Friction hysteresis results from an oscillating friction force at a contact interface. At nano-scale, this phenomenon is affected by the roughness of the contact interface and adhesion. In nanotribology, therefore, it is highly desirable to understand and predict this behavior to estimate the energy loss and possible wear. This paper presents a boundary element model (BEM) for the adhesive friction hysteresis contact at the interface of two bodies of arbitrary geometry. In the model, adhesion is represented by means of a Dugdale approximation of the total work of adhesion at local areas with a very small gap between the two surfaces. The amplitude of the oscillating tangential displacement is very small compared to the contact area which means that the interface does not experience gross-sliding between the two surfaces (the contact remains in the pre-sliding state). Hence, the frictional contact is divided into sticking and slipping regions, defined based on the local values for shear stress and normal pressure, and the rate of relative displacement. The model is first verified by comparing the numerical and analytical (Mindlin theory) solutions for the contact of a smooth ball and a flat of identical materials under a fixed normal force and an oscillating friction force. Then, the problem is solved at the smooth interface between a rigid ball and an elastic flat for various values of the work of adhesion. It is shown that as the work of adhesion increases, both static friction force and pre-sliding displacement increase due to the increase in the contact repulsive force. In addition, the rough interface between a glass ball against a silicon wafer and a DLC (Diamond-Like Carbon) coating is considered. Since adhesion depends on the interface roughness, the corresponding contact repulsive force is different for these interfaces. For the smoother interface, a larger contact repulsive force and consequently, a larger static friction force and pre-sliding displacement are obtained.
- Boundary element method