Elastomers small-strain properties

By the late 1940s, experimental researchers led by Leaderman and Tobolsky found that the small-strain properties of elastomers and thermoplastic melts were described by the theory of linear viscoelasticity developed by Boltzmann [B26] in the 1870s. This view is made clear in the monographs of Leaderman [L5] and Mark and Tobolsky [M7], which were published in this period. In the next two decades, this subject was developed in monographs by Tobolsky [T5] and, later. Ferry [F3]. 

So far, we have considered the elasticity of filler networks in elastomers and its reinforcing action at small strain amplitudes, where no fracture of filler-filler bonds appears. With increasing strain, a successive breakdown of the filler network takes place and the elastic modulus decreases rapidly if a critical strain amplitude is exceeded (Fig. 42). For a theoretical description of this behavior, the ultimate properties and fracture mechanics of CCA-filler clusters in elastomers have to be evaluated. This will be a basic tool for a quantitative understanding of stress softening phenomena and the role of fillers in internal friction of reinforced rubbers. 

The engineering property that is of interest for most of these applications, the modulus of elasticity, is the ratio of unit stress to corresponding unit strain in tension, compression, or shear. For rigid engineering materials, unique values are characteristic over the useful stress and temperature ranges of the material. This is not true of natural and synthetic rubbers. In particular, for sinusoidal deformations at small strains under essentially isothermal conditions, elastomers approximate a linear viscoelastic... 

A rubber-like solid is unique in that its physical properties resemble those of solids, liquids, and gases in various respects. It is solidlike in that it maintains dimensional stability, and its elastic response at small strains (<5%) is essentially Hookean. It behaves like a liquid because its coefficient of thermal expansion and isothermal compressibility are of the same order of magnitude as those of liquids. The implication of this is that the intermolecular forces in an elastomer are similar to those in liquids. It resembles gases in the sense that the stress in a deformed elastomer increases with increasing temperature, much as the pressure in a compressed gas increases with increasing temperature. This gas-like behavior was, in fact, what first provided the hint that rubbery stresses are entropic in origin. 

The equilibrium small-strain elastic behavior of an "incompressible" rubbery network polymer can be specified by a single number—either the shear modulus or the Young s modulus (which for an incompressible elastomer is equal to 3. This modulus being known, the stress-strain behavior in uniaxial tension, biaxial tension, shear, or compression can be calculated in a simple manner. (If compressibility is taken into account, two moduli are required and the bulk modulus. ) The relation between elastic properties and molecular architecture becomes a simple relation between two numbers the shear modulus and the cross-link density (or the... 

The mechanical orientability is the most prominent property of liquid-crystalline elastomers. Above a threshold stress (Sec. 3.3.1), small strains (about 20%-40%) are... 

The hardness of the composite samples increases, whereas the resilience decreases, with an increase in filler concentration. The hardness is a measure of elastic modulus at small strains. The increase in hardness is due to the drop in the mobility of the elastomer chains due to the distribution of metal particulate filler. The decrease in resilience is due to a decrease in damping properties of the composite caused by a decrease in NR content in the samples. 

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... 

The information on physical properties of radiation cross-linking of polybutadiene rubber and butadiene copolymers was obtained in a fashion similar to that for NR, namely, by stress-strain measurements. From Table 5.6, it is evident that the dose required for a full cure of these elastomers is lower than that for natural rubber. The addition of prorads allows further reduction of the cure dose with the actual value depending on the microstructure and macrostructure of the polymer and also on the type and concentration of the compounding ingredients, such as oils, processing aids, and antioxidants in the compound. For example, solution-polymerized polybutadiene rubber usually requires lower doses than emulsion-polymerized rubber because it contains smaller amount of impurities than the latter. Since the yield of scission G(S) is relatively small, particularly when oxygen is excluded, tensile... 

From the dynamic mechanical investigations we have derived a discontinuous jump of G and G" at the phase transformation isotropic to l.c. Additional information about the mechanical properties of the elastomers can be obtained by measurements of the retractive force of a strained sample. In Fig. 40 the retractive force divided by the cross-sectional area of the unstrained sample at the corresponding temperature, a° is measured at constant length of the sample as function of temperature. In the upper temperature range, T > T0 (Tc is indicated by the dashed line), the typical behavior of rubbers is observed, where the (nominal) stress depends linearly on temperature. Because of the small elongation of the sample, however, a decrease of ct° with increasing temperature is observed for X < 1.1. This indicates that the thermal expansion of the material predominates the retractive force due to entropy elasticity. Fork = 1.1 the nominal stress o° is independent on T, which is the so-called thermoelastic inversion point. In contrast to this normal behavior of the l.c. elastomer... 

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