Behavior viscoelastic

There are three fundamental test methods for characterization of the viscoelastic behavior of polymers creep, stress relaxation, and dynamic mechanical analysis. Although the primary focus for this chapter is DMA, it is useful first to discuss the fundamentals of creep and stress relaxation, not only because they are conceptually simpler but because most DMA instruments also are capable of operating in either a creep or stress relaxation mode. All three of the methods are related, and numerical techniques are available for calculating creep and stress relaxation data from dynamic mechanical data (Ferry 1980). 

In a creep test a sample is placed under a constant stress, and strain is recorded as a function of time. If an ideal elastic solid is subjected to a creep test, it will exhibit an immediate elastic strain in accordance with Hooke s law, but the strain will remain constant thereafter until the stress is removed, when the sample will return elastically to zero strain. An ideal liquid responds to a creep test quite differently. There is no initial elastic response, and there will be a continuously increasing strain with a slope inversely proportional to the viscosity the strain rate wUl remain constant. When the stress is removed, there is no elastic recovery— the liquid simply stops flowing in other words, the strain rate returns to zero. 

Because the strain in a creep test is time-dependent (while the stress is constant), creep data are commonly reported as a time-dependent creep compliance  

Note that (to a first approximation) the compliance is simply the inverse of the modulus. 

In a stress relaxation test a sample is quickly placed under a strain that is then held constant, and the resulting stress is recorded as a function of time. The response of an ideal elastic solid in stress relaxation is a stress that remains constant with time, while an ideal liquid responds with an immediate return to zero stress as soon as the test strain is imposed. Viscoelastic materials respond with a stress that decays with time. Stress relaxation data are commonly reported as a time-dependent stress relaxation modulus  

Finally, the rate dependent properties are usually modeled by a three-parameter solid which consists of a spring (m2) and a dashpot (h) in parallel connected to another spring (mj) in series. Viscoelastic properties may also be expressed in terms of the dynamic modulus G. A sinusoidal displacement of the form u = e is applied to the specimen 

The anisotropic viscoelastic properties in shear of the meniscus have been determined by subjecting discs of meniscal tissue to sinusoidal torsional loading [35] (Table B2.8). The specimens were cut in the three directions of orthotropic symmetry, i.e. circumferential, axial and radial. A definite correlation is seen with the orientation of the fibers and both the magnitude of the dynamic modulus IG I and the phase angle 8. 

The viscoelastic properties of the human intervertebral disc have been modeled [36, 37] using the three-parameter solid. The parameters were obtained by fitting experimentally obtained creep curves to analytical equations using linear regression (Table B2.9). 

The rate of creep and stress relaxation of TPs increases considerably with temperature those of the TSs (thermoset plastics) remain relatively unaffected up to fairly high temperatures. The rate of viscoelastic creep and stress relaxation at a given temperature may also vary significantly from one TP to an- 

Basics Creep data can be very useful to the designer. In the interest of sound design-procedure, the necessary long-term creep information should be obtained on the perspective specific plastic, under the conditions of product usage (Chapter 5, MECHANICAL PROPERTY, Long-Term Stress Relaxation/Creep). In addition to the creep data, a stress-strain diagram under similar conditions should be obtained. The combined information will provide the basis for calculating the predictability of the plastic performance. 

The factors that affect being able to design with creep data include a number of considerations. 

TTie strain readings of a creep test can be more accessible to a designer if they are presented as a creep modulus. In a viscoelastic material, namely plastic, the strain continues to increase with time while the stress level remains constant. Since the creep modulus equals stress divided by strain, we thus have the appearance of a changing modulus. 

The creep modulus, also known as the apparent modulus or viscous modulus when graphed on log-log paper, is normally a straight line and lends itself to extrapolation for longer periods of time. 

A crystalline material has a distinct melting point where there is a distinct entropy change in going from a disordered melt to a more ordered solid. Since an amorphous material remains disordered as it is cooled, it has no distinct melting point. Instead, its viscosity continues to increase imtil molecular motion ceases and it becomes a glass. Likewise, an amorphous polymer goes from a viscous liquid to a viscoelastic solid to an elastic brittle glass as it is cooled from its melt. 

Time response of different rheological systems to applied forces. The Maxwell model gives steady creep with some post stress recovery, representative of a polymer with no cross-linking. The Kelvin-Voigt model gives a retarded viscoelastic behavior expected from a cross-linked polymer. 

Thus far, the polymer melt has been considered as a purely viscous fluid. In a purely viscous fluid, the energy expended in deformation of the fluid is immediately dissipated and is non-recoverable. The other extreme is the purely elastic material where 

In fluids with time-dependent behavior, the effects of time can be either reversible or irreversible. If the time effects are reversible, the fluids are either thixotropic or rheopectic. Thixotropy is the continuous decrease of apparent viscosity with time under shear and the subsequent recovery of viscosity when the flow is discontinued. Rheopexy is the continuous increase of apparent viscosity with time under shear it is also described by the term anti-thixotropy. A good review on thixotropy was given by Mewis [45]. Polymer melts do exhibit some thixotropic effects however, thixotropy can also occur in inelastic fluids. The time scale of thixotropy is not necessarily associated with the time scale for viscoelastic relaxation. 

In the quantitative analysis of most extrusion problems, the polymer melt generally is considered to be a viscous, time-independent fluid. This assumption is, of course, a simplification, but it usually allows one to find a relatively straightforward solution to the problem. This assumption will be used throughout the rest of this book, unless indicated otherwise. In the analysis of any flow problem, however, it should be remembered that elastic effects may play a role. Also, some flow phenomena, such as extrudate swell, clearly cannot be analyzed unless the elastic behavior of 

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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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