Rubber elasticity stress-strain behaviour

There is a British standard19 giving guidance on the application of rubber testing to finite element analysis. Several of the models for stress strain behaviour are appraised and advice given on selection. The point is made that the models considered treat the rubber as a perfectly elastic material,... 

Treloar, L R. G. (1975). The Phytics of Rubber Elasticity (3rd edn). Oxford UniveTSity Press. An authoriutive text on the stress-strain behaviour of rubbers. (Relevant to Chapters 2 and 3.)... 

Elastic fracture mechanics can be applied to rubbers provided that allowance is made for their non-linear stress-strain behaviour. The steps are (a) replacing experimentally determined strain energy density remote from the crack and (b) replacing uq, the crack length in the unstrained state, by u = >n... 

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. 

Thus, this consideration shows that the thermoelasticity of the majority of the new models is considerably more complex than that of the phantom networks. However, the new models contain temperature-dependent parameters which are difficult to relate to molecular characteristics of a real rubber-elastic body. It is necessary to note that recent analysis by Gottlieb and Gaylord 63> has demonstrated that only the Gaylord tube model and the Flory constrained junction fluctuation model agree well with the experimental data on the uniaxial stress-strain response. On the other hand, their analysis has shown that all of the existing molecular theories cannot satisfactorily describe swelling behaviour with a physically reasonable set of parameters. The thermoelastic behaviour of the new models has not yet been analysed. 

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

Weakly crosslinked epoxy-amine networks above their Tg exhibit rubbery behaviour like vulcanized rubbers and the theory of rubber elasticity can be applied to their mechanical behaviour. The equilibrium stress-strain data can be correlated with the concentration of elastically active network chains (EANC) and other statistical characteristics of the gel. This correlation is important not only for verification of the theory but also for application of crosslinked epoxies above their Tg. 

Figure 5 demonstrates the different behaviour resulting from Eqs. (49) and (54) in the case of uniaxial compression. We also tested the elastic potential (Eq. (44)) in the two cases v = 1/2 and v = —1/4 by comparing the corresponding stress-strain relations with biaxial extension experiments which cover relatively small as well as large deformation regions for an isoprene rubber vulcanizate. In the rectan-... 

Rubber as an engineering material is unique in its physical behaviour. It exhibits physical properties that lie mid-way between a solid and liquid, giving the appearance of solidity, while possessing the ability to deform substantially. Most solid materials have an extensibility of only a few percent strain and only a portion of that is elastic, being typically Hookean in character, exhibiting a linear stress-strain relationship. Rubbers, however, may be extensible up to over 1000% strain, most of which is... 

In the field of rubber elasticity both experimentalists and theoreticians have mainly concentrated on the equilibrium stress-strain relation of these materials, i e on the stress as a function of strain at infinite time after the imposition of the strain > This approach is obviously impossible for polymer melts Another complication which has thwarted the comparison of stress-strain relations for networks and melts is that cross-linked networks can be stretched uniaxially more easily, because of their high elasticity, than polymer melts On the other hand, polymer melts can be subjected to large shear strains and networks cannot because of slippage at the shearing surface at relatively low strains These seem to be the main reasons why up to some time ago no experimental results were available to compare the nonlinear viscoelastic behaviour of these two types of material Yet, in the last decade, apparatuses have been built to measure the simple extension properties of polymer melts >. It has thus become possible to compare the stress-strain relation at large uniaxial extension of cross-linked rubbers and polymer melts ... 

The tensile stress-strain curve of a stretched NR sample is shown in Fig. 1. As expected, the mechanical behaviour appears to obey the concept of rubber-like elasticity, where the application of stress is considered to cause molecules to change from a coiled to an extended configuration... 

The properties of elastomeric materials are controlled by their molecular structure which has been discussed earlier (Section 4.4.5). They are basically all amorphous polymers above their glass transition and normally cross-linked. Their unique deformation behaviour has fascinated scientists for many years and there are even reports of investigations into the deformation of natural rubber from the beginning of the last century. Rubber elasticity is particularly amenable to analysis using thermodynamics, as an elastomer behaves essentially as an entropy spring . It is even possible to derive the form of the basic stress-strain relationship from first principles by considering the statistical thermodynamic behaviour of the molecular network. 

In reality the ideal elastic rubber does not exist. Real rubbery materials do have a small element of viscosity about their mechanical behaviour, even though their behaviour is dominated by the elastic element. Even so, real rubbers only demonstrate essentially elastic behaviour, i.e. instantaneous strain proportional to the applied stress, at small strains. 

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