Bulk compliance functions

In other words, independently of the viscoelastic history in the linear region, the tensile compliance function can readily be obtained from both the shear and bulk compliance functions. For viscoelastic solids and liquids above the glass transition temperature, the following relationships hold when t oo J t) t/T[ [Eq. (5.16)], D t) = y Jt [Eq. (5.21)], and D t)J t)/ >. These relations lead to r 3t that is, the elongational viscosity is three times the shear viscosity. It is noteworthy that the relatively high value of tensile viscosity facilitates film processing. 

As indicated in another section, the response to an isotropic pressure as a step function of time gives the bulk creep compliance B(t). However, the response to a sinusoidal pressure gives the complex bulk compliance ... 

As an example of bulk viscoelastic behavior, data for a poly(vinyl acetate) of moderately high molecular weight are shown in Fig. 2-9. Measurements by McKinney and Belcher of the storage and loss bulk compliance B and B" at various temperatures and pressures are plotted after reduction to a reference temperature and pressure of 50°C and 1 atm respectively (see Chapter 11). The complex bulk compliance is formally analogous to the complex shear compliance, but the two functions present several marked contrasts. 

An excellent reference describing appropriate ways of measuring the piezoelectric coefficients of bulk materials is the IEEE Standard for Piezoelectricity [1], In brief, the method entails choosing a sample with a geometry such that the desired resonance mode can be excited, and there is little overlap between modes. Then, the sample is electrically excited with an alternating field, and the impedance (or admittance, etc.) is measured as a function of frequency. Extrema in the electrical responses are observed near the resonance and antiresonance frequencies. As an example, consider the length extensional mode of a vibrator. Here the elastic compliance under constant field can be measured from... 

The Poisson ratio, like the bulk, tensile, and shear creep compliance, is an increasing function of time because the lateral contraction cannot develop instantaneously in uniaxial tension but takes an infinite time to reach its ultimate value. In response to a sinusoidal uniaxial stretch, the complete Poison ratio is obtained ... 

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady-state recoverable compliance) are functions of Af , (and to a lesser extent MWD). The glass transition temperature of rubbers is independent of molecular weight because chain ends for high polymers are too sparse to affect this bulk property (Figure 3.14 Bogoslovov et al., 2010). The behavior can be described by the empirical Fox-Hory equation (Fox and Flory, 1954) ... 

According to specific requirements, polymers have been used in devices for replacing deficient parts or assisting different functions of the body, thanks to the various physical and mechanical properties resulting from the bulk of the material, e.g. compliance. At this level, the user of polymers should also be aware of the fact that living tissues are in contact with polymers by their outermost surface. Thus, in addition to the classical properties for which polymers are used, the reactions and even the fate of the living tissues can be determined by the properties of the surface. To illustrate this, let us examine a simple in vitro experiment in which cells are grown in a polymeric vessel. Petri dishes are usually made of polystyrene, which is a transparent and... 

Once again the reader is reminded that, although all the equations in this chapter refer to deformation in shear, they are equally applicable to other types of deformation if the shear moduli, compliances, and spectra are replaced by the corresponding functions appropriate to extension or bulk compression, etc. 

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