Stress-strain behaviour rubbers

Determination of degree of crosslinking in natural rubber vulcanizates. IV. Stress-strain behaviour at large extensions. J. Appl. Pol. Sci. 2, 257 (1959). 

Rather surprisingly, all these kinds of deformation can be described in terms of a single modulus. This is a result of the assumption that rubber is virtually incompressible (i.e. bulk modulus much greater than shear modulus). Young s modulus E = 3G (for fdled rubbers the numerical factor may be in fact as high as 4). Indeed, these relationships by no means fully describe the complete stress strain behaviour of real rubbers but may be taken as first approximations. The shear stress relationship is usually good up to strains of 0.4 and the tension relationship approximately true up to 50% extension. 

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,... 

The term dynamic test is used here to describe the type of mechanical test in which the rubber is subjected to a cyclic deformation pattern from which the stress strain behaviour is calculated. It does not include cyclic tests in which the main objective is to fatigue the rubber, as these are considered in Chapter 12. Dynamic properties are important in a large number of engineering applications of rubber including springs and dampers and are generally much more useful from a design point of view than the results of many of the simpler static tests considered in Chapter 8. Nevertheless, they are even today very much less used than the "static" tests, principally because of the increased complexity and apparatus cost. 

Stress-strain measurements at uniaxial extension are the most frequently performed experiments on stress-strain behaviour, and the typical deviations from the phantom network behaviour, which can be observed in many experiments, provided the most important motivation for the development of theories of real networks. However, it has turned out that the stress-strain relations in uniaxial deformation are unable to distinguish between different models. This can be demonstrated by comparing Eqs. (49) and (54) with precise experimental data of Kawabata et al. on uniaxially stretched natural rubber crosslinked with sulphur. The corresponding stress-strain curves and the experimental points are shown in Fig. 4. The predictions of both... 

Read B.E., Dean G.D, Wright L. (2001) Modelling non-linear stress-strain behaviour of rubber-toughened plastics. Plastics, Rubber and Composites, Vol. 30, pp. 328. 

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.)... 

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... 

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... 

In reality the tensile stress-strain behaviour of rubber networks is better expressed by the semi-empirical equation ... 

None of these theories is, however, adequate to describe the stress—strain behaviour at large strains, a typical upper strain limit for the validity of the Gaussian theories being A 4 for natural rubber of... 

The statistical theory allows the stress-strain behaviour of a rubber to be predicted. The calculation is greatly simplified when the observation that rubbers tend to deform at constant volume is taken into account. This means that the product of the extension ratios must be unity... 

There are various test methods, one being the De Mattia Flex Test method which is suitable for rubbers that have reasonably stable stress-strain properties, at least after a period of cycling, and do not show undue stress softening or set, or highly viscous behaviour. The results obtained for some thermoplastic rubber should be treated with caution if the elongation at break is below,... 

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. 

Abstract The effects of the amount of rubber, the concentration of fibres and the state of the fibre/matrix interface upon the mechanical behaviour of short glass fibre-reinforced rubber-toughened nylon 6 ternary blends are described. First, tensile tests were carried out on different intermediate materials and then on the ternary blends to derive the stress-strain curves and document the damage mechanisms. Fracture toughness tests were implemented on compact tension specimens and the results were correlated to fractographic observations and acoustic emission analysis to assess the role of the different constituents. 

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]. 

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-... 

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