Viscoelasticity behavior

A variety of commercial instruments are available for the determination of the viscoelastic behavior of samples. Figure 3.15 shows one such apparatus, the Rheovibron Viscoelastometer. This instrument also takes advantage of the complementarity that exists between time and temperature It operates at four frequencies over a 175°C temperature range. With accessories, both the frequency range and the temperature range can be broadened still further. 

We have relied heavily on the use of models in discussing the viscoelastic behavior of polymers in the transient and dynamic experiments of the last few sections. The models were mechanical, however, and while they provide a way for understanding the phenomena involved, they do not explicitly relate these phenomena to molecular characteristics. To establish this connection is the objective of this section. 

These normal stresses are more pronounced for polymers with a very broad molecular weight distribution. Viscosities and viscoelastic behavior decrease with increasing temperature. In some cases a marked viscosity decrease with time is observed in solutions stored at constant temperature and 2ero shear. The decrease may be due to changes in polymer conformation. The rheological behavior of pure polyacrylamides over wide concentration ranges has been reviewed (5). 

The elongation of a stretched fiber is best described as a combination of instantaneous extension and a time-dependent extension or creep. This viscoelastic behavior is common to many textile fibers, including acetate. Conversely, recovery of viscoelastic fibers is typically described as a combination of immediate elastic recovery, delayed recovery, and permanent set or secondary creep. The permanent set is the residual extension that is not recoverable. These three components of recovery for acetate are given in Table 1 (4). The elastic recovery of acetate fibers alone and in blends has also been reported (5). In textile processing strains of more than 10% are avoided in order to produce a fabric of acceptable dimensional or shape stabiUty. 

Telechelic Ionomers. Low molecular weight polymers terminated by acid groups have been treated with metal bases to give ionomers in which the cations can be considered as connecting links in the backbones (67—71). The viscoelastic behavior of concentrated solutions has been linked to the neutralizing cation. 

Viscoelastic Measurement. A number of methods measure the various quantities that describe viscoelastic behavior. Some requite expensive commercial rheometers, others depend on custom-made research instmments, and a few requite only simple devices. Even quaHtative observations can be useful in the case of polymer melts, paints, and resins, where elasticity may indicate an inferior batch or unusable formulation. Eor example, the extmsion sweU of a material from a syringe can be observed with a microscope. The Weissenberg effect is seen in the separation of a cone and plate during viscosity measurements or the climbing of a resin up the stirrer shaft during polymerization or mixing. 

Eig. 7. Viscoelastic behavior of encapsulant materials (a) Newtonian fluid (b) non-Newtonian fluid. 

In Section 4.2.2 the central role of atomic diffusion in many aspects of materials science was underlined. This is equally true for polymers, but the nature of diffusion is quite different in these materials, because polymer chains get mutually entangled and one chain cannot cross another. An important aspect of viscoelastic behavior of polymer melts is memory such a material can be deformed by hundreds of per cent and still recover its original shape almost completely if the stress is removed after a short time (Ferry 1980). This underlies the use of shrink-fit cling-film in supermarkets. On the other hand, because of diffusion, if the original stress is maintained for a long time, the memory of the original shape fades. 

Fig. 22. Nomialized pull-off energy measured for polyethylene-polyethylene contact measured using the SFA. (a) P versus rate of crack propagation for PE-PE contact. Change in the rate of separation does not seem to affect the measured pull-off force, (b) Normalized pull-off energy, Pn as a function of contact time for PE-PE contact. At shorter contact times, P does not significantly depend on contact time. However, as the surfaces remain in contact for long times, the pull-off energy increases with time. In seinicrystalline PE, the crystalline domains act as physical crosslinks for the relatively mobile amorphous domains. These amorphous domains can interdiffuse across the interface and thereby increase the adhesion of the interface. This time dependence of the adhesion strength is different from viscoelastic behavior in the sense that it is independent of rate of crack propagation.

The typical viscoelastic response, as shown in Fig. 2.18, is the propagation of a shock due to the compression, followed by a relaxation to an equilibrium state. The relaxation response is a significant part of the total response. Relaxation times are typically in the 0.1 /is regime. At pressures over about 2 GPa, PMMA shows a change in relaxation time which may be indicative of mechanical failure. Anderson has recently extended this work to other polymers and found similar strong viscoelastic behavior [92A01]. 

Fig. 2.18. Polymeric solids are observed to respond to shock compression in a viscoelastic behavior. The figure shows a transmitted wave profile in UVIIA PMMA as measured with an imbedded VISAR mirror. Note that the early shock is followed by a rapid relaxation to a higher velocity, and a slow relaxation to higher velocities, (after Schuler and Nunziato [74S01]).

Some basic lamina and laminate behavioral characteristics were deliberately overlooked in the preceding discussion. Among them are plastic or nonlinear deformations, viscoelastic behavior, and wave propagation. 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

For those not familiar with this type information recognize that the viscoelastic behavior of plastics shows that their deformations are dependent on such factors as the time under load and temperature conditions. Therefore, when structural (load bearing) plastic products are to be designed, it must be remembered that the standard equations that have been historically available for designing steel springs, beams, plates, cylinders, etc. have all been derived under the assumptions that (1) the strains are small, (2) the modulus is constant, (3) the strains are independent of the loading rate or history and are immediately reversible, (4) the material is isotropic, and (5) the material behaves in the same way in tension and compression. 

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. 

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. 

There are several other comparable rheological experimental methods involving linear viscoelastic behavior. Among them are creep tests (constant stress), dynamic mechanical fatigue tests (forced periodic oscillation), and torsion pendulum tests (free oscillation). Viscoelastic data obtained from any of these techniques must be consistent data from the others. 

Fig. 2-24 Maxwell model used to explain viscoelastic behavior.

The Maxwell model is also called Maxwell fluid model. Briefly it is a mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus (E) in series with a dashpot of coefficient of viscosity (ji). It is an isostress model (with stress 5), the strain (f) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as d /dt = (l/E)d5/dt + (5/Jl)-This model is useful for the representation of stress relaxation and creep with Newtonian flow analysis. 

Here are some guidelines to mold living hinges with polypropylene (other plastics are similar but may require their own specific dimensions dependent upon their particular viscoelastic behavior) ... 

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