Further analysis of energy-based Indentation relationship among Young's modulus, nominal hardness, and Indentation work

In our previous study, we modeled the indentation performed on an elastic-plastic solid with a rigid conical indenter by using finite element analysis, and established arelationship between a nominal hardness/reduced Young's modulus (Hn/Er) andunloadingwork/totalindentation work (WeWt). The elasticity of the indenter was absorbed in Er= 1/[(1 - v2)/E + (1 - Vi2)/Ei,where Ei, and viare the Young's modulus and Poisson's ratio of the indenter, and E and v are those of the indented material.However,recalculation by directly introducing the elasticity of the indenter show that the use ofEralone cannot accurately reflect the combined elastic effect of the indenterand indented material, but the ratio η = [E/(1 - v2)]/[Ei/(1approximate Hn/Ec-We/Wtrelationship is almost independent ofselected η values over 0-0.3834, which can be used to give good estimates of η as verified by experimental results.