Extensional modulus, measurement

It has been suggested by Morgan [30] and others [28] that the sonic modulus (i.e. the extensional modulus measured at high frequencies by a wave-propagation technique) can be used to obtain a direct measure of molecular orientation in a manner analogous to the derivation of the so-called optical orientation function /o = (1 - sin2 0) from the birefringence. 

Detailed measurements of the extensional modulus of monofilaments have been made by longitudinal wave-propagation methods, where the relationship of the extensional modulus to molecular orientation and crystallinity has been examined. Early investigations using this technique were made by Hillier and Kolsky [24], Ballou and Smith [25], Nolle [26] and Hamburger [27]. 

The measurement of the extensional modulus was re-examined as a possible method for the measurement of molecular orientation in textile yarns by Charch and Moseley [28], Moseley [29] and Morgan [30], Morgan has developed Hamburger s pulse-propagation method. 

Three HIPS resins possessing distinct rheological properties were utilized in this study STYRON 1200, 1170, and 484. These resins have melt flow rates (MFR) of 5.0, 2.1, and 2.8 g/10 min (200T05kg) and will be referred to in the paper as HIPS 1, HIPS 2, and HIPS 3, respectively. The dynamic mechanical spectroscopy measurements (viscosity vs. frequency and temperature, loss and storage modulus vs. frequency and temperature) were performed on a TA Instruments ARES rheometer. The measurements were obtained at three different temperatures 170, 190, 210, and 2301C. The uniaxial extensional viscosity measurements were performed at three Hencky rates 0.1, and 10s on a SER (Sentmanat Extensional Rheometer, Xpansion Instruments) at 1701C. 

The extensional dynamic storage modulus E and the loss factor tan 8 for a series of linear polyethylene tapes of different draw ratios are shown in Fig. 30(a) and (b). There are two features worthy of particular note. First, the modulus at low temperatures is about 160 GPa, which is about one half of the theoretical modulus and the maximum value obtained from neutron diffraction and other measurements. Secondly, the a and y relaxations are both dearly visible even in the highest draw ratio material, although the magnitude of tan 5 for the y relaxation reduces with increasing draw ratio. 

The empirical temperature bandwidth constant (K), a measure of extensional damping effectiveness, is strongly affected by polymer secondary loss mechanisms. Polymers such as PMMA and PEMA form very effective damping materials because they possess broad temperature span lossy modulus curves. 

Generally, the operative frequency range for the torsional pendulum method is 0.01 to 50 Hz, the upper limit of the frequency defined by the dimensions of the oscillatory frequency relative to the dimensions of the sample. At higher investigative temperatures, the polymeric materials may undergo extensional deformation (creep) due to the weight of the inertia bar. Under such circumstances, a modified torsion pendulum apparatus may be used in which an inertia disk is attached directly onto the end of the sample (12). In addition, this method is frequently employed to measure the torsion modulus at low frequencies. 

In 1956 Thompson and Woods reported that dynamic experiments in extension indicated that orientation increased the temperature of the p transition, about 80°C, for oriented crystalline fibres, and reduced the drop in modulus occurring at higher temperatures. Subsequently nuclear magnetic resonance was used to demonstrate that orientation reduced molecular mobility above the glass transition temperature. Measurements of dynamic extensional and torsional moduli of hot stretched filaments and films were reported in 1963 by Pinnock and Ward, who found that the relations between measured compliances below the glass transition temperature were consistent with the deformation of an incompressible elastic solid. 

The extensional moduli parallel and perpendicular to the stretch direction of drawn films of cellulose acetate were measured by Wilson. Experiments were performed at 20°C for relative humidities of 65% and 100%. In each case the parallel modulus ( o) increased markedly with draw ratio while 90 showed a slight decrease. 

When a solid sample is subjected to extensional or compressional strain and the stress is measured, it is possible to determine Young s modulus in the region where stress is proportional to strain ... 

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