Sinusoidal oscillatory tests

The four commonly used techniques to extract information on the viscoelastic behavior of suspensions are creep-compliance measurements, stress-relaxation measurement, shear-wave velocity measurements, and sinusoidal oscillatory testing (25-27). In general, transient measurements are aimed at two types of measurements, namely, stress relaxation, which is to measure the time dependence of the shear stress for a constant small strain, and creep measurement, which is to measure the time dependence of the strain for a constant stress. 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

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. 

Typically, in dynamic oscillatory testing, a sinusoidal (oscillatory) small-amplitude stress is applied to the sample and the mechanical response measured as functions of both oscillatory frequency and, in some instances, temperature. 

Given that nonlinearities are ubiquitous, testing with oscillatory excitation is of less practical importance in contact mechanics than in other fields of material science. For instance, stick-slip motion is most easily studied by steadily pulling the object of interest across the supporting substrate. Oscillatory testing will result in complicated trajectories [17]. Sinusoidal excitation mostly... 

The elastic nature of a fluid is characterized by dynamic mechanical or stress relaxation techniques. Dynamic mechanical (oscillatory) testing is a procedure in which a sample is sinusoidally strained and the resultant stress is measured. The shear stress T varies with the same frequency as the shear rate... 

DMA measures the viscoelastic properties of a sample using either transient or dynamic oscillatory tests. Transient tests include creep and stress relaxation. In creep, a stress is applied to the sample and held constant, while deformation is measured versus time. After some time, the stress is removed and the recovery measured. In stress relaxation, a deformation is applied to the sample and held constant the degradation of the stress required to maintain the deformation is measured versus time. The most common test is the dynamic oscillatory test, where a sinusoidal stress (or strain) is applied to the material and the resultant sinusoidal strain (or stress) is measured. Also measured is the phase difference, 8, between the two sine waves. The phase lag will be 0° for a purely elastic material and 90° for a purely viscous material. Viscoelastic materials such as polymers will exhibit an intermediate phase difference. Since modulus equals stress divided by strain, the complex modulus, E, can be calculated. From E and 8, the storage modulus, E, the loss modulus, E", and tan 8 can be calculated ... 

If we perform an oscillatory test by applying a sine-wave-shaped input of either stress or strain, we can then, using suitable electronic methods, easily resolve (i.e. separate) the resulting sinusoidal strain or stress output into a certain amoimt of solid-like response, which is in phase with the input, and a corresponding amount of liquid-like response which is n/2 (i.e. 90°) out of phase with the input, see figure 8. 

Frequency sweeps are oscillatory tests performed at variables frequencies, keeping the amplitude and temperature at a constant value. For controlled shear strain tests, a sinusoidal strain is fixed with an amplitude in the viscoelastic linear region. These tests are used to investigate the time-dependent shear behavior. 

The TA Instruments CSL2 rheometer can perform low frequency oscillatory measurements as well as steady-state viscosity determinations, even though it has a simple mechanical system. The sinusoidal wave form is generated mathematically in the computer rather than with an electromechanical drive system. The stress is controlled, and the resulting strain is determined and stored in memory. The computer analyzes the wave form and calculates the viscosity and elasticity of the specimen at the frequency of the test. As of this writing (1996), the oscillation software covers a frequency range of 10-4 -40 Hz. This range could be increased as faster software and computers become available. 

In a series of experiments we have tested the type and range of entrainment of glycolytic oscillations by a periodic source of substrate realizing domains of entrainment by the fundamental frequency, one-half harmonic and one-third harmonic of a sinusoidal source of substrate. Furthermore, random variation of the substrate input was found to yield sustained oscillations of stable period. The demonstration of the subharmonic entrainment adds to the proof of the nonlinear nature of the glycolytic oscillator, since this behavior is not observed in linear systems. A comparison between the experimental results and computer simulations furthermore showed that the oscillatory dynamics of the glycolytic system can be described by the phosphofructokinase model. 

Dynamic Mechanical Testing - Film properties such as impact resistance and the cure response of thermosetting resins are conveniently investigated by dynamic measurements in which an oscillatory or torsional strain is applied to the sample with the stress and phase difference between the applied strain and measured stress being determined. In the present study, a Rheovibron Viscoelastometer was used which employed a sinusoidal strain at a... 

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... 

Dynamic Oscillatory Experiments The dynamic rheological properties of a polymeric solution can be determined by small-amplitude oscillation tests [2]. In small amplitude oscillatory measurements, a sinusoidally varying shear stress field is imposed on a fluid and the amplitude of the resulting shear strain and phase angle between the imposed stress and the strain is measured. The test is... 

Dynamic mechanical testing involves the application of an oscillatory strain 7(f) = 70 cos(cot) to a sample. The resulting sinusoidal stress cr(t) = (Tq cos(cot -E is measured and correlated against the input strain, and the viscous and elastic properties of the sample are simultaneously measured. 

Oscillatory shear flow properties (also referred to as dynamic viscoelastic properties) have long been used to investigate the viscoelastic properties of polymeric materials (Ferry 1980). Oscillatory shear flow measurement requires an instrument that can generate sinusoidal strain as an input to the fluid under test and record the stress resulting from the deformed fluid as an output. For such purposes, a parallel-plates flxture as well as a cone-and-plate flxture can be used the uniform shear rate in the radial direction that is necessary when conducting steady-state shear flow experiments is no longer necessary. 

In oscillatory shear flow, a sinusoidal strain is imposed on the fluid under test. If the viscoelastic behavior of the fluid is linear, the resulting stress will also vary sinusoidally, but it will be out of phase with the strain, as schematically shown in Figure 5.5. Since the sinusoidal motion can be represented in the complex domain, the following complex quantities may be defined ... 

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