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

Abstract

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.

Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials

“…The leading order of the derived scale ratio (H/E r )/ (W u /W t ) is found to be identical to that derived in our previous paper 7 for both linear-hardening and power-law hardened materials. Again, this ratio mainly depends on the half-included angle of conical indenter and slightly on Poisson's ratio.…”

“…7 The scale ratio for both linear and power-law hardening presented in this paper can be expressed equivalently as [2(1 À n) cot a]/3, and it is apparent that this ratio is independent of work hardening. Indeed, this ratio mainly depends on the half-included angle of conical indenter and slightly on Poisson's ratio.…”

“…Alkorta et al 4 and Malzbender 5 indicated that this method can incur significant error for soft materials, while Chen and Bull 6 found that when H/E r is larger than 0.1, significant deviation occurs in this relation. In our previous paper, 7 analytical approaches were adopted to uncover the physical nature of this scale ratio, and it was found that for elastic perfectly-plastic case, the scale ratio has the form [2(1 À n)…”

Solid particle erosion mechanisms of protective coatings for aerospace applications

“…H/E is known to be proportional to the index of plasticity through a linear relationship [25,205] and has been proposed to control SPE in terms of the transferred energy to the coated surface through the indentation process [73]. In the case of the coatings studied here, the linear relationship between H t /E r and R p is verified ( Figure 5.17).…”

“…The proportion of energy dissipated by plastic means during an indentation is known to be highly dependent on the geometry of the indenter [205]. For that reason, we chose to evaluate the materials index of plasticity (R p ), defined as the ratio of plastic work over the total work during an indentation test, using Berkovich and cube corner indenters.…”