Nanoindentation-derived elastic modulus of an amorphous polymer and its sensitivity to load-hold period and unloading st
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M.V. Swain Biomaterials Science Research Unit, Faculty of Dentistry, University of Sydney, Sydney Dental Hospital, Surry Hills, New South Wales 2010, Australia (Received 22 May 2007; accepted 20 August 2007)
An amorphous polymer was contacted by a Berkovich indenter using the same loading history but with four different unloading rates following a wide range of load-hold time periods. The strain-rate sensitivity index of the creeping solid was determined at each load-hold period based on two readily determinable parameters, which are the effective contact stiffness and strain rate at the onset of unloading. The measured strain-rate sensitivity index was found to increase with decreasing load-hold period, suggesting that the elastic moduli of the amorphous polymers determined by nanoindentation (together with the true contact area) depends significantly on the selection of the load-hold period. The rheological condition of the creeping solid under constant load changes substantially with time to affect the subsequent unloading recovery process. It is therefore advisable to control not only the unloading strain rate but also the load-hold period when testing time-dependent materials.
I. INTRODUCTION
Nanoindentation is a well-established technique for determining the local mechanical properties of classic time-independent materials such as metals and ceramics from the indentation load–displacement curves. On the basis of the Sneddon’s solution1 to the contact problem of an elastic half-space pressed by an axisymmetric punch, the technique derives the reduced elastic modulus as2 Er =
公 2
S
公A
,
(1)
where A is the projected area of the surface in contact with the indenter, S is the (elastic) contact stiffness, and  is a constant associated with the geometry of the indenter. Er is related to the Poisson’s ratio and the elastic modulus E of the material through the relationship 1/Er ⳱ (1 − 2)/E + (1 − i2)/Ei, where i and Ei are the and E values of the indenter. The contact area is determined as a function of the depth of contact hc based on the knowledge of the in-
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0079 J. Mater. Res., Vol. 23, No. 3, Mar 2008
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denter tip geometry. The contact depth (hc) is predicted most commonly by the method proposed by Oliver and Pharr,3 whereby hc is treated as a function of the peak load, peak displacement, and S. This method works well for a time-independent material that is elastic or elastic– plastic with an appreciable work-hardening characteristic. The accuracy of the method is compromised for a highly plastic and non-work-hardening material in the presence of a pileup of the material as a consequence of the plastic flow outside the contact perimeter.4 Based on recent nanoindentation studies of viscoelastic materials,5–10 this method appears to have even more limited applicability to materials exhibiting time-dependent behavior. Determining the hc of a
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