Stress relaxation, definition

If a crystal is exposed to stress in such a way that the strain is kept constant, the stress will decrease with time as shown in Figure 14-4. One concludes that stress relaxation has occurred. Conversely, strain does not remain constant under constant load. Time dependent (i.e., plastic) strain in stressed crystals is called creep. It was already mentioned that elastic strain due to the applied stress is usually less than 1%. Plastic strain definitely dominates beyond the elastic limit which, to a large extent, is due to dislocation formation and motion. Since the crystal lattice is conserved during this... 

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. 

In real food polymers, a distinction can be made between a viscoelastic solid, which contains some cross-links that are permanent, and a viscoelastic liquid, where, under the influence of stress, the relative movement of whole molecules will be observed. As shown in Figure 8.9, in the case of a viscoelastic solid, after application of the stress, the strain will eventually reach a constant value, and upon removal of the stress, the strain will finally return to the remaining value of food primary energy, which was not entirely dissipated. For a viscoelastic liquid, a permanent deformation will remain after removal of the stress. In the stress relaxation area, the deformation value will decay to zero for a viscoelastic liquid, whereas for a solid, it will reach a constant, nonzero value. It can also be seen as either a decreased value to the zero or a constant, nonzero value, as pointed out by the dashed line. Both values characterize the rheology parameters of foods under certain conditions. One of the reasons for this is that the factors of time-dependent foods are not necessarily related to their elastic modulus. This can be explained by the series of small deformations without rupture, which are dependent in different ways and are based on the primary molecular microstructure of foods. The time required for the stress to relax to a definite fraction of its initial value is the relaxation time. 

A stress-relaxation experiment is carried out by stretching the sample to some definite length at zero time and by measuring the force necessary to maintain that length as a function of time. The stress-relaxation measurements tend to yield the same sort of information that is obtained in creep experiments, but the results can be expressed in different ways. It is also possible, in principle, to calculate the stress-relaxation data from cre measurements, but this is rather complicated and not often d[Pg.929]

Stress relaxation is expressed as the change in force in the test piece as a percentage of the initial force, and there is not the confusion of definitions as with creep. Relaxation is not critically dependent on the applied strain for the. strain levels usually of interest but is very dependent on temperature. 

Any operational definition of apparent yield stress should take into account both the inevitable rheometrical limitations in its determination, and the characteristic time of the process to which it pertains. Such an operational definition has been proposed for a true yield stress in the context of the classical stress relaxation experiment [Spaans and Williams, 1995]. 

The stresses in the two experiments at the same time t are proportional to the imposed strains. Tliis fact leads to the definition of the stress-relaxation modulus at time t ... 

The reader will note that the definition of a phenomenological theory given at the start of this section has been satisfied by the Zener model. Measurements in creep, stress relaxation, or dynamic response are interrelated by three of the model parameters, say /r, and r. ... 

The stress relaxation mode is used for measurement of ultralow-frequency relaxation in polymers and composite structures, a primary indicator of the long-term performance of materials. This mode of operation provides definitive information for prediction of the long-term performance of materials by measuring the stress decay of a sample as a function of time and temperature at an operator-selected displacement (strain). 

In Chapter 4 we introduced linear viscoelasticity. In this scheme, observed creep or stress relaxation behaviour can be viewed as the defining characteristic of the material. The definition of the creep compliance function J t), which is given as the ratio of creep strain e t) to the constant stress o, may be recalled as... 

Once modifications to functions of this kind have been made, the Boltzmann superposition principle can no longer be assumed to apply, and there is no simple replacement for it. This marks a significant change in the level of difficulty when moving from linear to non-linear theory. In the linear case, the material behaviour is defined fully by single-step creep and stress relaxation, and the result of any other stress or strain history then can be calculated using the Boltzmann integral. In the non-linear case we have lost the Boltzmann equation, and it is not even clear what measurements are needed for a full definition of the material. 

However, the tube theory is still useful as it provides a simple qualitative picture that helps to analyze more complicated models as well as experiments. Thus, we proceed to investigate the effect CLF has on the stress relaxation using the definition of eqn [67]. The results of the described... 

Creep is defined as the time-dependent part of the strain which results from the application of a constant stress to a plastic. By comparing the definitions of creep and stress relaxation it can be seen that the two phenomena are closely related. Creep occurs when a constant stress is applied for an extended period whilst stress relaxation occurs during long-term exposure to a constant strain. 

Although 7i 1 is constant by definition during the stress relaxation experiment, 722 will in general change. The relation between axial extension and lateral contraction for a perfectly elastic solid is specified by Poisson s ratio /it ... 

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