Cyclic indentation of polymers: Instantaneous elastic modulus from reloading, energy analysis, and cyclic creep
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Cyclic indentation of polymers: Instantaneous elastic modulus from reloading, energy analysis, and cyclic creep Olga Smerdova1,a)
, Marina Pecora1, Marco Gigliotti1
1
Département Physique et Mécanique des Matériaux, Institut Pprime, CNRS, ISAE-ENSMA, Université de Poitiers, Futuroscope Chasseneuil F-86962, France a) Address all correspondence to this author. e-mail: [email protected] Received: 8 July 2019; accepted: 3 September 2019
An analysis of indentation cyclic behavior of polymers is carried out with the aim to tackle time-dependent behavior of polymer at several time scales by one test. The method consists in cycling the load between a positive close-to-zero value and a maximum peak value (10 mN in this study) for long time with constant loading rate. The short time scale is characterized through the instantaneous elastic modulus determined from reloading curves at each cycle. The advantages of determination of instantaneous elastic modulus from reloading instead of commonly used unloading curves are discussed. The energy dissipation describes viscoelasticity and plasticity at the time scale of one cycle. The evolution of both parameters with cycles along with the cyclic creep describes the long-time viscoelasticity. The cyclic indentation behavior of poly(methyl methacrylate), PR520 epoxy, and high-density polyethylene (HDPE) polymers is analyzed, and a comparison with the macroscopic cyclic behavior of HDPE is presented.
Introduction Nano- and micro-instrumented indentation techniques are now common to characterize the metallic materials. Some of the obvious advantages of these techniques are a small tested volume, which enables characterization of material gradients and heterogeneous materials, and a simple analysis method that provides hardness and elastic modulus [1]. However, when it comes to polymers, the application of the Oliver and Pharr method revealed to be questionable. Many authors [2, 3, 4, 5, 6, 7, 8, 9, 10] noticed difficulties in fitting of the unloading curve, which is necessary to obtain material stiffness and contact depth, since this curve presented a “nose,” i.e., negative stiffness at the beginning of the unloading. This is usually attributed to the viscoelastic behavior of polymers, which results in a retardation of material response to the loading phase superposed to the unloading recovery behavior. There are several ways to avoid the problem of negative stiffness and to improve the fitting of the unloading curve. For instance, a holding period is often introduced at the maximum load. However, the duration of hold has a significant impact on the values of elastic modulus and hardness [5, 6, 7]. A combination of minimal duration of hold and minimal unloading speed was suggested by Feng and Ngan [8] to obtain instantaneous elastic modulus clear of
ª Materials Research Society 2019
viscoelastic effects. Recently, Hardiman et al. [6] suggested to fit the unloading curve and to evaluate the stiffness not at the maximal load, but at the point of zero creep and relaxation drift, whe
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