Loading and unloading of a spherical contact: From elastic to elastic–perfectly plastic materials

In this study the frictionless contact of a power-law hardening elastic–plastic sphere in contact with a rigid flat has been investigated by the finite element method. The strain hardening exponent n varied from 0 to 1, with material properties changing from elastic–perfectly plastic to elastic. Parameters such as contact load, contact area under both loading and unloading have been calculated for a wide range of contact interferences. Based on the finite element results, analytical and dimensionless expressions of these contact parameters versus the contact interferences during loading have been presented. In addition, the load–deformation equations at unloading and the residual interference after complete unloading for a large range of maximum interferences are given.

► Semi-analytical dimensionless expressions for elastic–plastic spherical contacts.
► Solutions for a wide range of materials.
► Solutions for both loading and unloading are given.