The correlation between hardness and yield strength of hard materials

The correlation between hardness, H, and yield strength, Y, for hard materials is re-examined using an analytical approach to provide a physical interpretation, which explains the trends observed. Existing analytical predictions using the analogy of the spherical cavity fail to reproduce experimental and finite element results because the accommodation of the intrusion of the indenter due to surface deformation is not taken into account, while experiments made here and elsewhere indicate that the latter can be substantial. A simple modification is proposed, which accounts for this, and allows for a reasonable prediction of the relation between hardness and yield strength for materials, which have a well determined yield point and do not strain harden. The treatment also allows explaining the effect of indenter geometry on measured hardness for such materials.