Elastomer stress-strain properties

FE simulations of the stress-strain properties of fiUer-reinforced elastomers are an important tool for predicting the service live performance of mbber goods. Typical examples are the evaluation of rolling resistance of tires due to hysteresis energy losses, mainly in the tire tread or the adjustment of engine mounts in automotive applications. 

Figure 11. Comparison of the stress-strain properties of the thermoplastic elastomer HBIB-27 to that of inverted block copolymer HIB1-29.

The effects exerted by the filler on the stress-strain properties and the modulus of the vulcanizates are investigated on the standpoint of the part played by the rubber immobilized on the filler and of the behavior of the elastomer in the vicinity of the filler. 

Fig. 10. Compression stress-strain properties of various elastomeric syntactic foams129> (l)urethane elastomer binder and glass microspheres y = 640 kg/m3, void fraction 0.321 (2) polysulfide elastomer binder and phenolic microspheres y = 1500 kg/m3, void fraction 0.133 (3) silicone elastomer binder and glass microspheres y = 610 kg/m3, void fraction 0.407...

Rubber, vulcanized or thermoplastic Determination of tensile stress-strain properties Standard test methods for vulcanized rubber and thermoplastic elastomers-tension... 

To relate the physical properties of carbon black to rubber properties, we tested these tread blacks in the ASTM natural rubber recipe and in an SBR 1500 test recipe. In both elastomers, we checked standard stress/strain properties of modulus, tensile strength, and hardness. In the natural rubber recipe we also tested Firestone running temperature and rebound, and Goodyear rebound. In the SBR we checked percent swell, extrusion rate, viscosity, and laboratory abrasion. 

Ultimate stress-strain properties of amorphous elastomers... 

Stress-strain properties for unfilled and filled silicon rubbers are studied in the temperature range 150-473 K. In this range, the increase of the modulus with temperature is significantly lower than predicted by the simple statistical theory of rubber elasticity. A moderate increase of the modulus with increasing temperature can be explained by the decrease of the number of adsorption junctions in the elastomer matrix as well as by the decrease of the ability of filler particles to share deformation caused by a weakening of PDMS-Aerosil interactions at higher temperatures. 

Equation (4-46) predicts that the stress-strain properties of an elastomer that behaves like an entropy spring will depend only on the temperature, the density of the material, and the average molecular weight between cross-links. In terms of nominal strain this equation is approximately... 

The mechanical and thermal properties of a range of poly(ethylene)/po-ly(ethylene propylene) (PE/PEP) copolymers with different architectures have been compared [2]. The tensile stress-strain properties of PE-PEP-PE and PEP-PE-PEP triblocks and a PE-PEP diblock are similar to each other at high PE content. This is because the mechanical properties are determined predominantly by the behaviour of the more continuous PE phase. For lower PE contents there are major differences in the mechanical properties of polymers with different architectures, that form a cubic-packed sphere phase. PE-PEP-PE triblocks were found to be thermoplastic elastomers, whereas PEP-PE-PEP triblocks behaved like particulate filled rubber. The difference was proposed to result from bridging of PE domains across spheres in PE-PEP-PE triblocks, which acted as physical crosslinks due to anchorage of the PE blocks in the semicrystalline domains. No such arrangement is possible for the PEP-PE-PEP or PE-PEP copolymers [2]. 

The phantom network can account qualitatively for many properties of crosslinked elastomers, but the quantitative explanation of basic properties is wrong. For example, stress-strain properties, especially in simple extension, show departures from the phantom network results even at extension ratios covered by the Gaussian chain model. The explanation of these departures, phenomenologically described by the famous Mooney-Rivlin Eq. (1)... 

In highly polar elastomers use castor-based factice for highest compatibility, best stress-strain properties, and lowest volume swells. 

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. 

Most mechanical and civil engineering applications involving elastomers use the elastomer in compression and/or shear. In compression, a parameter known as shape factor (S—the ratio of one loaded area to the total force-free area) is required as well as the material modulus to predict the stress versus strain properties. In most cases, elastomer components are bonded to metal-constraining plates, so that the shape factor S remains essentially constant during and after compression. For example, the compression modulus E. for a squat block will be... 

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... 

Elastomers are solids, even if they are soft. Their atoms have distinct mean positions, which enables one to use the well-established theory of solids to make some statements about their properties in the linear portion of the stress-strain relation. For example, in the theory of solids the Debye or macroscopic theory is made compatible with lattice dynamics by equating the spectral density of states calculated from either theory in the long wavelength limit. The relation between the two macroscopic parameters, Young s modulus and Poisson s ratio, and the microscopic parameters, atomic mass and force constant, is established by this procedure. The only differences between this theory and the one which may be applied to elastomers is that (i) the elastomer does not have crystallographic symmetry, and (ii) dissipation terms must be included in the equations of motion. 

Studies have been made of the elastic (time-independent) properties of single-phase polyurethane elastomers, including those prepared from a diisocyanate, a triol, and a diol, such as dihydroxy-terminated poly (propylene oxide) (1,2), and also from dihydroxy-terminated polymers and a triisocyanate (3,4,5). In this paper, equilibrium stress-strain data for three polyurethane elastomers, carefully prepared and studied some years ago (6), are presented along with their shear moduli. For two of these elastomers, primarily, consideration is given to the contributions to the modulus of elastically active chains and topological interactions between such chains. Toward this end, the concentration of active chains, vc, is calculated from the sol fraction and the initial formulation which consisted of a diisocyanate, a triol, a dihydroxy-terminated polyether, and a small amount of monohydroxy polyether. As all active junctions are trifunctional, their concentration always... 

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. 

Figure 15.4 gives the stress-strain diagrams for a typical fiber, plastic, and elastomer and the average properties for each. The approximate relative area under the curve is fiber, 1 elastomers, 15 thermoplastics, 150. Coatings and adhesives, the two other types of end-uses for polymers, will vary considerably in their tensile properties, but many have moduli generally between elastomers and plastics. They must have some elongation and are usually of low crystallinity. 

Polymers are viscoelastic materials meaning they can act as liquids, the visco portion, and as solids, the elastic portion. Descriptions of the viscoelastic properties of materials generally falls within the area called rheology. Determination of the viscoelastic behavior of materials generally occurs through stress-strain and related measurements. Whether a material behaves as a viscous or elastic material depends on temperature, the particular polymer and its prior treatment, polymer structure, and the particular measurement or conditions applied to the material. The particular property demonstrated by a material under given conditions allows polymers to act as solid or viscous liquids, as plastics, elastomers, or fibers, etc. This chapter deals with the viscoelastic properties of polymers. 

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