Time-temperature superposition modified

One method for overcoming this difficulty is to introduce the modified (or reduced) time t which allows the use of integral relationships with different arguments. The definition of modified time is based on the principle of time-temperature superposition. This is the usual way to generalize temperature-dependent functions using the argument... 

The effects of strain rate and temperature are correlated, and can be modeled (Kinloch and Young, 1983, Kinloch, 1985). For different temperatures and strain rates, GIc and the time to failure, tf, were measured. Using the time-temperature superposition principle, shift factors (aT) applicable to the time to failure tf, were determine. Shift factors plotted against (T — Tg) are independent of the type of test used (Fig. 12.14). The construction of a typical master curve GIc versus tf/aT is shown in Fig. 12.15 (Hunston et al., 1984). The value of GIc may be predicted for any strain rate/temperature combination. This model can also be applied to rubber-modified epoxies (See chapter 13). 

In an earlier section, we have shown that the viscoelastic behavior of homogeneous block copolymers can be treated by the modified Rouse-Bueche-Zimm model. In addition, the Time-Temperature Superposition Principle has also been found to be valid for these systems. However, if the block copolymer shows microphase separation, these conclusions no longer apply. The basic tenet of the Time-Temperature Superposition Principle is valid only if all of the relaxation mechanisms are affected by temperature in the same manner. Materials obeying this Principle are said to be thermorheologically simple. In other words, relaxation times at one temperature are related to the corresponding relaxation times at a reference temperature by a constant ratio (the shift factor). For... 

Tobol sky and co-workers who also modified it to account for proportionality of modulus to absolute temperature (3). This has the effect of creating a slight vertical shift in the data. Ferry further modified the time-temperature superposition to account for changes in density at different temperatures which has the effect of creating an additional vertical shift factor (4). The effect of the temperature-density ratio on modulus is frequently ignored, however, since it is commonly nearly unity. 

Figure 46. Storage modulus, C/, of gluten - water mixtures in a time sweep test 10% strain, I Hz frequency). The master curve has been obtained by applying the time-temperature superposition principle. Temperatures considered 40 ( ), 50 ( ), 60 (0), 70 (O), 80 (A), and 90 ( ) °C (modified from [263])...

---