Elastomers stress-strain behaviour

Fig. 20. Types of stress-strain behaviour observed in cross-linked elastomers below Tg. Origins curves indicate amount of (ve-extetKion (sd matic)...

Blending of PLA with different thermoplastics and elastomers is an excellent alternative to copolymerization to improve PLA mechanical properties, in particular those related with the stress-strain behaviour, i.e. elastic modulus... 

In most cases simple determination of tensile strength is not sufficient. Elongation at break and often full stress-strain behaviour analysis is required. Elongation of the sample must be measured. Many problems are associated with the accurate measurement of extension of polymers [11]. There is a wide range of extensions to be measured, from less than 1% for stiff materials like GP polystyrene to over 1000% for certain elastomer systems. There is a significant... 

Menzel AM, Pleiner H, Brand HR (2009a) On the nonlinear stress-strain behaviour of nematic elastomers - materials of two coupled preferred directions. J Appl Phys 105 013503 1-13 Menzel AM, Pleiner H, Brand HR (2009b) Response of prestretched nematic elastomers to external fields. Eur Phys J E 30 371-377... 

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

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. 

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. 

Stress-Strain Relations for Viscoelastic Materials. The viscoelastic behaviour of an elastomer varies with temperature, pressure, and rate of strain. This elastic behaviour varies when stresses are repeatedly reversed. Hence any single mathematical model can only be expected to approximate the elastic behaviour of actual substances under limited conditions 2J. ... 

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]. 

A series of studies was also made by us, of the PUs cyclic stress-strain response. The range of structures achieved by us was widened by inclusion of DBDI, as a diisocyanate with a very strong tendency to packing due to its constitutional mobility. A systematic investigation (as shown in Table 4.5), was made of the effects of varying HS and SS chemistry, crosslinking and preparation procedures, on the hysteresis behaviour and Mullins effect of melt-cast polyurethane elastomers. The... 

The tensile stress-strain deformation pattern for polyurethane elastomers is similar to those of other elastomers, and Fig. 13.1 shows typical curves for urethane elastomers of different hardness. Typically, for elastomers, the shape of the curve changes with increasing deformation so that elastic behaviour over the full stress-strain range cannot be defined simply by Young s modulus. Figure 13.2 shows a stress-strain curve at low strain values. This curve can be described by the general equation... 

The non-linearity may arise for a variety of reasons. First, the linear theory has been developed for small strains, and to generalise it to large strain requires decisions on the appropriate definitions of both strain and stress, in effect making it necessary to create a new theory. Typical polymer applications may require the material to operate at strains in excess of 10%, and for elastomers the strains may be up to several hundred percent. Secondly, even at small strains linear behaviour may not be obtained. The behaviour may be quite rich, with the possibility of the polymer being initially linear but becoming non-linear at large times. 

Natural rubber (NR) is a well studied elastomer. Of particular interest is the ability of NR to crystallize, specifically the strain-induced crystallization that takes place whilst the material is stretched. Moreover, in many elastomer applications, network chain dynamics under external stress/strain are critical for determining ultimate performance. Thus, a study on how the strain-induced crystallization affects the dynamics of a rubbery material is of outmost importance. Lee et al [1] reported their initial findings on the role of uniaxial extension on the relaxation behavior of cross-linked polyisoprene by means of dielectric spectroscopy. Nonetheless, to our best knowledge no in-depth study of the effects of strain induced crystallization on the molecular dynamics of NR has been undertaken, analyzing the relaxation spectra and correlating the molecular motion of chains with its structure. Broadband dielectric spectroscopy (BDS) has been chosen in order to study the dynamic features of segmental dynamics, because it is a comparatively simple technique for the analysis of the relaxation behaviour over a suitable frequency interval. This study is important from a basic and practical point of view, since an elongated crosslinked polymer at equilibrium may be considered as a new anisotropic material whose distribution of relaxation times could be affected by the orientation of the chains. 

The properties of elastomeric materials are controlled by their molecular structure which has been discussed earlier (Section 4.5). They are basically all amorphous polymers above their glass transition and normally crosslinked. 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 nineteeth century. Elastomer deformation 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. 

Before briefly discussing each type it is necessary to consider the performance of thermoplastic elastomers, and the problem of defining service temperature limits for them. The structural features that convey the ability to be processed as a thermoplastic are also a limiting factor in their use. Since it is the pseudocrosslinks that allow these materials to develop elastomeric behaviour, any factor which interferes with the integrity of the pseudocrosslinks will weaken the material, and allow excessive creep or stress relaxation to occur under the sustained application of stress and strain. Temperature is obviously one such factor. 

In recent years, the behaviour of liquid crystalline polymers including elastomers has been a subject of considerable interest 104,105). It is known that small molecule liquid crystals turn into a macroscopic ordered state by external electric or magnetic fields. A similar behaviour seems to occur for liquid-crystalline polymer networks under mechanical stress or strain. 

Non-linear viscoelastic mechanical behaviour of a crosslinked sealant was interpreted as due to a Mullins effect. The Mullins effect was observed for a series of sealants under tensile and compression tests. The Mullins effect was partially removed after a mechanical test, when a long relaxation time was allowed, that is the modulus increased over time. Non-linear stress relaxation was observed for pre-strained filler sealants. Time-strain superposition was used to derive a model for the filled sealants. Relaxation over long periods demonstrates that the Mullins effect is caused by non-equilibrium with experimental conditions being faster than return to the initial state. If experiments were conducted over times of the order of a day there may be no Mullins effect. If a filled elastomer were only required to perform its function once per day then each response might be linear viscoelastic. 

The modulus at minimum and low strain amplitudes is due to the so-called filler network and it is accepted that the filler surface area, as well as the surface activity, play a major role in establishing a filler network, determining the effective contact area between filler particles and between filler particles and the elastomer matrix. The stress assisted disruption of the filler network causes the reduction of the modulus as the strain amplitude increases, giving rise to the non-linearity of the dynamic-mechanical behaviour of the rubber composite. This phenomenon is known as the Payne effect and it is (to a certain extent) reversible. The disruption and re-formation of the filler network is... 

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