhesive forces. (c) At least on the nanoscale, the roughness may be large compared to the particle size and therefore increase friction by presenting obstacles in the form of surface asperities to the smooth rolling motion of the particles. Configurations with large asperities should be unstable since the obstacles are worn off (or the particle is reincorporated into the surface). The influence of roughness—i.e., the asperity heights $h$ —has to be related to the particle size, here approximated by the thickness $g$ of the third body.
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Figure 3
Friction force as a function of contact area, roughness, and sliding distance. (a) The friction force plotted over the relative contact area reveals that a direct linear dependence between the two quantities exists only in the shear-band-like regime (SB), while the friction force of the cylindrical rollers does not vary with the contact area for a given normal load or even seems to be slightly negatively correlated. The dashed lines represent fits to the friction law in Eq. (3). (b) The friction of the rollers is instead correlated with the surface roughness divided by the third-body thickness, in accordance with Eq. (1) (solid black line). The light gray lines represent the data from the shear-band-like regime, for which the roughness data are much less reliable. (c) Subtracting the roughness-dependent term of Eq. (1) from the frictional force reveals a linear relation between the remaining partial friction force and the real contact area (solid black line). This explains the apparent, partially negative correlation between $F_{T}$ and $A_{c}$ : When the contact area increases after running in, it is counteracted by the roughness decreasing at the same time. The slope is indirectly related to the friction coefficient $μ_{0}^{r}$ of a flat surface. In (a)–(c) the root-mean-square deviation (RMSD) is provided as a goodness-of-fit measure. (d) The friction laws in this work [Eq. (1), solid lines, and Eq. (3), dashed lines] fit well to the friction force data plotted over the sliding distance. The arrow shows a point in time when two cylinders temporarily stick together, leading to the transient friction peak when the pure rolling motion is disturbed.
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Figure 4
(a) Cumulative wear volume as a function of sliding distance for different normal loads. Parts of the wear volume data are linearly dependent on the sliding distance in the steady-state regime. The slopes, representing the wear rates, however, seem to be comparable for different normal loads. (b) By plotting the wear volume as a function of $F_{N} s / H$ as in Archard's wear equation, the slopes should represent the wear coefficient $k$ , which would be independent of $F_{N}$ in Archard's model. The data show that this is not the case: The slopes are different, and the data do not collapse onto a single curve. (c) In the original derivation of this equation, it is $F_{N} / H = A_{c}$ . Therefore, we also plot the wear volume as a function of the integral over a direct measurement of the contact area but do not obtain a better correlation. (d) However, if we replace the normal load $F_{N}$ by the tangential friction force $F_{T}$ modified by a roughness term $h_{rms} / g$ , we obtain the same linear relation for all curves, including the running-in phase—although excluding the low-wear, shear-band-like regime—with a constant $k^{'} = 0.662$ [see Eq. (6)]. Note that the cylinders in the simulation with $F_{N} = 11.54 μ N$ start spanning across the periodic boundaries at $s = 0.5 μ m$ , forcing a rolling direction at an angle to the sliding direction. This adds a shear component which leads to bidirectional exchange of material between the first and third bodies and reduces the efficiency of the wear process to $k^{'} = 0.176$ . The resulting best fits are also shown in (a) as black lines (solid line for $k^{'} = 0.662$ and dashed line for $k^{'} = 0.176$ ) together with the RMSD as a goodness-of-fit measure for the solid lines.
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