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Contact-Patch-Size Distribution and Limits of Self-Affinity in Contacts between Randomly Rough Surfaces

Department of Materials Science and Engineering, Universität des Saarlandes, 66123 Saarbrücken, Germany
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Lubricants 2018, 6(4), 85; https://doi.org/10.3390/lubricants6040085
Received: 1 August 2018 / Revised: 30 August 2018 / Accepted: 31 August 2018 / Published: 20 September 2018
(This article belongs to the Special Issue Multiphysics and Multiscale Models of Tribology)
True contact between solids with randomly rough surfaces tends to occur at a large number of microscopic contact patches. Thus far, two scaling regimes have been identified for the number density n ( A ) of contact-patch sizes A in elastic, non-adhesive, self-affine contacts. At small A, n ( A ) is approximately constant, while n ( A ) decreases as a power law at large A. Using Green’s function molecular dynamics, we identify a characteristic (maximum) contact area A c above which a superexponential decay of n ( A ) becomes apparent if the contact pressure is below the pressure p cp at which contact percolates. We also find that A c increases with load relatively slowly far away from contact percolation. Results for A c can be estimated from the stress autocorrelation function G σ σ ( r ) with the following argument: the radius of characteristic contact patches, r c , cannot be so large that G σ σ ( r c ) is much less than p cp 2 . Our findings provide a possible mechanism for the breakdown of the proportionality between friction and wear with load at large contact pressures and/or for surfaces with a large roll-off wavelength. View Full-Text
Keywords: surface roughness; contact mechanics; friction; wear; Amontons’ law; Archard’s law surface roughness; contact mechanics; friction; wear; Amontons’ law; Archard’s law
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MDPI and ACS Style

Müser, M.H.; Wang, A. Contact-Patch-Size Distribution and Limits of Self-Affinity in Contacts between Randomly Rough Surfaces. Lubricants 2018, 6, 85.

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