Creep master curve

To determine the effect of the distribution of on creep, master curves for all the samples were drawn at 129 C instead of selecting T as the reference temperature. The temperature corrections were not used to draw the master curves shown in Figure 7 because these corrections, as mentioned earlier, were small and the experimental data did not extend to long ranges of temperature in the rubbery region. The characteristic creep time (t ) was taken as the time required to relax to a value of log E(t) = (log + log Er)/2, where Eg and E are the glassy and rubbery moduli, respectively. The slopes (n) of the master curves were determined at the time t. The characteristic creep time (t ) was found... 

Struik [3] originally proposed a method to model physical aging through the use of a momentary creep master curve obtained from a series of short term creep tests performed at various aging times. The momentary creep master curve was then used in conjunction with the effective time theory to predict long term creep in a polymer in the presence of physical aging. 

Figure 3-163. Creep Master Curves for Coupled GRPP Profax at 73 F, 5000 psi Stress"...

The creep data, measured as a ftinction of both time and temperature (T= —50. . . 80 °C), have been utilized to create creep master curves by adopting the TTS principle. Creep at other temperatures can be estimated by considering the shift factor (or) along the time scale (t) (cf. Eq. (13.11)). The modeling of creep behaviors is important from both fundamental and applications-driven perspectives. The Findley power law model has been proposed in order to evaluate the creep behavior of polymer blends and to predict the long-term deformation based on short-term experimental data. An empirical description for the creep compliance versus time is given by the Findley power law [32] ... 

Figure 13.10 Creep master curves constructed by considering Tref. = 30°C for POM and the POM/PU blend.

Figure 13.14 Creep master curves (compliance versus time) constructed by considering the TTS and selecting 30°C, and their fitting by the Findley power law equation.

Figure 9.7. Creep master curves referred at a and nanocomposites filled with 4.5 t%...

Master curves can be used to predict creep resistance, embrittlement, and other property changes over time at a given temperature, or the time it takes for the modulus or some other parameter to reach a critical value. For example, a mbber hose may burst or crack if its modulus exceeds a certain level, or an elastomeric mount may fail if creep is excessive. The time it takes to reach the critical value at a given temperature can be deduced from the master curve. Frequency-based master curves can be used to predict impact behavior or the damping abiUty of materials being considered for sound or vibration deadening. The theory, constmction, and use of master curves have been discussed (145,242,271,277,278,299,300). 

Extensive tests have shown that if the final creep strain is not large then a graph of Fractional Recovery against Reduced Time is a master curve which... 

To get accurate distributions of relaxation or retardation times, the expetimcntal data should cover about 10 or 15 decades of time. It is impossible to get experimental data covering such a great range of times at one temperature from a single type of experiment, such as creep or stress relaxation-t Therefore, master curves (discussed later) have been developed that cover the required time scales by combining data at different temperatures through the use of time-temperature superposition principles. 

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 ... 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

The time-temperature superposition principle has practical applications. Stress relaxation experiments are practical on a time scale of 10 to 10 seconds (10 to 10 hours), but stress relaxation data over much larger time periods, including fractions of a second for impacts and decades for creep, are necessary. Temperature is easily varied in stress relaxation experiments and, when used to shift experimental data over shorter time intervals, can provide a master curve over relatively large time intervals, as shown in Figure 5.65. The master curves for several crystalline and amorphous polymers are shown in Figure 5.66. 

The creep of a viscoelastic body or the stress relaxation of an elasacoviscous one is employed in the evaluation of T] and G. In such studies, the long-time behavior of a material at low temperatures resembles the short-time response at high temperatures. A means of superimposing data over a wide range of temperatures has resulted which permits the mechanical behavior of viscoelastic materials to be expressed as a master curve over a reduced time scale covering as much as twenty decades (powers of ten). 

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. 

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. 

Stress relaxation master curve. For the poly-a-methylstyrene stress relaxation data in Fig. 1.33 [8], create a master creep curve at Tg (204°C). Identify the glassy, rubbery, viscous and viscoelastic regions of the master curve. Identify each region with a spring-dashpot diagram. Develop a plot of the shift factor, log (ax) versus T, used to create your master curve log (ot) is the horizontal distance that the curve at temperature T was slid to coincide with the master curve. What is the relaxation time of the polymer at the glass transition temperature ... 

The master creep curve for the above data is generated by sliding the individual relaxation curves horizontally until they match with their neighbors, using a fixed scale for a hypothetical curve at 204°C. Since the curve does not exist for the desired temperature, we can interpolate between 208.6°C and 199.4°C. The resulting master curve is presented in Fig. 1.34. The amount each curve must be shifted from the master curve to its initial position is the shift factor, log (aT). The graph also shows the spring-dashpot models and the shift factor for a couple of temperatures. 

Figure 1.36 presents some creep modulus data for polystyrene at various temperatures [11], Create a master curve at 109.8°C by graphically sliding the curves at some temperatures horizontally until they line up. 

The analogy in the creep behaviour of various (glassy) polymers and other substances is illustrated in Figure 7.5 on each material measurements have been carried out over a broad range of temperatures, and all results coincide, after shifting, into a master curve with the equation ... 

FIG. 13.47 Small strain tensile creep curves of rigid PVC quenched from 90 °C (i.e. about 10 °C above Tg) to 40 °C and further kept at 40 0.1 °C for a period of 4 years. The different curves were measured for various values of time te elapsed after the quench. The master curve gives the result of a superposition by shifts that were almost horizontal the arrow indicates the shifting direction. The crosses refer to another sample quenched in the same way, but only measured for creep at a te of 1 day. From Struik (1977,1978). Courtesy of the author and of Elsevier Science Publishers. 

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