A Solution of Rigid Perfectly Plastic Deep Spherical Indentation based on Slip Line Theory

Abstract

During indentation it is often important to determine the relationship between the average pressure and the yield strength. This work uses slip line theory to determine this relationship for the case of a rigid sphere indenting a frictionless perfectly plastic half-space (i.e. no hardening). The results show that the ratio between the average contact pressure and the yield strength decreases as the depth of indentation is increased. Note that the slip-line analysis does not include the effects of pile-up or sink-in deformations. However, the slip-line theory has also been compared to data generated using the finite element method (FEM). The theory and the FEM results appear to agree well.