A three-dimensional fractal model of the normal contact characteristics of two contacting rough surfaces

According to the common characteristics of elastic mechanics and plastic mechanics expressions, a new model of asperity elastic–plastic contact is developed. The proposed model can solve the problem of discontinuous, leap, and non-monotone contact load and mean contact pressure and contact area in three separate phases, i.e., a perfectly elastic phase, elastoplastic phase, and fully plastic phase. The analytical model of normal contact stiffness considering the influence of the contact area distribution of the asperity and the elastoplastic deformation mechanism on the characteristics of the joint surface is further established by the fractal theory. In addition, the input energy of the asperity in the elastoplastic deformation stage is separated into stored energy and dissipated energy by introducing the loading and unloading model of the asperity. The analytical model of normal contact damping considering the deformation process of asperities and the elastoplastic deformation mechanism is further established. The effects of normal contact load, fractal dimension, fractal roughness, and plastic index on the normal contact stiffness and damping of the joint surface are studied by numerical simulation. The comparison of different models shows that the elastoplastic contact deformation mechanism has an obvious effect on the normal contact stiffness and damping. The normal contact stiffness and damping considering the elastoplastic deformation mechanism are greater than the normal contact stiffness and damping considering only the elastic and plastic states. Finally, the rationality of the present model is verified through model comparison and experimental comparison.