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. 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(sigma sigma)(r) with the following argument: the radius of characteristic contact patches, r(c), cannot be so large that G(sigma sigma)(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.