Experimental verification and theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation

The relationship between hardness (H), reduced modulus (Er), unloading work (Wu), and total work (Wt) of indentation is examined in detail experimentally and theoretically. Experimental study verifies the approximate linear relationship. Theoretical analysis confirms it. Furthermore, the solutions to the conical indentation in elastic-perfectly plastic solid, including elastic work (We), H, Wt, and Wu are obtained using Johnson’s expanding cavity model and Lamé solution. Consequently, it is found that the We should be distinguished from Wu, rather than their equivalence as suggested in ISO14577, and (H∕Er)∕(Wu∕Wt) depends mainly on the conical angle, which are also verified with numerical simulations.