Dynamic creep experiment

In a dynamic creep experiment, the shear strain for liquids can be written as (t)... 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

The mechanical response of polypropylene foam was studied over a wide range of strain rates and the linear and non-linear viscoelastic behaviour was analysed. The material was tested in creep and dynamic mechanical experiments and a correlation between strain rate effects and viscoelastic properties of the foam was obtained using viscoelasticity theory and separating strain and time effects. A scheme for the prediction of the stress-strain curve at any strain rate was developed in which a strain rate-dependent scaling factor was introduced. An energy absorption diagram was constructed. 14 refs. 

A complete description of the viscoelastic properties of a material requires information over very long times. Creep and stress relaxation measurements are limited by inertial and experimental limitations at short times and by the patience of the investigator and structural changes in the lest material at very long times. To supplement these methods, the stress or the strain can be varied sinusoidally in a dynamic mechanical experiment. The frequency of this alternation is u cycles/s or m(= 27ri ) rad/s. An alternating experiment at frequency w is qualitatively equivalent to a creep or stress relaxation measurement at a time t = (I /w) sec. 

Creep-compliance studies conducted in the linear viscoelastic range also provide valuable information on the viscoelastic behavior of foods (Sherman, 1970 Rao, 1992). The existence of linear viscoelastic range may also be determined from torque-sweep dynamic rheological experiments. The creep-compliance curves obtained at all values of applied stresses in linear viscoelastic range should superimpose on each other. In a creep experiment, an undeformed sample is suddenly subjected to a constant shearing stress, Oc. As shown in Figure 3 1, the strain (y) will increase with time and approach a steady state where the strain rate is constant. The data are analyzed in terms of creep-compliance, defined by the relation ... 

While creep experiments of the type described above are often ployed in the analysis of mechanical properties, they are not the only (mes used for that purpose. Two other important techniques are the stress-relaxation method and the measurement of dynamic properties. 

Dynamic measurements of viscoelastic behavior are based on a different conception. The nature of a stress-relaxation or a creep experiment is such tiiat no accurate measurements can be made for times leas than 1 sec in some cases 10 sec or more pass before the first measurement is made. Very often interesting phenomena of polymer viscoelasticity occur in a... 

Figure 4.156 illustrates the detailed technical drawing of a dynamic mechanical analyzer by TA Instraments. The sample is enclosed in a variable, constant-temperature environment, not shown, so that the recorded parameters are stress, strain, time, frequency, and temperature. This instrument can be used for resonant and defined-frequency operation. Even creep and stress relaxation measurements can be performed. In creep experiments, a constant stress is applied at time zero and the... 

This principle applies to all of the viscoelastic functions defined previously for stress relaxation, creep, and dynamic mechanical experiments. A most comprehensive discussion of TTS is provided in the text by Ferry (1980). An example of TTS is shown in Fig. 5.14 for the modulus data of Fig. 5.15, which were determined at various temperatures (Mercier et al. 1965) by both stress relaxation and creep measurements. The creep compliance data were converted to modulus by the relationship E(t) = VJ t). The single curve formed by superposition of the various curves shifted on the time axis to the given reference temperature (Tr) is referred to as a master curve. In this case... 

Fig. 3 Molecular weight dependence of the rjo or r) (a) = 0.01 rad s ) of linear (IUPAC5A) and long-chain branched polyethylenes. Filled symbols denote rio determined with creep experiments open symbols give rf from dynamic analysis at < = 0.01 rad s. A deviation from the solid line indicates the presence of LCB. Reprinted from [94], with kind permission from Elsevier...

Time-temperature equivalence in its simplest form implies that the viscoelastic behaviour at one temperature can be related to that at another temperature by a change in the timescale only. Consider the idealised double logarithmic plots of creep compliance versus time shown in Figure 7.7(a). The compliances at temperatures Ti and T2 can be superimposed exactly by a horizontal displacement log a, where a, is called the shift factor. Similarly (Figure 7.7(b)), in dynamic mechanical experiments, double logarithmic plots of tan 5 versus frequency show an equivalent shift with temperature. 

The identical function can be used in order to describe the result of a creep experiment on the system. One has just to substitute the dynamic compliance of the Debye-process by the associated elementary creep function, as given by Eq. (5.61). This leads to... 

The viscoelasticity of soft materials is probed via several types of experiment. In stress relaxation measurements, the strain is held constant and the decay of stress is monitored as a function of time. Usually the rate of decay decreases as time progresses. In creep experiments, the stress is held constant and the increase in strain is monitored. Generally, the strain increases rapidly at first and then the rate of increase becomes smaller. In addition to these measurements, many commercial rheometers are able to perform dynamic mechanical testing, where an oscillatory strain is applied to the specimen. If the frequency of deformation is (o and t denotes time, we can write the strain as... 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

H3.1 Dynamic or Oscillatory Testing of Complex Fluids H3.2 Measurement of Gel Rheoogy Dynamic Tests H3.3 Creep and Stress Relaxation Step-Change Experiments... 

F. Heslot, T. Baumberger, B. Caroli, and C Caroli, Creep, Stick-slip and Dry Friction Dynamics Experiments and a Heuristic Model, Phys. Rev., E49, 4973 (1994). 

This is because although 0 = (10), in general, cr(10) oQ (it will usually be less). In principle, the quantities we have defined, E(t), Dit), Gif), and J(i), provide a complete description of tensile and shear properties in creep and stress relaxation (and equivalent functions can be used to describe dynamic mechanical behavior). Obviously, we could fit individual sets of data to mathematical functions of various types, but what we would really like to do is develop a universal model that not only provides a good description of individual creep, stress relaxation and DMA experiments, but also allows us to relate modulus and compliance functions. It would also be nice to be able formulate this model in terms of parameters that could be related to molecular relaxation processes, to provide a link to molecular theories. 

Three types of experiments are used in the study of viscoelasticity. These involve creep, stress relaxation, and dynamic techniques. In creep studies a body is subjected to a constant stress and the sample dimensions are monitored as a function of lime. When the polymer is lirst loaded an immediate deformation occurs, followed by progressively slower dimensional changes as the sample creeps towards a limiting shape. Figure 1-3 shows examples of the different behaviors observed in such experiments. 

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