Apparent yield point

FIGURE 13.32 Apparent yield point, Py, versus relative humidity used to equilibrate the PVA binder used in the die pressing of AI2O3 powder. Data taken from Reed [6, p. 337]. 

The plastic behaviour of some metals, especially plain carbon steels, deviates from that described so far. Their stress-strain curve shows a so-called apparent yield point (also known as yield point phenomenon) (figure 3.5(b)) ... 

They are almost completely elastic until the upper yield strength Ren (UYS) is reached. At this stress, plastic deformation sets in rather suddenly, which is localised in so-called Liiders bands or flow lines. While the stress oscillates, these lines extend until they cover the whole specimen. The lowest stress occurring during this process is called lower yield strength i eL (lys). Why this localised plastic deformation occurs, will be explained in section 6.4.3. After the specimen has plastified completely, it behaves identical to a metal without apparent yield point. 

As already discussed, the interaction between dissolved atoms and a dislocation can cause pinning of the dislocation. Because the dissolved atoms can move through the lattice by diffusion, they can pin dislocations even if these do not move. This is especially so for interstitial atoms, for they have a large diffusivity. This is the cause of the apparent yield point of some metals and for the so-called Portevin-Le-Chdtelier effect (PLC) as we will see now. 

If the diffusivity (or the temperature) is raised even further, the speed of the dissolved atoms is so high that they simply accompany the dislocation during its movement. In this case, there is neither an apparent yield point nor serrated flow. 

In contrast to metals, polymers do not work-harden because no new obstacles are created when the molecules slide past each other. Heat generated during deformation causes a local increase in temperature, further easing plastic deformation. This results in a local softening of the material, similar to a metal with an apparent yield point (see section 6.4.3). Only if the plastic strain becomes larger does some hardening occur because the molecules become aligned in the direction of the applied stress. 

If the viscoelastic behavior is nonlinear, stress-strain curves at constant rate of loading or deformation will be so a fortiori, since they can depart from linearity even without this complication. Calculations by Van Holde show that the nonlinearity of tensile creep in nitrocellulose implies a stress-strain curve at constant rate of loading with a sharp change in slope at strains of about 5% which resembles the apparent yield points observed in such experiments on many textile fi-bers. 5 6... 

Direct Indicating Viscometer. This is a rotational type instrument powered by an electric motor or by a hand crank. Mud is contained in the annular space between two cylinders. The outer cylinder or rotor sleeve is driven at a constant rotational velocity its rotation in the mud produces a torque on the inner cylinder or bob. A torsion spring restrains the movement. A dial attached to the bob indicates its displacement. Instrument constants have been so adjusted that plastic viscosity, apparent viscosity, and yield point are obtained by using readings from rotor sleeve speeds of 300 and 600 rpm. 

Plastic viscosity (PV) is centipoises equals the 600 rpm reading minus the 300 rpm reading. Yield point (YP) in pounds per 100 ft equals the 300-rpm reading minus plastic viscosity. Apparent viscosity in centipoises equals the 600-rpm reading, divided by two. The interpretations of PV and YP measurements are presented in Figure 4-107. 

The three deformation regions are also apparent on the strength versus concentration relationships. The most dramatic drop of the yield point was observed at small filler concentrations (up to 0.15). On further filling the characteristic remained almost unchanged. 

TKPP Cone. Density Apparent Plastic Yield Point... 

Apparent vis.=18.5 cp, Plastic vis.=13.0 cp, Yield point=ll lb/100 ft.2 These values are characteristic of a superior, low-solids, drilling fluid that promotes a high drilling rate and good solids removal. In addition, maximum inhibition of hydrating clays is provided. 

In addition to the difference in the size distributions of droplets/particles produced, the overall production costs are apparently the point of differentiation among all atomization techniques under consideration. As the criteria for the evaluation of a specific atomization technique/system, the following factors are of importance high yields, minimum use of expensive gases, clean droplets/ particles, and high throughput. 

Kohlmeyer ( 0, reported that, although PbS(t) had an apparent boiling point of 1617 K, the vaporization did not yield... 

The yield is easily calculated by evaluating the derivatives of product concentration versus time and substrate concentration versus time and taking their ratio. Alternatively, product concentration is plotted against substrate concentration and the absolute value of the slope at any point is equal to the apparent yield. The important point to note here is that apparent yield ratios may be obtained even if specific consumption and production rates cannot be calculated because viable cell data are unavailable. For cases in which only endpoint data are available, an average apparent yield can be calculated. In this case, the apparent yield is simply the ratio of the change in the concentration of product to the change in the concentration of substrate ... 

We can define an apparent yield of product from substrate (Fps) as a measure of the efficiency of product formation that can be used to compare cells grown in different culture systems or in different media. Product P is a cellular product such as monoclonal antibody, while substrate S may be serum, glucose, glutamine, oxygen or any other important substrate. Analysis of the overall yield (from endpoint calculations) may allow for comparison of production efficiency between different reactors and culture conditions. Analysis of the yield at various time points allows for detection of changes in the mechanisms of product formation. Product yields are useful in identifying product degradation in culture (as evidenced by a decrease in Ypg for aU substrates). 

The Dynamic flow. The flow curves, n vs. u In Fig. 22, were not corrected for the apparent yield stress. For PP and LLDPE-A the curves nearly reached the Newtonian plateau and the Cole-Cole plots were found to be seml-clrcular Indicating that Oy = 0, However, for blends the situation Is less clear. Judging by the flow curves for BL, BL-1 and BL-2 at low deformation rates, the Newtonian plateau seems to be far away. This may Indicate the Incipient yield stress. To clarify this point n" vs. n was plotted In Fig. 23. An onset of the second relaxation mechanism Is visible. The long relaxation times In BL may only originate In the Interphase Interactions. These usually lead to the presence of the apparent yield stress. 

The high frequency cross point coordinates (Gjj, Uj ) were used for calculation of the Maxwellian zero-shear viscosity, tiom from Equation 38. For the neat polymers tiqh was In agreement with ng calculated from the shear and extenslonal responses. For BL, BL-1 and especially BL-2 ngfi < ng. The presence of an apparent yield stress Is the most likely explanation for the discrepancy. 

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