Elastic-Plastic Adhesive Contact of Rough Surfaces Based on Accurate FEA Study Using N-Point Asperity Model

Introduction

Contact of surfaces is inevitable in engineering applications, so this necessitates the study of surfaces and surface interactions. When studied on microscopic scale, all engineering surfaces are rough to some degree. When two surfaces are held or pressed together, contact occurs only at protuberances on either surface. These protuberances are called as asperities. As the contact occurs only at higher asperities, real contact area is very small and it is only a fraction of apparent contact area. In such a condition, the pressure in those contact spots is extremely high. So, modeling and study of contact between two rough surfaces is of immense importance in the field of science and engineering, and it is being carried out from last so many years for an improved understanding of phenomenon like friction, wear, adhesion, thermal and electrical conductance, etc.

Recently in micro electro-mechanical systems (MEMS), study of contact analysis has got a prime importance as these systems make use of miniaturized mechanical and electro-mechanical elements whose sizes range from 1 micron to several millimeters. And it has been known that while macro scale systems are more influenced by inertia effects, micro scale systems are more influenced by surface effects. One of the most important and almost unavoidable problems in MEMS is the adhesion. Adhesion is one of the surface interactions where sticking of two smooth and clean surfaces takes place when they come in contact with each other. Due to such sticking, it requires a definite normal force to separate them. This pull off force is called as adhesive forces which influences the frictional and wear characteristics, and morphology of contacts. Thus the study of adhesion becomes significantly more important in the contact applications involving smoother surfaces, lighter loads and smaller length scales.

To predict the force of adhesion between contacting elastic surfaces, there exists two widely known models viz. Johnson et al. (1971) model (JKR model) which considers adhesive force within expanded area of contact and Derjaguin et al. (1976) model (DMT model) which considers adhesive force just outside of contact area. In either case, the force of adhesion for an elastic sphere of radius R is given by CπRγ, where C is a constant, which is 1.5 and 2 for JKR and DMT models respectively, and γ the work of adhesion given by γ₁ + γ₂−γ₁₂, γ₁ and γ₂ being the surface energies for the two surfaces and γ₁₂ their interfacial energy. Tabor (1977) compared the assumptions and predictions of the JKR and DMT models and pointed out the inconsistencies between the two. Following the analysis of Tabor, Muller et al. (1980) showed that the two models can be considered as two opposite extremes of adhesive contact according to a dimensionless parameter called Tabor number, which may be interpreted as the ratio of the elastic deformation to the range of action of the adhesive forces. However, it has since been shown that the two models are the limiting cases of a generalized solution which can be seen in the work of authors like Greenwood (1997) and Johnson and Greenwood (1997). The JKR model is applicable to soft solids with large surface energy and radius. On the other hand, the DMT model is applicable to hard solids of small radius and low surface energy.