Analytical Interpretation of Brinell Hardness

Hardness, an experimentally determined quantity, cannot be related conveniently to other mechanical properties of a material. This note is aimed at deriving a better interpretation of the Brinell hardness in terms of some common mechanical properties such as Young’s modulus, Poisson’s ratio, and the yield point in shear. The Brinell hardness test can be idealized to that of a rigid frictionless sphere indenting a semi-infinite solid under a given load. Under the condition of Brinell hardness test, the maximum shear stress at any point in the elastic region along the axis of symmetry can be obtained from Terazawa’s solution. The Brinell hardness can then be interpreted as a measurement of the depth along the axis of symmetry where the maximum shear stress is equal to a given fraction of the yield point in shear, or the maximum shear stress expressed as a fraction of the yield point in shear at a given depth.