Broadband nanoindentation of glassy polymers: Part I. Viscoelasticity
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Rod S. Lakes Department of Engineering Physics, University of Wisconsin—Madison, Madison, Wisconsin 53706
Don S. Stone Materials Science Program, University of Wisconsin—Madison, Madison, Wisconsin 53706; and Department of Materials Science and Engineering, University of Wisconsin—Madison, Madison, Wisconsin 53706 (Received 17 February 2011; accepted 27 September 2011)
Protocols are developed to assess viscoelastic moduli from unloading slopes in Berkovich nanoindentation across four orders of magnitude in time scale (0.01–100 s unloading time). Measured viscoelastic moduli of glassy polymers poly(methyl methacrylate), polystyrene, and polycarbonate follow the same trends with frequency (1/unloading time) as viscoelastic moduli generated from dynamic mechanical analysis and broadband viscoelastic spectroscopy but are 18–50% higher. Included in the developed protocols is an experimental method based on measured indent area to remove from consideration indents for which viscoplastic deformation takes place during unloading. Ancillary measurements of indent area and depth reveal no detectable (;1%) change in area between 200 s and 4.9 days following removal of indenter.
I. INTRODUCTION
Polymers are known to exhibit viscoelastic behavior, meaning the relationship between stress and strain in these materials depends on time.1 The primary source of viscoelasticity comes from the thermally activated motions of polymer chains and side groups. Different relaxation processes become apparent at very different time scales and temperatures. Therefore, complete characterization of the viscoelastic behavior in polymers requires measurements over a wide range of time scale and temperatures. Many types of experiments are used to assess viscoelasticity in polymers.1 Creep is a common example of a transient type of experiment, in which a constant stress is applied and the increase in strain is measured with time. In a dynamic experiment, the response of a material to cyclic loading at various applied frequencies is analyzed. Interest in developing nanoindentation-based methods to measure viscoelastic moduli2–4 has increased recently largely because of interest in studying microscopic polymer systems, such as thin films and individual components in composites. Theory for the contact of an indenter against a viscoelastic half-space has been around for about 50 years.5–10 Of all indenter geometries, flat punches are easiest to analyze because the contact area does not change a)
during the experiment and the correspondence principle can be used. Flat punches have been used to generate viscoelastic properties using both dynamic and transient types of indentation experiments.11 However, punches have the disadvantage that they can probe only volumes of materials as small as the punch itself can be manufactured. Cone and pyramid geometries, on the other hand, offer the advantage of being able to probe arbitrarily small volumes. Specifically, to reduce the contact region of a flat end punch, one must use a new, smaller punch; but with a cone o
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