Viscoelasticity, linear dynamic mechanical testing

The incorporation of fillers to elastomeric compounds strongly modifies the viscoelastic behavior of the material at small strains and leads to the occurrence of a non-linear behavior known as Payne effect [49] characterized by a decrease in the storage modulus with an increase in the amplitude of small-strain oscillations in dynamic mechanical tests. This phenomenon has attracted considerable attention in the past decade on account of its importance for industrial applications [50-54]. The amplitude AG = G q—G ) of the Payne effect, where G q and G aie the maximum and minimum values of the storage modulus respectively, increases with the volume fo-action of filler as shown in silica-filled PDMS networks (Figure 4.7a). At a same silica loading, the PDMS network filled with untreated silica displays a much higher G value than the treated one and is much more resistant to the applied deformation (Figure 4.7b). 

There are several other comparable rheological experimental methods involving linear viscoelastic behavior. Among them are creep tests (constant stress), dynamic mechanical fatigue tests (forced periodic oscillation), and torsion pendulum tests (free oscillation). Viscoelastic data obtained from any of these techniques must be consistent data from the others. 

The mechanical response of polypropylene foam was studied over a wide range of strain rates and the linear and non-linear viscoelastic behaviour was analysed. The material was tested in creep and dynamic mechanical experiments and a correlation between strain rate effects and viscoelastic properties of the foam was obtained using viscoelasticity theory and separating strain and time effects. A scheme for the prediction of the stress-strain curve at any strain rate was developed in which a strain rate-dependent scaling factor was introduced. An energy absorption diagram was constructed. 14 refs. 

Dynamic mechanical measurements are performed at very small strains in order to ensure that linear viscoelasticity relations can be applied to the data. Stress-strain data involve large strain behavior and are accumulated in the nonlinear region. In other words, the tensile test itself alters the structure of the test specimen, which usually cannot be cycled back to its initial state. (Similarly, dynamic deformations at large strains test the fatigue resistance of the material.)... 

Two manifestations of linear viscoelasticity are creep and stress relaxation-, the respective two testing methods are known as transient tests. One can also apply sinusoidal load, an increasingly more used method of study of viscoelasticity by dynamic mechanical analysis (qv) (DMA). We shall now briefly discuss each of these three approaches. 

Mechanical testing procedures in common use involve other patterns of stress history than the simple creep and relaxation experiments on which the definitions of the transient viscoelastic functions are based, and the sinusoidally varying stress which is inherent in the definitions of the so-called dynamic properties. Certain relations between the behavior under coniplicated conditions and the basic viscoelastic functions are presented here together with some related problems. They are limited to linear viscoelastic systems and hence small strains, but in some cases could be extended to describe larger deformations, especially for simple extension. 

Generally, two different types of measurement are applied to determine the linear viscoelastic behavior, namely static (or equilibrium) and dynamic mechanical measurements. Static tests involve the imposition of a step change in stress and the observation of any subsequent development in time of the strain, whereas dynamic tests involve the application of a harmonically varying strain. In ordinary thermoplastic polymer systems, test conditions such as strain or frequency must be in the linear range otherwise, the results will be dependent on the experimental details rather than on the material under test. 

The linear viscoelastic master curve of a material serves as an important fingerprint for its mechanical behavior and the fine features of these master curves correlate with the particular materials molecular details. For these reasons, master curves are widely generated in practice. Below, we illustrate an example [38] of master curve generation where the original data were taken under dynamic testing. Fig. 2 shows the data. Fig. 3 shows the master curve obtained by means of the shift factor calculated from the data in Fig. 2. Finally, Fig. 4 shows a plot of the shift factor that is seen to display WLF-type behavior. 

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