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) equivalent to 1/[(1 - v(2))/E + (1 - v(i)(2))/E(i)], where E(i) and v(i) are 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 of E(r) alone cannot accurately reflect the combined elastic effect of the indenter and indented material, but the ratio eta = [E/(1 - v(2))]/[E(i)/(1 - v(i)(2))] 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) equivalent to 1/[(1 - v(2))/E + 1.32(1 - v(i)(2))/E(i)] = E(r)/[1 + 0.32 eta/(1 + eta)], and found that the approximate H(n)/E(c)-W(e)/W(t) relationship is almost independent of selected eta values over 0-0.3834, which can be used to give good estimates of E as verified by experimental results.