Stress-strain curve rubbers

Figure 8.2 shows a non-linear elastic solid. Rubbers have a stress-strain curve like this, extending to very large strains (of order 5). The material is still elastic if unloaded, it follows the same path down as it did up, and all the energy stored, per unit volume, during loading is recovered on unloading - that is why catapults can be as lethal as they are. 

Figure 7.12 Stress-strain curve for styrene-butadiene rubber...

FIGURE 12.18 Stress-strain curves of rubber-fiber composites developed for solid rocket motor insulator A, ethylene-propylene-diene monomer (EPDM) rubber-carbon fiber composites B, EPDM mbber-melamine fiber composites C, EPDM mbber-aramid fiber composites and D, EPDM rubber-aramid pulp composites. 1 and 2 stands for unaged and aged composites respectively. Carbon fiber- and melamine fiber-reinforced composites contain resorcinol, hexamine, and silica in the concentrations 10, 6 and 15, respectively and aramid fiber- and aramid pulp-based composites contain resorcinol, hexamine, and silica in the concentrations 5, 3 and 15, respectively. (From Rajeev, R.S., Bhowmick, A.K., De, S.K., and John, B., Internal communication. Rubber Technology Center, Indian Institute of Technology, Kharagpur, India, 2002.)... 

FIGURE 12.19 Stress-strain curves of some important tire-cords compared with that of rubber. (From Toyo Tire Talk, Vol. 11. Toyo Corporation, Japan. With permission.)... 

Figure 18.1 is the typical stress-strain curves of the filled rubber (SBR filled with fine carbon black, HAF),

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. 

FIGURE 22.8 Payne effect (left) and stress-strain curves right) of solution-based styrene-butadiene rubber (S-SBR) composites with fixed amounts of carbon black N220 and graphitized black N220g, as indicated. (From Kluppel, M. and Heinrich, G., Kautschuk, Gummi, Kunststoffe, 58, 217, 2005. With permission.)... 

FIGURE 28.9 Idealized cyclic stress-strain curve, showing the fuU viscoelastic curve together with its elastic component. (Redrawn from Andrew, C., Introduction to Rubber Technology, Knovel e-book publishers, 1999.)... 

FIGURE 38.2 Stress-strain curves of polyvinyl chloride-ground rubber tire (PVC-GRT) and PVC-Cl-GRT blends. (Reprinted from Naskar, A.K., Bhowmick, A.K., and De, S.K., J. Appl. Polym. ScL, 84, 622, 2002. With permission from Wiley InterScience.)... 

A typical stress-strain curve for a pure gum natural rubber vulcanizate (i.e., without carbon black or other fillers ) is shown in Fig. 83. The stress rises slowly up to an elongation of about 500 percent (length six times initial length), then rises rapidly to a value at break in the neighborhood of 3000 pounds per square inch based on the... 

Fig. 83.—Stress-strain curve for gum-vulcanized natural rubber. The tensile force given on the ordinate axis is referred to the initial cross section.

Fig. 96.—Theoretical and experimental stress-strain curves for simple elongation of gum-vulcanized rubber. (Treloar. )...

Anthony, Caston, and Guth obtained considerably better agreement between the experimental stress-strain curve for natural rubber similarly vulcanized and the theoretical equation over the range a = 1 to 4. KinelP found that the retractive force for vulcanized poly-chloroprene increased linearly with a — l/a up to a = 3.5. 

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... 

Work done by L. Mullins on the prestressing of filler-loaded vulcanisates showed that such prestressing gives a stress-strain curve approaching that of an unfilled rubber. This work has thrown much light on so called permanent set and the theory of filler reinforcement. See Stress Softening. 

The determination of the relationship of stress to strain when a rubber is deformed, the result being shown in the form of a stress-strain curve unless compression stress-strain is specifically stated, the expression normally applies to the tensile characteristics of a rubber. 

Atomic force microscopy and attenuated total reflection infrared spectroscopy were used to study the changes occurring in the micromorphology of a single strut of flexible polyurethane foam. A mathematical model of the deformation and orientation in the rubbery phase, but which takes account of the harder domains, is presented which may be successfully used to predict the shapes of the stress-strain curves for solid polyurethane elastomers with different hard phase contents. It may also be used for low density polyethylene at different temperatures. Yield and rubber crosslink density are given as explanations of departure from ideal elastic behaviour. 17 refs. 

A combination of an energy criterion and the failure envelope has been proposed by Darwell, Parker, and Leeming (22) for various doublebase propellants. Total work to failure was taken from the area beneath the stress-strain curve, but the biaxial failure envelope deviated from uniaxial behavior depending on the particular propellant formulation. Jones and Knauss (46) have similarly shown the dependence of failure properties on the stress state of composite rubber-based propellants. 

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