Glassy compliance

At very short times the compliance is low and essentially constant. This is the glassy state where chain motion requires longer times to be observed. 

At longer times an increase in compliance marks the relaxation of the glassy state to the rubbery state. Again, an increase of temperature through Tg would produce the same effect. 

Here the term ik is the retardation time. It is given by the product of the compliance of the spring and the viscosity of the dashpot. If we examine this function we see that as t -> 0 the compliance tends to zero and hence the elastic modulus tends to infinity. Whilst it is philosophically possible to simulate a material with an infinite elastic modulus, for most situations it is not a realistic model. We must conclude that we need an additional term in a single Kelvin model to represent a typical material. We can achieve this by connecting an additional spring in series to our model with a compliance Jg. This is known from the polymer literature as the standard linear solid and Jg is the glassy compliance ... 

The molecules of a liquid start to move relative to one another and the shear compliance increases rapidly after the shearing force has been applied for only c. 10 6 s. On the other hand, hard solids, such as diamond, sodium chloride crystals and materials at a low enough temperature to be in the glassy state, show only the above rapid elastic deformation, even after the shearing stress has been applied for a considerable time. 

Figure 4.16 Creep compliance (strain per unit imposed tensile stress) versus time for glassy polyvinylchloride after aging for various times after a quench from equilibrium at 90°C to a glassy state at 20°C. The master curve with many symbols is the superposition of all the curves and is obtained by a horizontal shift. The pluses were obtained by reheating to 90 C after 1000 days of aging, and then quenching again to 20°C, followed by one day of aging. This result shows that the aging process is thermoreversible. (From Struik 1976, with permission from the New York Academy of Sciences.)...

The evolution of the tensile creep compliance of a glassy epoxy resin at different aging times is shown, as an example, in Figure 12.22. The glasses were obtained by quenching the resin from Tg -I- 22°C to Tg — 9°C and were kept at this temperature for different intervals of time. The results obtained show that as the aging time increases, the values of J t) for comparable... 

The viscoelastic properties of the crystalline zones are significantly different from those of the amorphous phase, and consequently semicrystalline polymers may be considered to be made up of two phases each with its own viscoelastic properties. The best known model to study the viscoelastic behavior of polymers was developed for copolymers as ABS (acrylonitrile-butadiene-styrene triblock copolymer). In this system, spheres of rubber are immersed in a glassy matrix. Two cases can be considered. If the stress is uniform in a polyphase, the contribution of the phases to the complex tensile compliance should be additive. However, if the strain is uniform, then the contribution of the polyphases to the complex modulus is additive. The... 

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. 

Seitz [16] developed structure-property relationships for the mechanical properties, up to (Tg - 20K), of isotropic amorphous polymers which are glassy at room temperature, i.e., which have Tg>298K. If only the values of the properties at room temperature are of interest, equations 11.10 and 11.13 can be utilized to estimate v(298K) and B(298K), respectively and equations 11.2, 11.3, 11.4 and 11.7 can then be used to estimate the compliances and the other two moduli. If the temperature dependence of the mechanical properties is of interest, equations 11.10-11.12 must all be used to estimate v(T), for substitution into Equation 11.7. 

The correlations summarized above provide a general method to estimate the moduli, compliances and Poisson s ratio for glassy amorphous polymers, as functions of the structure of the polymeric repeat unit and the temperature of measurement. Independent correlations for B(T) and G(T) will now be discussed, and compared with the correlations presented above. 

The shape of the mastercurve is related to the polymer microstructure. That for polystyrene at 100 °C (Fig. 7.5b) shows a transition from a glassy compliance at Is to a rubbery one at times exceeding 10 s. It continues to 10 ° s, so it can be used for extrapolation to times longer than those accessible by experiment. Time-temperature superposition for semi-crystalline polymers, such as polyethylene, may be successful for a limited temperature range, i.e. 20°C-80°C. As polyethylene starts to recrystallise if heated within 50 °C of T, and residual stresses may start to relax, data for higher temperatures will not superimpose. 

Ideal yielding behaviour is approached by many glassy polymers well below their glass-transition temperatures, but even for these polymers the stress-strain curve is not completely linear even below the yield stress and the compliance is relatively high, so that the deformation before yielding is not negligible. Further departures from ideality involve a strain-rate and temperature dependence of the yield stress. These two features of behaviour are, of course, characteristic of viscoelastic behaviour. 

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