Analysis of Spherical Contact Models for Differential Hardness as a Function of Poisson's Ratio

A differential hardness is needed for a spherical indenter to avoid large deformations of it during an indentation process. Tabor proposes a criterion for this, where the ball hardness should be at least 2.5 times harder than the specimen. Later, five models expand the Tabor proposal, such that the critical interference corresponding to the inception of plastic deformation depends on the Poisson's ratio. This paper discusses the difference among these models, showing that they can be divided in two groups only. In addition, their similarity depending on the specific mechanical properties of tested material was used to make the conversion between yield stress and hardness.