Adhesion of an axisymmetric elastic body

Abstract

The adhesion forces between two bodies in contact were experimentally observed by Roberts (1968) and Kendall (1969). In these experiments it was noted that the contact areas at low loads were considerably larger than those predicted by Hertz theory. Several models were then introduced to add the adhesion effect to the Hertz model, such as the Johnson-Kendall-Roberts (JKR) model, the Derjaguin-Muller-Toporov (DMT) model and the Maugis model. The Maugis model also offers a transition between the JKR and DMT theories. These models were developed for axisymmetric elastic bodies, with ideal spherical surface profiles, which can be approximated by a single second-order term. Later, Zheng et al.(2007) developed a model that investigated the adhesion of axisymmetric elastic bodies whose surface profiles are ideally approximated by a single n-th order term. Since an actual surface profile may not be exactly described by a single paraboloid or a single higher-order term, it may not be obvious which model is more suitable to use. In this investigation, surface geometries of contacting bodies are approximated by a combination of second- and fourth-order terms and a transition region is established. It is shown that the need for using the transition model not only depends on the geometry of contacting bodies, but also on their material properties.