A Novel Model for Obtaining Equivalent Stress Distribution in Plastic Zone on Metallic Materials via Spherical Indentation

The classical contact mechanics provides elastic solutions for the load-depth relationship and stress distribution of the spherical indentation problem and verifies that the stress field of elastic-plastic indentation with an arbitrary blunt indenter approximates the expanding cavity model. This study reviews the stress solution of the elastic zone for spherical indentation using power-law hardening materials derived from predecessors based on the expanding cavity model and elastoplastic mechanics. Furthermore, the expression of von Mises equivalent stress distribution in the plastic zone beneath the spherical indenter is derived based on the analytical stress solution for an internally pressurized spherical shell. The numerical verification shows that the equivalent stresses calculated from finite element analysis are in good agreement with the theoretical solution of the elastic zone, but there are still significant deviations in the theoretical solution of the plastic zone. Therefore, to accurately characterize the equivalent stress distribution within the plastic zone of spherical indentation in power-law hardening materials, a novel dimensionless exponential function model is proposed based on a combination of the dimensional analysis and the finite element analysis. Finally, the equivalent stress distribution model is verified across a range of ductile metallic materials, with the results demonstrating good agreement between the finite element results and the model predictions.