Adhesive Contact of Elastically Deformable Spheres: A Computational Study of Pull-Off Force and Contact Radius

Abstract

Elastic spheres in contact deform around the contact region, due to intermolecular interaction forces. The deformed contacting surfaces change the distance between interacting molecules that in turn alters the force of interaction. Thus, the contact behavior of elastic spheres constitutes a nonlinear mathematical problem that defies the traditional analytical methods for general solution. Efficient computational techniques have enabled a detailed study of adhesive contact behavior of elastically deformable spheres with self-consistent solutions of a nonlinear integral governing equation. The present work extends the previous computational analysis to the quantities of practical interests such as the pull-off force and the radius of contact area. Trends of variations in the pull-off force as physical properties change are examined. Computationally determined radial positions as stress condition indicators suggest that the concept of contact radius is not clearly defined in the literature and can be confusing. It seems that some contact mechanics models would be consistent with the definition of the edge of contact area as the radial position for the local surface stress to change from compression to tension, whereas others would rather assume the contact radius as the radial position for the local tensile stress to reach its peak. The substantial quantitative deviation of self-consistently computed contact radius from the DMT model prediction suggests that models based on the assumption of a well-defined contact area having a constant gap may not be appropriate when describing cases of small values of Tabor's parameter.