Effect of surface cavities on static and dynamic adhesion to an elastomer

Abstract

The analysis of contact between two spherical surfaces introduced in the 19th century by Hertz was modified some 30 years ago by Johnson, Kendall and Roberts (JKR) to allow for adhesion between the two solids. Since then, the technique has been much used with various systems employing sphere/sphere and sphere/flat solid (sphere of infinite radius) geometry. We consider here the geometry in which one solid has a negative radius of curvature: a spherical solid contacts the second solid in a shallow spherical cavity. It is thus shown that the contact area of a rigid sphere on the smooth surface of an elastomer depends markedly on the flatness of the latter. Any neglect of cavities of large radius of curvature leads to an overestimate of the value of the intrinsic adhesion of Dupré, W0, and falsifies interpretation of separation kinetics under (variable) applied load. By allowing for the negaive radius of curvature of the cavities in the rubber, correction can be made leading to coherent values of W0 and debonding kinetics. The analysis may be of use for the assessment of flatness of surfaces and the increase in contact radius may prove beneficial for improving the precision of static adhesion tests.