Adhesion between a spherical indenter and an elastic solid with a compliant elastic coating

Abstract

The Johnson, Kendall and Roberts (JKR) adhesion theory is frequently applied to study the adhesion mechanics of thin compliant layers coated on to glass substrate in an atomic force microscope (AFM). These compliant layers are subjected to micro indentation in the AFM using a flat or spherical indenter. But, JKR theory is based on the contact of homogeneous, isotropic solids. The finite element analysis used by Sridhar et al (1997) (J. Phys. D: Appl. Phys. 30 1710-19) to study the adhesion mechanics of the three-layered crossed-cylinder arrangement of the surface force apparatus (SFA) has been extended to this AFM geometry. The effect of indenter elasticity is included for both spherical and flat punch probes. Computations of contact size and contact compliance each as a function of load are presented for a range of values of adhesion energy and elastic modulus ratio of layer and substrate.

On the two-dimensional solution of both adhesive and non-adhesive contact problems involving functionally graded materials

“…The accuracy of this model was validated experimentally and by comparison with numerical results produced using the finite element method (FEM). Johnson and Sridhar (2000) derived a JKR-like model to describe adhesive contacts between a solid comprising a homogeneously elastic coating bonded to a substrate and a rigid indenter. A selection of numerical results for a variety of different coatings were presented and the authors found that the JKR model using the elastic properties of the coating agreed well with their numerical results when the coating is thick whilst the JKR model using the elastic layers of the substrate agreed well with their obtained results when the coating was thin.…”

Formation of ultra-thin bi-molecular boundary adsorbed films

“…Surface adsorbed films act at the assumed smooth summits of surface features which are ubiquitous in any micro-scale contact according to some statistical distribution. If an analytical model for such a typical feature can be derived, then it may be included in an assumed statistical treatment of surface interactions in much the same manner as adhesion of asperities noted by Fuller and Tabor [24] and Johnson and Sridhar [25]. In fact, a combination of kinetic laws may be included in such an analysis as shown for adhesion, meniscus action and hydration by Rahnejat et al [26] and Teodorescu et al [23] for nano-scale lubricated impact dynamics of a diminutive roller and those of microelectromechanical systems (MEMS) gear teeth pairs respectively.…”

Axisymmetric indentation of a rigid cylinder on a layered compressible and incompressible halfspace

“…Problems concerning the investigation of strain and stress in elastic bodies in contact are the goal of researches devoted to theoretical models and applications in the industry; see, for example, [Li and Chou 1997;Johnson and Sridhar 2001;Wang et al 2004;Sburlati 2006].…”

“…A relative recent interest in contact mechanics (an exhaustive treatise of contact problems can be found in [Johnson 1985]) has focused on indentation problems upon layered solids with coating different from the substrate. This is of interest, for example, in the measurement of mechanical properties, such as hardness and elastic moduli, of surface films in not destructive experimental tests, also on the micro-or nanoscale.…”

“…We make the following hypotheses to approach the problem: the friction influences in a negligible way the normal stress distribution on the interface between the layer and the cylinder (see [Johnson 1985], for example); and we consider only the limit contact cases between the layer and the elastic substrate, that is, either perfect bonding or absence of friction.…”