Torsional measurements

The torsional measurements show only one maximum on the damping curve. This means that there is a good segmental miscibility between the networks in the UPR-BPA/DC system. 

The glass transition temperature according to dynamic torsional measurements is near -60 °C (Figure 25.17) for the rubbery phase, so that toughening above this temperature can be expected. The glass transition temperature of the... 

In a rotational viscometer the solution is filled in the annulus between two concentric cylinders of which either the external (Couette-Hatschek type) or the internal (Searle type) cylinder rotates and the other, which is connected to a torsion-measuring device, is kept in position. Let R, and Ro be the radii of the inner and outer cylinders, h the height of the cylinder which is immersed in the solution or its equivalent height if end effects are present, a> the angular velocity of the rotating cylinder, and T the torque (or moment of force) required to keep the velocity constant against the viscous resistance of the solution. It can be shown that the shearing stress (see, for example, Reiner, 1960) ... 

The losipescu torsion measurement results are given in Table 1, with an example stress-displacement curve shown in Figure 2. These values are indicative of a relatively torsion-resistant material, particularly given the low density of the carbon composite. The stress-displacement curves indicate little delamination or other failures until ultimate failure. 

Xsuda Y, Yasutake H, Ishijima A, Yanagida X (1996) Xorsional rigidity of single actin filaments and actin-actin bond breaking force under torsion measured directly by in vitro micromanipulation. Proc Natl Acad Sci USA 93 12937... 

Shear Modulus. The shear modulus determined from torsion measurements exhibits some dependence on temperature. For the Kevlar composite, the increase was 1.5, and for carbon fiber composite it was 1.2, from 293 to 4.2 K. Of course, both the damping and storage shear moduli represent tensorial quantities, and this must be included in the analysis. For anisotropic fibers, both the tensorial quantities of the fibers and those of the composite are involved. Here, only one tensor element, which was expected to be sensitive to temperature, was considered. 

The torsion measurements were carried out on a Rheometrics RMS 7200 (3) load frame, modified in our laboratory witii a computer controlled servo-motor. The sample and grips were housed witiiin a heater chamber for temperature control, with a measured oven stability [based on tiie range of measurements] of better tium ... 

Extensional measurements involve a simple loading process, but with compression and torsion measurements simplifying assumptions and/or corrections need to be applied to experimental data. In compression it is necessary to assume plane strain," and Poisson s ratio measurements may be performed either at constant strain or constant stress. For a non-linear viscoelastic polymer these two methods are not equivalent. 

Typical apparatus for torsional measurements is that described by Raumann - and in a modified form by Ladizesky and Ward. The sitmple is fastened betw een two clamps, the lower of which may be fixed in any required orientation, and the upper of which is attached rigidly to a small mirror and then to the lower end of a long phosphor-bronze strip. When the top of this strip is rotated both the suspension and the sample will twist, the former through an angle

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Hennig quotes room temperature values of extensional, transverse and torsional moduli for polyvinyl chloride, polymethylmethacrylate and polystyrene. Extensional data were obtained from d)mamic testing at 320 Hz, while torsional measurements were made at 1 Hz. These values, together with those of Robertson and Buenker on bisphenol A polycarbonate are summarised in Table 3. 

This complicated procedure, together with the inhomogeneity of stress and strain inherent to torsion of solid bodies, which precludes quantitative interpretation and observation of non-linear effects, must be regarded as a severe restriction on the utility of torsional testing in creep studies such as those discussed here. However, as already indicated, torsional measurements appear currently to offer the only route to the determination of all three shear compliances in materials with orthorhombic symmetry. 

Fig. 15. Measurement xmder tension E (storage modulus) and loss tangent of differently treated iPP in comparison to the torsion measurement G injection moulded and hot-...

Thermomechanicnl analysis (TMA) (a) peneiration, (b) extension, (c) flexure, and (d) torsional measurements. 

Erom a practical viewpoint, Eq. (29.4) can be used to describe the stress-strain relation of a material if vi/(A) is known. m/(A) can be obtained in the laboratory in various ways, such as pure shear experiments as described by Valanis and Landel [60], by torsional measurements as described by Kearsley and Zapas [62] and by a combination of tension and compression experiments as also described by Kearsley and Zapas [62]. Treloar and co-workers [63] have also shown that the VL function description of the mechanical response of rubber is a very good one. The reader is referred to the original literature for these methods. 

Finite Elasticity Theory The VL Representation. While the above description of the finite deformation behavior of elastic materials is very powerful, the limitation on it is that the material parameters W and W2 need to be determined in each geometry of deformation of interest. Hence, the torsional measurements described above only give values of Wi(/i, I2) and W2(/i, I2) for the condition of shear (torsion is anonhomogeneous shear) and that condition is/i = l2 = 3- -y. More measurements need to be made to obtain the parameters in extension, compression, etc. However, in 1967, Valanis and Landel (98) proposed a strain energy function that, rather than being a function of the invariants, is a function of the stretches Xj. The function was assumed to be separable in the stretches as... 

Because of this usefulness it is important to have relatively simple experiments available to obtain the VL function. Kearsley and Zapas (97) have shown that either simple extension combined with simple compression or torsion with normal force measurements can be used to obtain the VL function. Valanis and Landel (98) used pure shear measurements. The equations for the torsional measurements arise from the relationship between w X) and Wi and W2 given by... 

Thus, from torque and normal forces in torsional experiments, the VL function derivative can be obtained. Typical data for natural rubber are presented in Figures 30, 31, 32. The figures illustrate the sequence that would be used to obtain the VL ftmction. First, obtain torque and normal force data (Fig. 30) and use equations 47 and 48 to obtain the strain energy function derivatives Wi and W2 (some typical results shown in Fig. 31). Finally, data of the sort shown in Figure 31 are used to obtain the VL fimction derivative w X). Figure 32 shows such data obtained from torsional measurements on natural rubber samples cross-linked to different extents (102). 

J.-J. Pesce and G. B. McKenna, Prediction of the Sub-Yield Extension and Compression Responses of Glassy Polycarbonate from Torsional Measurements J. Rheol. 41, 929-942(1997). 

Frequently, a fiber is anisotropic, with different properties in different direc-tions. For practical purposes, the only types of deformation which can be readily measured are simple extension, torsion, and flexure. Extension and flexure should both measure Young s modulus E for elongation in the fiber direction, and should therefore yield the same result. Torsion measures the shear modulus G for a direction of slide perpendicular to the fiber direction, and in case of anisotropy these moduli E and G are not connected in any simple manner. Some examples of such behavior will be given in Chapter 16. 

The secondary dispersions, at -10 and —85 , presumably can be attributed to side group rearrangements as are the P mechanisms and other secondary effects discussed in Chapter 15. But it is difficult to guess the relative roles of volume and shear deformations in these motions. In shear (torsion) measurements at about 10 Hz, Schmieder and Wolf found secondary maxima in tan 6 at —30 and -100°C. No certain identification of these respective mechanisms can be made, since maxima in a and tan 6 are not really equivalent, and the respective frequency ranges are very different. If the secondary maxima in Fig. 18-17 do correspond to the secondary shear maxima, the temperature dependence of the associated relaxation times must be quite high. 

The data obtained by Brunetti et al. (2005) for lutetium trichloride agree more closely with the recommendations made in this work. Indeed, calculations from the data obtained in a series of six torsion measurements yield the mean values Agubff°(298, III law) = 303.0 kJ/mol and Asubff°(298, II law) = 305.6 kj/mol. These values should, however, be corrected to take into accoimt a comparatively high content of dimeric LU2CI6 molecules in the vapor phase. 

FIG. 81 Temperature dependencies of the (a) shear modulus and (b) loss tangent of LLDPE obtained from torsional measurement at 1 Hz for isotropic sample and oriented sample (Sor = 5). (From Ref. 111.)... 

Finally, there are some unique measurements of the mechanical torque connected with an elastic deformation of the nematic. Faetti et al. [63] determined the splay and bend elastic constants by means of such torsion measurements, and Grupp [ 139] made measurements of the twist elastic constant 22-... 

Finite Elasticity Theory The VL Representation. While the above description of the finite deformation behavior of elastic materials is very powerful, the limitation on it is that the material parameters Wi and W2 need to be determined in each geometry of deformation of interest. Hence, the torsional measurements described above only give values of Wi(/i, I2) and W2(/i, I2) for the condition of... 

One important issue in dealing with the nonlinear viscoelastic response of materials is the amount of data needed to determine the material parameters in the models. As noted above, even the general finite elasticity theory requires significant work to obtain the material parameters over the full three-dimensional deformation space. This is one reason that the VL framework is so attractive, when it works. Therefore, it is of interest to investigate whether or not the model can be extended to include compressibility. Pesce and McKenna (146) performed torsional tests on polycarbonate as described above. They then asked whether the VL function could be used to predict the tension and compression responses of the material. An important assumption in their approach was that the VL function determined from the torsional measurements using equations 45, 46, 47, 48, 49, 50, 51 (described immediately above) could be used to predict uniaxial data. When the incompressible equations 50 were applied to try to estimate the uniaxial stress-deformation data (isochronal), these equations did not work. However,... 

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