Rate of stress relaxation

C is the fractional chemical rate of stress relaxation per unit time... 

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 origin of the phenomenon of ageing lies in the fact that glasses are not in thermodynamic equilibrium their volume and entropy are too large, hence there is a tendency to volume reduction (volume retardation). Decreases of rates of stress relaxation and creep are consequences of this phenomenon. 

The equilibrium 20 is important not only in the synthesis of linear polysiloxanes but also in their applications. The effects of water vapor on inducing chain cleavage at high temperature are not only reduced molecular weights but also a dramatic increase in the rates of chemically induced stress relaxation at 250 °C in cross-linked poly(dimethylsiloxane) networks under load (70). Slow hydrolytic bond cleavage in cross-linked networks is seen even in studies of stress relaxation in air at room temperature, and appreciable rates of stress relaxation in the loaded networks are measured at temperatures as low as 70 (7i). The stress relaxation is greatly accelerated... 

The effects of simultaneous reptation and constraint release can be estimated if we assume the processes act independently. At time t followii a small shear strain y (and after the initial equilibration) the rate of stress relaxation, — da/dt, is the sum of two terms ... 

Figure 15 illustrates the comparison of ten-second tensile modulus E(10 sec) versus temperature of the amorphous and semicrystalline Nafion-Na as observed by dry state and underwater stress relaxation studies. It is evident that the rate of stress relaxation is faster and the relaxation temperature is lower in amorphous Nafion, relative to those of semicrystalline Nafion. 

Thermoreversibility of physical aging has been demonstrated in the time-dependent rate of stress relaxation as v/ell as in the damping behavior of the p-transition. 

A tactic polystyrene has a Tg of 100°C. What are the relative rates of stress relaxation of this polymer... 

Somewhat similar considerations were also applied to acto-myosin systems, for which enhanced fluidization was predicted due to actin-driven sliding of filaments.For actin networks, it has long been known that the addition of myosin motors can cause network contraction and eventually a macroscopic phase separation, a process dubbed super-precipitation. Under certain conditions, however, enhanced fluidization due to an increased rate of stress relaxation was foimd in solutions of non-CTOss-linked actin that was activated by minifilaments of skeletal muscle myosin II. The gels were foimd to soften at low frequencies. This can be explained by an increase in the rate of stress relaxation in the entangled networks when motors actively slide the filaments arormd the obstacles. This sliding can also lead to the formation of bundled or oriented/polar-ized states of actomyosin gels. There bave been a number of hydrodynamic-like theories developed for such fluidlike active gels. "... 

Creep resistance is of primary concern in rotating components of a turbine engine. High creep rates can lead to both excessive deformation and uncontrolled stresses. Creep resistance of fiber-reinforced ceramic matrix composites depend on relative creep rates of, stress-relaxation in, and load transfer between constituents. The tensile creep behavior of SiC/RBSN composites containing 24 vol% SiC monofilaments was studied in nitrogen at 1300 C at stress levels ranging from 90 to 150 MPa. Under the creep stress conditions the steady state creep rate ranged from 1.2 x 10 to 5.1 x 10 At stress levels below... 

Melt viscoelasticity is caused by physical entanglements of the molecules the stresses induced are of rubber elastic origin. The rate of stress relaxation is of viscous origin. Thus, low temperatures (or high relative molecular masses) promote long memories and hence large swell ratios high temperatures (or low relative molecular masses) promote short memories and hence small swell ratios. 

Let us consider these results. IS substances separating as an individual phase during the oligomer polymerization concentrate in the interstructural regions of the polymer and close to the solid surface, thus increasing the rate of stress relaxation. The adhesive interlayer can slide along the boundary polymolecular layer of surfactant relative to the substrates, with a drop in the internal stresses. 

Due to the biphasic nature and microporous structure of PVA-C, when it is tmder compression, fluid will flow out of the PVA-C structure gradually tmtil the hydrostatic pressure reaches equilibrium with the external load. This explains the observed results that, as the concentration of PVA increases, the available water content decreases and the stress relaxation and creep effect decrease [23, 51, 53]. For the rate of stress relaxation, both MiUon et al. [45] and Wong [23] found that after 1 h the PVA-C had relaxed to 45 % of its initial value but the relaxation still continued. Stammen et al. reported that the relaxation had attained equilibrium after 24 h [53]. 

The effect of strain level on the relaxation behaviour has also been investigated and is shown in Figure 10.8. It was observed that the increase in strain level from 20 to 200% does not have any effect on the rate of relaxation of the unfilled rubber and the composites. The effect of ageing on the stress decay was also investigated and the rate of stress relaxation was found to decrease after ageing and is shown in Figure 10.9. 

Figure 177 presents curves characterizing the kinetics of chemical relaxation and the accumulation of residual deformation in vulcanizates based on various raw rubbers. As we can see, the investigated vulcanizates are arranged in the following series according to rate of stress relaxation NK > SKB > SKS-30 > SKN-26, and according to rate of accumulation of residual deformation - in the series SKB > NK > SKN-26 > SKS-30. 

Fig. 183. Influence of iron naphthenate on the rate of stress relaxation of monosulfide natural rubber vulcanizate at lOO C. 1) Without iron naphthenate 2) with 21 0 iron naphthenate.

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