Linear viscoelastic region

For shear strains greater than approximately 2 the ratio cr(r)/> 0 for a concentrated polystyrene solution was reduced at all observable times. For the large strains, relaxation proceeded more rapidly at short times, but at longer times the residua] stress decayed with about the same time dependence as that in the linear viscoelastic region. 

LVE region, see Linear viscoelastic region Lyase, pectic characterized, 342 PGase assay, interference in,... 

Figure H3.2.4 Linear viscoelastic region as determined by the strain dependence of G (storage modulus) and G (loss modulus).

Real (viscoelastic) materials give an intermediate response that is an exponential curve. The exponential time constants associated with the curve are used to approximate the relaxation times of the material itself. Thus, the shape of the output curve is analyzed to give viscoelastic information, although this model fitting is only strictly legitimate in the linear viscoelastic region. Workers have shown that the mechanical parts of the models (springs and dashpots) can be associated with specific parts of a food s makeup. 

Butter and milk fat exhibit viscoelastic behavior at small stresses (Chwiej, 1969 Pijanowski et al., 1969 Shama and Sherman, 1970 Sherman 1976 Shukla and Rizvi, 1995). To probe this behavior, a very small stress or deformation is applied to a sample and the relationships between stress, strain and time are monitored. Viscoelastic testing is performed in the linear viscoelastic region (LVR) where a linear relationship between stress and strain exists and where the sample remains intact. Depending on the material, this region lies at a strain of less than 1.0% (Mulder and Walstra, 1974) or even less than 0.1% (Rohm and Weidinger, 1993). Figure 7.10 shows the small deformation test results for milk fat at 5°C. 

The derivation of fundamental linear viscoelastic properties from experimental data obtained in static and dynamic tests, and the relationships between these properties, are described by Barnes etal. (1989), Gunasekaran and Ak (2002) and Rao (1992). In the linear viscoelastic region, the moduli and viscosity coefficients from creep, stress relaxation and dynamic tests are interconvertible mathematically, and independent of the imposed stress or strain (Harnett, 1989). 

The Contribution of the Linear Viscoelastic Region to the Impact Properties of Thin Polymer Films... 

Although the difficulty in correlating dynamic mechanical and impact data has been noted (J, 2) because the former is measured in the linear viscoelastic region and the latter is measured presumably in the nonlinear region, it is nonetheless well documented (2-8) that various types of correlations do exist between these two measurements. 

As both referees pointed out, other reasons have been offered for energy dissipation during impact. In each case however some energy dissipating mechanism must be provided. The present work indicates that, at least for the samples used, this mechanism is provided by the dynamic mechanical dissipation factor. This in turn is attributed to the fact that at the high strain rates of impact the linear viscoelastic region is the largest, if not the only, contributor to the dissipation process. 

Consider two experiments carried out with identical samples of a viscoelastic material. In experiment (a) the sample is subjected to a stress CT for a time t. The resulting strain at f is ei, and the creep compliance measured at that time is D t) = e la. ln experiment (b) a sample is stressed to a level CT2 such that strain i is achieved immediately. The stress is then gradually decreased so that the strain remains at f for time t (i.e., the sample does not creep further). The stress on the material at time t will be a-i, and the corresponding relaxation modulus will be y 2(t) = CT3/C1. In measurements of this type, it can be expected that az> 0 > ct and Y t) (D(r)) , as indicated in Eq. (11-14). G(t) and Y t) are obtained directly only from stress relaxation measurements, while D(t) and J(t) require creep experiments for their direct observation. Tliese various parameters can be related in the linear viscoelastic region described in Section 11.5.2. 

The influence of temperature on the stress-strain behavior of polymers is generally opposite to that of straining rates. This is not surprising in view of the correspondence of time and temperature in the linear viscoelastic region (Section I l.5.2.iii). The curves in Fig. 11-23 are representative of the behavior of a partially crystalline plastic. 

Wu and Morbidelli (2001) extended the model of Shih et al. (1990) discussed in Chapter 2 to include gels that are intermediate between the strong-link and the weak-link regimes. In addition to the modulus, they also considered the critical strain, yc, at which the linear viscoelastic region ends ... 

Materials can show linear and nonlinear viscoelastic behavior. If the response of the sample (e.g., shear strain rate) is proportional to the strength of the defined signal (e.g., shear stress), i.e., if the superposition principle applies, then the measurements were undertaken in the linear viscoelastic range. For example, the increase in shear stress by a factor of two will double the shear strain rate. All differential equations (for example, Eq. (13)) are linear. The constants in these equations, such as viscosity or modulus of rigidity, will not change when the experimental parameters are varied. As a consequence, the range in which the experimental variables can be modified is usually quite small. It is important that the experimenter checks that the test variables indeed lie in the linear viscoelastic region. If this is achieved, the quality control of materials on the basis of viscoelastic properties is much more reproducible than the use of simple viscosity measurements. Non-linear viscoelasticity experiments are more difficult to model and hence rarely used compared to linear viscoelasticity models. 

Dynamic mechanical properties of all pure components and blends were measured as a function of percent strain and indicated a linear viscoelastic region up to approximately 30-35 percent. Therefore, all rheological experiments were conducted at a strain rate of 20 percent. In cases where thermal degradation occurred (as seen in time sweep), the heating chamber was continuously purged with liquid nitrogen. Frequency sweeps, and in some cases frequency-temperature sweeps, were performed on all pure components and blends. 

An advanced rheometric expansion system (ARES) is used to determine Tg of samples. Strain sweep experiments from 0.01 to 1% strain are conducted to ensure that experiments are carried out in the linear viscoelastic region. All experiments are done at a frequency of IHz and a strain level of 0.05%, which is in the linear region. Temperature sweeps are conducted at a heating rate of 5°C/min over a temperature range which covers the glassy and rubbery regions of the soy flour samples at different water activities. The temperature at which the loss modulus (G") was at a maximum is used to estimate the T . 

As an illustration. Figure 12.10 shows the variation of G and G" (measured in the linear viscoelastic region and at a frequency of 1 Hz) versus the water volume fraction cfr. 

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