Abstract
The indentation of a sphere into an elastoplastic half-space is considered, which is accompanied by pile-up / sink-in effects, extrusion of material around a sphere (formation of a bulk) and elastic sinking of the material. The evolution of studies of the indicated phenomena is shown. Based on the similarity of the deformation characteristics, expressions are obtained for determining the indentation depth, the depth of the residual crater, and the contact depth depending on the degree of loading. In this case, the influence of the characteristics of the hardened material — the yield strength and the hardening exponent — were taken into account. The radial boundary of the bulk is determined from the volume of the displaced material. Expressions are obtained for describing the profile of a loaded and unloaded crater.
Highlights
The operational performance of the joints of machine parts, including tightness, are determined of the relative contact area and the density of the gaps at the junction of rough surfaces [1, 2]
As indicated by the authors of [5], in the past many analytical, experimental, and numerical studies have been performed for modeling and predicting the properties of an elastoplastic contact, such as the contact radius, the average pressure, and the contact strength. Because of their complexity, no closed solution was proposed for elastoplastic contacts
Contact models can be divided into two main groups: indentation models and flattening models [7]
Summary
The operational performance of the joints of machine parts, including tightness, are determined of the relative contact area and the density of the gaps at the junction of rough surfaces [1, 2]. If the problem of determining the density of gaps is solved for an elastic contact of asperities, including under the mutual influence of asperities [2, 9, 10], for an elastic-plastic contact this solution is associated with “sink-in / pile-up” effects (Fig. 1). The method is based on the expression for contact stiffness obtained by Bulychev et al, who first proposed the kinetic indentation of materials (Fig. 2) in order to determine their mechanical properties. They studied the effect of elastic deformation depending on the E y ratio, the influence of the relative penetration depth h h R , the exponents of hardening, and the friction coefficient, but they did not present the results in a form convenient for engineering calculations. Earlier in [25], it was suggested that elastic deformations and plastic “bulk” should be described by separate equations or functions, but this was not realized
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
