Stress relaxation master curves

Figure 7.10 Stress relaxation master curve at a given temprature...

Figure 15 Stress-relaxation master curves for poly(a-methylstyrene) of various molecular weights. Reference temperature = 459 K. (From Ref. 160.)...

Figure 5.66 Stress-relaxation master curve for several polymers. From F. W. Billmeyer, Textbook of Polymer Science, 3rd ed. Copyright 1984 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

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 ... 

Figure 7.17. Stress relaxation master curve of (a) 7S enriched globulin fraction (b) IIS fiaction and the KWW equation in the glassy state (Copyright 1998 from Understanding phase transitions and chemical complexing reactions in 7S and IIS soy protein fractions by Morales-Diaz and Kokini (In Phase/State Transitions in Foods, Rao and Hartel (Eds.)). Reproduced by permission of Routledge/Taylor Franeis Group, LLC.)...

In this work we used polystyrene-based ionomers.-Since there is no crystallinity in this type of ionomer, only the effect of ionic interactions has been observed. Eisenberg et al. reported that for styrene-methacrylic acid ionomers, the position of the high inflection point in the stress relaxation master curve could be approximately predicted from the classical theory of rubber elasticity, assuming that each ion pah-acts as a crosslink up to ca. 6 mol %. Above 6 mol %, the deviation of data points from the calculated curve is very large. For sulfonated polystyrene ionomers, the inflection point in stress relaxation master curves and the rubbery plateau region in dynamic mechanical data seemed to follow the classical rubber theory at low ion content. Therefore, it is generally concluded that polystyrene-based ionomers with low ion content show a crosslinking effect due to multiplet formation. More... 

Figure 3-12. Stress relaxation master curve for N.B.S. polyisobutylene at 25°C (dotted line) and corresponding box-and-wedge distribution (solid lines). [Adapted from A. V. Tobolsky, Properties and Structure of Polymers, p. 128 and 151, by permission of John Wiley Sons, Inc.]...

Figure 3-19. Calculations of the viscosity from the stress relaxation master curve for NBS PIB at 25 °C (see Figure 3-12) via equation (3-89), showing the important contribution to the integral from the long-time data and the negligible contribution from the short-time modes in the glassy region.

Calculate the slope of a stress relaxation master curve at some time t when rmin < t < rmax where... 

A typical master curve is shown in Figure 6.2 (Santangelo and Roland, 1998) for dynamic shear data of a high molecular weight 1,4-polyisoprene measured over about a 160 range, yielding 15 decades of reduced frequency (the actual data spanned less than 5 decades). A tensile stress relaxation master curve for a polyurea rubber that spans 13 decades is displayed in Figure 6.6 (Knauss and Zhao, 2007). 

Figure 12.4. Flexural stress relaxation master curve for epoxy composites (T ef = 50°C). (x) Continuous transverse (A) particulate-filled (+) unfilled (O) foam. (Moehlenpah et al., 1970,1971.)...

In Figure 12.15 we show [51] the stress relaxation master curve at the reference temperature 20 C, presented as (7 vs. log t/aj), and the corresponding temperature shift factor log aj vs. T curve. For comparison, in Figure 12.16 we show also the values of ogaj from creep data... 

Figure 12.17 shows a master stress relaxation curve, presented as ((7 — (T.)/ (T — (7j) vs. log time. The value of a. is determined for t— oo by an approximation to the experimental stress relaxation master curve. This type of plot has been recommended by one of us [52-61]. It brings out the common features of stress relaxation curves for metals, polymers and other materials. This is true not only for experimental but also for computer generated stress relaxation curves [60-62]. For a discussion of these common features see also [62]. The type of plot recommended first in [52] is also being used successfully for instance by Wortmann and coworkers [63-66]. They investigated a variety of materials including wool fibers and also very stiff aramid fibers such as Kevlar. 

Figure 12.15 Stress relaxation master curve for PET/0.6PHB at the reference temperature 20 C (a) and temperature dependence of shift factor (b). The symbols in the master curve are the same as in Figure 12.14. (After [51].)...

L. H. Sperling, H. F. George, V. Huelck, and D. A. Thomas, Viscoelastic Behavior of Interpenetrating Polymer Networks Poly(ethyl acrylate)-Poly(methyl methacrylate), J. Appl. Polym. Sci. 14, 2815 (1970). Creep behavior of sequential IPNs. Stress relaxation. Master curves. 

FIGURE 16.13 The effects of molecular weight and crosslinking on stress-relaxation master curves. 

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