An analytical model of Brinell hardness for power-law hardening materials

Abstract

In the Brinell hardness test a hard spherical indenter is pressed into a metallic material. Due to the inhomogeneous distribution of stresses and strains the hardness measure is not a unique function of the material properties alone, but also depends on the setup geometry notably the diameter of the indenter. To this date there exists no analytic description of these interrelations. Therefore, it seems desirable to derive an analytical model which directly relates the material properties to the hardness value. Based on extensive numerical simulations analytic formulas are derived describing the dependence of Brinell hardness on the applied indentation load. The formulas are capable to represent the entire plastic range relevant for hardness measurements. Based on these results the indentation depths proposed in ISO 6506 can be directly related to a range of force-diameter indices, which serve as a means for selecting the appropriate Brinell test.