Tensile stress relaxation

Table 7-23 Examples of tensile stress relaxation of TP RPs at elevated temperatures...

Using this factorizability of response into a time-dependent and a strain-dependent function. Landel et ai. (61,62) have proposed a theory that would express tensile stress relaxation in the nonlinear regime as the product of a time-dependent modulus and a function of the strain ... 

Here m is the usual small-strain tensile stress-relaxation modulus as described and observed in linear viscoelastic response [i.e., the same E(l) as that discussed up to this point in the chapter). The nonlinearity function describes the shape of the isochronal stress-strain curve. It is a simple function of A, which, however, depends on the type of deformation. Thus for uniaxial extension,... 

Finally, tensile deformations provide the same information as shear deformation as long as the incompressibility assumption is not violated. In this case, the tensile stress relaxation modulus E(t) is directly related to the shear modulus E(t) = 3G(f), and all other relationships follow accordingly. 

Figure 2-10. A simple apparatus to measure tensile stress relaxation. The spring must be strong enough to stretch the sample very quickly.

Stress-strain curves are often measured by monitoring the tensile stress as a sample, originally at rest, is subjected to a constant tensile strain rate starting at t = 0. Show that, at any subsequent time during the constant-strain-rate period, the slope of the stress-strain curve is the tensile stress relaxation modulus ... 

Suppose that a material with a tensile stress relaxation modulus given as... 

Here again, [Pg.56]

Figure 3-11. Continuous distribution of relaxation times expressed as H r) and the corresponding tensile stress relaxation modulus E(t).

Figure 4-5. Construction of a master curve using tensile stress relaxation data gathered at five temperatures.

The buffering action of a coating in this situation is determined by the relaxation modulus of the coating material. The relaxation modulus may be measured on a film cast from the material by carrying out tensile-stress relaxation measurements with a suitable apparatus such as a Rheovibron dynamic viscoelastometer operated in a static mode. Figure 13 (inset) displays such measurements for the four coating materials used on the fibers measured in Figure 12. The measurements were carried out at 23 °C at small tensile strains, where the materials exhibit linear viscoelastic behavior. 

Figure 3.86 Tensile stress relaxation of FEP (MFR = 7) at constant strain at 23°OP ...

In an extrusion blow-moulded polyethylene container with a 1 mm wall, about 5 s elapse before crystallisation takes place at the inner surface (Eq. 5.2). During this time, the melt tensile stresses relax, so the microstructure will be spherulitic, even though the spherulites may be somewhat distorted. In contrast there is high orientation in the wall of a stretch blow-moulded PET bottle (Section 2.4.7) because crystallisation occurred while the preform was stretching. 

A typical master curve is shown in Figure 6.2 (Santangelo and Roland, 1998) for dynamic shear data of a high molecular weight 1,4-polyisoprene measured over about a 160 range, yielding 15 decades of reduced frequency (the actual data spanned less than 5 decades). A tensile stress relaxation master curve for a polyurea rubber that spans 13 decades is displayed in Figure 6.6 (Knauss and Zhao, 2007). 

Vleeshouwers, S., Jamieson, A. M., Simha, R., Effect of physical aging on tensile stress relaxation and tensile creep of cured EPON 828/epoxy adhesives in the linear viscoelastic region. Polymer Engineering and Science, 29(10), pp. 662-670 (1989). 

Geethamma, V.G. Pothen, Laly A. Rhao, Bhaskar Neelakantan, N.R. Thomas, Sabu. Tensile stress relaxation of short-coir- fiber -reinforced natural rubber composites. Journal of Applied Polymer Science, 94(1), 96-104 (2004). 

A straight section of polypropylene pipe is fixed rigidfy at its ends. Its tensile stress relaxation modulus at time t and coefficient of linear thermal expansion at 20°C are, respective. ... 

The tensile-stress relaxation modulus of a certain pofymer can be... 

Cavitation evolution dynamics in cylindrical liquid volumes under the axial loading by an exploding wire is studied experimentally aind theoretically. The method of dynamic head registration is used to study the structure of two phase flows formed and evaluate characteristic time of cavitation liquid fracture. As a result of numerical simulation of the experiments, which was performed in a single-velocity two-phase model approximation, the energy transformation mechanism is determined at shock interaction with a free real liquid surface. A two-phase model is suggested to describe the irreversible development of a cavitation zone formed as a result of the mentioned interaction. The model is based on practically instantaneous tensile--stress relaxation in a centered rarefaction wave and further inertial evolution of the process. 

Y.M. Boiko, W. Brostow, A.Y. Goldman, A.C. Ramamurthy, Tensile, stress relaxation and dynamic mechanical behaviour of polyethylene crystallized from highly deformed melts. Polymer, 36 (7), 1383-1392,1995. 

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)... 

This analysis turns out to be a simple extension of that for the deflection of a linear elastic cantilever. Young s modulus is replaced by the appropriate viscoelastic counterpart—in this case the tensile stress relaxation modulus. That this is the appropriate viscoelastic property to be employed can be thought of as arising from the fact that, when the cantilever is subjected to constant deflection, every element of it is subjected to a constant tensile strain (i.e. to tensile stress relaxation conditions). 

A nylon bolt of diameter 8 mm is used to join two rigid plates (Fig. 4.34). The nylon can be assumed to be linear viscoelastic with a tensile stress relaxation modulus... 

The tensile-stress relaxation modulus of a certain polymer can be approximated by an expression of the form given in eqn (4.S3). Relaxed and unrelaxed tensile moduli are r = O.SGPa and u = 1.5GPa, respectively, with relaxation time t 5s. The polymer is subjected to a constant rate of tensile strain e = 10 s" . Derive the stress-strain relation Boltzmann superposition principle. 

Bailor, F.V. Vamac elastomers - versatilty for auto applications. Rubber World 180, 1979. Blow, C.M., Exley, K., South Wart, D.W. Penetration of liquids in rubber. J IRI 3(1), 1969. Brown, R.P., Morrel, S.H., Norman, R.H. Tensile stress relaxation. J Inst Rubber Ind 4, 1973. Brumback, M.E., Clade, J.A. Airborne Rubber Seals Industrial maintenance. Thomson Delmar Eearning, 2003. 

Table 6-47. Tensile Stress Relaxation of TP Composites at Elevated Temperatures... 

Figure 18 Tensile stress relaxation modulus for PP homopolymer at 23 C 4.3.5 Dynamic Fatigue...

Figure 3-63. Tensile Stress Relaxation 40% Glass-Reinforced Nylons 6, 6/6, and 6/10 (Ref. 25)...

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