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

True contact between solids with randomly rough surfaces tends to occur at a large number of microscopic contact patches. So 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 Ac 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_σσ (r) with the following argument: the radius of characteristic contact patches, r_c, cannot be so large that G_σσ (r_c) is much less than p_c². 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.