Error Analysis In Nanoindentation
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evaluation of thin films and near surface mechanical properties [1,3]. The manufacturers claim sub-nanometre (0.04-0.1 nm) displacement and sub-micronewton (0.075 giN) load resolution for the most sensitive instruments. These high resolutions are achieved by use of a capacitance transducer to detect displacement changes, and load is applied by variation of an electromagnetic field on the indenter shaft. The voltage across the capacitance transducer and the loading coil is used to monitor changes in displacement and control the load. Most instruments can operate under load or displacement control although the former is more usual. In addition, the instruments have a small but finite compliance which must be known in order to determine the specimen compliance from the measured compliance. Furthermore, the exact shape of the indenter must also be known and is particularly critical at small (< 200 nm) displacements. Significant errors, therefore, are unlikely to arise because of the lack of resolution, but from errors in the calibration procedures for load and displacement and in the determination of instrument frame compliance and indenter shape. The environment in which the instrument is housed is another key factor which can lead to errors in the final result. In particular, any fluctuation in temperature can result in dimensional changes in the instrument which will affect displacement values, while mechanical vibrations will reduce the resolution of the instrument. It is likely, therefore, that calibration and operational errors will dominate the error budget and it is these factors which determine the overall accuracy of measurements. Estimation of the uncertainties in the various calibration constants must be determined in order 717 Mat. Res. Soc. Symp. Proc. Vol. 356 01995 Materials Research Society
to quote values of hardness and Young's modulus with a 95% confidence limit. Furthermore by carrying out such an analysis it should be possible to optimise measurement conditions to minimise errors. This paper describes the results of such a study carried out with materials having a range of hardness and Young's modulus values of 0.26 - 25 GPa and 60 - 600 GPa, respectively.
ERROR ANALYSIS
In nanoindentation the mechanical properties are calculated from the load-displacement data obtained during an indentation experiment. An assessment of calibration errors indicates that a simple summation of errors is not appropriate in this case, since compliance and area function are depended upon displacement. Thus the error analysis has been carried out using a cumulative approach. Errors in the raw data have been considered first, and then incorporated into the
calculated hardness and Young's modulus, through an appropriate procedure. Calibration Errors In carrying out the error analysis it was assumed that the input-output voltage data is correct, that is no error occurred during voltage readings. Thus, the load, P (mN), and the displacement, h (nm), can be determined by equations (1) and (2), respectively:
P- AVLLC
(
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