Indentation responses of time-dependent films on stiff substrates
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Robert F. Cook Materials Science and Engineering, University of Minnesota, Minneapolis, Minnesota 55455
John A. Emerson Sandia National Laboratories Albuquerque, New Mexico 87185
Neville R. Moody Sandia National Laboratories Livermore, California 94551 (Received 24 February 2004; accepted 20 May 2004)
A viscous-elastic-plastic indentation model was extended to a thin-film system, including the effect of stiffening due to a substrate of greater modulus. The system model includes a total of five material parameters: three for the film response (modulus, hardness, and time constant), one for the substrate response (modulus), and one representing the length-scale associated with the film-substrate interface. The substrate influence is incorporated into the elastic response of the film through a depth-weighted elastic modulus (based on a series sum of film and substrate contributions). Constant loading- and unloading-rate depth-sensing indentation tests were performed on polymer films on glass or metal substrates. Evidence of substrate influence was examined by normalization of the load-displacement traces. Comparisons were made between the model and experiments for indentation tests at different peak load levels and with varying degrees of substrate influence. A single set of five parameters was sufficient to characterize and predict the experimental load-displacement data over a large range of peak load levels and corresponding degrees of substrate influence.
I. INTRODUCTION
Depth-sensing indentation (DSI, sometimes called “nanoindentation”), in which the load and displacement are continuously monitored during a contact test, has developed into a standard technique for measurement of local mechanical responses of engineering materials. This development has been due in part to the availability of commercial instruments for small-scale contact testing, along with the rise of standard analytic techniques for property deconvolution.1 Such standard techniques have been used reliably for mechanical analysis of metals, glasses, ceramics, and composites.1–5 The standard analysis techniques rely on the (relative) time-independence of responses in the experimental timeframe. Many materials, including polymers and biological tissues, exhibit substantial time-dependent responses in an experimentally-relevant timeframe. Hallmarks of a time-
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2004.0308 J. Mater. Res., Vol. 19, No. 8, Aug 2004
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dependent response include creep at fixed load, stressrelaxation at fixed displacement, and rate-dependent responses. There are well-documented errors that result when such time-dependence is ignored in indentation analyses (including large apparent modulus values due to creep on unloading, and small apparent hardness values due to large viscous displacements6). Popular experimental approaches for treating indentation of time-dependent materials use a long hold time at peak load, aspiring t
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