Fractal modeling of normal contact stiffness for rough surface contact considering the elastic-plastic deformation

In this work, a new formulation of elastic-plastic contact model for the normal contact between rough surfaces is proposed based on the fractal theory. The surface topography is described using the modified one-variable Weierstrass-Mandelbrot fractal function. A new elastoplastic asperity contact model is developed based on the contact mechanics combined with the continuity and smoothness of mean contact pressure and contact load across different deformation regimes from elastic to elastoplastic, and from elastoplastic to fully plastic. The contact stiffness of a single asperity in the three deformation regimes of fully plastic, elastoplastic and elastic is derived, which changes smoothly at transit points between different deformation modes and overcomes the shortcoming of discontinuity derived from previous model. The contact stiffness and contact load of the whole surface in the three deformation regimes are formulated by integrating the micro-asperity contact. The difference between contact stiffness calculated from the plastic-elastoplastic-elastic three contact regimes and plastic-elastic two contact regimes is not obvious for surface with rougher topograph; however, for surface with smoother topograph, the two contact regimes predict a much smaller contact stiffness. The relationship of the normal contact stiffness and the normal contact force follows a power law function for the fractal surface contact considering three deformation regimes. The power exponent is nonlinearly dependent on the fractal dimension, which is different from the linear relationship for the purely elastic contact.