Relaxation modulus tensile

Several functions are used to characterize tire response of a material to an applied strain or stress [4T]. The tensile relaxation modulus E(t) describes tire response to tire application of a constant tensile strain l/e -. 

Figure I. Reduced tensile relaxation modulus, E0(t), of Kra-ton 102 cast from benzene solution at different temperatures as a function of time, t...

Figure 1 shows a plot of the reduced tensile relaxation modulus, Ep(t), against the time, t, in logarithmic coordinates for Kraton 102 cast from benzene. Similar plots were prepared for the results obtained on specimens cast from cyclohexane and tetrahydrofuran solution, respec-... 

Figure 10. Reduced tensile relaxation modulus of Kraton 102 cast from benzene solution as a function of t/a at 0°C (log a predicted by WLF equation)...

Stress relaxation experiments correspond to the situations in which the deformations sketched in Fig. 11-12 are imposed suddenly and held fixed while the resulting stresses are followed with time. The tensile relaxation modulus Y(t) is then obtained as... 

Laplace transform of the tensile relaxation modulus can be obtained from Eqs. (5.62) and (5.80). The pertinent expression is... 

Figure 8.8 Master curve showing the tensile relaxation modulus of polyisobutylene in the time domain at 25°C. (From Ref. 6.)...

Figure 12.30 Storage tensile relaxation modulus plotted versus temperature for several polyethylenes.

Find a Bode three-section contour for the data. That is, approach the experimental data by a contour formed by three horizontal segments alternating with three segments of slope +1. Find also, by Laplace inversion, the tensile relaxation modulus in the time domain. 

A thin rod of PMMA rigidly clamped at its ends is initially at 18°C. Suddenly it is heated to 60° C. Determine the stress 1 h after starting the experiment, knowing that at 18°C the tensile relaxation modulus is given by... 

Early experiments with elastomers showed that the relaxation toward equilibrium was sharply dependent on crosslink density. It was found that tightly crosslinked networks relaxed very quickly, whereas networks with low crosslink density exhibited relaxation that covered an extremely broad time scale. These early experiments were correlated in terms of the expression for the tensile relaxation modulus E(t) ... 

Figure 13. Excess microbending losses measured in the experiment of Figure 12 for various single mode and multimode fibers as a function of the 30-min, 23 °C tensile relaxation modulus of the coating material. The relaxation modulus-time relationships of the coating materials are depicted in the inset. (Reproduced with permission from Ref. 6. Copyright 1980 IEEE.)...

FIGURE 3.19 Logarithm of tensile relaxation modulus versus logarithm of time for unfractionated poly(methyl methacrylate) of My = 3.6 X 10 . (After McLoughlin, J. R. and Tobolsky, A. V. 1952. /. Colloid Sci.y 7, 555.)... 

Fig. 4.146 Tensile-relaxation modulus of polyethylene, high molecular weight, at different strain levels for the test temperature of 23 °C [13Gre].

Tensile relaxation modulus Tensile stress relaxation modulus Threshold energy of coagulation Activation energy Exchange energy of i-j contact Helmholtz free energy (F = E—TS)... 

The quantity in brackets is 2 E t)/2, where E t) is the tensile relaxation modulus or time-dependent Young s modulus. Hence,... 

In practice, most stress relaxation measurements on soft solids are made in siniple extension. For small deformations, the tensile relaxation modulus is obtained by inverting equation 3 with time-dependent force ... 

Fig. 16-8. Tensile relaxation modulus at 40.7 C for four polyethylene samples with different degrees of crystallinity indicated by numbers at right, plotted logarithmically. (Becker. )...

Develop an expression for the shear relaxation modulus assuming the tensile relaxation modulus can be represented by a Maxwell fluid. Hint Use Table 2.1. 

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