A hardness equation for sharp indentation of elastic-power-law strain-hardening materials

Abstract This investigation is predicated upon work by Mata et al. on the contact deformation regimes for strain-hardening materials. The results allow us to derive a general hardness equation for sharp indentation of elastic-power-law plastic materials. The formula H/σr = 1.440 + 0.264 ln(E/σr) is found to provide estimates of hardness H for a wide range of elastoplastic responses as long as the contact deformation regime lies within the elastic-plastic transition. This formulation is a modification to previous formulae derived for solids that do not exhibit strain hardening; where E is Young's modulus and the yield strength σys has been replaced by σr, the stress level in the uniaxial stress-strain curve at a characteristic strain ϵr of 0.1. The development of radial flow patterns is regarded as a necessary condition to the validity of the above equation. As the deformation underneath the indenter evolves to an uncontained mode, the radial flow patterns that are characteristic of the elastic-plastic transition are increasingly disrupted to a point where non-radial flow leads to piling-up of material at the contact boundary.