Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness meas
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J.H. Strader Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200
W.C. Oliver Agilent Technologies, Nanotechnologies Measurement Division, Oak Ridge, Tennessee 37830 (Received 4 August 2008; accepted 3 October 2008)
Experiments were performed on a (100) copper single crystal to examine the influences that small displacement oscillations used in continuous stiffness measurement techniques have on hardness and elastic-modulus measurements in nanoindentation experiments. For the commonly used 2-nm oscillation, significant errors were observed in the measured properties, especially the hardness, at penetration depths as large as 100 nm. The errors originate from the large amount of dynamic unloading that occurs in materials like copper that have high contact stiffness resulting from their high modulus-to-hardness ratios. A simple model for the loading and unloading behavior of an elastic–plastic material is presented that quantitatively describes the errors and can be used to partially correct for them. By correcting the data in accordance with model and performing measurements at smaller displacement oscillation amplitudes, the errors can be reduced. The observations have important implications for the interpretation of the indentation size effect. I. INTRODUCTION
Continuous stiffness measurement (CSM), also sometimes referred to as force modulation or dynamic stiffness measurement (DSM), is a convenient technique for measuring hardness and elastic modulus at small depths in nanoindentation experiments.1–4 An important advantage of the technique is that it allows basic mechanical properties like hardness and elastic modulus to be evaluated continuously as the indenter is driven in during loading, as opposed to the load-unload technique, which applies only to one specific depth as in the original Oliver–Pharr method,1 or the partial unloading methods that have been developed for spherical indentation by Field and Swain.5,6 CSM is usually implemented by applying a small, sinusoidally varying load to the primary load signal and measuring the amplitude and phase of the displacement oscillation at the same frequency by means of a frequency-specific amplifier.1,2 The stiffness, which for a)
Address all correspondence to this author. e-mail: [email protected] This author was an editor of this focus issue during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/jmr_policy DOI: 10.1557/JMR.2009.0096 J. Mater. Res., Vol. 24, No. 3, Mar 2009
an elastic contact is given by the ratio of the load amplitude to the displacement amplitude, can then be measured continuously during the loading cycle. By means of feedback control, the technique can also be implemented for experiments performed at constant displacement oscillation amplitudes, which are typically 1 or 2 nanometers. A basic assumption underlying almost all CSMs is that the amplitude of the oscillation is small enough that its
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