Stress-strain curves elastomer

Fig. 3. Stress—strain curve of typical polyesterether elastomer showing the three main regions (I, II, and III) (181), where A is the slope (Young s modulus)...

Proportion of Hard Segments. As expected, the modulus of styrenic block copolymers increases with the proportion of the hard polystyrene segments. The tensile behavior of otherwise similar block copolymers with a wide range of polystyrene contents shows a family of stress—strain curves (4,7,8). As the styrene content is increased, the products change from very weak, soft, mbbedike materials to strong elastomers, then to leathery materials, and finally to hard glassy thermoplastics. The latter have been commercialized as clear, high impact polystyrenes under the trade name K-Resin (39) (Phillips Petroleum Co.). Other types of thermoplastic elastomers show similar behavior that is, as the ratio of the hard to soft phase is increased, the product in turn becomes harder. 

Figure 2.2 Stress-strain curve of polyester elastomer containing 58 wt% PBT. A, slope = Young s modulus B, yield stress. (Reprinted with permission from ref. 190, p. 96. Copyright 1988 John Wiley Sons, Inc.)...

Flexural modulus is the force required to deform a material in the elastic bending region. It is essentially a way to characterize stiffness. Urethane elastomers and rigid foams are usually tested in flexural mode via three-point bending and tite flexural (or flex ) modulus is obtained from the initial, linear portion of the resultant stress-strain curve. 

Density is also found to increase in this region, thus providing additional evidence of crystallisation. Certain synthetic elastomers do not undergo this strain-induced crystallisation. Styrene-butadiene, for example, is a random copolymer and hence lacks the molecular regularity necessary to form crystallites on extension. For this material, the stress-strain curve has a different appearance, as seen in Figure 7.12. 

However, not all properties are improved by filler. One notable feature of the mechanical behaviour of filled elastomers is the phenomenon of stresssoftening. This manifests itself as a loss of stiffness when the composite material is stretched and then unloaded. In a regime of repeated loading and unloading, it is found that part of the second stress-strain curve falls below the original curve (see Figure 7.13). This is the direct opposite of what happens to metals, and the underlying reasons for it are not yet fully understood. 

Figure 7.13 Typical stress-strain curve for a filled elastomer...

FIG. 11 Stress-strain curves for (a) a pristine polyurethane elastomer (b) a polyurethane-clay nanocomposite prepared from organomontmorillonite (5 wt%). (From Ref. 66.)... 

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 1. Stress-time data from stress-strain curves measured in simple tension at 30°C on the LHT-240 polyurethane elastomer at seven extension rates, A from 9.4 X t° 9.4 min 1. Key 0,9, stress as a function of time ( — 1)/X, at the indicated values of strain, ( — 1).

Figure 4 shows stress-strain curves measured at an extension rate of 94% per minute on the TIPA elastomer at 30°, —30°, and —40°C. With a decrease in temperature from 30° to -40°C, the ultimate elongation increases from 170% to 600%. The modulus Ecr(l), evaluated from a one-minute stress-strain isochrone, obtained from plots like shown in Figure 1, increases from 1.29 MPa at 30°C to only 1.95 MPa at —40°C. This small increase in the modulus and the large increase in the engineering stress and elongation at fracture results from viscoelastic processes. 

Figure 4. Stress-strain curves for the TIP A polyurethane elastomer measured at the indicated temperatures at an extension rate of 0.94 min 1. Arrows indicate...

Figure 4. Stress-strain curves for SIN S containing 40% castor oil elastomer (21). Discontinuous curve adapted from sequential IPN synthesis (1) COPEN (2) COPEUN (3) COPUN (4) 40/60 COPEN/PSN (S) 40/60 COPEUN/PSN (6) 40/60 COPUN/PSN (7) 40/60 COPUN/PSN...

Of prime interest are the tensile properties summarized in Table 4, and typical of stress-strain curves exhibited by thermoplastic elastomers. The elongation and strength at break were measured above 1000% and 50 MPA, respectively. Both the tensile modulus and the stress at yield increased by increasing the PCL relative content whereas, as expected, the ultimate elongation at break slightly decreased. 

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. 

Figure 10.8 Stress-strain curves for 6% crosslinked poly(n-butyl acrylate) elastomer for the sample and control specimen (strain rate= lOOmm/min, room temperature). Adapted from Kushner et al. (2007). Copyright 2007 American Chemical Society.

A spring with a modulus of G, and a dashpot containing a liquid with a viscosity of rj, have been used as models for Hookean elastic solids and Newtonian liquids, respectively. In these models, the spring stores energy in a reversible process, and the dashpot dissipates energy as heat in an irreversible process. Figure 5.3 is a stress-strain curve for a typical elastomer the straight... 

Figure 5.3 Stress-strain curve for a typical elastomer. The dashed line indicates Hookean behavior.

The stress-strain curves of the vulcanizates with 40 phr filler loading are shown in Fig. 28. SBR reinforced with plasma-coated carbon black shows a slight improvement in tensile strength relative to SBR with uncoated carbon black. Polyacetylene-coated carbon black can better interact chemically and physically with the elastomer and thus contributes extra to the reinforcement of the elastomer. 

Smith,T.L., Frederick, . E. Ultimate tensile properties of elastomers. IV. Dependence of the failure envelope, maximum extensibility, and equilibrium stress-strain curve on network characteristics. J. Appl. Phys. 36,2996-3005 (1965). 

An important feature of filled elastomers is the stress softening whereby an elastomer exhibits lower tensile properties at extensions less than those previously applied. As a result of this effect, a hysteresis loop on the stress-strain curve is observed. This effect is irreversible it is not connected with relaxation processes but the internal structure changes during stress softening. The reinforcement results from the polymer-filler interaction which include both physical and chemical bonds. Thus, deforma-tional properties and strength of filled rubbers are closely connected with the polymer-particle interactions and the ability of these bonds to become reformed under stress. 

The success of the developed model in predicting uniaxial and equi-biaxi-al stress strain curves correctly emphasizes the role of filler networking in deriving a constitutive material law of reinforced rubbers that covers the deformation behavior up to large strains. Since different deformation modes can be described with a single set of material parameters, the model appears well suited for being implemented into a finite element (FE) code for simulations of three-dimensional, complex deformations of elastomer materials in the quasi-static Emit. 

The stress-strain curve for unfilled NR exhibits a large increase in stress at higher deformations. NR displays, due to its uniform microstructure, a very unique important characteristic, that is, the ability to crystallise under strain, a phenomenon known as strain-induced crystallization. This phenomenon is responsible for the large and abrupt increase in the reduced stress observed at higher deformation corresponding, in fact, to a self-toughening of the elastomer because the crystallites act as additional cross-links in the network. This process can be better visualized by using a Mooney-Rivlin representation, based on the so-called Mooney-Rivlin equation ... 

A linear relationship exists between the toughness (integrated stress-strain curve) and the dynamic mechanical dissipation factor. The types of materials that fit this relationship include glassy polymers, elastomers, and an impregnated fabric. The existence of this relationship indicates that toughness arises from the molecular motions which give rise to the dynamic mechanical properties. 

Polymeric materials show a wide range of stress-strain characteristics. One characteristic of polymers that is markedly different from metals and ceramics is that their mechanical properties are highly time- and temperature-dependent. An elastomer or a rubbery polymer shows a stress-strain curve that is nonlinear. 

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