The equivalence of axisymmetric indentation model for three-dimensional indentation hardness

Nix and Gao [J. Mech. Phys. Solids46, 411 (1998)] established an important relation between the microindentation hardness and indentation depth for axisymmetric indenters. We use the conventional theory of mechanism-based strain gradient plasticity [Huang et al., Int. J. Plast.20, 753 (2004)] established from the Taylor dislocation model [Taylor, Proc. R. Soc. London A145, 362 (1934); Taylor, J. Inst. Met.62, 307 (1938)] to study the Berkovich and other triangular pyramid indenters. The three-dimensional finite element analysis shows that the widely used equivalence of equal base area leads to significant errors, particularly in microindentation. A new equivalence of equal angle is proposed for triangular pyramid indenters, and it has been validated for a large range of indenter angles and indentation depths.