Mechanical contact between rough surfaces at low load

A model is developed to describe the initial contact between rough surfaces. The Greenwood-Williamson statistical approach is used with exponential or Weibull asperity height distributions, and modified with the relative displacement between the surfaces referenced to the initial contact of the highest asperity (within a given area) at zero load. This form provides a framework for investigating contact at low loads or contact over small area e.g. as found in microfabricated structures. The approach gives the expected number of asperities touching, the real area of contact and the normal force in terms of the indentation. The model results show that for hard surface materials (e.g. Silicon), very few asperities may be in contact at low loads (∼1 µN) even over large nominal surface areas (∼20 × 20 µm2), in accordance with observations drawn from microfabrication experiments. This suggests an analytical means to bridge nanoscale concepts and approaches (e.g. superlubricity, friction at a single asperity) to microscale structures.