Stress relaxation recovery after

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. 

As with the elastic solid we can see that as the stress is applied the strain increases up to a time t = t. Once the stress is removed we see partial recovery of the strain. Some of the strain has been dissipated in viscous flow. Laboratory measurements often show a high frequency oscillation at short times after a stress is applied or removed just as is observed with the stress relaxation experiment. We can replace a Kelvin model by a distribution of retardation times ... 

After this rather extensive discussion of the experimental verification of eqs. (2.11), (2.20) and (2.22), where the interrelations of steady flow properties with dynamic properties and shear recovery are scrutinized, a few words should be added with respect to stress-relaxation after cessation of steady shear flow. As pointed out above, Lodge predicted a decrease of the extinction angle during stress relaxation (4). That this... 

Creep, stress relaxation and set are all methods of investigating the result of an applied stress or strain as a function of time. Creep is the measurement of the increase of strain with time under constant force stress relaxation is the measurement of change of stress with time under constant strain and set is the measurement of recovery after the removal of an applied stress or strain. It is important to appreciate that there are two distinct causes for the phenomena of creep, relaxation and set, the first physical and the second chemical. The physical effect is due to rubbers being viscoelastic, as discussed in Chapter 9, and the response to a stress or strain is not instantaneous but develops with time. The chemical effect is due to ageing of the rubber by oxidative chain scission, further crosslinking or other reaction. 

The rubber industry has traditionally paid more attention to measuring the recovery after removal of an applied stress or strain, i.e. set, than to creep or stress relaxation. This is partly because relatively simple apparatus is required and it is a convenient way to get an indication of the state of cure, but also because it appears at first sight that set is the important parameter when judging sealing efficiency. Set correlates with relaxation only generally and it is actually the force exerted by a seal that usually matters, rather than the amount it would recover if released. 

Fig. 5.2. Typical stress-relaxation curve for a polymer TFT (a). Ratio of reversible to total stress after one-day recovery for the same device (b). The device was a PQT-12 TFT on thermal Si02 biased at VG = —20 V and VDS = —1 V.

Fig. 5.1 Idealized representation of the transient change in fiber and matrix stress that occurs during the isothermal tensile creep and creep recovery of a fiber-reinforced ceramic (the loading and unloading transients have been exaggerated for clarity). It is assumed that the fibers have a much higher creep resistance than the matrix. The matrix stress reaches a maximum at the end of the initial loading transient. After full application of the creep load, the matrix stress relaxes and the fiber stress increases. Upon specimen unloading, elastic contraction of the composite occurs, followed by a time-dependent decrease in fiber stress and increase in matrix stress. Overall, creep tends to increase the difference in stress between constituents and recovery tends to minimize the difference in stress. After Wu and Holmes.15...

The temporary network model predicts many qualitative features of viscoelastic stresses, including a positive first normal stress difference in shear, gradual stress relaxation after cessation of flow, and elastic recovery of strain after removal of stress. It predicts that the time-dependent extensional viscosity rj rises steeply whenever the elongation rate, s, exceeds 1/2ti, where x is the longest relaxation time. This prediction is accurate for some melts, namely ones with multiple long side branches (see Fig. 3-10). (For melts composed of unbranched molecules, the rise in rj is much less dramatic, as shown in Fig. 3-39.) However, even for branched melts, the temporary network model is unrealistic in that it predicts that rj rises to infinity, whereas the data must level eventually off. A hint of this leveling off can be seen in the data of Fig. 3-10. A more realistic version of the temporary network model... 

The degree of stress relaxation can be used to predict the capping tendency of a formulation. It occurs when the upper punch begins to move upwards in the die after reaching Upon removal of upper punch the tablet when outside the die will expand in the axial and radial directions to relieve stress resulting from ela.stic recovery after compaction which could eventually lead to problems like capping and lamination (163). 

Viscoelastic foams show a stress-relaxation phenomenon, i.e., delay of complete deformation recovery after compression. These foams usually take 2 to 30 seconds to recover after 50% compression. In contrast, HR foams and conventional flexible polyurethane foams show very short deformation-recovery times, e.g., less than 1 second. This means that these foams have low viscoelasticity or small energy absorption. 

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. 

Figure 3.19 Recovery under a fuUy confined condition. The recovered stress for the pure SMP and foam after stress-controlled programming with two pre-stresses is shown. The inset shows the long-term stress relaxation of the foam programmed by a 47 kPa compressive stress. Source [41] Reproduced with permission from Elsevier...

DMA measures the viscoelastic properties of a sample using either transient or dynamic oscillatory tests. Transient tests include creep and stress relaxation. In creep, a stress is applied to the sample and held constant, while deformation is measured versus time. After some time, the stress is removed and the recovery measured. In stress relaxation, a deformation is applied to the sample and held constant the degradation of the stress required to maintain the deformation is measured versus time. The most common test is the dynamic oscillatory test, where a sinusoidal stress (or strain) is applied to the material and the resultant sinusoidal strain (or stress) is measured. Also measured is the phase difference, 8, between the two sine waves. The phase lag will be 0° for a purely elastic material and 90° for a purely viscous material. Viscoelastic materials such as polymers will exhibit an intermediate phase difference. Since modulus equals stress divided by strain, the complex modulus, E, can be calculated. From E and 8, the storage modulus, E, the loss modulus, E", and tan 8 can be calculated ... 

After stretching the sample to Em = 200% at Thigh, stress-relaxation was allowed to occur. Once the stress relaxed, the sample was cooled under constant stress to Tiow. After releasing the stress to zero a stress-free recovery module was applied. 

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