Influence of the stiffness of the measurement system on the elastic adhesional contact

An elastic contact theory is described to reveal the effects of the stiffness of the measurement system on the adhesion behavior. The point contact is treated in an elastic continuum limit, taking into account the energy change from the surface to the interface within the contact region. The contact area is determined under Hertz's assumptions. The stiffness of the measurement system is taken into account and the total energy is defined as E(total) = E(elastic) + E(interface) + E(stiffness). The contact radius, the displacement, the force, and the total energy are normalized and their relationships are discussed. In the limit when the stiffness is infinite, our approach conforms to the Johnson-Kendall-Roberts (JKR) theory. The force at the initial contact is discussed as well as the force required to separate samples. The ratio of these forces can be written as a function of only one parameter (kappa), which is concerned with the stiffness. A simple asymptotic relation is derived between the force ratio and the parameter kappa. It is suggested that the radius of the contact tip can be estimated from Young's modulus, the Poisson ratio, the stiffness, the separation force, and the force ratio. The force curves and their hysteresis loops are deduced and discussed.