Small-amplitude oscillatory testing

Using plateau storage modulus (G t obtained from small amplitude oscillatory tests to calculate molecular weight between cross-links (Wfc)... 

The relaxation times, t, and corresponding moduli, G, constitute what is called the distribution or spectrum of relaxation times. The relaxation spectrum given in Eq. (3-40) is a distinctive feature of the Rouse model that can be tested experimentally. A simple type of rheological experiment from which this spectrum can be obtained is small-amplitude oscillatory deformation, discussed in Section 1.3.1.4. In this test, at low frequencies, (o < /x, the Rouse model predicts the usual terminal relaxation behavior G — Gco rf, and G" = Gcnxi. More significantly, at higher frequencies, where co is in the range 1/t, oj < 1/tat, the Rouse model predicts a power-law frequency dependence of G and G" ... 

Small-Amplitude Oscillatory Motion ( Dynamic Testing )... 

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... 

Small amplitude oscillatory shear measurements, creep and creep recovery tests are examples of small perturbation tests carried out on hydrogels. The principle of small amplitude oscillatory shear measurements is shown in Fig. 2. 

Small amplitude oscillatory measurements were conducted in shear using a strain-controlled ARES-LS rheometer equipped with 25mm parallel plate geometry. Testing was conducted to determine the viscoelastic fingerprint of the resins at 230°C. All measurements were conducted in the linear viscoelastic regime under nitrogen. 

The most popular dynamic test procedure for viscoelastic behavior is the application of an oscillatory stress of small amplitude. This shear stress applied produces a corresponding strain in the material. If the material were an ideal Hookean body, the shear stress and shear strain rate waves would be in phase (Fig. 14A), whereas for an ideal Newtonian sample, there would be a phase shift of 90° (Fig. 14B), because for Newtonian bodies the shear strain is at a maximum, when a maximum of stress is present. The shear strain, when assuming an oscillating sine fimction, is at a maximum in the middle of the slope, because there is the steepest increase in shear strain due to the change in direction. For a typical viscoelastic material, the phase shift will have a value between >0° and <90° (Fig. 14C). 

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. 

The viscoelastic parameters are generally measured by dynamic oscillatory measurements. Apparatus of three different configurations can be used cone and plate, parallel plates, or concentric cylinders. In the case of cone and plate geometry, the test material is contained between a cone and a plate with the angle between cone and plate being small (<4°). The bottom member undergoes forced harmonic oscillations about its axis and this motion is transmitted through the test material to the top member, the motion of which is constrained by a torsion bar. The relevant measurements are the amplitude ratio of the motions of the two members and the associated phase lag. From this information it is relatively simple to determine G and G". 

Conventional wear test configurations can be adapted to fretting. Ball-on-flat, block-on-ring, and crossed cylinders can be modified so that the sliding motion can be made oscillatory and the amplitude small (less than 100 tm). 

Dispersed systems, i.e. suspensions, emulsions and foams, are ubiquitous in industry and daily life. Their mechanical properties are often tested using oscillatory rheological experiments in the linear regime as a function of temperature and frequency [29]. The complex response function is described in terms of its real part (G ) and imaginary part (G"). Physical properties like relaxation times or phase transitions of the non-perturbated samples can be evaluated. The linear rheology is characterized by the measurement of the viscoelastic moduli G and G" as a function of angular frequency at a small strain amplitude. The basics of linear rheology are described in detail in several textbooks [8, 29] and will not be repeated here. The relations between structure and linear viscoelastic properties of dispersed systems are well known [4,7, 26]. 

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