Partial slip in mesoscale contacts: Dependence on contact size

Abstract

Using acoustic resonators, we have studied the occurrence and the magnitude of partial slip between glass spheres and polymer surfaces. The measurement relies on the shifts of resonance frequency and bandwidth, Δf and ΔΓ, induced by the contact as well as the dependence of Δf and ΔΓ on the amplitude of oscillation. One often finds a decrease of Δf at elevated amplitudes, which goes back to partial slip (also "microslip"). Building on two different models of partial slip, we derive the frequency-amplitude relation from the force-displacement relation. In accordance with both models, the bandwidth is found to increase with amplitude in the partial slip regime. For the highest amplitudes and largest spheres investigated, one observes a decrease of bandwidth with amplitude, which is interpreted as a transition to gross slip. Deviating from both models of partial slip, Δf is sometimes found to be independent of amplitude in the low-amplitude range. Constant Δf implies linear force-displacement relations. The critical amplitude for the onset of partial slip depends on the contact radius, where partial slip is more pronounced for larger contacts. This finding can be explained by a smooth stress profile at the edge of the contact with no singularity. The stress at the edge might be lowered by nanoscale roughness, by capillary forces, or by the inability of the two surfaces to reestablish a sticking contact at the turning point of the oscillation.