Experimental Methods for Shear Measurements

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 two basic types of mechanical deformation, from a physical and molecular standpoint, are shear and dilatation. The experimental methods described in the preceding three chapters yield information primarily about shear only in extension measurements on hard solids does a perceptible volume change influence the results. By combining shear and extension measurements, the bulk properties can be calculated by difference, as for example in creep by equation 55 of Chapter 1, but the subtraction is unfavorable for achieving a precise result. Alternatively, bulk properties can be measured directly, or they can be obtained by combining data on shear and bulk longitudinal def ormations (corresponding to the modulus M discussed in Chapter 1), where the subtraction does not involve such a loss of precision. Methods for such measurements will now be described. They have been reviewed in more detail by Marvin and McKinney. ... 

The deep-channel surface viscometer is a frequently used experimental method for measuring interfacial shear viscosity owing to its sensitivity (irish S 10 surface poises) and relatively simple analytical theory. The main drawback of this technique is the necessity of placing a small tracer particle within the interfacial flow field for tracking the central surface velocity. This may be particularly cumbersome with heavy-oil systems, for which the particle may require several hours or more to execute a complete revolution, as well as with liquid -liquid systems, for which the placement of the particle at the interface may be difficult. For more details, see Refs. 58 and 151-156. 

By solving Eqs. (4) and (7) simultaneously, the mass flux can be calculated provided the wall shear stress is known as a function of particle superficial volume flow rate. Botterill and Bessant (1973) have proposed several relationships for shear stress, however, these are not general. LaNauze (1976) also proposed a method to measure this shear stress experimentally. 

Shear cell measurements offer several pieces of information that permit a better understanding of the material flow characteristics. Two parameters, the shear index, n, and the tensile strength, S, determined by fitting simplified shear cell data to Eq. (6), are reported in Table 2. Because of the experimental method, only a poor estimate of the tensile strength is obtained in many cases. The shear index estimate, however, is quite reliable based on the standard error of the estimate shown in parenthesis in Table 2. The shear index is a simple measure of the flowability of a material and is used here for comparison purposes because it is reasonably reliable [50] and easy to determine. The effective angle of internal... 

The authors state that their approach that leads to Eq. (13.171) does not take into account that during the first loading of the fibre viscoelastic and plastic deformation contribute to the shear deformation. Therefore they have applied a slightly different method for the calculation of the tensile strength as a function of the initial modulus. However, there is still room for a slight discrepancy between the theoretical and experimental results as the derivation of Eq. (13.171) is based on the application of a single orientation angle as a measure of the whole distribution in the fibre. 

Also in 1963 Raumann reported measurements on specimens prepared from amorphous sheets stretched below the glass transition temperature. The experimental method was identical with that reported earlier for polyethylene. Major features were that as the result of orientation q increased to over five times the isotropic value, and the shear modulus at 90° dropped to about half the isotropic shear modulus other moduli showed only small variations from the isotropic values (Ladizesky and Ward have commented that Raumann s torsional moduli are probably in error, owing to her assumptions of the validity of the St. Venant theory, and an inadequate correction for tensile stress). 

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