Adhesive Contact on Randomly Rough Surfaces Based on the Double-Hertz Model

Abstract

A cohesive zone model for rough surface adhesion is established by combining the double-Hertz model (Greenwood, J. A., and Johnson, K. L., 1998, “An Alternative to the Maugis Model of Adhesion Between Elastic Spheres,” J. Phys. D: Appl. Phys., 31, pp. 3279–3290) and the multiple asperity contact model (Greenwood, J. A., and Williamson, J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. Lond. A, 295, pp. 300–319). The rough surface is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian distributed heights. By applying the double-Hertz theory to each individual asperity of the rough surface, the total normal forces for the rough surface are derived for loading and unloading stages, respectively, and a prominent adhesion hysteresis associated with dissipation energy is revealed. A dimensionless Tabor parameter is also introduced to account for general material properties. Our analysis results show that both the total pull-off force and the energy dissipation due to adhesive hysteresis are influenced by the surface roughness only through a single adhesion parameter, which measures statistically a competition between compressive and adhesive forces exerted by asperities with different heights. It is also found that smoother surfaces with a small adhesion parameter result in higher energy dissipation and pull-off force, while rougher surfaces with a large adhesion parameter lead to lower energy dissipation and pull-off force.