Adhesive contact on randomly rough surfaces based on the double-hertz model

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.