Microscopic basis of Archard's wear law
In plain words
The amount of material lost by wear grows in proportion to load and sliding distance, but the proportionality constant varies by a factor of a million between materials and cannot be predicted. Its link to what happens at single contacts is unclear.
Precise statement
Archard's law $V = K N s / H$ (wear volume V, load N, sliding distance s, hardness H) has an empirical dimensionless coefficient K spanning roughly $1e-8 \text{ to } 1e-2$. Derive K from asperity-scale mechanisms, including the critical junction size $d*$ proportional to $G w / \tau_j^{2}$ (shear modulus G, surface energy w, junction strength $\tau_j$) below which junctions deform plastically instead of shedding debris, and predict wear rates for specified material pairs.
What would settle it
A multiscale theory predicting K for several metal and ceramic pairs that matches measured wear rates without adjustable parameters.
Status in the literature
Unverified note
Atomistic simulations since 2016 identify a critical junction size for debris formation; quantitative prediction of K for real surfaces is lacking (2026).