Adhesive Contact of Elastic Solids with Self-Affine Fractal Rough Surfaces

Abstract

The elastic adhesive contact of self-affine fractal rough surfaces against a rigid flat is simulated using the finite element method. An array of nonlinear springs, of which the force-separation law obeys the Lennard–Jones potential, is introduced to account for the interfacial adhesion. For fractal rough surfaces, the interfacial interaction is generally attractive for large mean gaps, but turns repulsive as the gap continuously shrinks. The interfacial interactions at the turning point corresponding to the spontaneous contact are shown for various surfaces. For relatively smooth surfaces, the probability density distributions of repulsion and attraction are nearly symmetric. However, for rougher surfaces, the simulation results suggest a uniform distribution for attraction but a monotonously decreasing distribution with a long tail for repulsion. The pull-off force rises with increasing ratio of the work of adhesion to the equilibrium distance, whereas decreases for solids with a higher elastic modulus and a larger surface roughness. The current study will be helpful for understanding the adhesion of various types of rough solids.