Adhesive Contact of Rough Elastic Solids Based on an Incremental Model

This paper advances a contact model for rough elastic solids in the presence of adhesion. Based on the JKR energy balance method and an incremental contact model, the adhesive contact of rough surfaces is modeled as a combination of loading in the absence of adhesion and unloading keeping a constant real contact area due to adhesion. The relations between the normal load, the real contact area, and the average interfacial separation are presented, and the contact processes of Gaussian rough surfaces are thoroughly discussed. For solids with large work of adhesion and relatively smooth surfaces, full stick might happen spontaneously. While for solids with lower work of adhesion and rougher surfaces, initial contact generates only limited contact area, and external compression is required to increase the contact area further. When a critical area is achieved, the contact area will increase spontaneously again even without compression. Once the separation shrinks to a critical value, instability will be triggered with a sharp increment of contact area and an abrupt fall in normal load. The current study presents a simple method to determine the bonding strength of macroscopic rough solids.