Extended JKR theory on adhesive contact of a spherical tip onto a film on a substrate

The conventional JKR theory was extended to the adhesive contact of a rigid sphere onto an elastic film perfectly bonded to a rigid substrate. An elasticity problem of axisymmetric indentation on an elastic film was revisited, in which the force-depth relations for both flat and spherical indentations were obtained in a simple form. With the obtained force-depth relations, the energy release rate at the debonding of a spherical tip from an elastic film was expressed in terms of pull-off force, elastic constants, and geometric parameters. The adhesion energy between a spherical tip and an elastic film can be measured as the critical energy release rate at the instability of debonding. This study suggests that when the critical radius of contact is larger than the thickness of an elastic film, the extended JKR theory should be used in place of the conventional JKR theory to correctly evaluate the adhesion energy between the spherical tip and the elastic film.