Viscoelastic effects during unloading in depth-sensing indentation
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With polypropylene as a prototype viscoelastic material at room temperature, it was found that a “nose” may appear in the unloading segment of the load–displacement curve during nanoindentation when the holding time at peak load is short and/or the unloading rate is small, and when the peak load is high enough. The load at which the nose appears was also found to decrease linearly with decreasing unloading rate. A linear viscoelasticity analysis was performed to interpret this effect. The analysis predicts a linear variation between the nose load and the unloading rate, and the slope of such a linear variation is also shown to be proportional to the viscosity parameter of the material. Thus, by measuring the slope of the nose-load versus unloading rate plot at a given temperature, the viscosity parameter of the specimen can be found. This is a new way of measuring the viscosity parameter of a material in addition to the existing method of force modulation and noting the frequency response of the displacement.
I. INTRODUCTION
In the past decade nanoindentation has been established as a standard method for probing mechanical properties including hardness and elastic modulus at the submicron length scale. In the celebrated method for elastic modulus measurement by Oliver and Pharr,1 the tip–sample contact stiffness S and contact area Ac at the onset of unload are measured. The tip–sample reduced modulus Er is then calculated from the contact mechanics relation: Er =
公 2
S
公Ac
.
(1)
Here, Ac is the contact area at full load and is therefore not the residual indent area after unload. This is particularly important for materials like glass or polymers, in which the residual indent size after unload could be significantly smaller than the contact size at full load. Thus, the requirement for area measurement in hardness and elastic modulus measurement is different. Since hardness is defined as the load divided by the residual indent area, we are more concerned with the residual indent area after unload, which can be measured by atomic force microscopy (AFM), for example. This is the prime reason for incorporating AFM on the same platform as indentation in the newest nanoindenters such as the Hysitron (Hysitron Inc., Minneapolis, MN) or the CSM (CSM Instruments SA, Peseux, Switzerland) setups. In elastic modulus measurement, currently the only way of 2604
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J. Mater. Res., Vol. 17, No. 10, Oct 2002 Downloaded: 07 Feb 2015
measuring the contact area Ac under load is to use the area–depth function Ac ⳱ f (hc) of the tip, and the contact depth hc (see Fig. 1) is obtained using the Oliver–Pharr formula: P , (2) hc = h − ⑀ S where ⑀ is a constant depending on the indenter geometry (⑀ ⳱ 0.75 for the Berkovich tip). Equations (1) and (2) are purely results of elastic contact mechanics. In nanoindentation, it is often found that significant viscoelastic effects in general are present at full load. A consequence of pure elasticity is that the contact size or indenter displacement will decrease s
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