Elastic range polymers

In general, the behavior of all classes of polymer behavior is Hookean before the yield point. The reversible recoverable elongation before the yield point, called the elastic range, is primarily the result of bending and stretching of covalent bonds in the polymer backbone. This useful portion of the stress-strain curve may also include some recoverable uncoiling of polymer chains. Irreversible slippage of polymer chains is the predominant mechanism after the yield point. 

It is important to note that the behavior of polymers below the yield point is Hookean and essentially reversible for short-term service. Thus this range, which is associated with stretching and bending of covalent bonds, is called the elastic range. The area under the stress-strain curve is a measure of toughness. 

The molecular movements of the chain determine the elastic range of polymers. In this unique state of rubber like elasticity there is freedom of the micro-Brownian motion of the chain units and a high relaxation time for the macro-Brownian motion of the entire chain. This state can be described as a liquid with a fixed structure U6). 

Dissolution measurements under the microscope, therefore, are a powerful tool for selecting solvents or plasticizers. Measurements of elastic range extension give insight into structural changes caused by plasticizers. Thermal diffusivity and heat conductivity measurements are recommended to detect side group and other transitions in polymers and other substances. 

The ratio of tensile stress to corresponding strain below the proportional limit. Many polymers/blends do not obey Hooke s law through out the elastic range but deviate therefrom even at stresses well below the yield stress. However, stress-strain curves almost always show a linear region at low stresses, and a straight line drawn tangent to this portion of the curve permits calculation of tensile modulus. 

The ratio of stress to deformation within the elastic range of a material. It can be determined by tensile test, compression test, and bending test. Because of the viscoelastic characteristics of polymers, time-dependenee is an important consideration... 

Even in the apparently linear range, the response to stress should be considered as viscoelastic rather than elastic. Most polymers that behave in a linear, viscoelastic manner at small strains (< 1 %) behave in a nonlinear fashion at strains of the order of 1 % or more. However, in a fibrous composite, the resin may behave quite differently than it would in bulk. Stress and strain concentrations may exceed the limiting values for linearity in localized regions. Thus the composite may exhibit nonlinearity (Ashton, 1969 Trachte and DiBenedetto, 1968), as is the case with particulate-filled polymers (Section 12.1.2). Although nonlinearity at low strains is characteristic, Halpin and Pagano (1969) have predicted constitutive relations for isotropic linear viscoelastic systems, and verified their prediction using specimens of fiber-reinforced rubbers. 

This result demonstrates that the frictional force per unit area (frictional stress) is related to the normal pressure P instead of the load W by the power law. For solid friction, eq. (11.1) is also valid, with a = 1. A polymer gel is easily deformable, with a typical elasticity ranging from 1 to 1000 kPa, owing to the presence... 

Like all cementations materials, polymer concretes are inflexible and tend to brittleness. The modulus of elasticity range from 10 to 10 psi and flexural strength from 500 to 1000 psi. Tensile strengths vary from 150 to 400 psi and compressive strengths range from 1800 to 5000 psi. 

Catalysts on the basis of complexes of cobalt or iron salts [e.g., cobalt(II) chloride/ pyridine, cobalt(II) acetate/AlR2Cl] yield mixed structures with more than 20% 1,2 double bonds and rubber elastic-like polymers [325,326]. Rare earth catalysts have also been described [327]. A crystalline c/ -1,4 polymer with a melting point of 198°C and a molecular weight of 100 000 is obtained with aluminum alkyls/neodymium compounds at a molar ratio of 31 1. The yield is in the range of 30%. Cobalt(II) acetate in combination with diethylaluminum chloride or rhodium salts also yields a cis-, A polymer [328,329]. 

The aforementioned discussion assumed that a propagating flaw was the cause of failure. It would be better if the flaw never existed. Many modern impact modifiers are designed to prevent the formation of the flaw. The approach here is to prevent the polymer phase from yieMng by extending the elastic range of the polymer by control of monomers. 

It appeared that a successful modeling of mechanical properties of crystalline polymers within the elastic range requires a consideration of lamellae thickness and crystallinity but also the lamellae width and length. Varying elastic properties of the amorphous phase are to be considered when the constraints between lamellar crystals change due to differentiated solidification conditions. 

The Poisson s ratio can be determined provided the adhesive displacement is measured in the longitudinal and transversal directions. This property is very difficult to measure experimentally, especially in the elastic range. For polymers, the Poisson s ratio varies between 0.3 and 0.5. For temperatures below the glass transition temperature (Tg), the value is close to 0.3. When the adhesive is above Tg or in the plastic region, the Poisson s ratio is about 0.5. Table 19.1 gives the values for several adhesives. One way to determine the Poisson s ratio is to deduce it from the measurement of the Young s modulus and the shear modulus (see Sect. 19.5). 

We will now investigate how the occurrence and interplay of the structural phase of elastic, flexible polymers depends on the mutual interaction range between nonbonded monomers [127,128,135,136]. For this purpose, we consider the single-polymer model (6.8), consisting of the FEME potential (1.39) for the bonded interaction and a truncated Leimar(Hones... 

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