A simple theory of static and dynamic hardness

Abstract When a hard spherical indenter is pressed into the surface of a softer metal, plastic flow of the metal specimen occurs and an indentation is formed. When the indenter is removed it is found that the permanent indentation is spherical in shape, but that its radius of curvature is greater than that of the indenter. It is generally held that this ‘shallowing’ effect is due to the release of elastic stresses in the material around the indentation. It is clear that if the recovery is truly elastic it should be reversible and that a second application and removal of the indenter under the original load should not change the size or shape of the indentation. Experiments show that this is the case. This means that when the original load is reapplied, the deformation of the indenter and the recovered indentation is elastic and should conform with Hertz’s equations for the elastic deformation of spherical surfaces. Measurements show that there is, in fact, close agreement between the observed deformation and that calculated from Hertz’s equations. These results have been applied to the case of indentations formed in a metal surface by an impacting indenter. The energy involved in the elastic recovery of the impacting surfaces is found to account for the energy of rebound of the indenter. This analysis explains a number of empirical relations observed in dynamic hardness measurements, and, in particular, reproduces the calibration characteristics of the rebound scleroscope. The results also show that for very soft metals the dynamic hardness is very much higher than the static hardness, and it is suggested that in rapid deformation of soft metals, forces of a quasi-viscous nature are involved. In the third part of the paper a simple theory of hardness is given, based on the theoretical work of Hencky and Ishlinsky. It is shown experimentally that for a material incapable of appreciable work-hardening, the mean pressure Pm required to produce plastic yielding is related to the elastic limit Y of the material by a relation Pm = cY, where c is a constant having a value between 2·6 and 3. An empirical method is described which takes into account the work-hardening produced in metals by the indentation process itself. This results in a general relation between hardness measurements and the stress-strain characteristic of the metal, and there is close agreement between the theory and the observed results. In addition, the theory explains the empirical laws of Meyer.