Viscoelasticity Unear

Two contributions to the tensile stress growth function, t/J, should be distinguished one due to the Unear viscoelastic response, and the other originating in... 

To account for the nonideal nature of real soUds and liquids, the theory of Unear viscoelasticity provides a generaUzation of the two classical approaches to the mechanics of the continuum-that is, the theory of elasticity and the theory of hydromechanics of viscous Uquids. Simulation of the ideal boundary properties elastic and viscous requires mechanical models that contain a combination of the ideal element spring to describe the elastic behavior as expressed by Hooke s law, and the ideal element dash pot (damper) to simulate the viscosity of an ideal Newton Uquid, as expressed by the law of internal friction of a liquid. The former foUows the equation F = D -x (where F = force, x = extension, and D = directional force or spring constant). As D is time-invariant, the spring element stores mechanical energy without losses. The force F then corresponds to the stress a, while the extension x corresponds to the strain e to yield a = E - e. 

B. UNEAR VISCOELASTIC BEHAVIOR IN BULK (VOLUMINAL) DEFORMATION... 

N. W. Tschoegl, The Theory of Unear Viscoelastic Behavior, Academic Press, 1980, Chapter 9. 

Abstract This chapter deals with the non-linear viscoelastic behaviour of rubber-rubber blend composites and nanocomposites with fillers of different particle size. The dynamic viscoelastic behaviour of the composites has been discussed with reference to the filler geometry, distribution, size and loading. The filler characteristics such as particle size, geometry, specific surface area and the surface structural features are found to be the key parameters influencing the Payne effect. Non-Unear decrease of storage modulus with increasing strain has been observed for the unfilled vulcanizates. The addition of spherical or near-spherical filler particles always increase the level of both the linear and the non-linear viscoelastic properties. However, the addition of high-aspect-ratio, fiber-like fillers increase the elasticity as well as the viscosity. 

With either pure, unfilled elastomers or slightly filled rubber compounds (typically filler volume fraction lower than 10 %) however, a Unear viscoelastic region is observable within the experimental window of most dynamic rheometers providing the strain amplitude does not exceed 10—20 %. 

Principle. The quantity, E (s), in transform space is analogous to the usual Young s modulus for a Unear elastic materials. Here, the Unear differential relation between stress and strain for a viscoelastic polymer has been transformed into a linear elastic relation between stress and strain in the transform space. It will be shown in the next chapter that the same result can be obtained from integral expressions of viscoelasticity without recourse to mechanical models, so that the result is general and not limited to use of a particular mechanical model. Therefore, the simple transform operation allows the solution of many viscoelastic boundary value problems using results from elementary solid mechanics and from more advanced elasticity approaches to solids such as two and three dimensional problems as well as plates, shells, etc. See Chapters 8 and 9 for more details on solving problems in the transform domain. 

Figure 5.5 Schematic of the sinusoidally applied strain and the resulting out-of-phase sinusoidal stress response of a Unear viscoelastic fluid.

Park, S.-J., Larson, R. G. Modeling the Unear viscoelastic properties of metallocene catalyzed high density polyethylenes with long-chain branching./. Rheol, (2005) 49, pp. 523-536... 

Fisher and Denn (1976) presented the Unearized stability analysis for the isothermal viscoelastic case as an extension of the steady-state case presented in Section 9.1.3. The analysis showed (Fig. 9.14) that the critical draw ratio depends on the power-law index, n, and on the viscoelastic parameter a /", where a is defined in Eq. 9.83. Three regions are shown in Figure 9.14 stable, unstable, and unattainable. The lower boundary of the unattainable region is described by the relationship Dr = 1 At low values of the parameter... 

Tschoegl, N.W. The phenomenological theory of Unear viscoelastic behavior an introduction. Springer, BerUn (1989)... 

Rheology. Dynamic and steady shear measurements were done with an Rheometric Al S rheometer. 25mm parallel plate fixtures were used for the dynamic shear experiments frequency sweeps over the frequency range O.Ol-lOOHz were made between 120 - 260lfc using film specimens. All measurements were made within the Unear viscoelastic Umit, which was determined from strain sweeps. Steady shear experiments as a function of shear rate were made between 150 - 2801C with a 25 mm cone-and-plate fixture. The shear rate range used was 0.001 to 25 s. ... 

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