Characterization of elastic modulus and hardness of brittle solids by instrumented indentation

The reduced elastic modulus E_r and indentation hardness H_IT of various brittle solids including ceramics, semiconductors, glasses, single crystals, and laser material were evaluated using nanoindentation. Various analysis procedures were compared such as Oliver & Pharr and nominal hardness-based methods, which require area function of the indenter, and other methods based on energy, displacement, contact depth, and contact stiffness, which do not require calibration of the indenter. Elastic recovery of the imprint by the Knoop indenter was also utilized to evaluate elastic moduli of brittle solids. Expressions relating H_IT/E_r and dimensionless nanoindentation variables (e.g., the ratio of elastic work over total work and the ratio of permanent displacement over maximum displacement) are found to be nonlinear rather than linear for brittle solids. The plastic hardness H_p of brittle solids (except traditional glasses) extracted based on E_r is found to be proportional to \(E_{\mathrm{r}}\sqrt {H_{\text{IT}}}\) $$E_{\mathrm{r}}\sqrt{H_{\text{IT}}}$$ .