Stress relaxation behavior

The relaxation behavior of individual chains depends on the simultaneous or cooperative relaxation of neighboring chains. If these are the same, different, or mixed in type, differences in stress-relaxation behavior may be expected. Thus, stress-relaxation experiments may be expected to reveal even the most intimate extents of chain mixing or segregation (Horino et al, 1965 Manabe et a/., 1969, 1971 Soen et a/., 1966 Takayanagi, 1972 Takayanagi et al, 1963 Tobolsky and Aklonis, 1964 Tobolsky and DuPre, 1968). 

In this equation represents the glassy modulus (3 x lO dyn/cm ), T in is a characteristic relaxation time, E2 represents the rubbery plateau modulus, and E it) is the relaxation modulus as a function of time. 

It may be that in PVC/NBR materials the nearest neighbor chain composition is nearly (but not quite) random. 

One further point should be made. The WLF equation can correctly predict the relaxation behavior of incompatible systems, but for temperature ranges limited to one transition. For incompatible polyblends that exhibit two transitions, the equation will yield satisfactory results if applied to each transition separately. 

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Eig. 10. Stress relaxation behavior at 105°C of the phosphor bron2e alloy C521, in the A, reHef annealed HR04 and roUed B, H04, tempers compared to C,... 

When a viscoelastic material is subjected to a constant strain, the stress initially induced within it decays in a time-dependent manner. This behavior is called stress relaxation. The viscoelastic stress relaxation behavior is typical of many TPs. The material specimen is a system to which a strain-versus-time profile is applied as input and from which a stress-versus-time profile is obtained as an output. Initially the material is subjected to a constant strain that is maintained for a long period of time. An immediate initial stress gradually approaches zero as time passes. The material responds with an immediate initial stress that decreases with time. When the applied strain is removed, the material responds with an immediate decrease in stress that may result in a change from tensile to compressive stress. The residual stress then gradually approaches zero. 

The stress-relaxation behavior of a material is normally determined in either the tensile or the flexural mode. In these experiments, a material specimen is rapidly elongated or compressed to produce a specified strain level and the load exerted by the specimen on the test apparatus is measured as a function of time. Specimens of certain plastics may fail during tensile or flexural stress-relaxation experiments. 

Viscoelastic stress-relaxation data are usually presented in one of two ways. In the first, the stress manifested as a function of time. Families of such curves may be presented at each temperature of interest. Each curve representing the stress-relaxation behavior of the material at a different level of... 

Creep and stress relation Creep and stress relaxation behavior for plastics are closely related to each other and one can be predicted from knowledge of the other. Therefore, such deformations in plastics can be predicted by the use of standard elastic stress analysis formulas where the elastic constants E and y can be replaced by their viscoelastic equivalents given in Eqs. 2-19 and 2-20. 

Similar results were observed in the stress-relaxation experiments which are shown in Figure 2. The 5- and 10-day samples relax to the same stress level. The major difference in stress-relaxation behavior among the different samples occurs during the very beginning of the relaxation process. For that reason, and in order to better illustrate the first minutes of relaxation, the time scale is logarithmic. 

Very simple models can illustrate the general creep and stress-relaxation behavior of polymers except that the time scales are greatly collapsed in the models compared to actual materials. In the models most of the in-... 

Figure 17 Calculated stress-relaxation behavior at 298 K for five uncross-linked elastomers of M = 200,000 EP, ethylene-propylene (56 44) styrene-butadiene (23.5 76.5), SB natural rubber, N butyl and dimethyl siloxane.

Water is a natural plasticizer for many polar polymers such as the nylons (23K). polyester resins (239), and cellulosic polymers (240). It strongly shifts in epoxies (241.242). Thus the creep and stress-relaxation behavior of such polymers can be strongly dependent on the relative humidity or the atmosphere. 

The mechanical properties of two-phase polymeric systems, such as block and graft polymers and polyblends, are discussed in detail in Chapter 7. However, the creep and stress-relaxation behavior of these materials will be examined at this point. Most of the systems of practical interest consist of a combination of a rubbery phase and a rigid phase. In many cases the rigid phase is polystyrene since such materials are tough, yet low in price. 

Mow, V. C., Ateshian, G. A., Lai, W. M., and Gu, W. Y. (1998). Effects of fixed charges on the stress-relaxation behavior of hydrated soft tissues in a confined compression problem. International Journal of Solids Structures, 35 4945-4962. 

The Kelvin-Voigt model, also known as the Voigt model, consists of a Newtonian damper and Hookean elastic spring connected in parallel, as shown in the picture. It is used to explain the stress relaxation behaviors of polymers. 

Stress relaxation is the decrease in load of a material held at a fixed displacement. Figure 15.22 shows the spring and dashpot in series that can be used to model the stress relaxation behavior. Using this model one... 

Background At elevated temperatures the rapid application of a sustained creep load to a fiber-reinforced ceramic typically produces an instantaneous elastic strain, followed by time-dependent creep deformation. Because the elastic constants, creep rates and stress-relaxation behavior of the fibers and matrix typically differ, a time-dependent redistribution in stress between the fibers and matrix will occur during creep. Even in the absence of an applied load, stress redistribution can occur if differences in the thermal expansion coefficients of the fibers and matrix generate residual stresses when a component is heated. For temperatures sufficient to cause the creep deformation of either constituent, this mismatch in creep resistance causes a progres-... 

Further aspects of the viscoelastic behavior of ESIs which have been reported to date include linear stress relaxation behavior of amorphous ESI [40] and the creep behavior of amorphous ESI in the glass transition region [41]. Chen et al. [42]... 

Neither simple mechanical model approximates the behavior of real polymeric materials very well. The Kelvin element does not display stress relaxation under constant strain conditions and the Maxwell model does not exhibit full recovery of strain when the stress is removed. A combination of the two mechanical models can be used, however, to represent both the creep and stress relaxation behaviors... 

As shown in Fig. 9, the stress relaxation curves of all AEC/AA solutions collapse into one curve when the solutions were presheared with the same rate. Because the stress relaxation is at the molecular level and the chiro-optical properties reflect the suprastructural level, it is expected that the lyotropic solutions with different chiro-optical properties have the same stress relaxation behavior in both the tumbling and flow-align regions. 

Undervacuum Stress Relaxation Studies. The stress relaxation behavior of the Nafion system presents some unusual characteristics. The relaxation master curves of the precursor, as well as of Nafion in its acid and salt forms, are very broad and are characterized by a wide distribution of relaxation times. The individual stress relaxation curves and the master curves for the precursor (45), Nafion acid and Nafion-K (46), are shown in Figures 14, 15 and 16 with the reference temperatures Indicated in the captions. Time-temperature superposition of stress relaxation data appears to be valid in the precursor and in the dry Nafion acid, at least over the time scale of the experiments. In the case of Nafion-K, time-temperature superposition is not valid, because it leads to a breakdown at low temperatures, which is reestablished at high temperatures (above ISO C). Similar behavior was also observed for a low molecular weight (5x10 ) styrene ionomer. The addition of small amounts of water to the Nafion acid can lead to a breakdown in the time-temperature superposition. The Influence of crystallinity and of strong ionic interaction will be discussed in the section on underwater stress relaxation studies. 

We can predict tg for stress relaxation failure, where the failure occurs during stress releocation process under a constant strain. From observation of rubbery polymers, we can approximate the stress relaxation behavior by following ecjuation. 

The conversion of strain mismatch into stress is a function of the stress relaxation modulus exhibited by the polymer. A predictive stress model must incorporate the complex dependencies of the modulus and stress relaxation behavior on temperature, glass transition temperature, degree of cure, crosslink density, solvent-plasticization, and reaction kinetics. 

Under-water stress relaxation of the Nafion acid and Nafion-Na samples with an equivalent weight of 1200 was carried out by Kyu and Eisenberg (40). The degree of neutralization of the Nafion-Na was measured to be ca. 80%. Time-temperature superposed master curves of the two systems, reduced to a reference temperature of 50°C, are shown in Figure 6. The under-water stress relaxation behavior of Nafion acid resembles that of Nafion-Na, except for the fact that the elastic modulus is somewhat lower in the acid. This latter feature may be due to the difference in the degree of water absorption of the acid and salt samples (26,31). The swelling of Nafion acid is greater than that of Nafion-Na, which yields a material of lower modulus. 

The resemblance of the under-water stress relaxation curves and the dissimilarity of the stress relaxation behavior of the Nafion acid and the salt in the dry state may be explained as follows. The phase separated hydrophilic regions are expected to contain a substantial fraction of the ether side chains which are anchored in the ionic domains by their polar end groups. In the dry state, the coulombic interactions within the ionic aggregates are so strong that these domains probably serve as effective crosslinks. This would not only reduce the mobility of molecules within the domains but would also control the mobility of the fluorocarbon matrix through the side chains this, in turn, leads to the rise in the primary relaxation temperature. 

Note that the stress relaxation behavior is exponential in time. Now the value of a model is evident we leam that the mark of a viscoelastic fluid in a stress-relaxation experiment is exponential decay of the stress. 

Now one may associate these relaxation times with the relaxation times of a generalized Maxwell model. Thus the stress relaxation behavior for the bead-and-spring model is given as... 

The first step in the project was to perform an extensive set of experimental tests on the actual glass-filled PTFE that was used in the gasket. Specifically, uniaxial tension and compression experiments at different strain rates and different final strain levels were performed. Both the loading and unloading behavior was examined. A few select stress relaxation experiments were also performed to directly probe the stress relaxation behavior of the material. Examples of the experimental data obtained from these tests are shown in Figs. 11.13 to 11.16. 

Example 14.6 A polymer is represented by a series arrangement of two Maxwell elements with parameters Ej = 3 x 10 N/m, tj = 1 s, Ej = 5 X 10 N/m, and tj = 10 s. Sketch the stress relaxation behavior of this polymer over several decades (at least seven) of time. 

Figure5.il Stress response for a material that exhibits a combination of elastic and stress relaxation behavior when a constant strain is applied for a time t.

Pothan, Laly A. Neelakantan, N.R. Rao, Bhaskar Thomas, Sabu. Stress relaxation behavior of banana fiber-reinforced polyester composites, Journal of Reinforced Plastics and Composites, 23(2), 153-165 (2004). 

Boe] Mechanical tests with Larson-Miller parameters applying, conductivity measurements Stress relaxation behavior, hardness, electrical conductivity... 

Dynamic Mechanical Analysis and Stress Relaxation Behavior. Samples were compression molded into bars of the dimensions 38.xl2.5x0.78 0.007 mm and 65.x9.7xl.7 0.007 mm in a Carver laboratory hot press model C. A TA Instruments 983 DMA, which was operated in the fixed frequency mode, was used to characterize the storage and loss moduli as a function of temperature. Samples were scanned at fi-equencies from 0.05 to 10.0 Hz over a temperature range from -150 C to above the glass transition temperature. The displacement was 0.4 - 0.6 mm. Stress relaxation curves were determined for the same size samples at a constant strain. The sample was displaced for 10.0 minutes and then allowed to recover for 10.0 minutes. The stress data were taken in five degree increments. A microprocessor controlled Liquid Nitrogen Cooling Accessory (LNCA) was used for sub-ambient operations. 

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