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A discrete retardation time spectrum consists of individual value pairs showing a limited total number k of Kelvin/Voigt models connected in series, e. g. with k = 5. In this case, the discrete retardation time spectrum consists of 5 individual value pairs, e. g. expressed in terms of the retardation time-dependent creep compliances Ji (Λi), here with i = 1 to 5. A corresponding example, but using the relaxation time-dependent relaxation moduli, is explained in Chapter 7.3.3.3b, see Table 7.1 and Figure 7.9.

The shape of both exponential functions, the creep and creep recovery curve, is determined by the spectrum of retardation times. For many polymers, the range of retardation times spreads over several decades, and frequently up to much more than 100 s. Often Λi values up to 1000 s (= approx. 17min) or 10,000 s (= approx. 167min = almost 3h) can be found, and sometimes periods which are even longer. Therefore, for samples showing highly viscous or viscoelastic behavior, retardation times of at least half an hour should be taken into account.

Summing up the individual creep compliances Ji(Λi), the function of the time-dependent creep compliance J(t) can be determined in the form of a fitting function:

Equation 6.14

J(t) = Σi (1 / Gi) ⋅ [1 – exp(-t /Λi)]

= (1 / G1) ⋅ [1 – exp(–t /Λ1)] + (1 / G2) ⋅ [1 – exp(–t /Λ2)] + (1 / G3) ⋅ [1 – exp(–t /Λ3)] + ...

The discrete retardation time spectrum can be illustrated in a diagram displaying an individual point for each individual value pair (Λi / Ji). Usually, the Λi values [s] are presented on the x-axis and the Ji values [Pa-1] on the y-axis (similar to Figure 7.9). In the same diagram, the calculated fitting function J(t) may be displayed; here, time t [s] is shown on the x-axis and the J-values [Pa-1] on the y-axis, using the same scale for Λi and t, and also the same scale for Ji and J on the other axis.