Correlation between yield stress and hardness of nickel-silicon-boron-based alloys by nanoindentation

Based on the relation proposed by Tabor in 1951, which connects the ultimate tensile strength and the yield stress of classical materials to the Brinell or Vickers hardness numbers by a simple factor of proportionality, we propose an extended analytical model for the determination of the yield stress of brittle materials using nanoindentation data. This model considers the nanoindentation hardness calculated from the projected actual contact area between the indenter and the material which is representative of the real mean pressure exerted by the indenter compared to classical hardness numbers. A coefficient is introduced in the model to integrate the extent of the elastic recovery of the indented material occurring after the withdrawal of the indenter. This is possible by using the criterion defined by the residual to maximum indenter displacements ratio, this criterion being already related to the deformation mode under indentation. Indeed, this criterion allows identifying the piling-up deformation observed for complete or fully plastic deformation materials or the sinking-in deformation for purely elastic materials. The proposed model thus allows a good estimation of the yield stress of brittle materials for which classical tensile tests are not applicable. The model is validated on a variety of amorphous nickel-silicon-based alloy ribbons, i.e., Ni89Si9B2, Ni78Si9B13 and Ni68Fe3Cr7Si8B14 on which both nanoindentation tests and tensile experiments have been performed.