Dynamic tensile compliance

A full description of the relation between (Tzz t) and ezz t) is provided by the complex dynamic tensile compliance jD, defined as... 

Identical relationships apply to the compliance in a dynamic tensile experiment. Equations (3.79) and (3.80) are plotted in Fig. 3.13. 

The viscoelastic properties of materials in other modes of deformation may also be described in terms of a complex modulus or a compliance. In the case of dynamic tensile tests, the complex modulus is given by... 

We note that, in principle, the main physical discussions related to filler networking in this paper do not change if a sinusoidal tensile or uniaxial compres-sional stress (amplitude 0) is imposed on the rubber material. In some examples the complex dynamic modulus is then denoted with E = E + iE" and the compliance with C = C - iC". All theoretical considerations use the shearing modulus G. ... 

This is because although 0 = (10), in general, cr(10) oQ (it will usually be less). In principle, the quantities we have defined, E(t), Dit), Gif), and J(i), provide a complete description of tensile and shear properties in creep and stress relaxation (and equivalent functions can be used to describe dynamic mechanical behavior). Obviously, we could fit individual sets of data to mathematical functions of various types, but what we would really like to do is develop a universal model that not only provides a good description of individual creep, stress relaxation and DMA experiments, but also allows us to relate modulus and compliance functions. It would also be nice to be able formulate this model in terms of parameters that could be related to molecular relaxation processes, to provide a link to molecular theories. 

Characterization. Opacity of a sample was determined from its absorption at 700 nm. Dynamic mechanical characterization was carried out with an automated Rheovibron DDV-IIC (IMASS) in the tensile mode with a heating rate cf 1.5°/min data taken at 11 Hz are reported here. The same sample was used for the entire temperature range of -100° to 150°C. Because of the magnitude of the load cell compliance, properties of our samples in the glassy region below about -40°C were not viewed in any quantitative sense. 

The viscoelastic response of equilibrium rubber networks can be obtained by measuring the shear and tensile moduli or compliances as a function of time, or the corresponding dynamic moduli and compliances as a function of frequency. As discussed in Section 5.2, the measurements of any viscoelastic function can be converted to another viscoelastic function. 

This mechanical model is depicted in Fig. 21. The Eqs. (15) and (17) have been confirmed for aromatic polyamide fibers by a variety of experiments. Figure 22 shows the dynamic compliance versus the orientation parameter measured during extension of medium and high-modulus PpPTA fibers. It confirms the linear relation (15) and yields e = 240 G Nm and go = 2 G Nm . It has been shown that the tensile curves of the second and higher extensions of an aramid fiber are well described by Eq. (17) [143]. A relation between the strain and the dynamic... 

We write the dynamic compliance as a function, D uj), because it varies generally with the frequency. To completely characterize the viscoelastic tensile properties of a given sample, one does indeed require to know the complete functional dependence. 

Dynamic mechanical analysis (DMA) was performed to determine the influence of the polymer constitution on tensile modulus and mechanical relaxation behavior. For this purpose, a Perkin Elmer DMA-7 was run in tensile mode at an oscillation frequency of 1 Hz with a static stress level of 5 x lO Pa and a superposed oscillatory stress of 4 x 10 Pa. With this stress controlled instrument, the strain and phase difference between stress and strain are the measured outputs. Typically, the resulting strain levels ranged from 0.05% to 0.2% when the sample dimensions were 8 mm x 2 mm x 0.1 mm. A gaseous helium purge and a heating rate of 3°C min" were employed. The temperature scale was calibrated with indium, and the force and compliance calibrations were performed according to conventional methods. 

The indicated equilibrium compliance of 10 7 1 cm /djme corresponds to an equilibrium shear modulus of 12 x 10 dynes/cm, close to but considerably higher than that found. This may reflect an unexpected difficulty in preparing reproducible samples or it may reflect a different sample histoiy. The tensile specimens were tested shortly after preparation while the dynamic mechanical properties were measured some l8 months after preparation. 

Fig. 4. The dynamic compliance, 533 = / as a function of > during tensile deformation of the fibre. A, A Fibre 1 , fibre 2 O, , fibre 3. Open symbols...

It is worth noting that dynamic strain softening is observed on filled vulcanizates whatever is the strain mode, i.e., shearing, tensile of uniaxial compression. The shear modulus G =G +iG" is explicitly considered here, but the same considerations would in principle apply as well to the tensile modulus E =E +iE" or the compliance / =/A/."... 

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