Relaxation test

The relaxation behaviour, i.e. the stress relief at imposed deformations, is included in the assessment of long-term behaviour of plastic geomem- 

In individual cases even a sudden brittle failure was observed in HDPE geomembranes manufactured from true high density PE-resins, when they were exposed to a stress over a large area (EPA 1992). This phenomenon, however, seems to occur solely in extremely eold weather. The brittle cracks extend and branch out and propagate rapidly over the whole surface. This kind of cracking is dealt with in the technical literature under the term rapid crack propagation (RCP) as an independent meehanism of stress cracking. 

Various deformation, however, are imposed unavoidably on geomembranes during the installation and operational phase, even if they are handled and installed correctly. The imposed deformations also result in stresses which are partially relieved over the course of time by stress relaxation. Chapter 4 deals with creep, relaxation and deformation behaviour of HDPE geomembranes in more detail. Since imposed deformations represent a frequent and a likely event, not only particularly stress crack resistant resins should be chosen but the relaxation behaviour of the geomembranes should be checked as well. 

The test of relaxation behaviour is described in (outdated) DIN 53441 1984 Testing of Plastics, Stress Relaxation Test. The principle of the test method is that an elongation is imposed on the test specimen by a uniaxial tensile force which is then kept constant. The force necessary to 

According to the requirements of die BAM certification guidelines the first measured value has to be determined after one minute, thus fi - to = 1 min or 5 6 s. The measurement is carried out over 1000 hours. Then the ratio of the stress in 1000 hours, o(1000h), to the stress in one minute, o(lmin), is determined. The stress relaxation must be so great that the stress reduction is at least 50 %  

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Creep, creep mpture, and stress relaxation tests are multiple-point tests requiring long periods of time (1000 h min) to generate useflil data these are standard tests for determining more fundamental polymer properties (202,203). Data for these tests are generated under several... 

Accurately performed relaxation tests in which the strain in the material was maintained constant and the decaying stress monitored, would give slightly lower values than those values obtained from the isometric data. 

Stress relaxation. In a stress-relaxation test a plastic is deformed by a fixed amount and the stress required to maintain this deformation is measured over a period of time (Fig. 2-33) where (a) recovery after creep, (b) strain increment caused by a stress step function, and (c) strain with stress applied (1) continuously and (2) intermittently. The maximum stress occurs as soon as the deformation takes place and decreases gradually with time from this value. From a practical standpoint, creep measurements are generally considered more important than stress-relaxation tests and are also easier to conduct. 

With crystalline plastics, the main effect of the crystallinity is to broaden the distribution of the relaxation times and extend the relaxation stress too much longer periods. This pattern holds true at both the higher and low extremes of crystallinity (Chapter 6). With some plastics, their degree of crystallinity can change during the course of a stress-relaxation test. This behavior tends to make the Boltzmann superposition principle difficult to apply. 

The basic viscoelastic theory assumes a timewise linear relationship between stress and strain. Based on this assumption and using mechanical models thought to represent the behavior of a plastic material, it can be shown that the stress, at any time t, in a plastic held at a constant strain (relaxation test), is given by ... 

Thus, by determining values of a0/o ) from a relaxation test, creep strains can be calculated using Eq. 2-17 in the form of ... 

The trend of this factor is generally consistent with plastics behaviors. However, stress-relaxation information has to be interrelated with the individual behavior of the plastics, as derived from the relaxation-test data (Chapter 2). 

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. 

Stress relaxation tests are alternative ways of measuring the same basic phenomenon in viscoelastic polymers as creep tests, Le. the time-dependent nature of their response to an applied stress. As such, they have also been of value in understanding the behaviour of these materials. The essence of stress relaxation tests is that strain increases with time for a given stress, so that if stress is decreased with time in a controlled manner ( relaxed ), a state... 

Creep and stress-relaxation tests measure the dimensional stability of a material, and because the tests can be of long duration, such tests are of great practical importance. Creep measurements, especially, are of interest to engineers in any application where the polymer must sustain loads for long periods. Creep and stress relaxation are also of major importance to anyone interested in the theory of or molecular origins of Viscoelasticity. 

If the deformations and stresses are small and the time dependence is weak, creep ami stress-relaxation tests are essentially the inverse of one another. Otherwise data from one kind of test can be used to calculate the other by fairly complex methods to be described later. However, to a first approximation the interconversion from creep to stress relaxation, or vice versa, is given by a simple equation (3) ... 

Although nearly all creep and stress-relaxation tests are made in uniaxial tension, it is possible to make biaxial tests in which two stresses are applied at 90° to one another, as discussed in Section VI. In a uniaxial test there is a contraction in the transverse direction, but in a biaxial test the transverse contraction is reduced or even prevented. As a result, biaxial creep is less than uniaxial creep--in cquihiaxial loading it is roughly hall as much for equivalent loading conditions. In the linear region the biaxial strain 2 in each direction is (255.256)... 

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. 

Moreover, real polymers are thought to have five regions that relate the stress relaxation modulus of fluid and solid models to temperature as shown in Fig. 3.13. In a stress relaxation test the polymer is strained instantaneously to a strain e, and the resulting stress is measured as it relaxes with time. Below the a solid model should be used. Above the Tg but near the 7/, a rubbery viscoelastic model should be used, and at high temperatures well above the rubbery plateau a fluid model may be used. These regions of stress relaxation modulus relate to the specific volume as a function of temperature and can be related to the Williams-Landel-Ferry (WLF) equation [10]. 

The observation that the first order rate "constant" is not constant for the perturbation and relaxation test intervals leads to the conclusion that a simple first- order model is not sufficient to explain the behavior in this dynamically-perturbed system and another model should be proposed and tested. Often, the new models are in themselves more complex and require more information for verification than was originally collected. Thus, the direct approach may require the iteration of new experiments with additional sampling. 

Table 9.5 Stress relaxation test parameters of cooked potatoes from different cultivars... 

Constant strain for stress relaxation tests and constant load creep tests may be conducted in simple devices. Temperature control is critical since the results are usually applied as a spectral representation for structural analysis or research purposes. Figure 8 illustrates a multistation creep tester with automated data recorders. Strain and load endurance tests are conducted in similar devices, but the conditions existing at failure and time to failure are normally the only data required. The endurance tests are used frequently to supplement the constant displacement rate tests for routine evaluation. 

Stress relaxation has been mentioned in the context of several plasticity instruments. ASTM D6048140 gives background information about techniques and theory of stress relaxation testing and interpretation of results. Mention is made of the Mooney and capillary rheometers. 

ASTM D6048, 2002. Stress relaxation testing of raw rubber, unvulcanised rubber compounds and thermoplastic elastomers. 

If data is needed for the more sophisticated viscoelastic models now being introduced then results from forced vibration dynamic tests (Chapter 9) or stress relaxation tests (Chapter 10), as appropriate, would be used. 

There are two reasons for using a tensile stress/strain test other than the standard method as typified by ISO 37. First, it can be sensibly argued that a more useful measure of stiffness is the so-called relaxed modulus, i.e. the stress at a given elongation after a fixed time of relaxation this is essentially a short term stress relaxation test. Secondly, it may be more convenient for quality control purposes to have a simple test in which only one parameter is measured. 

Stress relaxation measurements can also be used as a general guide to ageing, and it is particularly relaxation due to chemical effects which is then studied. Such measurements are normally made in tension and will be considered in Chapter 15 as an ageing test. Hence, in this section, only relaxation tests in compression will be discussed as this mode of deformation is the only one commonly used and standardised to directly estimate the relaxation of rubbers in service. For an application in tension, the methods described in Chapter 15 could, of course, be adapted. It must be appreciated that the methods in compression do not only measure relaxation due to physical effects, especially when elevated temperatures and liquid environments are used, so that the distinction is a little blurred. 

Tahir and Birley24 have considered the tangent modulus at intervals on the stress relaxation curve and compared it to the modulus of the initial loading curve to derive what they termed the Modulus Enhancement Factor, hence adding to the information which can be gained from a stress relaxation test. 

The critical phase of either a creep test or a stress relaxation test is in the first few seconds. It is here that the transducer can be overloaded or the optical encoder can give a noisy response. Most controlled-strain instruments will give an audible error signal if the transducer is overloaded. For controlled-stress instruments, the noise level is determined by the resolution of the optical encoder. 

The sample must have reached steady state before cessation of the test or the application of a second step. Steady state in a creep test is seen as a constant slope in the strain curve. A constant slope in the stress curve may also be seen in a stress relaxation test, but often the signal is lost in the noise. A material that is liquid-like in real time will need a test period of 5 to 10 min. A stress relaxation test is likely to be somewhat shorter than a creep test since the signal inevitably decays into the noise at some point. A creep test will last indefinitely but will probably reach steady state within an hour. For a material that is a solid in real time, all experiments should be longer as molecular motion is, by definition, slower. Viscoelastic materials will lie in between these extremes. Polymer melts can take 1 hr or more to respond in a creep test, but somewhat less time in a stress relaxation test. 

Stress relaxation tests need not have a second step, although some workers recommend a second step in the opposite direction. The Boltzmann superposition principle for polymers allows for multiple step-change tests of both types (stress or strain) as long as the linear limit of the polymer is not exceeded (Ferry, 1980). 

A good diagnostic for creep and stress relaxation tests is to plot them on the same scales as a function of either compliance (J) or modulus (G), respectively. If the curves superimpose, then all the data collected is in the linear region. As the sample is overtaxed, the curves will no longer superimpose and some flow is said to have occurred. These data can still be useful as a part of equilibrium flow. The viscosity data from the steady-state part of the response are calculated and used to build the complete flow curve (see equilibrium flow test in unit hi.2). 

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