Partial-slip frictional response of rough surfaces.

If two elastic bodies with rough surfaces are first pressed against each other and then loaded tangentially, sliding will occur at the boundary of the contact area while the inner parts may still stick. With increasing tangential force, the sliding parts will expand while the sticking parts shrink and finally vanish. In this paper, we study the fractions of the contact area, tangential force and tangential stiffness, associated with the sticking portion of the contact area, as a function of the total applied tangential force up to the onset of full sliding. For the numerical analysis randomly rough, fractal surfaces are used, with the Hurst exponent H ranging from 0.1 to 0.9. Numerical simulations by boundary element method are compared with an analytical analysis in the framework of the Greenwood and Williamson (GW) model. In both cases, a universal linear dependency between the real contact area fraction in stick condition and the applied tangential force is found, regardless of the Hurst exponent of the rough surfaces. Regarding the dependence of the differential tangential stiffness on the tangential force, a linear relation is found in the GW case. For randomly rough surfaces, a nonlinear relation depending on H is derived.