Broadband nanoindentation of glassy polymers: Part II. Viscoplasticity
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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)
The relationship between hardness and flow stress in glassy polymers is examined. Materials studied include poly(methylmethacrylate), polystyrene, and polycarbonate. Properties are strongly rate dependent, so broadband nanoindentation creep (BNC) is used to measure hardness across a broad range of indentation strain rates (104 to 10 s1). Molybdenum (Mo) is also studied to serve as a “control” whose rate-dependent hardness properties have been measured previously and whose flow stress, unlike the polymers, is pressure insensitive. The BNC hardness data are converted to uniaxial flow stress using two methods based on the usual Tabor–Marsh–Johnson correlation. With both methods the resulting BNC-derived uniaxial flow stress data agree closely with literature compression uniaxial flow stress data for all materials. For the polymers, the BNC hardness data depend on initial rate of loading, indicating that the measured properties are path dependent. Path dependence is not detected in Mo. I. INTRODUCTION
Polymers are noted for their pronounced time- and temperature-dependent mechanical properties, including yield. Rate and temperature effects in the yield stress are a consequence of the mechanisms for plastic flow, which involve thermally activated chain rearrangements and side group motions.1,2 Although rate and temperature effects are important in their own right, they can also be used as “fingerprints” to help gain insight into deformation mechanisms and polymer structure (e.g., Refs. 3–7). Approaches involving uniaxial compression, tension, or shear experiments are well established for bulk specimens to assess the temperature and rate dependence of yielding. It is desired to extend studies of rate and temperature dependence of yielding to microscopic polymer systems including thin films8,9 and components in biological materials.10,11 One way to do this is to rely on indentation creep, which has been used for more than 50 years in polymers.12,13 Indentation creep involves pushing a hard (typically diamond), pyramid- or sphere-shaped indenter into the specimen until a predetermined load is reached, then holding the load constant. The constant load portion of the experiment is analyzed. At constant load, the indenter continues to a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.364 J. Mater. Res., Vol. 27, No. 2, Jan 28, 2012
penetrate so that area of contact grows as a function of time. The pressure, or hardness, beneath the indenter and the rate of penetration both decrease with time giving rise to a spectrum of hardness versus strain rate. A similar experiment is impression creep in which the end of a right circu
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