Predictions of frame compliance and apex morphology in sharp nanoindentations

If all components in a nanoindentation system are well calibrated and a reference material has unique hardness, H and reduced modulus, Er independent of the indentation depths, the load, L and the penetration depth, h in the indentation loading curve of the reference material can be correlated by L=Kh2. Here the constant K is expressed by H, Er and indenter geometry constants. By using H and Er of a fused silica and the Berkovich geometry, an analytical expression for the indentation loading curve could be derived. To compare with this analytical loading curve, experimental indentation data were measured with two commercial nanoindenters. The experimental loading curves shifted leftward or rightward from the analytical loading curve and this depth deviation was attributed to improper calibration of the nanoindenters. Quantitative calibrations of frame compliance and indenter bluntness were tried for the raw nanoindentation data and this resulted in consistent nanoindentation data regardless of the used nanoindenters.