Relaxation and Creep Tests

One of the fundamental methods used to characterize the viscoelastic time-dependent behavior of a polymer is the relaxation test. In a relaxation test, a constant strain is applied quasi-statically to a uniaxial tensile (or compression or torsion) bar at zero time. That is, the bar is suddenly stretched to a new position and rigidly fixed such that the strain remains constant for the duration of the test. The sudden strain must not induce any dynamic or inertia effects (which explains the term quasi-static, i.e., the loading motion is sufficiently slow that inertia effects can be ignored). 

In a relaxation test, it is also normal to assume that the material has no previous stress or strain history or if one did exist, the effect has been nullified in some way. One method to accomplish this for polymers is to anneal the sample at a suitable temperature sufficient to remove any previous history and then to cool very slowly. The nature of such a process will become obvious in later sections. 

If a polymer is loaded in the described manner, the stress needed to maintain the constant strain will decrease with time. Eventually, the stress will go to zero for an ideal thermoplastic polymer but will decrease to a constant value for a crosslinked polymer. The strain input and the stress 

Obviously, if the stress is a function of time and the strain is constant, the modulus will also vary with time. The modulus so obtained is defined as the relaxation modulus of the polymer and is given by. 

The latter equation is the uniaxial stress-strain relation for a polymer analogous to Hooke s law for a material that is time independent but is valid only for the case of a constant input of strain. The relaxation test provides the defining equation for the material property identified as the relaxation modulus. More general differential and integral stress-strain relations for an arbitrary loading will be developed in later Chapters. 

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The master curves obtained from specimens cast from tetrahydro-furan solution at 2 and 4% strain, respectively, are slightly different. These differences, however, are probably within the experimental error. An idea of the reproducibility can be obtained from Figure 4, which shows the master curves of the creep compliances obtained on specimens cut from two sheets of Kraton 102 cast from benzene solution. Although the method of preparation appeared to be identical, there are noticeable differences between the two curves. Even larger differences exist between these curves and the master curve obtained from the relaxation data after conversion to creep. Again, there were no apparent differences in the method of preparation of the sheets from which the specimens for the relaxation and creep tests were cut. 

Measurement of set is effectively restricted to rubbers and flexible cellular materials, where it has traditionally been paid rather more attention than stress relaxation and creep tests. Its popularity has a lot to do with the simple apparatus required. If set is measured on plastics it is usually made by following recovery after removal of load in a creep test. 

In previous chapters, relaxation and creep testing was introduced and the relaxation modulus and creep compliance were defined as the stress output for a constant strain input (relaxation) and the strain output for a constant stress input (creep). A question naturally arises as how the output could be found if a variable input of either strain or stress were to occur. One could, of course, attempt to solve a general differential equation if the variation is specified but such an approach could, in some cases, be quite tedious. 

The derivation of fundamental linear viscoelastic properties from experimental data obtained in static and dynamic tests, and the relationships between these properties, are described by Barnes etal. (1989), Gunasekaran and Ak (2002) and Rao (1992). In the linear viscoelastic region, the moduli and viscosity coefficients from creep, stress relaxation and dynamic tests are interconvertible mathematically, and independent of the imposed stress or strain (Harnett, 1989). 

Stress relaxation and creep are measured with the aid of two distinct experimental methods, which are frequently used in the mechanical testing of solid polymers, especially over longer periods. 

Dynamic testing is the most commonly used one in the study of polymer properties. Because of its widespread usage, dynamic data have been analyzed in terms of six different functions, as opposed to a single one in stress relaxation and creep. The experiment involves (1) imposition (on a specimen of the material) of either a shear stress or a shear strain which varies sinusoidally with time, and (2) study of the corresponding response. 

Creep. In general, polymers exhibit a degree of visco-elastic behaviour and thus for full characterisation of such a material a knowledge of its rate dependent response is necessary. To determine the long-term behaviour of a material either stress relaxation or creep tests may be used. The former involves monitoring the time-dependent change in stress which results from the application of a constant strain to a specimen at constant temperature. Conversely,... 

We have already referred to various kinds of data on mechanical behavior of polymers. We are now going to consider methods of acquisition of such information. The most fi equently used are the so-called quasistatic methods which involve relatively slow loading. Tension, compression, and flexure belong here. The quasistatic methods have to be distinguished from so-called transient tests which include stress relaxation and creep. There are also impact tests and dynamic mechanical procedures which will be defined later. 

Raman and IR spectroscopy have been used in a number of studies of molecular load distributions and deformation mechanisms in PP, usually in combination with a mechanical loading device (tension or compression). The topics studied include true loads on atomic bonds, chain scission under stress, stress relaxation and creep, residual stresses, and stresses along aramid fibers in a PP matrix during pull-out testing. 

By using dynamic mechanical analysis (DMA), tensile, compression, bending and torsion tests can be carried out under static or dynamic conditions. Elastic moduli can also be obtained by DMA. With DMA, measurements of constant stress or constant strain can also be made. Thus thermal expansion coefficients, stress relaxation and creep can be investigated by DMA. Here we only give an example of the measurement of the thermal expansion coefficient. In Figure 4.96, the thermal expansion curves of Fe-Co-Si-B amorphous alloy are plotted. Curves 1 and 2 are the measured results for a relaxed glass and as-quenched glass. 

Compression set, which is a measure of the recovery of rubber after release from compressive forces, is a combination of creep and stress relaxation and, since tests are conducted at elevated temperatures, the chemical processes of stress relaxation are likely to predominate. Compression set test conditions have been specified by seal users, and are considered by some engineers to be an excellent indicator of sealing efficiency. Compression tests are used in service specifications as a measure of cross-linking. 

The deformation mechanisms associated with relaxation and creep are related to the long chain molecular structure of the polymer. Continuous loading gradually induces strain accumulation in creep as the polymer molecules rotate and unwind to accommodate the load. Similarly, in relaxation at a constant strain, the initial sudden strain occurs more rapidly than can be accommodated by the molecular structure. However, with time the molecules will again rotate and unwind so that less stress is needed to maintain the same strain level. It is also clear from these tests that polymers have some characteristics of a solid and some characteristics of a fluid. In a relaxation test, the ratio of the initial stress and strain is. 

In this section, elementary mechanical models that can describe some aspects of viscoelastic polymeric behavior are presented. Although these simple models cannot represent the behavior of real polymers over their complete history of use, they are very helpful to gain physical understanding of the phenomena of creep, relaxation and other test procedures and to better understand the relationship between stress and strain for a viscoelastic material. Undoubtedly, the first models were developed on the basis of observations and not just as a mathematical exercise. Generalized mechanical models are presented later in Chapter 5. 

Apart from relaxation and creep experiments, two major types of test mode can be used to monitor the viscoelastic properties of polymers, namely temperature sweep and frequency sweep tests. These experiments are usually performed at short strains (<0.5% of active length) so as to be within the linear region when a sinusoidal stress a (Eq. (12.3)) (i.e., force per area unit) is applied to a viscoelastic material the resultant strain (i.e., unitary relative geometric displacement) appears out-of-phase (Eq. (12.4)), with the angle d being a> the angular frequency... 

For this Paper tests have been carried out with a fine zincoxide fraction with a median size of 0,8/tm. The experiments show that also dry bulk solids show relaxation and creeping. Another time dependent effect in contrast to a relaxation, where the stresses decrease after a previous consolidation, is a stress increase after a previous relief. 

The results of four corresponding creep experiments applying the time-dependent load values fromO Fig. 34.20 indicate that the predicted strain limit of tan y = l was not exceeded in either one of the creep tests and the congruence between relaxation and creep becomes better in the long-term scale (O Fig. 34.21). 

Relaxation of the residual stresses induced by autofrettage at 720 MPa (104,400 psi) in reactor tubes k = 2.4), of AISI 4333 M6 at a uniform temperature of 300°C has been studied and it was concluded, on the basis of creep tests for 10,000 h, that after 5.7 years 60% of the original stress would remain (161). 

Dynamic loading in the present context is taken to include deformation rates above those achieved on the standard laboratorytesting machine (commonly designated as static or quasi-static). These slower tests may encounter minimal time-dependent effects, such as creep and stress-relaxation, and therefore are in a sense dynamic. Thus the terms static and dynamic can be overlapping. 

There are two further related sets of tests that can be used to give information on the mechanical properties of viscoelastic polymers, namely creep and stress relaxation. In a creep test, a constant load is applied to the specimen and the elongation is measured as a function of time. In a stress relaxation test, the specimen is strained quickly to a fixed amount and the stress needed to maintain this strain is also measured as a function of time. 

Although creep, stress relaxation, and constant-rate tests are most often measured in tension, they can be measured in shear (19-22), compression (23,24), flexure (19), or under biaxial conditions. The latter can be applied... 

Time is the major (actor in determining the mechanical properties of a polymer. This is seen directly in creep and stress-relaxation experiments. These tests cover long periods of time, so that they are sensitive to the types of molecular motions that require long times. Tfrey give little direct information on the types of molecular motion that take place at short times. However, by using the time-temperature superposition principle and the WLF equations, access to these short times can be achieved even though they may not easily be attainable by direct experimentation. 

When a plastic is subjected to an external load the observed stiffness changes with time. In a creep test the load is kept constant leading to an increase in strain. In a stress-relaxation test the deflection (frequently compression) is kept constant so that the stress is observed to relax. The changes will be primarily due to physical effects, and the strains may be reversible if sufficient time is allowed. At long durations the applied load can lead to failure, known as creep-rupture or stress-rupture. 

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