Effect of elastic surface deformation on the relation between hardness and yield strength

The use of an analytical approach to determine the relation between hardness and yield strength for materials with a high ratio of yield strength to Young's modulus is re-examined. It is shown that predictions using the analogy of the spherical cavity fail to reproduce experimental and finite element results because the surface deflection that occurs during loading is not taken into account. A modification is proposed to allow this. This gives a greatly improved prediction of the relationship between the hardness and yield strength of a material. It also enables the effect of the indenter shape on the measured hardness to be incorporated and explains why in some very hard materials, indentation is observed to be completely elastic.