Reduced shear, creep compliance

FIGURE 5.2 Reduced shear creep compliance curves Jp(t) cm /dyn, determined on Epon 1007/DDS at seven temperatures, as indicated, presented logarithmically as a function of logarithmic time t. 

FIGURE 5.3 Reduced shear creep compliance curves Jp(f) of Epon 1007/DDS shifted to superimpose with the curve at the reference temperature 100.7°C shown logarithmically versus the logarithm of the reduced time r/aj-. 

FIGURE 5.4 Comparison of reduced shear creep compliance curves of Epon 828, 1001, 1002, 1004, and 1007/DDS plotted logarithmically against time at the reference temperatures indicated that are close to the respective TgS. 

Torsional creep measurements were made on the urethane-crosslinked polybutadiene elastomers at temperatures between —68 C and 25 C. The average molecular weight of a networks chain. Me, is 3400, 5200, and 8300 for TB-1, TB-2, and TB-3, respectively. The reduced shear creep compliance Jpit/ax) curves obtained for the three samples are shown in Figure 5.13. The reference temperatures are chosen to be 7.4°C, 0.0 C, and 17.0°C for TB-1, TB-2, and TB-3, respectively, so that superposition is achieved at shorter times... 

FIGURE 5.13 The logarithm of the reduced shear creep compliance curves, Jp t) (in Pa ), for the three urethane-end Unked polybutadiene elastomers displayed as a function of the logarithm of the reduced time t/ap (in seconds). The reference temperatures of reduction are chosen so that superposition is achieved at short times in the primary softening dispersion, (o) TB-1, 74 C, ( ) TB-2, 0°C, (e) TB-3, 17°C. 

FIGURE 6 Reduced shear creep compliance curves cmVdyne, determined on Epon... 

FIGURE 11 Logarithmic plot of the reduced shear creep compliance curves Jp t) (in cmVdyne = lOPa ) against the reduced time I/oy (in seconds).The reference temperature of reduction. To, is -20.0 C for all curves. Data points are shown only for Sample 11-A. 

Torsional creep measurements were made on the urethane-crosslinked polybutadiene elastomers at temperatures between -68 and 25°C.The average molecular weight of a networks chain. Me, is 3400, 5200, and 8300 for TB-1, TB-2, and TB-3 respectively. The reduced shear creep compliance Jp(t/ar) curves obtained for the three samples are shown in Fig. 18. The reference temperatures are chosen to be 7.4,0.0, and 17.0°C for TB-1, TB-2, and TB-3 respectively so that superposition is achieved at shorter times in the primary softening dispersion. The most loosely urethane-crosslinked TB-3 has the largest 7e = 2.5 x lO Pa There is a plateau intermediate between the glassy compliance 7g (not reached in these measurements) and /e, and its level is about 2.0 X 10 Pa in all three samples. The network chain density does not affect the form of the time-dependent response up to and including the intermediate plateau in the Jp(t) curves. Only the terminal dispersion, i.e., the approach to /e, is influenced. The shift factors, Uj, that were used to obtain the... 

FIGURE 20 Double logarithmic plot of the reduce shear creep compliance curves Jp(t) (in Pa" ) as a function of the logarithm of the reduced retardation time, t/Or, for five elastomers at To = 0°C. Solid line (HTPB-2), long dashed line (Viton), short dashed line (PB-2), dashed-dotted line (PB-1), dotted line (HTSBR). 

The logarithm of the reduced shear creep compliance Jp t/aj) of several elastomers are compared at 0°C in Rg. 20 as a function of the logarithm reduced time-scale log(i/flr)- The elastomers include (1) the urethane-crosslinked polybutadiene elastomer, TB-2, described in Subsection B (2)... 

As an example of the concentration dependence of viscoelastic properties in Fig. 16.11 the shear creep compliance of poly(vinyl acetate) is plotted vs. time for solutions of poly(vinyl acetate) in diethyl phthalate with indicated volume fractions of polymer, reduced to 40 °C with the aid of the time temperature superposition principle (Oyanagi and Ferry, 1966). From this figure it becomes clear that the curves are parallel. We may conclude that the various may be shifted over the time axis to one curve, e.g. to the curve for pure polymer. In general it appears that viscoelastic properties measured at various concentrations may be reduced to one single curve at one concentration with the aid of a time-concentration superposition principle, which resembles the time-temperature superposition principle (see, e.g. Ferry, General references, 1980, Chap. 17). The Doolittle equation reads for this reduction ... 

FIG. 16.11 Shear creep compliance of poly(vinyl acetate), M = 240 kg/mol, and four solutions in diethyl phthalate with indicated values of the polymer volume fraction, John Wiley Sons, Inc. 

The Epons 828,1001,1002,1004, and 1007 fully cured with stoichiometeric amounts of DDS are examples of well-characterized networks. Therefore, mechanical measurements on them offer insight into the viscoelastic properties of rubber networks. The shear creep compliance J t) of these Epons were measured above their glass temperatures [11, 12, 14]. From the statistical theory of rubber elasticity [1-5, 29-33] the equilibrium modulus Ge is proportional to the product Tp, where p is the density at temperature T, and hence the equilibrium compliance is proportional to (Tpy Thus J t) is expected to be proportional to and J(t)Tp is the quantity which should be compared at different temperatures. Actually the reduced creep compliance... 

The storage and loss shear moduli, G and G", vs. oscillation frequency ta, and the creep compliance J vs. time t, measured at each concentration and tanperature, were temperature shifted with respect to frequency or time. These temperature master curves at each concentration were then shifted to overlap one another along the frequency or time axis. The dynamic shear moduli master curves as a function of reduced frequency (oa ac are shown in fig. 4.4, and the shear creep compliance master curves as a function of reduced time tlajUc are shown in fig. 4.5. Master curves... 

FIG. 15-3. Recoverable shear creep compliance and retardation spectrum of l 3 5-tri-a-naphthyl benzene, reduced to 64.2°C from measurements at that temperature and above (open circles) and at four other temperatures as indicated. (Points for spectrum calculated in several different ways.) (Plazek and Magill. )... 

FIG. 14-9. Creep compliance of samples F, H, I, and J of Fig. 14-4 in shear with small deformations, reduced to 30 C. Pips refer to measurements at different temperatures from —50 to 90 C. (Plazek. )... 

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