Stress-relaxation and

The purpose of these comparisons is simply to point out how complete the parallel is between the Rouse molecular model and the mechanical models we discussed earlier. While the summations in the stress relaxation and creep expressions were included to give better agreement with experiment, the summations in the Rouse theory arise naturally from a consideration of different modes of vibration. It should be noted that all of these modes are overtones of the same fundamental and do not arise from considering different relaxation processes. As we have noted before, different types of encumbrance have different effects on the displacement of the molecules. The mechanical models correct for this in a way the simple Rouse model does not. Allowing for more than one value of f, along the lines of Example 3.7, is one of the ways the Rouse theory has been modified to generate two sets of Tp values. The results of this development are comparable to summing multiple effects in the mechanical models. In all cases the more elaborate expressions describe experimental results better. 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

The Metravib Micromecanalyser is an inverted torsional pendulum, but unlike the torsional pendulums described eadier, it can be operated as a forced-vibration instmment. It is fully computerized and automatically determines G, and tan 5 as a function of temperature at low frequencies (10 1 Hz). Stress relaxation and creep measurements are also possible. The temperature range is —170 to 400°C. The Micromecanalyser probably has been used more for the characterization of glasses and metals than for polymers, but has proved useful for determining glassy-state relaxations and microstmctures of polymer blends (285) and latex films (286). 

Stress Relaxation. Another important consequence of the viscoelastic nature of plastics is that if they are subjected to a particular strain and this strain is held constant it is found that as time progresses, the stress necessary to maintain this strain decreases. This is termed stress relaxation and is of vital importance in the design of gaskets, seals, springs and snap-fit assemblies. This subject will also be considered in greater detail in the next chapter. 

The thorough and persistent work on precursor decay (the dependence of Hugoniot elastic limit on propagation distance) of Duvall s Washington State University group was successful in demonstrating that precursor attenuation was due to both stress relaxation and hydrodynamic attenuation. Typical data on crystalline LiF is shown in Fig. 2.7. Observed plastic strain... 

Dynamic loading in the present context is taken to include deformation rates above those achieved on the standard laboratorytesting machine (commonly designated as static or quasi-static). These slower tests may encounter minimal time-dependent effects, such as creep and stress-relaxation, and therefore are in a sense dynamic. Thus the terms static and dynamic can be overlapping. 

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. 

Failure can be considered as an actual rupture (stress-rupture) or an excessive creep deformation. Correlation of stress relaxation and creep data has been covered as well as a brief treatment of the equivalent elastic problem. The method of the equivalent elastic problem is of major assistance to designers of plastic products since, by knowing the elastic solution to a problem, the viscoelastic solution can be readily deduced by simply replacing elastic physical constants with viscoelastic constants. 

The time/temperature-dependent change in mechanical properties results from stress relaxation and other viscoelastic phenomena that are typical of these plastics. When the change is an unwanted limitation it is called creep. When the change is skillfully adapted to use in the overall design, it is referred to as plastic memory. 

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

Gillen, K.T., M. Celina, and R. Bernstein, Validation of improved methods for predicting long-term elastomeric seal lifetimes from compression stress-relaxation and oxygen consumption techniques. Polymer Degradation and Stability, 82(1), 25-35, 2003. 

Figure 4. Experimental setup for stress-relaxation and cross-linking at constant simple extension. Key A, electron accelerator B, beam aperture C, force transducer D, thermostated box E, sample F, stretching device G, connecting rods.

Although creep, stress relaxation, and constant-rate tests are most often measured in tension, they can be measured in shear (19-22), compression (23,24), flexure (19), or under biaxial conditions. The latter can be applied... 

Star-shaped polymer molecules with long branches not only increase the viscosity in the molten state and the steady-state compliance, but the star polymers also decrease the rate of stress relaxation (and creep) compared to a linear polymer (169). The decrease in creep and relaxation rate of star-shaped molecules can be due to extra entanglements because of the many long branches, or the effect can be due to the suppression of reptation of the branches. Linear polymers can reptate, but the bulky center of the star and the different directions of the branch chains from the center make reptation difficult. 

The use of soluble zinc soap activators such as zinc 2-ethyl hexanoate instead of conventional stearic acid gives efficiency of vulcanisation and ensures that stress relaxation and creep properties are optimised. Zinc soaps, including the new high efficiency activating types, do not bloom from the compound, either during processing or subsequently during service. 

Olefin fiber production, economic aspects of, 11 242-243 Olefin fibers, 11 224-246 applications of, 11 243-244 creep, stress relaxation, and elastic recovery in, 11 227-228 extrusion of, 11 231-234 hard-elastic, 11 242 high-strength, 11 241-242 manufacture and processing of,... 

Static Load Creep, Stress-Relaxation and Creep-Rupture... 

To the best of our knowledge, the supercoil conformation of the monoden-dron jacketed polystyrene is one of the first observations of a defined tertiary structure in synthetic polymers. The plectoneme conformation could be caused by underwinding or overwinding of a backbone from its equilibrium state [168]. Quick evaporation of the solvent certainly can cause a residual torsion in the molecule as it contracted in itself. Unlike macroconformations of biomolecules, where the tertiary structures are often stabilized by specific interactions between side groups, the supercoil of the monodendron jacketed polymers is metastable. Eventually, annealing offered a path for the stress relaxation and allowed the structural defects to heal [86]. 

The large scale molecular motions which take place in the rubber plateau and terminal zones of an uncross-linked linear polymer give rise to stress relaxation and thereby energy dissipation. For narrow molecular weight distribution elastomers non-catastrophic rupture of the material is caused by the disentanglement processes which occur in the terminal zone, e.g., by the reptation process. In practical terms it means that the green strength of the elastomer is poor. 

It has been reported (4-6) that elastomers undergo very longterm relaxation processes in stress relaxation and creep experiments. The long time behavior of shear modulus can be represented by (18)... 

Tschoegl,N. W. Stress relaxation and creep in dilute polymer solutions. J. Chem. Phys. 44,2331-2334(1966). 

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