Micro and macro contact mechanics for interacting asperities

Contact of rough surfaces at micro and macro scales is studied in this paper. The asperities at micro scale are characterised by small radius of curvature whereas the waviness is characterised by large radius of curvature. When two rough surfaces come in contact, on the micro scale, of asperities contacts in a very small area leave large gaps between the surfaces; whereas on the macro scale the surfaces conform to each other under the application of load without gaps. Contact at micro scale is modelled by superposition of Hertzian stress fields of individual asperity contacts and the waviness at macro scale is modelled as a mixed boundary problem of rough punch indentation where displacements of uneven profile are prescribed along the region of contact. In both the cases for simplification the roughness is assigned to one surface making the other surface perfectly flat an assumption often made in contact mechanics of rough bodies. The motivation for modelling the asperities at micro scales comes from the preliminary results obtained from photoelastic experiments. Numerical results are presented based on the analytical results available for Hertzian contacts. The motivation for modelling the asperities at macro scales comes from the results available in literature for flat contacts from solving mixed boundary elasticity problems. A condition of full stick is assumed along the contact which is a common assumption made for rough contacts. The numerical results are presented for both the cases of rough contact at micro and macro scales.