Time-dependent tensile modulus

Fig. 5.14. Time dependent tensile modulus of PIB. Measurements at the indicated temperatures (left) and master-curve, constructed for a reference temperature T = 298 K right). The insert displays the applied shifts. Data from Castiff and Tobolsky...

A second method in mechanical tests is the stress relaxation experiment. Here, a certain constant strain is instantaneously imposed on a sample and the stress induced by this procedure is measured as a function of time. Figure 6.2 schematically shows the possible shape of a stress relaxation curve for an uniaxially deformed sample. The tensile stress has its maximum directly after the deformation act and then it decays. Anelastic components first produce a downward step. If the sample can flow, the stress will further decrease and finally vanish completely. The result of such an experiment can be described by the time-dependent tensile modulus E t), defined as... 

Although time-temperature superposition is applicable to any viscoelastic response test (creep, dynamic, etc.), here, we will focus on its application to stress relaxation. Figure 16.12 shows tensile stress relaxation data at various temperatures for polyisobutylene, plotted in the form of a time-dependent tensile (Young s) modulus E t) versus, time on a log-log scale ... 

Many polymeric materials are susceptible to time-dependent deformation when the stress level is maintained constant such deformation is termed viscoelastic creep. This type of deformation may be significant even at room temperature and under modest stresses that lie below the yield strength of the material. For example, automobile tires may develop flat spots on their contact surfaces when the automobile is parked for prolonged time periods. Creep tests on polymers are conducted in the same manner as for metals (Chapter 8) that is, a stress (normally tensile) is applied instantaneously and is maintained at a constant level while strain is measured as a function of time. Furthermore, the tests are performed under isothermal conditions. Creep results are represented as a time-dependent creep modulus E t), defined by ... 

Returning to the Maxwell element, suppose we rapidly deform the system to some state of strain and secure it in such a way that it retains the initial deformation. Because the material possesses the capability to flow, some internal relaxation will occur such that less force will be required with the passage of time to sustain the deformation. Our goal with the Maxwell model is to calculate how the stress varies with time, or, expressing the stress relative to the constant strain, to describe the time-dependent modulus. Such an experiment can readily be performed on a polymer sample, the results yielding a time-dependent stress relaxation modulus. In principle, the experiment could be conducted in either a tensile or shear mode measuring E(t) or G(t), respectively. We shall discuss the Maxwell model in terms of shear. 

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 ... 

Stress relaxation is the time-dependent change in stress after an instantaneous and constant deformation and constant temperature. As the shape of the specimen does not change during stress relaxation, this is a pure relaxation phenomenon in the sense defined at the beginning of this section. It is common use to call the time dependent ratio of tensile stress to strain the relaxation modulus, E, and to present the results of the experiments in the form of E as a function of time. This quantity should be distinguished, however, from the tensile modulus E as determined in elastic deformations, because stress relaxation does not occur upon deformation of an ideal rubber. 

Because of the time dependence of polymer properties, it is important that the time scale used in our standard tests corresponds exactly with that of the moment loading. That is, if the moment is to be a sustained load, then the tensile test should also be at very long loading, for example, in the equilibrium modulus region. 

As mentioned earlier, the DMTA technique measures molecular motion in adhesives, and not heat changes as with DSC. Many adhesives exhibit time-dependent, reversible viscoelastic properties in deformation. Hence a viscoelactic material can be characterized by measuring its elastic modulus as a function of temperature. The modulus depends both on the method and the time of measurement. Dynamic mechanical tests are characterized by application of a small stress in a time-varying periodic or sinusoidal fashion. For viscoelastic materials when a sinusoidal deformation is applied, the stress is not in phase with displacement. A complex tensile modulus E ) or shear modulus (G ) can be obtained ... 

Loads on a fabricated product can produce different t3q>es of stresses within the material. There are basically static loads (tensile, modulus, flexural, compression, shear, etc.) and dynamic loads (creep, fatigue torsion, rapid loading, etc.). The magnitude of these stresses depends on many factors such as applied forces/loads, angle of loads, rate and point of application of each load, geometry of the structure, manner in which the structure is supported, and time at temperature. The behavior of the material in response to these induced stresses determines the performance of the structure. 

The tensile creep behaviour of specially oriented sheets of LDPE was studied by Gupta and Ward. However, their data took the form of a dependence of isochronous modulus on temperature time dependence and non-linearity being ignored. The interpretation of such data is reviewed elsewhere in this book. 

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