On the Measurement of Creep by Nanoindentation with Continuous Stiffness Techniques
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On the Measurement of Creep by Nanoindentation with Continuous Stiffness Techniques Andrei Rar1,2, Sangjoon Sohn2, Warren C. Oliver3, David L. Goldsby4, Terry E. Tullis4 and George M. Pharr1,2 1 Oak Ridge National Laboratory, Metals and Ceramics Division, Oak Ridge, TN 37831, U.S.A. 2 The University of Tennessee, Department of Materials Science and Engineering, Knoxville, TN 37996, U.S.A. 3 MTS, Nano Instruments Innovation Center, Oak Ridge, TN 37831, U.S.A. 4 Department of Geological Sciences, Brown University, Providence, RI 02912, U.S.A. ABSTRACT Measurement of material creep parameters by means of nanoindentation using continuous stiffness techniques avoids the problems associated with thermal drift that often plague creep measurements based on the time dependence of the indentation depth alone [1,2]. Problems with thermal drift are negligible from a practical point of view during continuous stiffness measurements because the contact stiffness can be measured over a short time period, typically less than one second, during which time the displacements due to thermal drift are minimal. Determination of the time dependence of the indentation depth from the stiffness data relies on the well-known relation between contact stiffness and the square root of the contact area. For pyramidal indenters, the true indentation contact depth must be proportional to the contact stiffness, leading to the assumption that indentation depth is also proportional to the contact stiffness. In this study, we critically examine this assumption using data obtained from experiments on a relatively soft material, epoxy, and a relatively hard material, fused quartz. The results show that just after initial load application, the change in contact area may be different than that expected from the change in indentation depth. One possible explanation for the observed behavior is examined by finite element modeling.
INTRODUCTION The measurement of creep behavior by nanoindentation is attractive for at least two reasons. First, because of the localized nature of the measurements, nanoindentation can be used to study the creep of thin films and small microstructural features. Second, because of the relatively high stresses that are applied and the high sensitivity of the displacement measurements, the technique can be used to examine creep of materials with low creep rates, such as the room temperature creep of minerals [2]. Referring to the diagram in Fig. 1, it is convenient to define the indentation creep rate as
ε& =
dh / dt , h
where h is indentation depth [3]. It has been shown that in many circumstances, the creep rate measured in this way is related to the mean contact pressure under the indenter in exactly the same way that uniaxial creep rate is related to the uniaxial creep stress in a simple tension test [3,4].
(1)
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α
Fig. 1. Schematic illustration of contact geometry for indentation by a self-similar conical indenter.
h*
a
h
For materials with low creep rates at room temperature, such as quartz, measurement
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