Normal Contact Model for Elastic and Plastic Mechanics of Rough Surfaces

An elastic and plastic mechanical model is proposed to characterize the normal contact of rough surfaces. The contact process is considered as three separated contact regimes, i.e., the fully elastic, mixed elastic–plastic and fully plastic ones. The Hertzian elastic contact solutions and the classical fully plastic contact model of Abbott and Firestone are used to model the contact behaviors of fully elastically deformed asperities and fully plastically deformed ones, respectively. For the mixed elastic–plastic regime, an improved Hermit interpolation method is applied to enforce the continuity and smoothness at the critical contact interference, and to decrease the interpolation waving effect by transforming the physical quantities of contact load into logarithmic coordinates. The contact model of rough surfaces is formulated by using the Greenwood and Williamson’s statistics analysis. Comparisons with the CEB, ZMC and KE models are then performed to examine the effects of plasticity index and mean separation. Agreeing well with the ZMC model, our results show that the total contact load of rough surfaces decreases with the increase in mean separation, and the difference between the prediction results of elastic models and the plastic ones also decreases, indicating that the contact behaviors mainly dominated by plastically deformed asperities have been changed to be controlled by elastically deformed ones. Larger plasticity index represents more plastically deformed asperities, inducing normal contact behaviors mainly dominated by plastic solutions.