Exponential Series Representation of Master Curves

Variation of the relaxation modulus and creep compliance of a Maxwell model on linear-linear (left) and log-log (right) scales are shown in Figs. 7.15-7.16. Notice the rapid decay of the modulus as the time approaches the selected relaxation time and the flow at long times due to the fluid nature of the Maxwell model. The behavior of the modulus and compliance for a simple Maxwell element is similar to that for many polymers in the glassy and transition region. 

If several Maxwell models are used in series to represent polymer response, as in the generalized Maxwell model (see Chapter 6), and if the spring moduli and relaxation times are judiciously chosen, the transition region broadens as shown in Fig. 7.17. The parameters used for the curves 

Curves without E decay rapidly at larger times, while curves with the E term are constant at long time as indicated. Parameters in Table 1. 

While the above description suggests that various master curve shapes can be represented by generalized Maxwell or Kelvin models, it does not mean that the determination of the proper values of the spring moduli or relaxation times to obtain a precise fit is trivial. 

Examination of the relaxation modulus of a generalized Maxwell model demonstrates the complexity. That is. 

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