Strain oscillatory

FT rheometry is a powerful technique to document the nonlinear viscoelastic behavior of pure polymers as observed when performing large amplitude oscillatory strain (LAOS) experiments. When implemented on appropriate instmments, this test technique can readUy be applied on complex polymer systems, for instance, filled mbber compounds, in order to yield significant and reliable information. Any simple polymer can exhibit nonlinear viscoelastic properties when submitted to sufficiently large strain in such a case the observed behavior is so-called extrinsic... 

For the continuous mode, we utilized a dynamic rheological technique, Fourier transform mechanical spectroscopy (FTMS) (77,75), which provided a powerful method for monitoring, simultaneously, the evolving dynamic moduli at several frequencies during the course of photo-cross-linking. In this technique, an oscillatory strain, y, was applied to the sample, such that... 

Viscoelasticity is studied using dynamic mechanical analysis. When we apply a small oscillatory strain and measure the resulting stress. Purely elastic materials have stress and strain in phase, so that the response of one caused by the other is immediate. In purely viscous material the phase delay between stress and strain reach 90 degree phase lag. 

One frequently deals with the linear effects of anisotropy which are induced by oscillatory velocity gradients or by oscillatory strains... 

The most common dynamic method is oscillatory testing, in which the sample is subjected to a sinusoidal oscillatory strain, and the resulting oscillatory stress measured. The more sophisticated rotational viscometers have the additional capability of dynamically testing liquid-like materials using small angle oscillatory shear. A parallel disc viscometer can be set up for testing solid-like materials (e.g., butter), in oscillatory shear. Some UTM-type solids rheometers, in which the moving crosshead can be made to reciprocate sinusoidally, can be used to test solid-like materials in oscillatory deformation in compression, tension or shear. 

Fig. 24. G and G" obtained using small amplitude oscillatory strain for PCLC10 before and after large-amplitude shear. See text for conditions of large amplitude shear. Master curves obtained by application of time-temperature superposition and shifted to T0=55 °C. From Ref. [54].

Finally, one of the most useful ways of measuring viscoelastic properties is dynamic mechanical analysis, or DMA. In this type of experiment, an oscillating stress is applied to the sample and the response is measured as a function of the frequency of the oscillation. By using different instruments this frequency can be varied over an enormous range. Actually, the sample is usually stretched a little bit and oscillated about this strain also, the stress necessary to produce an oscillatory strain of a given magnitude is the quantity usually measured. If the sample being oscillated happens to be perfectly elastic, so that its response is instantaneous, then the stress and strain would be completely in-phase. If a sinusoidal shear strain is imposed on the sample we have (Equation 13-72) ... 

Kevlar aramid fiber has good vibration damping characteristics. Dynamic (commonly sinusoidal) perturbations are used to study the damping behavior of a material. The material is subjected to an oscillatory strain. We can characterize the damping behavior in terms of a quantity called the logarithmic decrement, A, which is defined as the natural logarithm of the ratio of amplitudes of successive vibrations, i.e. 

For oscillatory strains less than approximately 0.03-0.04, the suspensions showed linear viscoelastic response with the plateau modulus. Go, being independent of frequency (Chow and Zukoski, 1995b). Because Go increases exponentially with volume... 

No influence of strain on the viscoelastic properties was found. A strain sweep to 14% oscillatory strain was performed with frequencies ranging from 1 rad/sec to 10 rad/sec. and gave an essentially linear viscoelastic respons. 

In the rheological structure of most food systems there is a viscous element present, and the deformation curves are often highly influenced by the rate of the imposed strain. This is due to the fact that the material relaxes (or flows) while tested under compression and the resultant deformation of this flow is dependent on the nature of the viscous element (Szczesniak, 1963 Peleg and Bagley, 1983). In the viscoelastic food systems, where during processing it is caused to oscillate sinusoidally, the strain curve may or may not be a sine wave. In cases when a periodic oscillatory strain is applied on a food system like fluid material, oscillating stress can be observed. The ideal elastic solid produces a shear stress wave in phase with... 

Oscillatory strain (solid curve and left axis) and oscillatory stress (dashed curve and right axis) are in-phase for a Hookean solid. 

Giacomin, A. Dealy, J. (1993) Large amplitude oscillatory strain measurements, in Collyer, A. A. (Ed.) Techniques in Rheological Measurements, London Chapman Hall. Giacomin, A., Samurkas, T. Dealy, J. (1989) Polym. Eng Sci., 29, 499. 

Oscillatory measurements using the cone-and-plate viscometer are sometimes carried out to demonstrate the elastic behavior of a viscoelastic fluid [10]. The fluid in the viscometer is subjected to an oscillatory strain imposed on the bottom surface while the response of the shearing stress is measured on the top surface. If the phase shift between the input strain and the output stress is 90°, the sample is purely viscous if it is 0°, the sample is completely elastic. A measured phase shift between 0° and 90° demonstrates that the fluid is viscoelastic. 

During oscillation, the complex shear modulus, G, is defined as the ratio of oscillatory stress to oscillatory strain... 

FIGURE 3.14 Temperature dependence of storage and loss moduli, G and G", and loss tangent, tan (5, for an HR sample measured at an oscillatory strain rate of 15 Hz. The temperature range extended from —40 to 60°C. The loss tangent peak appears in the vicinity of room temperature. 

The viscoelastic behavior is evaluated by means of two types of methods static tests and dynamic tests. In the first calegtuy a step change of stress or strain is applied and the stress or strain response is recorded as a function of time. Stress relaxation, creep compliance, and creep recovery are static methods. The dynamic tests involve the imposition of an oscillatory strain or stress. Every technique is described in the following sections. 

Then the gradual floe destruction produces a shear-thinning behavior, until no Hoes remain but single particles, and the flow becomes Newtonian. In fact, the motion of the droplets under oscillatory strains has been observed by means of diffusing wave spectroscopy (31). Near the yield point, only a small fraction of drops flow while the rest remain as solid blocks. 

Such theories may be used to determine the degree of spherulite deformation from experimental patterns, and have been used for interpreting rates of deformation from light scattering motion pictures. They have been used more recently for explaining the results of dynamic light scattering measurements where samples are subjected to an oscillatory strain. ... 

---