Mechanical properties characterization of a viscoelastic solid using low-frequency large-amplitude oscillatory indentati
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M.V. Swain Biomaterials Science Research Unit, Faculty of Dentistry, University of Sydney, Surry Hills, NSW 2010, Australia (Received 3 October 2007; accepted 4 December 2007)
A viscoelastic solid was contacted by a pointed indenter using low-frequency large-amplitude sinusoidal load functions to determine its contact stiffness in a manner similar to that of the continuous stiffness measurement (CSM) technique but in a quasi-static condition. The contact stiffness of a viscoelastic solid determined by the CSM technique, or the dynamic stiffness, is known, from previous CSM-based studies, to overestimate the quasi-static contact stiffness. The contact stiffness of a viscoelastic solid determined in a quasi-static manner is thus hypothesized to help predict the contact depth more accurately. A new analysis procedure based on truncated Fourier series fitting was developed specifically to process the large amplitude sinusoidal indentation data. The elastic modulus of the material characterized in this work was in agreement with that determined by dynamic mechanical analysis, thereby providing evidence for the validity of the present method in characterizing other viscoelastic materials.
I. INTRODUCTION
Nanoindentation is a powerful tool for probing the mechanical properties of materials at nanometer length scales. The technique deduces the reduced elastic modulus as1–3 Er =
公 2
S
公A
,
(1)
where A is the projected area of the sample surface in contact with the indenter, S is the contact stiffness, and  is a constant associated with the geometry of the indenter. Er is related to Poisson’s ratio and the elastic modulus E of the sample through the relation 1/Er ⳱ (1 − 2)/E + (1 − i2)/Ei, where i and Ei are Poisson’s ratio and elastic modulus of the indenter, respectively. For a material whose behavior is independent of its deformation rate, S is determined as the slope of the load (F) versus displacement (h) curve at the onset of quasistatic unloading.
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0211 J. Mater. Res., Vol. 23, No. 6, Jun 2008
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For a creeping solid, however, the slope of the initial unloading curve exceeds the contact stiffness under the influence of creep deformation.4 The load on the sample may be held constant for some period prior to unloading so as to exhaust the creep deformation and hence to reduce the extent of contact stiffness overestimation. In practice, the use of a long maximum load-hold period (to exhaust creep) can compromise the accuracy of the displacement data due to thermal drift, which is often unavoidable in indentation testing at nanometer length scales. A new method of determining the contact stiffness that does not require a long load-hold period was developed for linear viscoelastic and power-law creep solids by Feng and Ngan.4,5 This method determines the contact stiffness as S=
冉冋 冏 册 dP dh
−1
t+
h˙共t−t 兲 − F˙共t+t 兲
t
冊
−1
,
(2)
where h˙(t−t
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