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K.Y. Zeng Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore

L. Shen Institute of Materials Research and Engineering, Singapore 117602, Singapore (Received 27 January 2005; accepted 25 March 2005)

A five-step indentation scheme is proposed to extract the elastic and viscoelastic properties of polymeric materials using a sharp indenter. In the formulation, analytical solutions to the elastic-viscoelastic deformation based on the concept of “effective indenters” proposed by both Pharr and Bolshakov [Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002)] and Sakai [Elastic recovery in the unloading process of pyramidal microindentation. J. Mater. Res. 18, 1631 (2003)] were derived. Indentation experiments on polymethylmethacrylate following the five-step scheme were performed. The elastic-viscoelastic parameters were extracted by fitting the solution based on Sakai’s effective indenter to the experimental results using a genetic algorithm. It was found that the solution based on Sakai’s effective indenter was able to correctly extract the elastic properties. Based on this prediction and the experimental results, Pharr and Bolshakov’s effective indenter profile could be determined. The extracted elastic-viscoelastic parameters using the solution based on Pharr and Bolshakov’s effective indenter were independent of the reloading levels. I. INTRODUCTION

The nanoindentation technique has drawn much interest recently for both its efficiency and versatility in measuring the mechanical properties of small volumes of materials and thin films. However, the application of nanoindentation to polymeric materials is still a challenging issue. Since the unloading curve of polymers depends not only on the holding time but also on the unloading rate, the widely used Oliver & Pharr method1 is greatly limited. It is well known that when the unloading rate is low, the initial slope of the unloading curve, which is defined as the contact stiffness, may even become negative, causing the so-called “nose” effect. It is believed that the viscoelasticity and/or viscoplasticity of polymeric materials are responsible for this phenomenon. Several methods have been proposed to study the indentation of polymers. Cheng et al.2 derived an analytical solution to the indentation on polymers with a flatended punch based on the standard viscoelastic solid model. This model is able to predict short-time creep behavior of polymers. Recently, Zhang et al.3 derived a

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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0200 J. Mater. Res., Vol. 20, No. 6, Jun 2005

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semi-analytical solution to the indentation creep of a polymeric film/substrate system with a flat-ended punch based on a more complicated generalized Kelvin model. This model is able to predict relatively long-time creep behavior of polymers. For these flat-ended punch indentation studies, the instantaneous plastic deforma