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

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

Tribology International 111 (2017) 52–56 Contents lists available at ScienceDirect Tribology International journal homepage: /locate/triboint E?ect of ?ne-scale roughness on the tractions between contacting bodies Junki Joea,?, M. Scaraggib, J.R. Barbera a Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA b DII, Universitá del Salento, 73100 Monteroni-Lecce, Italy MARK ARTICLE INFO Keywords: Contact mechanics Surface roughness Adhesion ABSTRACT Perssons theory for the elastic contact of rough surfaces is modi?ed to include the compliance associated with an interface force law such as the Lennard-Jones law. We determine the e?ect of adding a small packet of waves on the probability distribution function [PDF] of the local interfacial gap (including the e?ect 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 modi?ed interfacial force law describing the in?uence of just the ?ne-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 modi?ed interface energy. 1. Introduction Surfaces are rarely atomically smooth and numerous authors have attempted to predict the e?ect of surface roughness on the contact of nominally plane surfaces. Many of these theories are based on models of the roughness as a set of non-in