Accurate measurement of tip-sample contact size during nanoindentation of viscoelastic materials
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lypropylene (PP) and amorphous selenium (a-Se) were used as prototype materials at room temperature to explore the problems that may exist in the accurate measurement of the reduced modulus of viscoelastic materials using depth-sensing nanoindentation. As has been reported previously by others, we observed that a “nose” in the load–displacement curve may occur during unloading, indicating significant creep effects at the onset of unloading. To accurately measure the elastic modulus in viscoelastic materials like PP or a-Se, both the contact stiffness and the contact area at the onset of unloading must be determined accurately. The issue of removing the influence of creep on the measurement of the contact stiffness using the Oliver–Pharr method has been addressed in a previous paper by Feng and Ngan. In this work, the effect of creep on contact-depth measurement is considered. Removal of creep effects in both contact stiffness and contact-area measurement leads to satisfactory prediction of the reduced moduli in PP and a-Se.
I. INTRODUCTION
A decade ago, Oliver and Pharr1 proposed a novel method to determine the hardness and elastic modulus of a material using depth-sensing indentation. The Oliver– Pharr method has since become a standard method in the analysis software of commercially available nanoindenters supplied by, for example, MTS, Hysitron, CSM Instruments SA, MicroMaterials, etc. In the Oliver–Pharr scheme, it is assumed that, during the unloading process, the contact between the tip and the surface is purely elastic. The result is the well-known formula for obtaining the contact depth hc:
Pmax , S
hc = hmax − ⑀
(1)
where hmax is the maximum indenter displacement at the onset of unloading, Pmax is the load before unloading, S is the contact stiffness at the onset of unloading, and ⑀ is a constant (⑀ ⳱ 0.75 for Berkovich tip). S is measured by fitting the load (P) versus displacement (h) curve during unloading to the empirical equation P ⳱ a(h − hf)m, where a, hf, and m are fitting parameters.1,2 Once the contact depth hc is calculated from Eq. (1), the contact area Ac can be obtained from the known shape function J. Mater. Res., Vol. 18, No. 5, May 2003
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of the indenter tip, and finally, the reduced modulus, Er can be obtained from the classical contact mechanics result Er =
公 2
S
公Ac
.
(2)
Both Eq. (1) and (2) are based on the assumption that the tip–sample contact is purely elastic. Unfortunately, in many cases, the contact between the tip and the sample is far from purely elastic. Creep effects during indentation have been reported by many researchers.3–17 It is well known that creep effects during unloading may cause the contact stiffness to be overestimated.3,4,8 In extreme cases of viscosity becoming the dominant factor during unloading, as would happen when the unloading rate is low or the hold before unloading is too short or the full load is large enough, the indenter displacement may continue to increase for a short while during t
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