A study of the elastic—plastic deformation of heavily deformed spherical contacts

Abstract

Abstract

This work uses a finite-element analysis and analytical equations to model elastic—plastic large deformations of spheres in contact with rigid flat surfaces. No strain hardening in the sphere or friction between the surfaces has been considered. The case considered here is of a deformable sphere compressed by a rigid flat as opposed to the reverse case of a rigid spherical indenter penetrating a deformable surface. Most previous works only deal with elastic or elasto-plastic deformation at much smaller deformations. A model for predicting the contact area, pressure, and force is proposed based on the finite element modelling (FEM) simulations and analytical equations derived from volume conservation. The analytical volume conservation approach is similar to that used to model the barrelling of compressed cylinders. The most important aspect of the model is the resulting equation relating the average pressure to the yield strength during fully plastic deformation. The results are compared with existing models and experimental data.