Creep compliance master curve

Fig. 22. Lower envelope of creep compliance master curve as well as experimental compliance curve for 342.2° C ( ) and 350.4° C ( ) Dashed lines represent best" straight line of slope 1 obtained by substracting lower envelope from experimental...

Figure 12.3 Creep compliance master curve for PET/0.6PHB at the reference temperature 20°C. (After [36].)...

Figure 12.8 Creep compliance master curves (a) and stress-time shift factor (b). The master curve obtained using the stress-time superposition is indicated by short dashes the point symbols are the same as in Figure 12.7. The master curve obtained by using the temperature-time superposition is shown by long dashes (b cf. Figure 12.3) after [36].

Figure 12.10 Creep compliance master curves for different materials pure PP (1) a blend of 90% PP + iq% PLC (2) a blend of 80% PP + 20% PLC (3) pure PLC (cf. Figure 12.3) (4). The symbols are the same as in Figure 12.9. (After [50].)...

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. 7.3 Creep Compliance Master Curve for an Epoxy at 120 ° C. (Data from Brinson (1965).)...

Figure 10.10 Time-temperature shear creep compliance master curve (Sullivan). 

Figure 9.10. Creep compliance master curves at a reference temperature of 50°C for neat PP and relative nanocomposites with various contents of carbon nanotubes (CNT) [36]...

As expected, the creep compliance master curves indicated a lower compliance for all the iiaiiocomposites at shorter times (up to 10" s) as compared to neat PP. However, it is interesting to note that the creep compliance curves for Iiaiiocomposites with 0.5, 1, and 2.5 wt% of MWNT showed a cross over at about 10 s. The iianocomposite with 5 wt% of MWNTs showed the lowest compliance over the entire time range when compared to all the other compositions. This peculiar behavior was tentatively explained by the authors considering that two competing factors may concur in determining the overall creep response (i) the size of the spherulites/crystallites (which is a consequence of incorporation of nanotubes and hence inter-phase effects), (ii) the thermal expansion coefficient (which depends on the amount of nanotubes). 

Because of the uncertainties involved in the decomposition, this procedure would not appear to be a practical way to determine the AHa value needed for Equation 8. It does, however, demonstrate three important points (1) it is the compliances of the mechanisms that are additive (2) T0 and AHa can be obtained from plots such as those shown in Figures 7 and 8 of shift data determined in either relaxation or creep experiments without decomposition of compliance master curves (3) Equation 8 describes time-temperature superposition in Kraton 102 adequately within the experimental accuracy. 

Master curves are important since they give directly the response to be expected at other times at that temperature. In addition, such curves are required to calculate the distribution of relaxation times as discussed earlier. Master curves can be made from stress relaxation data, dynamic mechanical data, or creep data (and, though less straightforwardly, from constant-strain-rate data and from dielectric response data). Figure 9 shows master curves for the compliance of poly(n. v-isoprene) of different molecular weights. The master curves were constructed from creep curves such as those shown in Figure 10 (32). The reference temperature 7, for the... 

Rgure 9 Master curves for creep compliance of polyisoprene of various molecular weights at a reference temperature of - 3()0C ... 

Figure 4. Master curves of the tensile creep compliance, Dp(t), of Kraton 102 cast from benzene solution, as functions of time, t,...

The master curves obtained from specimens cast from tetrahydro-furan solution at 2 and 4% strain, respectively, are slightly different. These differences, however, are probably within the experimental error. An idea of the reproducibility can be obtained from Figure 4, which shows the master curves of the creep compliances obtained on specimens cut from two sheets of Kraton 102 cast from benzene solution. Although the method of preparation appeared to be identical, there are noticeable differences between the two curves. Even larger differences exist between these curves and the master curve obtained from the relaxation data after conversion to creep. Again, there were no apparent differences in the method of preparation of the sheets from which the specimens for the relaxation and creep tests were cut. 

Figure 4.16 Creep compliance (strain per unit imposed tensile stress) versus time for glassy polyvinylchloride after aging for various times after a quench from equilibrium at 90°C to a glassy state at 20°C. The master curve with many symbols is the superposition of all the curves and is obtained by a horizontal shift. The pluses were obtained by reheating to 90 C after 1000 days of aging, and then quenching again to 20°C, followed by one day of aging. This result shows that the aging process is thermoreversible. (From Struik 1976, with permission from the New York Academy of Sciences.)...

One can also construct master curves from the data. Figure 14.21 shows that values of Dts for two PBMA samples of veiy differoit molar masses, each obtained at three different temperatures, can be reduced to two master curves using WLF parameters obtained 40 years previously by Feny and co-workers [56] in creep compliance measurements on PBMA. This figure also emphasizes the strong dependence of Detr on M , for the polymer. 

FIGURE 6.9 Loss tangent of polyisobutylene measured by dynamic mechanical spectroscopy and calculated from the recoverable creep compliance. These are not master curves the abscissa is the actual frequency (Plazek et al., 1995). 

Many viscoelastic parameters of polymers can be used to obtain master curves such as creep compliance relaxation modulus E, E", C, G" and loss factor tan d. These viscoelastic variables of polymers are dependent on temperature, frequency and relaxation time. As an example. Figure 4.65 shows the experimental results and Figure 4.66 shows the master curve of PMMA. The parameter chosen is the storage moduli. The following procedure is recommended for the master curve measurement. 

Here is an example of the minimum data procedure for the application of the time-stress correspondence. In Figure 17 we show creep compliance of the same PET/0.6PHB PLC as a fimction of logarithmic time. This is a master curve—and only two sets of experimental data (for two stress levels) have been used to create it. 

Fig. 17. Master curve of creep compliance of PET/0.6PHB for

Figure 15.8 shows the creep data obtained for PC in the temperature range 130-155 C. The logarithm of creep compliance (S) is shown as a function of the logarithm of decay time. One of the curves is selected as the reference (in this case, T = 145 °C), then the other curves are shifted along the log time axis and superimposed upon the reference curve. The final master curve based on creep data is shown in Figure 15.9. The curve shows that at small time intervals the material exhibits relatively low compliance (or high modulus). At longer times, viscous flow occurs and the material exhibits a high compliance (or modulus). Thus this master curve clearly demonstrates the effects of time on the mechanical properties of PC.

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