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 (Hn/Er) and unloading work/total indentation work (We/Wt). The elasticity of the indenter was absorbed in Er ≡ 1/[(1 - v2)/E + (1 - vi2)/Ei], where Ei and vi 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 Er alone cannot accurately reflect the combined elastic effect of the indenter and indented material, but the ratio η = [E/(1 - v2)]/[Ei/(1 - vi2)] would influence the Hn/Er–We/Wt relationship. Thereby, we replaced Er with a combined Young’s modulus Ec = 1/[(1 - v2)/E + 1.32(1 - vi2)/Ei] = Er/[1 + 0.32η/(1 + v)], and found that the approximate Hn/Ec–We/Wt 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.
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Ma, D., Ong, C.W. Further analysis of energy-based indentation relationship among Young’s modulus, nominal hardness, and indentation work. Journal of Materials Research 25, 1131–1136 (2010). https://doi.org/10.1557/JMR.2010.0137
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DOI: https://doi.org/10.1557/JMR.2010.0137