Dynamic Mechanical Behaviour

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 early attempts to interpret the dynamic mechanical behaviour in structural terms include that of Smith et al. where the plateau modulus was correlated with the fraction of non-crystalline material f, determined by NMR. Plots of the plateau compliances at —60 °C and —160 °C as a function of f suggested a modified Takay-anagi series model, with a constant amount of non-crystalline material in parallel with the simple series model. The modd showed good internal consistency, with values for the compliances of the non-ciystalline regions which were acceptable in physical terms. 

The debate moved forward a further stage with the observation that the average crystal length (sometimes termed the longitudinal crystal thidcness), determined 

A Takayanagi-type model (Fig. 31) can be used to quantify the relationship with the storage modulus at —50 °C (in the plateau region between the a and y-relaxations). It can be shown that 

In the case of the y relaxation, it was concluded that there are two mechanisms for the change in modulus and hence for tan 5. The first is an increase in the efficiency of stress transfer (i.e. the shear lag factor) with falling temperature due to the quenching of molecular motions. These are predominantly if not entirely in the non-crystalline regions. Secondly, the quenching of these molecular motions also gives rise to an 

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Any motion occurring within any polymer system leads to a change of the dynamic mechanical behaviour, in particular its mechanical loss. This makes the dynamic mechanical measurements the most appropriate technique for studying solid-state transitions. However, in order to assign the molecular motions involved in the considered transition from only the dynamic mechanical results, it is necessary to perform systematic studies on a large series of compounds with gradual modification of their chemical structure. Such an approach has been used in some cases, but it requires lots of effort in synthesising the various compounds. 

Fig. 29 Temperature dependence of the dynamic mechanical behaviour, at 11 Hz, for the alternating copolymer B1T1 (from [26])...

This WLF equation enables us to calculate the time (frequency) change at constant temperature, which - as far as the dynamic-mechanical behaviour is concerned - is equivalent to a certain temperature change at constant time (frequency). For temperatures below Tg deviations from the WILF equation are of course to be expected. This has been stated, for instance, by Rusch and Beck (1969). 

The dynamic mechanical behaviour of ultra high modulus polypropylene is shown in Fig. 32. As in LPE, the modulus is temperature dependent, rising to a value of 25 GPa at —140 °C, which is rather more than half (he value of 42 GPa obtained from crystal measurements. Although the a and y relaxations of the isotropic polymer can be seen in the highly drawn material, the -relaxation is undetectable. On annealing, the modulus at high temperatures is markedly reduced, and a P-relaxa-... 

Dynamic Mechanical Behaviour of Atactic Polystyrene, High-impact Polystyrene and Other Styrenic Polymers... 

Gibson, A.G. at al. (1978). Dynamic mechanical behaviour and longitudinal crystal thickness measurements on ultra-high modulus linear polyethylene a quantitative model for the elastic modulus. Polymer, Vol. 19 (1978), pp. 683-693 Hong, K. et al. (2004). A model treating tensile deformation of semi-crystalline polymers Quasi-static stress-strain relationship and viscous stress determined for a sample of... 

In many cases, a comprehensive characterization of the rheological properties of systems, such as concentrated colloidal dispersions, can require measurements of dynamic mechanical behaviour at frequencies outside the range of conventional, commercially available, rheometers (typically 10 Hz to 10 Hz). In particular, consideration of the relative time scales of particle-fluid displacement and interfacial polarization mechanisms in such systems reveals the need for enhanced high frequency ranges (above ca. 10 Hz). 

Y.M. Boiko, W. Brostow, A.Y. Goldman, A.C. Ramamurthy, Tensile, stress relaxation and dynamic mechanical behaviour of polyethylene crystallized from highly deformed melts. Polymer, 36 (7), 1383-1392,1995. 

Determination of the flow behaviour and the structure of SBS solutions have been the subject of many investi tions (see e.g. [363-367]). However, the dynamic mechanical behaviour of solutions has been little reported. Pico and Williams [368] describe the gelation behaviour of highly concentrated SBS... 

The gelling behaviour of aqueous agarose gels has beat extenavely studied by Nishinari et al. [166,204,520-5293 with various measuring tediniques (stress relaxation, dynamic mechanical behaviour, differential anning calorimetry, optical rotation etc). 

Figure 1.2 The effects of temperature on the dynamic mechanical behaviour of one polyester/glass fibre composite (isophthalic polyester Neste S 560 Z, E-glass, manufactured by pultrusion). The DSC method gives the Tg of the pure S 560 Z resin casting as 135°C. Owing to certain additives, the Tg of the FRP material in question could not be determined with DSC.

Dynamic-mechanical behaviour was investigated in the shear mode for nanocomposites based on IR and containing 60 phr of a furnace CB (N326) and various amounts of OC. ° A pronounced Payne effect was detected, particularly at OC concentrations above the threshold required to have a change in the filler networking mode. 

IR based nanocomposites. In situ silica was prepared in IR with the solution process.Swelling experiments evidenced good polymer-filler adhesion, in the presence of coupling agents. The dynamic-mechanical behaviour was found to be increasingly non-linear for silica contents higher than 20 wt%. 

The modulus at minimum and low strain amplitudes is due to the so-called filler network and it is accepted that the filler surface area, as well as the surface activity, play a major role in establishing a filler network, determining the effective contact area between filler particles and between filler particles and the elastomer matrix. The stress assisted disruption of the filler network causes the reduction of the modulus as the strain amplitude increases, giving rise to the non-linearity of the dynamic-mechanical behaviour of the rubber composite. This phenomenon is known as the Payne effect and it is (to a certain extent) reversible. The disruption and re-formation of the filler network is... 

Pothan LA, Thomas S (2003) Polarity parameters and dynamic mechanical behaviour of chemically modified banana fiber reinforced polyester composites. Compos Sci Technol 63 1231-1240... 

Yamada, N. Yoshinaga, I. Katayama, S., Synthesis and Dynamic Mechanical Behaviour of Inorganic-Organic Hybrids Containing Various Inorganic Components. J. Mater. Chem. 1997,7,1491-1495. 

The aggregate model also has been used with success to describe the mechanical anisoti opy of several liquid crystalline polymers. Ward and co-workers [56] examined the dynamic mechanical behaviour of several thermotropic polyesters in tension and shear over a wide temperature range, and used the single-phase aggregate model to relate quantitatively the fall in tensile modulus with temperature to the corresponding fall in shear modulus. 

As the temperature and strain rate in a polymer change, the nature of the stress-strain curve can alter remarkably. It is therefore natural to seek correlations between the area beneath the stress-strain curve and the impact strength, and between dynamic mechanical behaviour and the impact strength. Attempts to make such correlations directly have met with mixed success [121], which is not surprising in view of the complex quantitative interpretations of impact strength suggested above. 

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