Elongational compliance

The modulus 5 is a measure of stiffness or hardness of an object. The compliance T is a measure of its softness. In regions far from transitions, the elongation compliance J is defined as in Eq. 22 ... 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

The presence of spherulites or smaller crystallites is comparable to cross-linking and affects not only the moduli and compliances, but also the ultimate properties such as yield strength and ultimate elongation. 

The first assumption involved in using the Boltzmann superposition principle is that elongation is proportional to stress, that is, compliance is independent of stress. The second assumption is that the elongation created by a given load is independent of the elongation caused by any previous load. Therefore, deformation resulting from a complex loading history is obtained as the sum of the deformations that can be attributed to each separate load. 

When dash pot and spring elements are connected in parallel they simulate the simplest mechanical representation of a viscoelastic solid. The element is referred to as a Voigt or Kelvin solid, and it is shown in Fig. 3.10(c). The strain as a function of time for an applied force for this element is shown in Fig. 3.11. After a force (or stress) elongates or compresses a Voigt solid, releasing the force causes a delay in the recovery due to the viscous drag represented by the dash pot. Due to this time-dependent response the Voigt model is often used to model recoverable creep in solid polymers. Creep is a constant stress phenomenon where the strain is monitored as a function of time. The function that is usually calculated is the creep compliance/(f) /(f) is the instantaneous time-dependent strain e(t) divided by the initial and constant stress o. ... 

In other words, independently of the viscoelastic history in the linear region, the tensile compliance function can readily be obtained from both the shear and bulk compliance functions. For viscoelastic solids and liquids above the glass transition temperature, the following relationships hold when t oo J t) t/T[ [Eq. (5.16)], D t) = y Jt [Eq. (5.21)], and D t)J t)/ >. These relations lead to r 3t that is, the elongational viscosity is three times the shear viscosity. It is noteworthy that the relatively high value of tensile viscosity facilitates film processing. 

There are a great number of techniques for the experimental determination of viscoelastic functions. The techniques most frequently found in the literature are devoted to measuring the relaxation modulus, the creep compliance function, and the components of the complex modulus in either shear, elongational, or flexural mode (1-4). Although the relaxation modulus and creep compliance functions are defined in the time domain, whereas the complex viscoelastic functions are given in the frequency domain, it is possible, in principle, by using Fourier transform, to pass from the time domain to the frequency domain, or vice versa, as discussed earlier. 

In addition to elongation flow, material can also exhibit elastic behavior. Two parameters that have been proposed " to quantify this property are (1) recoverable shear RS and (2) compliance C. These can be derived from ... 

Purchased membranes were initially tested for compliance with the specifications designed to assure their suitability for winding operations (thickness, tensile strength and elongation) and for their performance characteristics (flux and salt rejection)... 

In the Bueehe-Halpin theory the necessity of a strong filler-rubber bond follows naturally from the requirement of a low creep compliance. On the other hand the hysteresis criterion of failure, Eq. (32), does not make the need for filler-rubber adhesion immediately obvious. It is clear, however, that Hb cannot exceed Ub. In absence of a strong filler-rubber bond, the stress will never attain a high value the only way for Ub to become large would be for eb to increase considerably. There is no reason, however, why under these conditions eb should be much greater than in the unfilled rubber at the same test conditions and, in any case, it will be limited by the so-called ultimate elongation . This is the maximum value of eh on the failure envelope and is a fundamental property of polymeric networks. The ultimate extension ratio is given by theory (2/7) as the square root of the number of statistical links per network chain, n,... 

Since the linear viscoelasticity of a material is described with a material function G(t), any experiment which gives full information on G(t) is sufficient it is not necessary to give the stresses corresponding to various strain histories. We will restrict the discussion to incompressible isotropic materials. In this case, different types of deformation such as elongation and shear give equivalent information in the range of linear viscoelasticity. Several types of experiments measure relaxation modulus, creep compliance, complex modulus etc which are equivalent to the relaxation modulus (1). 

Elastic modulus and percent elongation to assess their compliance and stretchability, respectively... 

Tensile test tcn.sile strength modulus, elongation to break compliance... 

These relations enable one to relate the shear viscoelastic functions to their tensile counterparts. At high compliance levels, rubbers are highly incompressible, and the proportional relation between the tensile and shear moduli and compliances holds. However, at lower compliances approaching Jg, the Poison ratio fi (which in an elongational deformation is -(Mw/dM, where w is the specimen s width and / is its length) is less than Eqs. (28) and (29) are then no longer exact. For a glass ju T. When G(t) = K(t), E t) = 2.25 Gif). 

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