Volume-strain behaviour

Stress/strain behaviour in the elastic region, i.e. below the yield stress, as a function of volume fraction, 4>, contact angle, 0, and film thickness, h, was examined [51]. The yield stress, t , and shear modulus, G, were both found to be directly proportional to the interfacial tension and inversely proportional to the droplet radius. The yield stress was found to increase sharply with increasing <(>, and usually with increasing 6. A finite film thickness also had the tendency to increase the yield stress. These effects are due to the resulting increase in droplet deformation which induces a higher resistance to flow, as the droplets cannot easily slip past one another. 

In a later study [56], the effect of gas volume fraction (foam rheology was investigated. Two models were considered one in which the liquid was confined to the Plateau borders, with thin films of negligible thickness and the second, which involves a finite (strain-dependent) film thickness. For small deformations, no differences were observed in the stress/strain results for the two cases. This was attributed to the film thickness being very much smaller than the cell size. Thus, it was possible to neglect the effect of finite film thickness on stress/strain behaviour, for small strains. 

The stress-strain behaviour of thermoelastoplastics is as a rule a nonlinear onell7> 118). It strongly depends on many factors, the most important being the volume... 

From the dynamic mechanical measurements of Stachurski and Ward this process is seen to occur at 50°C in the region of 150 Hz. Clayton et al. concluded therefore that the tensile creep behaviour observed at low draw ratio could be the result of the cone easy shear process occurring in their time scale at 20°C. The observed anisotropy of time dependence of S33 and S22 dS33/dt > dS22/dt) leads to a low value of (0) compared with (90), which is consistent with the above conclusion. Furthermore, calculation of the variation of volume strain with time during tensile creep at 0° and 90° (made possible by the measurement of both lateral and axial strains) showed that at 0° the... 

The statistical theory allows the stress-strain behaviour of an elastomer to be predicted. The calculation is greatly simplified when the observation that elastomers tend to deform at constant volume is taken into account. This means that the product of the extension ratios must be unity... 

Figure 7.19 Effect of volume fraction of steel fibres on the stress-strain behaviour of concrete [44].

An equilibrium model may not be representative of the true situation commonly faced in the laboratory. The relaxation behaviour of the samples becomes progressively longer with increasing volume fraction. It is quite reasonable to suppose that, at high particle concentrations and low electrolyte concentrations, the relaxation times become so long that it is impractical to allow all the stresses and strains to relax from the sample prior to measurement. Stress relaxation studies for a range of particles that show nearly complete relaxation is shown in Figure 5.16.21... 

We have expressed the relaxation behaviour in terms of the number of chains per unit volume. At this stage we are considering the polymer in an undiluted state. Suppose we now apply a step strain to the melt in the linear regime. Two different zones of behaviour can be seen relative to the time re. This is the time at which the tube constraints begin to affect the relaxation of the chain ... 

It should be noted that the theory described above is strictly vahd only close to Tc for an ideal crystal of infinite size, with translational invariance over the whole volume. Real crystals can only approach this behaviour to a certain extent. Flere the crystal quality plays an essential role. Furthermore, the coupling of the order parameter to the macroscopic strain often leads to a positive feedback, which makes the transition discontinuous. In fact, from NMR investigations there is not a single example of a second order phase transition known where the soft mode really has reached zero frequency at Tc. The reason for this might also be technical It is extremely difficult to achieve a zero temperature gradient throughout the sample, especially close to a phase transition where the transition enthalpy requires a heat flow that can only occur when the temperature gradient is different from zero. 

The strain rate dependence of the yield stress is shown at various temperatures in Fig. 20. To go further in the analysis, it is interesting to use the Eyring approach presented in Sect. 2.2.1.1. For this purpose, the ratio oy/T, K is plotted versus log( , s-1) at various temperatures in Fig. 21. A linear dependence is observed at each temperature, in agreement with the Eyring expression. However, the slopes show two different temperature regimes at low and high temperatures. Of course, the activation volume, Vo, directly related to the slope, reflects the change in behaviour, as shown in Fig. 22. At low temperature, the activation volume is small (around 0.1 nm3) and independent of temperature, whereas it increases rapidly above room temperature... 

Very important phenomena in polymer behaviour, such as viscoelasticity, stress, strain, volume and enthalpy relaxation, ageing, etc., are characterised by time-dependence of the polymer properties. 

This problem falls into a category of strongly coupled fluid-structure interaction (FSI) problems due to comparable stiffnesses of the container and its liquid content. Hence, accurate prediction of containers behaviour requires a liquid-container interaction model. Here, a two-system FSI model based on the Finite Volume Method is employed, and a good agreement is found between measured and predicted pressure and strain histories. 

---