The accurate calculation of real contact area between rough surfaces is a key issue in tribology. In this paper, based on the geometrical information of total contact area and the number of contact patches with respect to surface separation, a new method is proposed to determine the relation between real contact area and normal load. The contact of rough surfaces is treated as an accumulation of equivalent circular contacts with varying average contact radius. For a realistic range of separation, the proposed model predicts a linear relation between real contact area and load, and coincides well with direct finite element calculations. Moreover, this model is general and not confined to isotropic Gaussian surfaces.

The measurement of real contact area between rough surfaces is one of the most challenging problems in contact mechanics and is of importance to understand some physical mechanisms in tribology. Based on the frustrated total internal reflection, a new apparatus is designed to measure the real contact area. For metallic samples with various surface topographies, the relation between normal load and real contact area is measured. The unloading process is firstly considered to distinguish the contribution of elasticity and plasticity in contact of rough surfaces. It is found that both elasticity and plasticity are involved throughout the continuous loading process, different from some present understanding and assumptions that they play at different loading stages. A quantitative parameter is proposed to indicate the contribution of plasticity. The present work not only provides an experimental method to measure real contact area but figures out how elastic and plastic deformation works in contact of rough surfaces.

In this paper, an incremental equivalent contact model is developed for elastic-perfectly plastic solids with rough surfaces. The contact of rough surface is modeled by the accumulation of circular contacts with varying radius, which is estimated from the geometrical contact area and the number of contact patches. For three typical rough surfaces with various mechanical properties, the present model gives accurate predictions of the load-area relation, which are verified by direct finite element simulations. An approximately linear load-area relation is observed for elastic-plastic contact up to a large contact fraction of 15%, and the influence of yield stress is addressed.

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Classical laws of friction suggest that friction force is proportional to the normal load and independent of the nominal contact area. As a great improvement in this subject, it is now widely accepted that friction force is proportional to the real contact area, and much work has been conducted based on this hypothesis. In present study, this hypothesis will be carefully revisited by measuring the friction force and real contact area in-site and real-time at both normal loading and unloading stages. Our experiments reveal that the linear relation always holds between friction force and normal load. However, for the relation between friction force and real contact area, the linearity holds only at the loading stage while fails at the unloading stage. This study may improve our understanding of the origin of friction.