Elastic punching of material during flattening of a spherical asperity and restoration of the imprint in unloading

Abstract

The development of the methodology previously proposed by the authors for determining the displacements of half-space points under the action of an axisymmetric load described by a parabola is presented. It is shown that when the sphere is flattened, the pressure distribution on the contact area is a function of complex shape, which can be represented by a combination of several equations for description in adjacent sections. The knowledge and description of the contact pressure distribution function is of practical importance in solving the issues of elastic punching of the material, the magnitude of the elastic recovery of the contact print during unloading, and determining the curvature of its profile. Equations are proposed for determining displacements inside and outside the contact area when describing the distribution of contact pressure by analytical functions and when using a discrete distribution of contact pressure. The accuracy of the obtained results depends on the rate of the approximating functions to the actual pressure distribution at the contact area. At the same time, the goals of the problems to be solved should be considered. When determining elastic recovery in the center of the contact area, it is sufficient to use a uniform distribution of contact pressure. When determining the profile of the restored contact print and its curvature, increased accuracy of approximating functions is required.