In 1975, Fuller and Tabor have shown that roughness can destroy macroscopic adhesion. This means that in spite of the presence of adhesion at the microscopic scale, the macrosopic force of adhesion vanishes. The mechanism of vanishing macroscopic adhesion is very simple: during approach of elastic bodies, asperities are elastically deformed so strongly that after unloading they destroy the microscopic adhesive junctions. However, both in the moment of formation of microscopic adhesive junctions in the loading phase and their destruction during unloading, mechanical energy disappears. This means that the microscopic adhesion makes the contact dissipative even if there is no macroscopic force of adhesion. In particular, the force-distance dependency during indentation and pull-off do not coincide with each other showing some "adhesive hysteresis". When a ball rolls on such rough surface, there will be a final energy dissipation due to formation of a new contact at the frontline of the contact and its destruction at the rear part. Thus, microscopic adhesion will lead to appearance of rolling friction in an apparently non-adhesive contact. In the present paper, we calculate the approach and pull-off dependencies of force on distance, the dissipated energy in one loading-unloading cycle and estimate the force of rolling friction due to microscopic adhesion.

According the JKR theory of adhesive contact, changes of the contact configuration after formation of the adhesive neck and before detaching are completely reversible. This means, that after formation of the initial contact, the force-distance dependencies should coincide, independently on the direction of the process (indentation or pull-off). In the majority of real systems, this invariance is not observed. The reasons for this may be either plastic deformation in the contacting bodies or surface roughness. One further mechanism of irreversibility (and corresponding energy dissipation) may be chemical heterogeneity of the contact interface leading to the spatial dependence of the specific work of adhesion. In the present paper, this "chemical" mechanism is analyzed on a simple example of an axisymmetric contact (with axisymmetric heterogeneity). It is shown that in the asymptotic case of a "microscopic heterogeneity", the system follows, during both indentation and pull-off, JKR curves, however, corresponding to different specific surface energies. After the turning point of the movement, the contact area first does not change and the transition from one JKR curve to the other occurs via a linear dependency of the force on indentation depth. The macroscopic behavior is not sensitive to the absolute and relative widths of the regions with different surface energy but depends mainly on the values of the specific surface energy.

The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one-dimensional integrals.