Multi-stage contact model between fractal rough surfaces based on multi-scale asperity deformation

• Multi-stage contact model of interface as variation of contact degree is proposed. • Asperity deformation depends on contact force and shows nonlinearity at length scale. • Each contact stage is distinct as various deformation modes of multi-scale asperities. • Inherent critical contact force between two stages of surface is decided by morphology. A novel multi-stage contact model of fractal rough surfaces is proposed in this paper. Actual asperity deformation depending on contact degree is derived at length scale, based on which, the actual deformation mode of asperity is analyzed. In accordance with deformation modes of multi-scale asperities, the contact behavior of the whole surface is distinguished into five stages as the increment of contact force. A complete model of contact characteristics across multi-stage is established, and the corresponding mathematical analytical solution of each stage is provided. Accordingly, the relationship between contact force, normal stiffness, and real contact area are analyzed under the effects of fractal factors. The simulation results of the developed model are also compared with that of available models and experimental data.