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

The relationship between hardness (H), reduced modulus (E_r), unloading work (W_u), and total work (W_t) 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 (W_e), H, W_t, and W_u are obtained using Johnson's expanding cavity model and Laḿ solution. Consequently, it is found that the We should be distinguished from W_u, rather than their equivalence as suggested in ISO14577, and (H/E_r)/(W_uW_t) depends mainly on the conical angle, which are also verified with numerical simulations.