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

Abstract

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[sub n]/E[sub r]) and unloading work/total indentation work (W[sub e]/W[sub t]). The elasticity of the indenter was absorbed in E [sub r] ≡ 1/[(1 − ν²)/E + (1 − ν[sub i]²)/E [sub i]], where E[sub i] and ν[sub 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[sub r] alone cannot accurately reflect the combined elastic effect of the indenter and indented material, but the ratio η = [E/(1 − ν²)]/[E [sub i/(1 − ν[sub i]²)] would influence the H[sub n]/E[sub r]–W[sub e]/W[sub t] relationship. Thereby, we replaced E r with a combined Young’s modulus E[sub c] ≡ 1/[(1 − ν²)/E + 1.32(1 − ν[sub i]²)/E[sub i]] = E [sub r]/[1 + 0.32η/(1 + η)], and found that the approximate H[sub n]/E[sub c]–W[sub e]/W [sub 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.