Probing Friction-Wear Coupling Across Scales: Molecular Dynamics Insights from K/μ

Abstract

At engineering scales, Amontons–Coulomb friction (with coefficient of friction μ) and Archard wear (with wear coefficient K) can be treated as coupled under standard assumptions. Whether this coupling survives downscaling, however, remains unclear. We develop a composite diagnostic, K/μ, that algebraically links Archard’s and Amontons–Coulomb’s forms through K/μ ≈ VH/W, where V is wear volume, W is the work of friction, and H is hardness. The construct removes explicit normal-load scaling and enables a joint self-consistency check of the two laws at the nanoscale. We then test it using molecular dynamics simulations of aluminum films indented and abraded by three rigid diamond asperities, spanning asperity spacing (close, intermediate, and wide) and speed (2.5–100 m/s). The parameters respond differently to configuration and speed: apparent hardness increases with spacing and with speed; wear volume is weakly speed-dependent but peaks at intermediate spacing; and the work of friction grows with speed and spacing yet does not mirror the wear ordering. The friction coefficient remains in a narrow band (1.0–1.4) across conditions, while the wear coefficient varies by five times. The resulting K/μ magnitudes lie in the 0.2–1.0 range. Compared with laboratory-scale bands, these nanoscale K/μ values are considerably larger, suggesting that the classical friction–wear coupling does not carry over unchanged to multi-asperity nanoscale contacts.