Viscoelastic process

Figure 4 shows stress-strain curves measured at an extension rate of 94% per minute on the TIPA elastomer at 30°, —30°, and —40°C. With a decrease in temperature from 30° to -40°C, the ultimate elongation increases from 170% to 600%. The modulus Ecr(l), evaluated from a one-minute stress-strain isochrone, obtained from plots like shown in Figure 1, increases from 1.29 MPa at 30°C to only 1.95 MPa at —40°C. This small increase in the modulus and the large increase in the engineering stress and elongation at fracture results from viscoelastic processes. 

The MRC cycle calls for a 182°C cure temperature. The effect of cure temperature on residual stress was investigated by curing specimens at four other cure temperatures (171, 165, 160, and 149°C) while holding the dwell time (4 hours) constant. In Figure 8.18 the dimensionless curvature for these specimens is plotted versus the cure temperature. The curvature is reduced as the cure temperature is decreased with significant reduction in curvature obtained for dwell temperatures of 165°C or less. The final curvature as predicted by the viscoelastic process model is overlaid with the experimental data in Figure 8.18 and is shown to capture the trend. 

The rates of relaxation and retardation processes above the glass temperature are strongly dependent on the viscosity and thus on the fraction of free volume present. Because the viscosity not only depends on temperature but also on static pressure (the glass transition temperature increases approximately 1 °C per 20 bar of pressure) it is not surprising that pressure also affects the viscoelastic processes. A qualitatively relation analogous to Eq. (13.121) can be readily derived (Ferry, 1980) ... 

Fig. 11 shows master curves extrapolated with the model. These have the same general features as master curves plotted by shifting data isotherms. The two differ slightly because different assumptions are involved. The conventional method of shifting data makes all isotherms congruent the same viscoelastic processes are assumed at all temperatures. The phenomenological model is not limited to this assumption. When the thermal spread varies with frequency, the model extrapolates to isotherms like fig. 11. Note... 

The friction coefficient is customarily obtained from either the relaxation or retardation spectrum, H x) or L x), respectively. At short times, i.e., on the transition from the glassy-like to the rubbery plateau, the viscoelastic processes obey Rouse dynamics, and the relaxation modulus is given by Eq. (11.45). Since H x) = —dG/d nx t, one obtains... 

Images like these reveal that the recovery after 24 h for HDPE is substantial however, complete recovery is not observed [74], Interestingly, the dynamics of the recovery depends on the indentation rate, but not the magnitude of the applied load, which points at viscoelastic processes that play an important role in particular low loading rates (Fig. 4.26). 

The tearing or rupture energy measured by Rivlin and Thomas73 on black mixes shows humps or maxima at characteristic rates of tearing, except at higher temperatures. This is the result of a viscoelastic process which was shown not to exist in gum rubbers. 

As has already been stated, the verified possibility of extending the reduced variables principles to ABS resins makes it possible to treat these typical heterophase systems as blends of amorphous homophase polymers and plasticizers. One possible explanation is that over the experimental y range it is not possible to separate the contributions of the two different phases, and the materials will behave as homophase polymer. In fact, long-time molten polymer rheology experiments measure viscoelastic processes over the entire molecule, and, as a consequence, molecular compatibility is evaluated (13). On the other hand, high frequency and/or low temperature tests involve the main chain as well as the side chains of the polymer system the segmental miscibility of the polymer-polymer system is then evaluated. It is important in experimental measurements of polymer compatibility to evaluate the actual size of the volume subject to the test. 

When this occurs, and when AG and are large enough, considerable work will be dissipated in the viscoelastic process that constitutes fibril formation, before fibril rupture. That is to say. Equations (lb) or (3b) constitute the necessary condition for high strength. This may be considered a local "all-or-nothing" criterion. There will be a critical level of interfacial force, and of free... 

Such models are much too simple to describe the complex viscoelastic behavior of a polymer, nor do they provide any real insight into the molecular mechanism of the process, but in certain instances they can prove useful in assisting the understanding of the viscoelastic process. 

A polymer will noimally have several viscoelastic processes, each (MM being caused by the onset of a particular form of molecular motion. These occur normally at widely spaced temperatures. 

The application to movements within a solid polymer must take into account the elastic distortion of the surrounding molecules, as outlined above for a monatomic system, plus the energy needed to facilitate molecular rotation. One way in which this is thought to happen in polyethylene is indicated in Figure 4.38. Within the amorphous region of solid polyethylene, molecular movement can occur by short sections of the molecule flipping from one equilibrium position to another like a crankshaft. Bonds 1 and 7 are colinear it will be seen that four atoms can then flip round by rotations around bonds 1 and 7. The onset of this mechanism is one explanation of the y-viscoelastic process in pofyethylene. 

The horizontal logarithmic time scale shifts that are required to superpose the data obtained at different temperature are the logarithms of the Ut shift factors. The Uj values thus reflect the principal temperature dependence of the viscoelastic process. It was possible to represent the time-scale temperature dependences of the three samples with a single VFTH Eq. (33) in which only one parameter T , which reflects the change in Tg, varies with the level of crosslinking. The fit achieved is shown in Fig. 12. The atmosphere in which the measurements were made is important since samples measured in air contain the moisture absorbed under ambient conditions, whereas those measured in rough vacuum (use about symbol - lO torr = 1.3 Pa) are at least partially... 

Several theories exist correlating the DBT obtained from impact tests to structural variables expressed in terms of thermodynamic parameters such as Tg of the polymer (76) using impact strength as a measure of toughness. It is doubtful, however, that any viscoelastic process can play such an important role because fracture is a highly localized process and the contributions to Tg come from the entire volume of the test specimen, whereas the contribution to fracture energy... 

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