Non-linear finite element constitutive modeling of indentation into super- and ultrahard materials: The plastic deformation of the diamond tip and the ratio of hardness to tensile yield strength of super- and ultrahard nanocomposites

Using a non-linear constitutive material model for super- (H ≥ 40 GPa) and ultrahard (H ≥ 80 GPa) materials that accounts for the pressure enhancement of elastic moduli and of plastic resistance, we present the effect of plastic deformation and resultant blunting of the diamond indenter, and discuss the limitations to the measurement on ultrahard materials by means of nano-indentation. We further show that the ratio of the hardness H to plastic resistance Y in tension amounts to about 2.4 for the super- and 2.84 for ultrahard nanocomposites, although the ratio of hardness to Young's modulus is relatively high. These results are briefly discussed in terms of the expanding cavity model and the elastic–plastic transition.