ИСТИНА

A model of adhesive contact between an indenter, whose shape is described by the power-law function, and an elastic half-space is suggested. The model is based on the solution of an axisymmetric contact problem with the piecewise constant additional load applied outside the contact region. Calculation is carried out for the case when the dependence of the adhesive force on the gap between the surfaces is specified in the form of the Lennard–Jones potential. The results obtained at various numbers N of steps in the piecewise constant approximation, including N = 1, which corresponds to the known Maugis–Dugdale model of adhesion, are compared. The results indicate that the Maugis–Dugdale model can be used to describe the force-distance curves obtained in the process of approach and removal of parabolic indenters and indenters with the shape described by higher-order functions in the case of the contact between the indenter with the half-space. If the surfaces are separated and only interact via adhesive forces, the use of approximations with a small number of steps, including the Maugis–Dugdale model, leads to a significant error, in particular to an overestimated size of the adhesive hysteresis loop. For the conical indenter, the use of the Maugis–Dugdale model results in an error, even in the case when surfaces are in contact. The results of calculations performed using the Lennard–Jones potential are compared to the results obtained with using linear and exponential potentials. The particular shape of the adhesive potential is shown to have no pronounced effect on the approach–separation curves, especially in the case of the contact between surfaces, provided that the maximum value of the adhesive pressure and the specific adhesive energy coincide for all functions that describe the shape of the adhesive potential.