Nanoindentation hardness measurements using real-shape indenters: application to extremely hard and elastic materials

Abstract

We study the technique of nanoindentation hardness measurement applied to extremely hard and elastic thin films. We do the study with the aid of Hertz’s solutions for elastic contacts. The effect of different apical angles in ideally sharp conical diamond indenters is analyzed. In addition, the blunt tip shape of practical diamond indenters is discussed. The area function of the tip of real indenters is deduced from experimental nanoindentation measurements performed with these indenters on fused quartz. Triangular-base pyramidal indenters with Berkovich and cube corner geometries are considered. Theoretical hardness values applying Hertz’s and Oliver and Pharr’s methods of analysis are obtained and compared with the experimental data deduced from nanoindentation measurements performed on very hard and elastic ta-C films. The theoretical analysis shows a necessary dependence of the calculated hardness values with the apical angle of the indenter in totally elastic materials and to some extent in elastoplastic materials. Moreover, when the indenter tip is blunt or when there are inaccuracies in the measured area function of the indenter tip, hardness values decrease for very small penetration depths. Besides, in these films, because of their very small thickness, measured hardness values also decrease for measurements with penetration depths larger than a fraction of film thickness, due to the effects of the softer substrate.