Viscoelastic behavior, laws

When the magnitude of deformation is not too great, viscoelastic behavior of plastics is often observed to be linear, i.e., the elastic part of the response is Hookean and the viscous part is Newtonian. Hookean response relates to the modulus of elasticity where the ratio of normal stress to corresponding strain occurs below the proportional limit of the material where it follows Hooke s law. Newtonian response is where the stress-strain curve is a straight line. 

A borderline case of viscoelastic behavior is the so-called linear viscoelastic behavior. which is observed upon small deformations / and deformation rates . For such behavior the viscous contribution follows the Newton Law of friction (r = )... 

Several researchers reported viscoelastic behavior of yeast suspensions. Labuza et al. [9] reported shear-thinning behavior of baker s yeast (S. cerevisiae) in the range of 1 to 100 reciprocal seconds at yeast concentrations above 10.5% (w/w). The power law model was successfully applied. More recently, Mancini and Moresi [10] also measured the rheological properties of baker s yeast using different rheometers in the concentration range of 25 to 200 g dm. While the Haake rotational viscometer confirmed Labuza s results on the pseudoplastic character of yeast suspension, the dynamic stress rheometer revealed definitive Newtonian behavior. This discrepancy was attributed to the lower sensitivity of Haake viscometer in the range of viscosity tested (1.5 to 12 mPa s). Speers et al. [11] used a controlled shear-rate rheometer with a cone-and-plate system to measure viscosity of... 

We have proposed the use of a quadratic blending law of the double reptation type to express the viscoelastic behavior of [SIS-SI] blends based on the viscoelastic behavior of the diblock and the (Ptribiock copolymers. It may be expressed as Eq. (15), where triblock is the volume fraction of the triblock copolymer in the [SIS-SI] blend. 

In 1983, Steinbom and Flock studied the rheology of crude oils and water-in-oil emulsions (58). Emulsions with high proportions of water exhibited pseudoplastic behavior and were only slightly time dependent at higher shear rates. Omar et al. also measured the rheological characteristics of Saudi crude oil emulsions (59). NonNewtonian emulsions exhibit pseudoplastic behavior and followed a power-law model. Mohammed et al. studied crude oil emulsions using a biconical bob rheometer suspended at the interface (60). More stable emulsions displayed viscoelastic behavior and a solid-like interface. Demulsifiers changed the solid-like interface into a liquid one. 

The various models were invented explicitly to provide a method of mathematical analysis of polymeric viscoelastic behavior. The Maxwell element expresses a combination of Hooke s and Newton s laws. For the spring,... 

Ghoneim and Chen(33) developed a viscoelastic-viscoplastic law based on the assumption that the total strain rate tensor can be decomposed into a viscoelastic and a viscoplastic component. A linear viscoelasticity model is used in conjunction with a modified plasticity model in which hardening is assumed to be a function of viscoplastic strains as well as the total strain rate. The resulting finite-element algorithm is then used to analyze the strain rate and pressure effects on the mechanical behavior of a viscoelastic-viscoplastic material. 

The Larson-Miller and other similar methods have been widely used for metals but here it is important to note that difficulties arise for fiber reinforced composite laminates because the constants are only valid for one configuration of the plies and a more general approach is needed. Dillard (1981) developed an incremental viscoelastic time dependent lamination theory approach that included the Tsai-Hill failure law modified to account for delayed failures using the Zhurkov time dependent failure model that will be discussed in the next section. The advantage of the Dillard approach is that information on the viscoelastic behavior as well as the delayed failure behavior of 0°, 10° and 90° plies can be used to predict the behavior of general laminate configurations. 

The rheological properties of polymer blends - and especially of thermosetting polymer blends - share a close relationship to the morphology and reactions involved. Moreover, these properties can cause changes in shear or strain conditions that may lead to dramatic variations in the phase structure and other properties of polymer blends. The time-temperature superposition principle (WLF-type equations) and power laws have been widely applied to the linear viscoelastic behavior of both neat polymers and blends, despite the fact that they may reflect different types of structure transitions for either thermoplastic or thermosetting resins. 

The dashed line (c) in Fig. 2 corresponds to a typical stress (force) versus strain (displacement) curve for a material which obeys Hooke s Law (elastic) and curve (b) represents a viscoelastic behavior. It can be observed from the figure that the curve from the thermoplastic material is almost linear for a force (stress) below 300 N. In the linear region of the curve, the material behaves like an elastic material and obeys Hooke s Law. The curve in Fig. 2 can be represented by the following equation ... 

If the adhesive material exhibits viscoelastic behavior, then the high stress magnitudes observed at the overlap end region of bonded joints are expected to diminish in time due to the creep process. For example, Weitsman (1981) utilized the nonlinear viscoelastic power-law response, which describes a stress-enhanced creep process to illustrate time-dependent... 

Because of their complex structure the mechanical behavior of polymeric materials is not well described by the classical constitutive equations Hooke s law (for elastic solids) or Newton s law (for viscous liquids). Polymeric materials are said to be viscoelastic inasmuch as they exhibit both viscous and elastic responses. This viscoelastic behavior has played a key role in the development of the understanding of polymer structure. Viscoelasticity is also important in the understanding of various measuring devices needed for rheometric measurements. In the fluid dynamics of polymeric liquids, viscoelasticity also plays a crucial role. " Also in the polymer-processing industry it is necessary to include the role of viscoelastic behavior in careful analysis and design. Finally there are important connections between viscoelasticity and flow birefringence. ... 

Intcrmolecular Contributions. Increasing concentration reduces the effects of excluded volume and intramolecular, hydrodynamic on viscoelastic properties (Section 5). Internal viscosity and finite extensibilty have already been eliminated as primary causes of shear rate dependence in the viscosity. Thus, none of the intramolecular mechanisms, even abetted by an increased effective viscosity in the molecular environment, can account for the increase in shear rate dependence with concentration, e.g., the dependence of power-law exponent on coil overlap c[r/] (Fig. 8.9). Changes in intermolecular interaction with increased shear rate seems to be the only reasonable source of enhanced shear rate dependence, at least with respect to the early deviations from Newtonian behavior and through a substantial portion of the power law regime. 

Both polymeric and some biological reactors often contain non-Newtonian liquids in which viscosity is a function of shear rate. Basically, three types of non-Newtonian liquids are encountered power-law fluids, which consist of pseudoplastic and dilatant fluids viscoplastic (Bingham plastic) fluids and viscoelastic fluids with time-dependent viscosity. Viscoelastic fluids are encountered in bread dough and fluids containing long-chain polymers such as polyamide and polyacrylonitrite that exhibit coelastic flow behavior. These... 

The major characteristic of a polymeric reactor that is different from most other types of reactors discussed earlier is the viscous and often non-Newtonian behavior of the fluid. Shear-dependent rheological properties cause difficulties in the estimation of the design parameters, particularly when the viscosity is also time-dependent. While significant literature on the design parameters for a mechanically agitated vessel containing power-law fluid is available, similar information for viscoelastic fluid is lacking. 

---