Slow Vertical Motions of a Spherical Indenter on an Elastic Half-Space

摘要

The dynamic frictionless contact problem for a homogeneous, isotropic elastic half-space and a rigid spherical indenter is studied. An approximate solution to the problem is obtained under the assumption that the contact area and the contact pressure under the punch are slowly varied during the time of travel of the Rayleigh wave along a distance comparable with the diameter of the contact area. First- and second-order asymptotic models of vertical oscillations of a spherical indenter are explicitly constructed. The first-order asymptotic model is considered in detail. The results obtained can be applied for assessing the apparent effect of energy dissipation in nanoindentation testing performed in oscillatory mode for perfectly elastic materials.