Stress relaxation time

Stress relaxation time, obtained from rheograms based on viscometric flows, is used to define a dimensionless parameter called the Deborah number , which quantifies the elastic character of a fluid... 

Not only are the creep compliance and the stress relaxation shear modulus related but in turn the shear modulus is related to the tensile modulus which itself is related to the stress relaxation time 0. It is therefore in theory possible to predict creep-temperature relationships from WLF data although in practice these are still best determined by experiment. 

This integral equation can be solved exactly with the stress relaxation time approximated as... 

The observations above can be rapidly turned into a semi-quantitative theory for star-polymer stress-relaxation [24] which is amenable to more quantitative refinement [25]. The key observation is that the diffusion equation for stress-re-lease, which arises in linear polymers via the passage of free ends out of deformed tube segment, is now modified in star polymers by the potential of Eq. (16). Apart from small displacements of the end, the diffusion to any position s along the arm will now need to be activated and so is exponentially suppressed. Each position along the arm, s, will possess its own characteristic stress relaxation time T(s) given approximately by... 

Work in groups of three. The shift factor, or, in the WLF Equation [Eq. (5.76)], is actually a ratio of stress relaxation times, f , in the polymer at an elevated temperature, T, relative to some reference temperature. To, and can be related via an Arrhenius-type expression to the activation energy for relaxation, Erei as... 

Note that the model given in Ref. 47) takes into account the distortion of potential barriers in activation flow under the action of stress. Relaxation time is 0k = 0k exp (—mWk) (here mk = yk/RT where yk is constant, R is gas constant, T is temperature). Normally, two Maxwell s elements (N = 2) and one viscous element with vis-... 

This Rouse stress relaxation time is half of the end-to-end vector correlation time because stress relaxation is determined from a quadratic function of the amplitudes of normal modes (see Problem 8.36). 

This Zimm stress relaxation time is half of the Zimm end-to-end vector correlation time. 

The Rouse time tr is the longest stress relaxation time [Eq. (8.18)]. 

The relaxation time of the Kuhn monomer tq is the shortest stress relaxation time in the Rouse model, given by Eq. (8.56) with p N ... 

Stress Relaxation - Time-dependent decrease in stress in a solid material as a result of changes in internal or external conditions. Also called... 

The ratio shear viscosity to shear modulus is often symbolised by the time x = ti / G. For the Maxwell model, x is called the stress relaxation time. In the Kelvin model x is a measure of the time required for the extension of the spring to its equilibrium length under a constant stress. X is called the retardation time. 

An alternative method that has provided interesting data is to run a 90° peel test but begin this test at 0.1 in. (2.5 mm)/min, then stop the tensile tester under stress but allow the recorder to continue. It will be necessary to reduce the speed of the recorder, as the test may take minutes. Stress relaxation will be shown by the rate of drop of the peel value obtained when the tester was stopped. A useful value of stress relaxation time is that time taken when the applied stress has been reduced to 40% of its original value. 

FIGURE 9.5 Average stress relaxation time of PVAc versus free-volume fraction. The solid line indicates the behavior expected from the DooUttle equation at A, 308 K , 303 K. (From Ferguson and Cowie [2008].)... 

Figure 1.4 Variation of shear modulus (Co) and stress relaxation time (Tr) as a function of temperature at different concentrations (in wt%) of surfactant in water (from Ref [37]).

Roughly speaking, the plateau modulus G depends on the number density of the entanglement points, and so the large deviation in the exponent for the viscosity from the prediction may originate from the deviation in the exponent for the stress relaxation time. It can be seen from Figure 7.7a that the slope of the double-logarithmic plot of the relaxation times Tr and vs. concentration at 35 °C is close... 

Thus, our results above 40 °C can be explained semiquantitatively by modification of Hoffmann s theory. However, it is still difficult to determine which model is more appropriate between the ghost-like crossing proposed by Shikata and the sliding of connections proposed by Appel from the stress-relaxation time alone. 

With 10% pre-strain, which is about 3% higher than the yield strain, a tendency similar to 30% pre-strain is observed. Therefore, as long as the pre-strain is over the yield strain, a certain amount of shape fixity can be realized. Of course, as the pre-strain increases, the shape fixity ratio also increases. For example, at the zero stress relaxation time, the shape fixity is about 62.5% for the 10% pre-strain level, which is lower than the corresponding shape fixity of 73% for the 30% pre-strain level. It is also observed that the shape fixity with 10% pre-strain plateaus earlier than that with 30% pre-strain as the stress relaxation time increases, possibly due to less viscoelastic and viscoplastic deformation with the lower pre-strain level. 

---