Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model

Abstract

The objective of this paper is to apply the expanding cavity model to study the conical or spherical indentation response of hydrostatic pressure dependent plastic solids. To this end, the elastic–perfectly plastic stress and displacement fields in a hollow sphere subjected to internal pressure are first obtained by assuming that the material obeys the Drucker–Prager yield criterion. Attention is focussed on the influence of the pressure sensitivity index of the material on the above fields as well as the development of plastic flow in the sphere. These results are then employed to extend the expanding cavity model of indentation to pressure dependent plastic solids. It is found that the size of the plastically deformed region surrounding the indented zone enhances significantly with the pressure sensitivity index of the material. Also, the mean contact pressure normalized by the compressive yield stress increases strongly when the material exhibits a pressure dependent plastic behaviour.