The Effect of Adhesion on the Contact of an Elastica with a Rigid Surface

Abstract

The understanding of topics such as friction, wear, lubrication, and adhesive bonds is dependent on the ability to measure surface and interfacial energies. The surface energies of liquids may be measured accurately using a variety of techniques; however, surface energies of solids are much more difficult to accurately measure. In an attempt to develop a method that can be used to measure surface and interfacial energies of solids, this thesis proposes the use of a elastica. The elastica acts as an extremely flexible beam and provides a structure that will permit measurable deformation of the solid by relatively small surface attractions. The ends of the elastica are lifted, bent, and clamped vertically at an equal height and specified distance apart. They are then moved downward, allowing the strip to make contact with a flat, rigid, horizontal surface.

Two adhesion models are investigated. First, a JKR-type analysis, which examines the effect of adhesion forces that exist within the area of contact between the elastica and the rigid surface, is considered. Various values for the work of adhesion are examined. A DMT-type analysis, which assumes that the adhesion forces act in the region just outside of the contact area, is also considered. Results are obtained for linear and constant forces. Various values for the maximum DMT force and the vertical separation between the elastica and the rigid substrate at which the adhesion forces terminate are examined. Results from the two types of analyses are compared.