Contact of rough surfaces: Modeling adhesion in advanced multiasperity models

Surface roughness affects several tribological phenomena and in particular adhesion. For many years, multiasperity models have been the most used in the study of rough contacts notwithstanding their evident limitations. In this work, we propose a fair assessment of improved asperity models with adhesion modeled according to the Derjaguin, Muller and Toporov theory, which assumes attractive forces do not deform the surface profiles. Results are given for three enhanced asperity models: the discrete Greenwood and Williamson model, where the effective heights and curvatures of the surface asperities are used rather than a statistical description; the interacting Hertzian asperities model, where the elastic coupling effects are included; the interacting and coalescing Hertzian asperities model, where the coalescence of contact spots is also conveniently considered. A comparison with advanced contact mechanics theories shows that only the interacting and coalescing Hertzian asperities model correctly captures the physics of the problem at all roughness scales.