Tensile compliance function

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. 

This is because although 0 = (10), in general, cr(10) oQ (it will usually be less). In principle, the quantities we have defined, E(t), Dit), Gif), and J(i), provide a complete description of tensile and shear properties in creep and stress relaxation (and equivalent functions can be used to describe dynamic mechanical behavior). Obviously, we could fit individual sets of data to mathematical functions of various types, but what we would really like to do is develop a universal model that not only provides a good description of individual creep, stress relaxation and DMA experiments, but also allows us to relate modulus and compliance functions. It would also be nice to be able formulate this model in terms of parameters that could be related to molecular relaxation processes, to provide a link to molecular theories. 

In the above considerations, a sinusoidal shear strain is applied to the sample. It should be clear that a sinusoidal shear stress could also be applied resulting in corresponding compliance functions J and J". The former results from the deformation in phase with the stress, while the latter corresponds to the out-of-phase deformation. The value of tan 5 remains the same, as can be seen from the curves in Figure 2-13, where we can easily imagine the stress as the applied variable and strain as the measured variable. Tensile stress is equally applicable and definitions of E (co), E" (o), D"(co), D co), etc. are completely analogous to the derived shear parameters. At a given frequency, the value of tan 8 is always the same for any of these quantities, i.e., tan 8 = E"/E = D"/D . 

Two test cases are used to validate the linear viscoelastic analysis capability implemented in the present finite-element program named NOVA. In the first case, the tensile creep strain in a single eight-noded quadrilateral element was computed for both the plane-stress and plane-strain cases using the program NOVA. The results were then compared to the analytical solution for the plane-strain case presented in Reference 49. A uniform uniaxial tensile load of 13.79 MPa was applied on the test specimen. A three-parameter solid model was used to represent the tensile compliance of the adhesive. The Poisson s ratio was assumed to remain constant with time. The following time-dependent functions were used in Reference 49 to represent the tensile compliance for FM-73M at 72 °C ... 

Figure 13. Plot of the time-dependent dielectric constant as a function of time for different values of the tensile compliance given in the legend.

In the previous two sections we discussed the effects of representing a single-exponential time-dependent compliance on dielectric behavior. It is well known that the time dependence of the tensile compliance of glassy materials such as polymers cannot be represented as a single exponential function. The decay can, however, be represented by a distribution of exponential functions. A considerable effort has been made in studying the origins and shapes of tensile compliance with time. In this work we simply asssume that an approximation to these distributions can take the form... 

Figure 21. Plot of log(tensile compliance) as a function of log(time) for different levels of c and / = 8. Points indicate spacing and half the points used in the calculations.

Figure 3. Reduced tensile creep compliance, DD(t), of Kraton 102 cast from benzene solution, at different temperatures as a function of time, t (Sheet I)...

Consider the tensile experiment of Fig. 11 -12a as a creep study in which a steady stress To is suddenly applied to the polymer specimen. In general, the resulting strain c(t) will be a function of time starting from the imposition of the load. The results of creep experiments are often expressed in terms of compliances rather than moduli. Tlie tensile creep compliance D(t) is... 

The Poisson ratio, like the bulk, tensile, and shear creep compliance, is an increasing function of time because the lateral contraction cannot develop instantaneously in uniaxial tension but takes an infinite time to reach its ultimate value. In response to a sinusoidal uniaxial stretch, the complete Poison ratio is obtained ... 

Have the PPI component function as a flexible spacer of a terminally placed, rigid, crystallizable component derived primarily from gly-colide so as to allow for facile molecular entanglement to create pseudo-crosslinks, which in turn maximize the interfacing of the amorphous and crystalline fractions of the copolymer, leading to high compliance witiiout compromising tensile strength... 

The viscoelastic response of equilibrium rubber networks can be obtained by measuring the shear and tensile moduli or compliances as a function of time, or the corresponding dynamic moduli and compliances as a function of frequency. As discussed in Section 5.2, the measurements of any viscoelastic function can be converted to another viscoelastic function. 

A material, which can be described as an SLS, was found to have unrelaxed and relaxed Young s modulus values of 70 and 50 GPa, respectively. Determine the relaxation and retardation times. Plot graphically the compliance of the material as a function of time, under the action of a constant uniaxial tensile stress. 

For orthorhombic symmetry on the other hand, tensile creep and lateral compliance measurements on specimens cut from oriented sheet will yield only 6 of the 9 required creep functions those not accessible by this method being Suit), Sssit) and S66(t)- The two shear compliances 555(1) and Seeit) can be obtained by torsional creep experiments, but these need to be carefully designed and involve complex experimental procedures. The only possibility for measurement of Su(t) on sheet appears to be by compressive creep techniques, however, one would expect substantial experimental difficulties largely associated with strain measurement and specimen geometry. There appears to be no reported evaluation of the full characterisation of creep for the case of orthorhombic synunetry. 

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). 

Creep measurements involve measuring a constant tensile or flexural load to a respective specimen (as discussed previously) and measuring the strain as a function of time. In a typical creep plot, percentage creep strain is plotted against time. The apparent creep modulus at a particular time can be calculated by dividing the stress by strain at that particular time. Creep compliance is determined by dividing the strain by stress. For a tensile test, the simplest way to measure extension is to make two gauge marks on the tensile specimen and note the distance between the marks at different intervals. However, accurate measurement of extension requires an optical or laser extensometer. In a flexural measurement, the strain is usually calculated with the help of a linear variable differential transformer system. 

As the stress-strain linearity limit of most thermoplastics and their blends is very low, nonlinear viscoelastic behavior of heterogeneous blends needs to be considered in most cases. The nonlinearity is at least partly ascribed to the fact that the strain-induced expansion of materials with Poisson s ratio smaller than 0.5 markedly enhances the fractional free volume (240). Consequently, the retardation times are perpetually shortened in the course of a tensile creep in proportion to the achieved strain. Thus, knowledge of creep behavior over appropriate intervals of time and stress is of great practical importance. The handling and storage of the compliance curves D (t,a) in a graphical form is impractical, so numerous empirical functions have been proposed (241), eg. 

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