Normal stress differences experimental methods

This section describes two common experimental methods for evaluating i], Fj, and IG as functions of shear rate. The experiments involved are the steady capillary and the cone-and-plate viscometric flows. As noted in the previous section, in the former, only the steady shear viscosity function can be determined for shear rates greater than unity, while in the latter, all three viscometric functions can be determined, but only at very low shear rates. Capillary shear viscosity measurements are much better developed and understood, and certainly much more widely used for the analysis of polymer processing flows, than normal stress difference measurements. It must be emphasized that the results obtained by both viscometric experiments are independent of any constitutive equation. In fact, one reason to conduct viscometric experiments is to test the validity of any given constitutive equation, and clearly the same constitutive equation parameters have to fit the experimental results obtained with all viscometric flows. 

The relative ease in the experimental measurements of viscosity functions renders them amenable to extensive study in comparison to the normal stress functions. Hence, there have been attempts [90-93] to find methods for the prediction of the normal stress difference om the viscosity function. 

In this section, we present another experimental method that also employs a capillary die. However, this method allows one to determine not only shear viscosity but also normal stress differences in steady-state shear flow by continuously supplying a polymeric... 

Figure 12.4 gives log versus log y plots for CaC03-filled PP composites with varying amounts of CaC03 at 200 °C, where denotes steady-state first normal stress difference that was determined from the exit pressure method described in Chapter 5. Note that the experimental data used to calculate values of given in Figure 12.4... 

Slit rheometers are more difficult to build and use but are preferred for research studies, because the flat flow channel makes it possible to mount pressure sensors and to make optical measurements. It has been proposed that measurement of the exit pressure or hole pressure [129] might be used to infer the first normal stress difference using a slit rheometer [9,p. 309], but these approaches have been little used because of the difficulty of measuring the small pressures or pressure differences involved. As in the case of capillary rheometers, there are established methods for calculating the true wall shear stress and shear rate from experimental slit data [9, 81]. 

Experimental determination of viscosity and normal stress coefficients Since the range of rj may extend from 10 2 to 1011 N s/m2 and the normal stress coefficients, Tj and Tj, cover also a wide range of values, a number of different experimental techniques have been developed to cover this wide range. Some methods are listed in Table 15.2. 

Another experimental method that is as important as continuous-flow capillary rheometry is slit rheometry. The basic idea of slit rheometry is the same as that of continuous-flow capillary rheometry insofar as the measurement of wall normal stress along the die axis is concerned. But, there is a significant theoretical difference between the two methods, as we will make clear, and also in the die design. The slit rheometer has some advantages over the continuous-flow capillary rheometer in the way that transducers can be mounted on the die wall, but there are also some disadvantages. 

The procedure described, involving the variation of the laser energy, has some advantages relative to the alternative method of using several solutions with different transmittances. First, it provides a check for multiphoton effects simply by analyzing the quality of the linear correlations obtained. It should be stressed that the excellent correlations in figure 13.7 are typical, that is, correlation factors are usually better than 0.9995. Second, the method requires considerably less sample (only one solution is needed). Third, the analysis of experimental data is also conceptually simpler, because no normalization is required. 

The Jenike shear cell has been considered for long time the testing cell for establishing standard procedures in industrial applications and research. It has been recognized as one of the standards for testing bulk solids in the United States and in Europe, being especially focused on cohesive powders. The complexity of this method is such that errors due to poor technique can easily arise. A reference material has therefore been produced with which laboratories can verify both their equipment and experimental technique. The reference material consists of 3 kg of limestone powder packed in a polyethylene jar. It is accompanied by a certificate giving shear stress as a function of normal applied stress for four different powder compaction stresses. 

The effect of the flUer concentration was studied (up to 84% — in copolymer of butadience with acrylic acid) in the presence of 0-84% solid filler on the temperature dependence of parameters of mechanical dynamic properties. For the first time a principle was stated in that wodc to the effect that the filler influence m dso be described by the reduction method similar to temperature reduction. For this, use was made of an equation equivalent in its form to the WLF equation but with different numerical values of the constants Ci and C2. Its most generd result is the stress-strain representation in a twice-normalized state-by temperature and by concentration of the flUer. However, not all the parameters can be represented in the concentration-invariable form by the use of tl same method of filler concentration reduction. Specifically, the effect of the filter at the initial section of the stress-strain curve is greater than was predicted by the gemtal reduction method. The relative strain at rapture can also be represented in the concentration invariant from, if tiie vertical shift of the experimental curves is used in addition to tiie commm horizontal one. The author has proposed empirical formulas descrfliing the concentrational dependence of the reduction coefficient. 

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