Stress distribution model for the entire plastic zone of conical indentation with power-law hardening materials

Abstract

<p indent="0mm">The classical contact mechanics provides an elastic conical indentation solution, and verifies that the strain field of elastic-plastic indentation with an arbitrary blunt indenter mostly satisfies the expanding cavity model. This study reviews the stress solution of the elastic zone for conical indentation using power-law hardening materials derived from predecessors based on the expanding cavity model and elastic-plastic mechanics. Furthermore, the expression of von-Mises equivalent stress in the plastic zone of conical indentation is determined according to the plastic stress solution of an internally pressurized thick spherical shell. The numerical verification revealed that the calculated equivalent stresses via finite element analysis are consistent with the theoretical solution of the elastic zone for conical indentation. However, a clear deviation in the entire plastic zone for the power-law hardening materials is still observed. Furthermore, to accurately describe the equivalent stress in the entire plastic zone of conical indentation for power-law hardening materials, a novel model for the indented stress distribution is established by combining the dimensional analysis method and finite element simulation. Finally, the stress model was verified using a wide range of ductile materials. The comparison results revealed that all of the calculated equivalent stresses are consistent with the model predictions for the entire plastic zone.