Hybrid Atomistic/Continuum Study of Contact and Friction Between Rough Solids

A hybrid simulation method is used to study the effect of atomic structure and self-affine roughness on non-adhesive contact and friction between two-dimensional surfaces. Rough-on-flat and rough-on-rough contact are compared as a function of system size up to several micrometers. In order to contrast elastic and plastic behavior, interactions within the deformable substrate are either harmonic or Lennard-Jones. The ratio of lattice constants in the solids is varied to examine the effect of commensurability. In all cases the true area of contact rises linearly with load, but the slope is much larger than expected from continuum calculations. These calculations considered a continuous distribution of surface heights that is appropriate for large scales, rather than the discrete height distribution of the crystalline surfaces used here. The ratio of contact area to load depends on the ratio of lattice constants in the solids and varies with system size in small systems that deform plastically. While some dislocations are observed, plasticity is dominated by an asperity flattening mechanism where surface atoms are displaced into a lower layer. The kinetic friction rises linearly with load and is independent of system size, as predicted by Amontons's laws. Variations in friction with commensurability are smaller for rough surfaces than for flat surfaces, because most of the contact area is in small patches. Asperity flattening increases patch sizes and thus the effect of commensurability on friction. Rough-on-rough contact leads to additional friction associated with the local slope of the contacting regions.