Stress-strain curves systems

Using both condensation-cured and addition-cured model systems, it has been shown that the modulus depends on the molecular weight of the polymer and that the modulus at mpture increases with increased junction functionahty (259). However, if a bimodal distribution of chain lengths is employed, an anomalously high modulus at high extensions is observed. Finite extensibihty of the short chains has been proposed as the origin of this upturn in the stress—strain curve. 

Figure 18.17 shows that the characteristics of the stress-strain curve depend mainly on the value of n the smaller the n value, the more rapid the upturn. Anyway, this non-Gaussian treatment indicates that if the rubber has the idealized molecular network strucmre in the system, the stress-strain relation will show the inverse S shape. However, the real mbber vulcanizate (SBR) that does not crystallize under extension at room temperature and other mbbers (NR, IR, and BR at high temperature) do not show the stress upturn at all, and as a result, their tensile strength and strain at break are all 2-3 MPa and 400%-500%. It means that the stress-strain relation of the real (noncrystallizing) rubber vulcanizate obeys the Gaussian rather than the non-Gaussian theory. 

Nevertheless, it is obviously shown in Figure 18.1 that the stress-strain curve of the filled mbber gives the clear stress upturn, thus its tensile strength becomes 30 MPa. Therefore, the fundamental question is what happens or what stmcture is produced in the carbon black-filled mbber under large extension, which newly generates the stress upturn. In the case of the fine carbon black-fiUed system, when carbon blacks are dispersed ideally, the carbon gel makes the continuous phase at the... 

Incidentally, as is well known, in the unvulcanized state of the filled mbber, the stress upturn does not appear even in the carbon content of = 0.2-0.25. For understanding this phenomenon, we must consider the discontinuity between the SH layers, in addition to the very low modulus of the unvulcanized mbber. Actually, as we discussed earlier, carbon blacks disperse as an aggregate of carbon particles, then the continuity of carbon gels consisting of aggregates must be much poorer than the theoretical calculation based on the perfect dispersion of carbon particles. In this case, the stress cannot be transmitted from carbon gel to carbon gel through such a very soft medium, and as a result, the stress-strain curve of the system is rather similar to the characteristics of the... 

These experimental results show conclusively that the deformation factor occurring in the theoretical equation of state offers only a crude approximation to the form of the actual equilibrium stress-strain curve. The reasons behind the observed deviation are not known. It does appear, however, from observations on other rubberlike systems that the type of deviation observed is general. Similar deviations are indicated in TutyP rubber (essentially a cross-linked polyisobutylene) and even in polyamides having network structures and exhibiting rubberlike behavior at high temperatures (see Sec. 4b). 

Recent work has focused on a variety of thermoplastic elastomers and modified thermoplastic polyimides based on the aminopropyl end functionality present in suitably equilibrated polydimethylsiloxanes. Characteristic of these are the urea linked materials described in references 22-25. The chemistry is summarized in Scheme 7. A characteristic stress-strain curve and dynamic mechanical behavior for the urea linked systems in provided in Figures 3 and 4. It was of interest to note that the ultimate properties of the soluble, processible, urea linked copolymers were equivalent to some of the best silica reinforced, chemically crosslinked, silicone rubber... 

Figure 10.1. USAXS observation during straining of an SBS block copolymer. Right monitor Intensity maxima on an ellipse. Raw-data coordinate system (x,y) and radial cuts for data analysis are indicated. Middle Videotaping of sample. Left Stress-strain curve. Control booth of beamline BW4, HASYLAB, Hamburg...

The material properties used in the simulations pertain to a new X70/X80 steel with an acicular ferrite microstructure and a uniaxial stress-strain curve described by er, =tr0(l + / )", where ep is the plastic strain, tr0 = 595 MPa is the yield stress, e0=ff0l E the yield strain, and n = 0.059 the work hardening coefficient. The Poisson s ratio is 0.3 and Young s modulus 201.88 OPa. The system s temperature is 0 = 300 K. We assume the hydrogen lattice diffusion coefficient at this temperature to be D = 1.271x10 m2/s. The partial molar volume of hydrogen in solid solution is... 

Figure 5.68 Effect of increasing strain rate and decreasing temperature on stress-strain curves for polyethylene. Reprinted, by permission, from F. Rodriguez, Principles of Polymer Systems, p. 249, 2nd ed. Copyright 1982 by Hemisphere Publishing Corporation.

Figure 6. Stress-strain curves for 50-volume rayon composite with and without HRH system...

For the considered systems, the stress-strain curves and the derived quantities yield stress, ay, plastic flow stress, erpf, and strain softening, have been studied [53,60] in a temperature range from - 110 °C to typically (Ta - 20)°C. Indeed, for temperatures closer to Ta, the experimental results are less reliable as some creep behaviour can to occur. 

Determination of the Elastic and Viscous Stress-Strain Curves for Model Collagen Fiber Systems... 

There is overwhelming evidence that the aramide fibres possess a radially oriented system of crystalline supramolecular structure (see Fig. 19.1). The background of the properties, the filament structure, has been studied by Northolt et al. (1974-2005), Baltussen et al. (1996-2001), Picken et al. (2001), Sikkema et al. (2001, 2003), Dobb (1977-1985) and others. The aramid fibres (and the "rigid" extended chain fibres in general) are exceptional insofar as they were - with the rubbers - the first polymer fibres whose experimental stress-strain curve can very well be described by a consistent theory. 

On the basis of what has been discussed, we are in the position to provide a unified understanding and approach to the composite elastic modulus, yield stress, and stress-strain curve of polymers dispersed with particles in uniaxial compression. The interaction between filler particles is treated by a mean field analysis, and the system as a whole is macroscopically homogeneous. Effective Young s modulus (JE0) of the composite is given by [44]... 

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