Viscosity and Relaxation by D. R. Uhlmann

By D. R. Uhlmann

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1977). Normalization of Eqs. (116) and (117) gives the retardation function for the generalized Burgers model: * 1 D " ΛΕ(0)-ΛΕ(ΟΟ) - β - £ ^ ( 1) 1 8 Figures 27 and 28 show the six-term fit (m = 6) of Eq. (118) to the retardation function measured by Rekhson et al. (1977). 7 A continuous spectrum of retardation times is obtained by a method similar to that for stress relaxation times. Although approximation methods are available (Ferry, 1970) we have used the method proposed and described in Subsection E.

Rekhson and S. M. Rekhson (1986a). They applied it to the data on the stress relaxation function obtained by Rekhson et al. (1977) using a temperature scanning technique. T h e measurements were started at 300°C below the glass transition temperature. At these low temperatures, only the very short relaxation times are active and can be monitored conveniently. The spectrum for their data is shown in Fig. 22. All ten iterations were unable to smooth the short-relaxation-time peaks that therefore seem to be real.

T h e total stress is the sum of the responses to e(tx) s(t) and e(t2), - h) - 2Ge{h)*{t2 = 2Ge{tx)*{t = 2Ge(tl)mt - tl) - ψο2 - -/,)*(/ h m t given by, - t2) -12)\ (where t > t2) (203) (204) = 2Ge(tl)S(t) or in terms of derivatives with respect to time; s(t) = 2Ge{tx)[<*{t Therefore s(t) - tx) - Ψ(ί2 - tl)*{t - t2)], t > t2. (205) = 0 for / > t2 only if *(/-fx) = * ( f t/T (t/T)h 2 - * 2 ) . F r o m three functions e~ , e~ , and E " = 1w ; - e ~ ' the first satisfies the condition (206). / T/ (206) used for ^ ( 0 .

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