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

Nix and Gao [J. Mech. Phys. Solids 46, 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 [Y. Huang et al., Int. J. Plast. 20, 753 (2004)] established from the Taylor dislocation model [G. I. Taylor, Proc. R. Soc. London A 145, 362 (1934); G.I. 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.