Apparent yield stress

This means that in the range of stresses which are lower than the apparent yield stress (x < Y), a mechanism of plastic flow ( creeping flow) occurs differing completely from that in the common range. 

Galgali and his colleagues [46] have also shown that the typical rheological response in nanocomposites arises from frictional interactions between the silicate layers and not from the immobilization of confined polymer chains between the silicate layers. They have also shown a dramatic decrease in the creep compliance for the PP-based nanocomposite with 9 wt% MMT. They showed a dramatic three orders of magnitude drop in the zero shear viscosity beyond the apparent yield stress, suggesting that the solid-like behavior in the quiescent state is a result of the percolated structure of the layered silicate. 

One feature of the Maxwell model is that it allows the complete relaxation of any applied strain, i.e. we do not observe any energy stored in the sample, and all the energy stored in the springs is dissipated in flow. Such a material is termed a viscoelastic fluid or viscoelastic liquid. However, it is feasible for a material to show an apparent yield stress at low shear rates or stresses (Section 6.2). We can think of this as an elastic response at low stresses or strains regardless of the application time (over all practical timescales). We can only obtain such a response by removing one of the dashpots from the viscoelastic model in Figure 4.8. When a... 

The durability of the particle network structure imder the action of a stress may also be time-dependent. In addition, even at stresses below the apparent yield stress, flow may also take place, although the viscosity is several orders of magnitude higher than the viscosity of the disperse medium. This so-called creeping flow is depicted in Fig. 11 where r (. is the creep viscosity. In practice this phenomenon is insignificant in the treatment of filled polymer melts, but may be relevant, for example, in consideration of cold flow of filled elastomers. 

Pseudoplastic. A material of this type appears to have a yield stress beyond which flow commences and increases sharply with increase in stress. In practice, such substances are found to exhibit flow at all shear stresses, although the ratio of flow to force increases negligibly until the force exceeds the apparent yield stress. 

Data from viscometers are often presented as a linear plot of shear stress versus shear rate, sometimes called a rheogram (Figure HI.1.2). This type of plot allows the viewer to see directly if there is Newtonian behavior because the plot will take the form of a straight line through the origin. A non-Newtonian response is, by definition, nonlinear and may or may not pass through the origin. If the sample has an apparent yield stress, then the line or curve will... 

Two protocols are presented for non-Newtonian fluids. Basic Protocol 1 is for time-independent non-Newtonian fluids and is a ramped type of test that is suitable for time-independent materials. The test is a nonequilibrium linear procedure, referred to as a ramped or stepped flow test. A nonquantitative value for apparent yield stress is generated with this type of protocol, and any model fitting should be done with linear models (e.g., Newtonian, Herschel-Bulkley unithit). 

Measuring the Viscosity of Non-Newtonian Fluids The exact start and end poin ts of the ramp can be decided from the ramp performed in Basic Protocol 1. A stress of 1/lOth to l/100th of the apparent yield stress to the nearest order of magnitude should be set. 

If a sample shows a very sharp drop in viscosity over a narrow stress range, then it can be considered to have an apparent yield stress. 

Much more effort has gone into relating hardness value to the yield stress of fats than to their elastic properties. For example, the International Dairy Federation proposed (Walstra, 1980) that penetration depth be converted to an apparent yield stress (AYS) for sharp-ended cones according to the equation ... 

Hardness and apparent yield stress can be calculated from penetration test data, while sectility test data can be converted to a yield stress and a pseudo-Bingham plastic viscosity (Dixon and Williams, 1977). 

FIGURE 12.24 Viscosity (at y 50 sec ) and apparent yield stress (at y = 1 sec ) versus suspension solids fraction for ion-exchanged kaolinite. Data taken from Langs-... 

The Casson body model " is a semiempirical model used to describe shear thinning behavior after an apparent yield stress has been exceeded. It is, in fact, a combination of the apparent yield stress with the power law model, whereby the power law index n is arbitrarily set to 0.5 ... 

A more general mathematical description of shear thinning materials comprising an apparent yield stress is given by the Herschel-Bulkley model ... 

Shear thinning of concentrated suspensions is typical for submicron particles dispersed in a low viscosity Newtonian fluid.At low shear strain rates. Brownian motion leads to a random distribution of the particles in the suspension, and particle collision will result in viscous behavior. At high shear strain rates, however, particles will arrange in layers, which can slide over each other in the direction of flow. This results in a reduced viscosity of the system in agreement with the principles of shear thinning. A pro-noimced apparent yield stress can be found for shear thinning suspensions, if the Brownian motion is suppressed by electrostatic repulsion forces, which result in three-dimensional crystal-like structures of the particles with low mobility. 

Flow of hexagonal liquid crystalline systems is presumably a function of the alignment of the rod-like aggregates along their long axis in the direction of flow.f " The shear thinning flow process can be accompanied by an apparent yield stress. Viscoelastic behavior has also been reported. ... 

Cubic liquid crystalline systems have been described as clear, stiff gelsJ As such, they show shear thinning after an apparent yield stress has been exceeded. The viscoelastic properties are also typical for the gel character a broad linear viscoelastic range and a frequency-independent elastic component, which is considerably higher than the viscous component, are observed. ... 

The convenient way of data examination for presence of the apparent yield stress Is by means of the modified Casson plot (51) ... 

Once the values of F(u) are known either Equation 20 or) 21 can be used. The advantage of Equation 20 is that only F needs to be corrected for the apparent yield stress. If Equation 21 Is to be used both Gg and G" must be corrected Independently and then ... 

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. 

The apparent yield stress. Ihe complex viscosity n vs. oi for PP blends with LLDPE-B and LLDPE-C Is shown In Fig. 26. The plot clearly Indicates possible yield stress behavior especially for blends containing 50% PP. Ihe apparent yield stress In dynamic flow data was calculated using Equation 23, with F G or F G". The yield stress values as well as the assumed matrix material for calculating F are listed In Table V. For both systems the maximum value of the apparent yield stress occurred at 50% PP. In fact, there Is a direct correlation - In a given system the yielding Is primarily observed In blends having a co-contlnuous structure. As before (53 ) Gy > Gy... 

In the last column of Table V the directly measured shear stress values at yield are listed. These measurements were carried out In RSR, setting the desired level of stress and recording the strain after 200 s. The results are shown In Fig. 27. There Is good agreement between Gy and Oy for System-1 but not for system-2. The two sets of experiments are carried out on a different time scale. Since, according to Equation 24, the apparent yield stress In blends depends on time one should not expect the same results from the dynamic and creep measurements. Furthermore, the differences In less viscous System-2 are expected to be larger than those for System-1. 

Table V. Apparent yield stress for PP blended with LLDPE-B or LLDPE-C...

Figure 29. Storage shear modulus vs. frequency for System 1. The points are experimental, uncorrected for the apparent yield stress, the lines computed from the relaxation spectrum.

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