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 a relationship between a nominal hardness/reduced Young’s modulus (H_n/E_r) and unloading work/total indentation work (W_e/W_t). The elasticity of the indenter was absorbed in E_r ≡ 1/[(1 − ν²)/E + (1 − ν_i²)/E_i], where E_i and ν_i are the Young’s modulus and Poisson’s ratio of the indenter, and E and ν are those of the indented material. However, recalculation by directly introducing the elasticity of the indenter show that the use of E_r alone cannot accurately reflect the combined elastic effect of the indenter and indented material, but the ratio η = [E/(1 − ν²)]/[E_i/(1 − ν_i²)] would influence the H_n/E_r–W_e/W_t relationship. Thereby, we replaced E_r with a combined Young’s modulus E_c ≡ 1/[(1 − ν²)/E + 1.32(1 − ν_i²)/E_i] = E_r/[1 + 0.32η/(1 + η)], and found that the approximate H_n/E_c–W_e/W_t relationship is almost independent of selected η values over 0–0.3834, which can be used to give good estimates of E as verified by experimental results.