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- Calibration (1)
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A recently developed theoretical model represents the generalization of the indentation of a sphere into an infinite homogeneous halfspace to the problem of a Hertzian load acting on a halfspace covered with one or more films having different elastic properties. The model allows the analytical calculation of the complete elastic stress field and the deformations within the films and the substrate. Some results of the model shall be confirmed by nanoindentation experiments using an UMIS-2000 nanoindenter into Si3N4/SiO2 and SiO2/ Si3N4 double layers on BK7 glass and Si(100) single crystal. The materials used allow accurate measurements due to their homogeneous, amorphous structure as well as low surface and interface roughness. After the determination of the instrument compliance and the real, depth dependent indenter radius the measured loaddepth data are compared with calculated results. It is shown that measurement results can be correctly interpreted by the model. The onset of plastic deformation is investigated for the same samples by multiple partial unloading experiments with a 4-µm radius diamond sphere. The critical load at which a first deviation from a wholly elastic response occurs is used for a stress calculation with the model. The mechanical behavior of the different film combinations is interpreted by means of the von Mises comparison stress. The measured results, together with the analytical modeling, allow an optimization of the thickness and modulus of the individual layers to get a maximum mechanical stability.
The accuracy and comparability of nanoindentation results depend significantly on the calibration of area function and instrument compliance. The area function results should not depend on the reference material used or on the calibration method (direct or indirect). This has been investigated for 18 different Berkovich tips. A novel calibration method is proposed that confirms the material independence of the area function and gives a force-dependent instrument compliance function. An agreement between direct and indirect calibration could only be achieved by considering a radial displacement correction. Further, it is shown that the transition range from a spherical cap to the correct face angle of the pyramid can extend to a depth of more than 250 nm. A better parameter for the indenter than the tip radius is the offset of the contact radius to the radius of an ideal tip at a depth where the correct face angle is reached.
An extensive comparison between the conventional Vickers hardness at 500 mN and indentation hardness measured with Vickers indenters at 500 mN is presented for up to 20 different materials and for three different instruments. Additionally, the indentation modulus is compared to Young’s modulus, which was measured with alternative methods or taken from the literature. It is shown that the agreement between the results from depth-sensing indentation and the reference values can be improved by additional corrections, for the calculation of the indentation area. With corrections the mean hardness difference to the Vickers hardness reference as average of all investigated materials can be reduced to about 10 % although disturbing pile-up or sink-in effects can still not be considered. For the modulus, the mean difference was only about 6 %.