A simple stress field solution for conical indentation

Abstract

Classical contact mechanics has revealed the theoretical conical indentation solution of a stress field for ideal elastic–plastic materials based on the expansion cavity model and elastoplastic theory. This study proposes an equivalent stress analytical equation for the representative volume element of the median energy density point under conical indentation. For materials whose constitutive relations conform to power-law hardening, the equivalent stress solution is defined as the characteristic stress factor, and a simple stress field solution characterized by the logarithmic distribution law of dimensionless stress for conical indentation is presented. The verification results of finite element analysis showed that the proposed solution can uniformly describe the distribution of equivalent stress and three principal stresses in the material deformation region near the cone tip.