Journal of Adhesion Science and Technology, Vol.10, No.1, 17-31, 1996
Effect of the stiffness of the measurement system on adhesion force curves in the elastic continuum limit
An elastic contact theory is described to reveal the effects of the stiffness of the measurement system on the pin-on-disk adhesional contact. The pin is assumed to be elastic and the plane is assumed to be rigid and smooth. The total energy is assumed to be the sum of the following four terms: (i) an elastic energy for the pin, (ii) the specific energy of adhesion in the area of the contact which is expressed as the difference between the surface energies and the interface energy, (iii) the energy for the surface-surface interaction, and (iv) another elastic term for the measurement system such as the cantilever of the atomic force microscope (AFM). The contact area is determined under Hertz's assumptions. A Lennard-Jones type potential is used for the surface-surface interaction. The pressure distribution within the contact region is determined as the superimposition of Hertz's pressure distribution and Boussinesq's distribution. In the limit when the stiffness is infinite, our approach conforms to the Muller-Yushchenko-Derjaguin (MYD) theory. In the limit when the surface-surface interaction is negligible, our approach conforms to our previous analytical theory. In the limit when the stiffness is infinite and the surface-surface interaction is negligible, our approach conforms to the Johnson-Kendall-Roberts (JKR) theory. Although the results are not presented in an analytical form, the simultaneous equations are expressed with normalized parameters. The normalized equations are numerically resolved. The normalized relationships between the distance and the force (force curve) are presented. It is suggested that the normalized force curve can be determined by only two parameters - the normalized stiffness of the measurement system and the normalized distance which is used in the expression of the Lennard-Jones potential. It is suggested that the force at the initial contact decreases with decreasing stiffness and then the minimum force changes from -1.5 to about -2.4 pi Delta gamma R. The minimum force is not equal to the force at separation, but it approaches the separation force with decreasing stiffness.