Investigation of the hydrostatic and plastic zones in hardness measurement using finite element simulation

The aim of this research was to evaluate the effect of the strain hardening of a homogeneous metallic material on the size and shape of hydrostatic and plastic zones forming in the indentation process with a spherical indenter. Precise measurements and finite element calculations (FEM) were performed for indentations and the results were compared with those of the expanding cavity model (ECM). We concluded that in the range of <i>d</i>/<i>D</i> (impression diameter/indenter diameter) = 0.42-0.5 there is a good agreement between the measured and FEM-calculated hardness results if the strain hardening effect is properly taken into account. The results show that the ECM model underestimates the size of the hydrostatic zone and overestimates that of the plastic deformation region. We have also proved that the hydrostatic and plastic zones have a more complex shape than a hemisphere. In the investigated cases, the ratio of the plastic and hydrostatic volumes beneath the indenter is nearly independent of the <i>d</i>/<i>D</i> ratio in the range of 0.42-0.5, and its value is around 6. In these cases, the calculated geometry and size of the hydrostatic and plastic zones can be assumed to be close to their actual values. These results demonstrate that the reliability of hardness measurement performed by spherical indenter is highest when the <i>d</i>/<i>D</i> ratio of 0.42-0.5 is fulfilled, within the <i>d</i>/<i>D</i> range of 0.24-0.6 allowed by the standard. In this paper, we provided a well-defined and reproducible way to define the boundary between the hydrostatic core and the plastic zone (for a homogeneous structure with a spherical indenter) taking into account strain hardening.