Shear elastic component

To add to this picture it should be realised that so far only the viscous component of behaviour has been referred to. Since plastics are viscoelastic there will also be an elastic component which will influence the behaviour of the fluid. This means that there will be a shear modulus, G, and, if the channel section is not uniform, a tensile modulus, , to consider. If yr and er are the recoverable shear and tensile strains respectively then... 

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

The Maxwell Model. The first model of viscoelasticity was proposed by Maxwell in 1867, and it assumes that the viscous and elastic components occur in series, as in Figure 5.60a. We will develop the model for the case of shear, but the results are equally general for the case of tension. The mathematical development of the Maxwell model is fairly straightforward when we consider that the applied shear stress, r, is the same on both the elastic, Xe, and viscous, Xy, elements. 

More modem versions of the Defo test have vacuum preparation of the test piece and computerised control but although they measure both the viscous and elastic components, it is still a compression test at low shear rate. Isayev et al27 described an instrument and method to discriminate between materials by measuring the elastic recovery at very short times. 

The low shear rheology measurements also show a rapid increase in the viscoelastic properties (modulus and zero shear viscosity) with increase of bentonite concentration above the gel point (> 30 g dm bentonite). Several models have been proposed to account for the elastic properties of concentrated dispersions, of which that originally proposed by van den Tempel (25) and later developed by Papenhuizen (26) seems to be the most appropriate for the present system. According to this model, if the interaction energy minimum between adjacent particles is sufficiently negative, a three-dimensional network structure may ensue, giving an elastic component. Various models can be used to represent the three dimensional structure, the simplest of which would be either an ideal network where all particles are... 

Figure 4.4 Components of the shear elastic modulus extracted from admittance vs frequency measurements using a 1S.6 /Mn-thick polyisobutyiene-coated TSM resonator. Lines are literature values for the polyisobuiylene modulus (44) at 5 MHz. (Reprinted with permisskm. See Ref. [66] 1991 IEEE.)...

Following Kupradze (1963), we will demonstrate that the radiation conditions for the potential (compressional wave) and solenoidal (shear wave) components of the elastic field can be formulated as follows ... 

Cubic liquid crystalline systems have been described as clear, stiff gelsJ As such, they show shear thinning after an apparent yield stress has been exceeded. The viscoelastic properties are also typical for the gel character a broad linear viscoelastic range and a frequency-independent elastic component, which is considerably higher than the viscous component, are observed. ... 

Equations [3.6.16 and 17] define the interfacial viscous and elastic components if surfaces are deformed by shear. Their counterparts refer to deformation by dilation (extension), or compression. Now we are concerned with relative extensions AAI A, or, infinitesimally, d In A. As before, for purely elastic surfaces the following two options should be considered (a) there is a network-type elasticity, as in a two-dimensional gel and (b) such a skin is absent elasticity is of the Gibbs... 

For simplicity, consider the isotropic linear elastic description of the problem. The total stress is obtained by summing up the contributions of the constituent dislocations. If we consider the shear stress components for concreteness, then the total stress for the boundary with dislocation spacing D is... 

Within an optics-type approach, one considers the resonator as an acoustic cavity. The term acoustic in this context always pertains to shear waves, never to longitudinal waves. This distinction is important in hquids, shear waves rapidly decay because the elastic part of the shear modulus is zero. Shear waves therefore provide for surface specificity. Longitudinal waves, on the contrary, propagate because the elastic component of the compressional modulus is nonzero. 

In these cases the relative velocity of the shearing plates is not constant but varies in a sinusoidal manner so that the shear strain and the rate of shear strain are both cyclic, and the shear stress is also sinusoidal. For non-Newtonian fluids, the stress is out of phase with the rate of strain. In this situation a measured complex viscosity (rf) contains both the shear viscosity, or dynamic viscosity (t] ), related to the ordinary steady-state viscosity that measures the rate of energy dissipation, and an elastic component (the imaginary viscosity ij" that measures an elasticity or stored energy) ... 

Further consequences of the yield stress [i.e., the plug flow] are (i) a drastic reduction of the extrudate swell, B = d/d (d is diameter of the extrudate, d that of the die) [see, e.g., Crowson and FoUces, 1980 Utracki et al, 1984], and (ii) significant increase of the entrance-exit pressure drop, Pg (also known as Bagley correction). For single-phase fluids, these parameters have been related to elasticity by molecular mechanisms [Tanner, 1970 Cogswell, 1972 Laun and Schuch, 1989]. However, in multiphase systems, both B and P depend primarily on the inter-domain interactions and morphology, not on deformation of the macromolecular coils. Thus, in multiphase systems [i.e., blends, filled systems, or composites], only direct measures of elasticity, such as that of Nj, or G should be used. It is customary to plot the measure of the elastic component versus that of the shear components, viz., vs. 

The first term represents the elastic component that is related to Poisson s effect by the equation = (1 — 2vei) 3 introduced above, where 3 is the elastic component of axial tme strain. The second term, P, corresponding to plastic shear, is usually considered to be zero in metals, but we showed elsewhere (32) that it can be slightly negative in some polymers, due to the compaction of macromolecular chains subjected to strain-induced orientation. The last term , measures the contribution of cavitation and/or crazing to the macroscopic volume change of the tensile specimen (33). 

On the other hand, in a non-Newtonian fluid, the viscosity depends on the shear rate. Besides showing very high non-Newtonian viscosities, polymers exhibit a complex viscoelastic flow behavior, that is, their flow exhibits memory , as it includes an elastic component in addition to the purely viscous flow. Rheological properties are those that define the flow behavior, such as the viscosity and the melt elasticity, and they determine how easy or difficult is to process these materials, as well as the performance of the polymer in some applications. The rheology of the polymers and its effect on the processing of these materials are studied in Chapters 22 and 23. 

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