Viscoelastic behavior, illustrations

In this approach the reviews concerned the rheology involving the linear viscoelastic behavior of plastics and how such behavior is affected by temperature. Next is to extend this knowledge to the complex behavior of crystalline plastics, and finally illustrate how experimental data were applied to a practical example of the long-time mechanical stability. 

Figure 1-8 Maxwell Model (Left) and Kelvin-Voigt Model (Right) Illustrate Mechanical Analogs of Viscoelastic Behavior.

The shearing characteristics of non-Newtonian fluids are illustrated in Fig. 7. Curves A and B represent viscoelastic behavior. Curve C illustrates the behavior if the fluid thins with increasing shear, generally referred to as shear thinning or pseudoplasticity. The opposite effect of shear thickening or dilatancy is shown as curve D. 

Figure 2.24 Five regions of viscoelastic behavior for a linear, amorphous polymer I (a to b), II (b to c), III (c to d), IV (d to e), and V ( e to f). Also illustrated are effects of crystallinity (dotted line) and cross-linking (dashed line).

The behavior observed in the stress-strain curve corresponds to viscoelastic behavior that is typical of polymeric materials. The viscoelastic behavior is highly dependent on the temperature at which the test is performed and its relationship to the Tg of the sample. It is also dependent on the rate of deformation, as mentioned previously. In general, very rapid deformation does not allow time for molecular rearrangement to occur and results in behavior characteristic of a more brittle material. The effects of temperature and rate of testing on plastic materials are illustrated in Figs. 3.54 and 3.55, respectively. 

The damping function, g(s), in Eq. (6.30) accounts for lack of proportionality between stress and strain. The product, g(e)e, quantifies the nonlinear elasticity (g(e) = 1 for linear viscoelastic behavior). Separability of time and strain is illustrated for 1,4-polyisoprene in Figures 6.4 and 6.5 the time-dependence of the stress relaxation is the same for shear strains of varying amplimde and for different modes of deformation (Fuller, 1988). 

Figure 3-55. A Maxwell model used to illustrate viscoelastic behavior.

This section considers the behavior of polymeric liquids in steady, simple shear flows - the shear-rate dependence of viscosity and the development of differences in normal stress. Also considered in this section is an elastic-recoil phenomenon, called die swell, that is important in melt processing. These properties belong to the realm of nonlinear viscoelastic behavior. In contrast to linear viscoelasticity, neither strain nor strain rate is always small, Boltzmann superposition no longer applies, and, as illustrated in Fig. 3.16, the chains are displaced significantly from their equilibrium conformations. The large-scale organization of the chains (i.e. the physical structure of the liquid, so to speak) is altered by the flow. The effects of finite strain appear, much as they do when a polymer network is deformed appreciably. 

When anisotropy is present in the fluid state, the phenomenon described in Chapter 3 becomes more complex. We attempt to illustrate this complexity with a few aspects of viscoelastic behavior taken from the literature on lyotropic polypeptide LCPs (rod-like o -helical macromolecules in helicogenic solvents). For example, when c < ci, conventional viscosity-versus-shear-rate behavior is observed (see Chapter 3). Contrary to intuition, however, Fig. 5.29 shows that, at any given shear rate, the viscosity decreases with increasing concentration of polymer when the polypeptide concentration c exceeds that required for uniform LC formation. 

The surface forces, of van der Waals type for rubber-like materials, are able to grandly modify the stress tensor provided by the contact of a blunt asperity applied against the flat and smooth surface of a rubber sample. It will be shown how the coupling of surface adhesion properties and bulk viscoelastic behavior of rubber-like material allows us to solve adherence problems. This will be illustrated through three examples the spontaneous peeling due to the intervention of internal stresses the no-rebound of balls on the smooth surfoce of a soft elastomer and the adhesive contact and rolling of a rigid cylinder under a smooth-surfaced sheet of rubber. 

It seems desirable at this point to familiarize the reader with some concrete examples of the viscoelastic phenomena defined in the preceding chapter, and to provide an idea of their character as exhibited by various types of polymeric systems. Linear viscoelastic behavior in shear will be illustrated in considerable detail, with a few additional examples of bulk viscoelastic behavior and nonlinear phenomena. The examples are accompanied by some qualitative remarks about molecular interpretation, anticipating Chapters 9 and 10 where molecular theories will be discussed more quantitatively. 

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