Direct measurement of indentation frame compliance
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Lubos Prchlik Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
James F. Smith MicroMaterials Limited, Unit 3, Wrexham Technology Park, Wrexham LL13 7YP, United Kingdom (Received 16 June 2003; accepted 13 October 2003)
Accurate determination of frame compliance is an essential component of instrumented micro- and nanoindentation experiments. In load frames of finite stiffness, the load applied via the indenter induces displacement in both the sample and the load frame. Frame compliance must be identified and subtracted from the total indenter displacement to account properly for sample deformation. Current experimental procedures, in which the frame compliance is inferred from the elastic unloading indentation response of a reference sample, are based on several assumptions and simplifications that can propagate significant uncertainty with respect to subsequent analyses of mechanical behavior of the sample. We outline a new procedure that measures the compliance of the load frame, and identify the effects of load, loading direction, and loading rate on the measured compliance, as well as several possible sources of uncertainty in other available methods of frame compliance determination.
I. INTRODUCTION
Recent developments in the analysis of instrumented or depth-sensing indentation present the opportunity to quantify both the elastic and plastic mechanical properties of materials, including elastic modulus E, yield strength y, and strain hardening exponent n.1–4 The calculation of plastic mechanical properties requires that indentation data are obtained with accuracy and precision greater than that required for determination of only elastic properties.3,5,6 The accuracy of the indentation load– displacement (P–h) response is defined by the calibration of three factors: load P, displacement h, and load frame compliance Cf. Although the calibration of Cf , a measure of the load frame displacement incurred per unit applied load, is as crucial to the accuracy of the data as the basic force and displacement transducer calibrations, its proper implementation has received relatively little attention. Indentation instruments are designed to minimize this compliance, and most manufacturers estimate the magnitude of Cf according to the method of Oliver and Pharr1 and modifications thereof. Commercial instruments exhibit Cf in the range of 10−5 to 10−7 m/N, which means that the instrument displaces as much as 10 nm for a maximum applied load Pmax of 10 mN in nanoindentation experiments (the equivalent of 10 m displacement for Pmax ⳱ J. Mater. Res., Vol. 19, No. 1, Jan 2004
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10 N during microindentation). Such displacements comprise a significant fraction of indentation depth for many natural and engineered materials currently studied via indentation. The level of accuracy attained in the calibration of Cf significantly affects the quantitative interpretation of the P–h response. Because frame comp
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