Effect of fine-scale roughness on the tractions between contacting bodies

Persson's theory for the elastic contact of rough surfaces is modified to include the compliance associated with an interface force law such as the Lennard-Jones law. We determine the effect of adding a small packet of waves on the probability distribution function [PDF] of the local interfacial gap (including the effect of elastic deformation). This procedure is then used iteratively to develop an algorithm for determining the PDF for a rough surface with a prescribed power spectral density. The results show that for untruncated quasi-fractal surfaces, the PDF then converges at large wavenumber, in contrast to the result when only elastic deformation is taken into account. If the roughness is restricted to wavenumbers greater than a certain critical value, the algorithm predicts a converged relation between nominal traction and mean gap that can be regarded as a modified interfacial force law describing the influence of just the fine-scale roughness on the contact. In particular, the area under the resulting curve can be interpreted as a measure of interface energy as reduced by this roughness. The remaining macroscopic features of the surface can then be described using the JKR methodology in combination with this modified interface energy.