Yield strain magnitudes

A tensile test on the peel arm is used to obtain the parameters of elastic modulus, plastic modulus and yield strain. In this test, it has been necessary to use an extensometer for measuring strain at small magnitudes (i.e. up to about 2%) in order to obtain sufficient accuracy in the determination of Ei. It is also important to continue the tensile test to fracture, in order to define enough of the plastic region for an accurate... 

Here Av is the shear-activation volume of the polymer at 293 K, values of which are listed for prominent glassy homo-polymers in Table 8.3, and f(0)/yu(0) is the threshold yield strain in shear at 0 K, which is 0.11 for most glassy polymers, except PS, for which it is 0.12 (Table 8.2). In eqs. (11.46) and (11.51) sq is the preexponential factor that incorporates a frequency factor based on the eigenfre-quency of a plastic relaxation cluster and has typically a magnitude of 1.40 X 10 s for tensile flow in glassy polymers (see Chapter 8). 

FIGURE 8.5 Creep response of conical bone for three different stress levels. When a low stress is applied to the bone, the strain remains constant over time, and there is no permanent deformation after unloading. For stresses just below yield, strains increase with time at a constant rate, and a small permanent deformation exists after unloading. As the magnitude of the stress is increased, the rate of creep increases, and a larger permanent deformation exists after unloading. (From R. 108.)... 

As a pipeline is heated, strains of such a magnitude are iaduced iato it as to accommodate the thermal expansion of the pipe caused by temperature. In the elastic range, these strains are proportional to the stresses. Above the yield stress, the internal strains stiU absorb the thermal expansions, but the stress, g computed from strain 2 by elastic theory, is a fictitious stress. The actual stress is and it depends on the shape of the stress-strain curve. Failure, however, does not occur until is reached which corresponds to a fictitious stress of many times the yield stress. 

If the material is perfectly plastic, i.e., if the yield function is independent of k and a, then = 0 and the magnitude of the plastic strain rate cannot be determined from (5.81). Only its direction is determined by the normality condition (5.80), its magnitude being determined by kinematical constraints on the local motion. 

Likewise, the longer the duration of material stress or strain, the more time for viscous flow to occur. Finally, the greater the material stress or strain, the greater the likelihood of viscous flow and significant permanent deformation. For example, when a TP product is loaded or deformed beyond a certain point, the material comprising it yields and immediate or eventually fails. Conversely, as the temperature or the duration or magnitude of material stress or strain decreases, viscous flow becomes less likely and less significant as a contributor to the overall response of the material and the essentially instantaneous elastic deformation mechanism becomes predominant. 

Rupture. Rupture strain decreases steadily with increases in the duration of stress. Alternately, the magnitude of stress needed to cause rupture decreases as the duration of stress increases. Figure 2-31 shows the development first of damage and then of yielding in a PVC compound as a function of its being under sustained stress. The decay at the onset of the first damage and of yield... 

Some important conditions concerning the estimation of error should be pointed out. First, modulus measurements of rectangular bars are made in torsion and the calculations contain assumptions that may depend on geometry. How this influences error, particularly at low torque levels is not known. Second, the strains were kept constant at 0.1% other strains might not yield the same results. On the other hand one would expect an inverse proportionality to exist between the magnitudes of error and strain. Thirdly, these errors were estimated for a frequency of 1Hz. 

In each of the named cases, hardness is a variation on strength and depends on a specific state of stress related to it, occurring in the tested material under the applied force. If the magnitude of this stress is less than a certain boundary value known as the yield point, then the strain of the material is reversible, in other words, it is elastic. On exceeding the yield point the material is subjected to irreversible strain on removal of the load, or to failure. In some materials, especially those of imperfect structure, failure occurs even at a strain below that corresponding to the yield point. These are termed brittle. 

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