Long Linear viscoelastic behavior

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. 

The mean times t and tw will be called the number-average and weight-average relaxation times of the terminal region, and tw/t can be regarded as a measure of the breadth of the terminal relaxation time distribution. It should be emphasized that these relationships are merely consequences of linear viscoelastic behavior and depend in no way on assumptions about molecular behavior. The observed relationships between properties such as rj0, J°, and G and molecular parameters provides the primary evidence for judging molecular theories of the long relaxation times in concentrated systems. 

Wood-Adams, P. Dealy, J.M. deGroot, A.W. Redwine, O.D. Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 2000, 33 (20), 7489-7499. Trinkle, S. Friedrich, C. Van Gurp-Palmen plot a way to characterize polydispersity of linear polymers. Rheol. Acta 2001, 40 (4), 322-328. Trinkle, S. Walter, P. Friedrich, C. Van Gurp-Palmen plot. II. Classification of long chain branched polymers by their topology. Rheol. Acta 2002, 41 (1-2), 103-113. 

The above examples refer to linear viscoelastic behavior under small stresses. At higher shear stresses, the shear relaxation times also increase with elapsed time but to a lesser extent. Other aspects of the changes in viscoelastic properties with elapsed time, including prediction of properties after long time periods, have been discussed in detail by Struik. 

We are interested here only in linear viscoelastic behavior, which means that Oq must be sufficiently small that the strain will stay within the linear range until steady-state is reached. At long times, the shear rate approaches a steady value and the creep compliance thus becomes linear with time. The slope of the linear asymptote is 1 / r)o, and the intercept of its extrapolation to zero time is called the steady-state compliance /f. 

Effect of Long-Chain Branching on Linear Viscoelastic Behavior... 

Linear viscoelasticity Linear viscoelastic theory and its application to static stress analysis is now developed. According to this theory, material is linearly viscoelastic if, when it is stressed below some limiting stress (about half the short-time yield stress), small strains are at any time almost linearly proportional to the imposed stresses. Portions of the creep data typify such behavior and furnish the basis for fairly accurate predictions concerning the deformation of plastics when subjected to loads over long periods of time. It should be noted that linear behavior, as defined, does not always persist throughout the time span over which the data are acquired i.e., the theory is not valid in nonlinear regions and other prediction methods must be used in such cases. 

New heterocyclic polymers designed especially for service at elevated temperatures have intriguing properties, some of which are in contrast to properties usually associated with linear noncrystalline polymers. These polymers have sometimes been described as stiff chains because of the long inflexible repeat units of which they are comprised. Relatively few quantitative studies have yet appeared in the dilute solution properties or the viscoelastic behavior of the new heterocyclic polymers—partly because of the difficulties inherent in working with the poorly soluble materials. Some studies on the polyimide with the (idealized) structure ... 

In the solid state deformation, the nonlinear viscoelastic effect is most clearly shown in the yield behavior. The type of stresses applied to a system has little effect on the linear viscoelastic relaxation, but becomes very important as the stress level increases. At high stress levels, the contribution from the external work done on a lattice cell has to be included in the nonlinear viscoelastic analysis. By taking into account the long range cooperative interaction, the external work can,... 

The main question is in the near future, will we be able to predict the viscoelastic behavior of linear polymers whatever the molecular weight distribution, encompassing the broadest dispersion from oligomers to very long molecules The... 

Normally a logarithmic time scale is used to plot the creep curve, as shown in Figure 3.9b, so that the time dependence of strain after long periods can be included. If a material is linearly viscoelastic (Equation 3.17), then at any selected time each line in a family of creep curves (with equally spaced stress levels) should be offset along the strain axis by the same amount. Although this type of behavior maybe observed for plastics at low strains and short times, in most cases the behavior is nonlinear, as indicated in Figure 3.9c. 

Measurements of linear and nonlinear viscoelastic behavior of elastomers have a long history. Instead of reviewing the works done in the past by various workers... 

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