Torsional modulus measurement

Mechanical Properties. Dynamic mechanical properties were determined both in torsion and tension. For torsional modulus measurements, a rectangular sample with dimensions of 45 by 12.5 mm was cut from the extruded sheet. Then the sample was mounted on the Rheometrics Mechanical Spectrometer (RMS 800) using the solid fixtures. The frequency of oscillation was 10 rad/sec and the strain was 0.1% for most samples. The auto tension mode was used to keep a small amount of tension on the sample during heating. In the temperature sweep experiments the temperature was raised at a rate of 5°C to 8°C per minute until the modulus of a given sample dropped remarkably. The elastic component of the torsional modulus, G, of the samples was measured as a function of temperature. For the dynamic tensile modulus measurements a Rheometrics Solid Analyzer (RSA II) was used. The frequency used was 10 Hz and the strain was 0.5 % for all tests. 

From the torsional modulus measurements, it is clear that by blending Vectra with Ultem the torsional modulus of the Ultem sheets can be greatly enhanced. G of the neat Ultem sheet is around 1.5 GPa, but G of the Ultem/Vectra blend sheets (with a Vectra content ranging from 10% to 30%) is in the range of 50 to 70 GPa, i.e. about 30 to 45 times higher than that of neat Ultem sheet. The existence of Vectra microfibrils improves G of the blend sheet for temperatures up to the glass transition temperature of Ultem. 

Much more information can be obtained by examining the mechanical properties of a viscoelastic material over an extensive temperature range. A convenient nondestmctive method is the measurement of torsional modulus. A number of instmments are available (13—18). More details on use and interpretation of these measurements may be found in references 8 and 19—25. An increase in modulus value means an increase in polymer hardness or stiffness. The various regions of elastic behavior are shown in Figure 1. Curve A of Figure 1 is that of a soft polymer, curve B of a hard polymer. To a close approximation both are transpositions of each other on the temperature scale. A copolymer curve would fall between those of the homopolymers, with the displacement depending on the amount of hard monomer in the copolymer (26—28). 

Mechanical Properties. Although wool has a compHcated hierarchical stmcture (see Fig. 1), the mechanical properties of the fiber are largely understood in terms of a two-phase composite model (27—29). In these models, water-impenetrable crystalline regions (generally associated with the intermediate filaments) oriented parallel to the fiber axis are embedded in a water-sensitive matrix to form a semicrystalline biopolymer. The parallel arrangement of these filaments produces a fiber that is highly anisotropic. Whereas the longitudinal modulus of the fiber decreases by a factor of 3 from dry to wet, the torsional modulus, a measure of the matrix stiffness, decreases by a factor of 10 (30). 

Some important conditions concerning the estimation of error should be pointed out. First, modulus measurements of rectangular bars are made in torsion and the calculations contain assumptions that may depend on geometry. How this influences error, particularly at low torque levels is not known. Second, the strains were kept constant at 0.1% other strains might not yield the same results. On the other hand one would expect an inverse proportionality to exist between the magnitudes of error and strain. Thirdly, these errors were estimated for a frequency of 1Hz. 

The value of the modulus and the shape of the modulus curve allow deductions concerning not only the state of aggregation but also the structure of polymers. Thus, by means of torsion-oscillation measurements, one can determine the proportions of amorphous and crystalline regions, crosslinking and chemical non-uniformity, and can distinguish random copolymers from block copolymers. This procedure is also very suitable for the investigation of plasticized or filled polymers, as well as for the characterization of mixtures of different polymers (polymer blends). 

Fig. 8. Apparent torsional modulus (period"2 in arbitrary units) measured at various end loads. Specimen correctly aligned 9 Specimen displaced at one end by 2 microns, parallel to its thin dimension, x Specimen displaced at one end by 10 microns.

Generally, the operative frequency range for the torsional pendulum method is 0.01 to 50 Hz, the upper limit of the frequency defined by the dimensions of the oscillatory frequency relative to the dimensions of the sample. At higher investigative temperatures, the polymeric materials may undergo extensional deformation (creep) due to the weight of the inertia bar. Under such circumstances, a modified torsion pendulum apparatus may be used in which an inertia disk is attached directly onto the end of the sample (12). In addition, this method is frequently employed to measure the torsion modulus at low frequencies. 

Measurement of low-temperature flexibility was significantly advanced by the method of Clash and Berg. This assessment of torsional modulus was adopted as an ASTM procedure (41). By its use, it can be shown that plasticizing with linear molecular structures enhances the low-temperature flex most efficiently (i.e., lower plasticizer concentration has a more pronounced effect) chain branching and ringed aromatic moieties show lower efficiency. Increasing any compatible plasticizer s concentration in the composition lowers the temperature at which brittleness develops. However, this formulation approach may sacrifice the optimum in other properties, such as tensile strength, modulus, or hand. 

Modulus changes at low temperatures can be monitored by the torsional modulus or Gehman test of ISO 1432 (BS903, Part A13) and by measurement of hardness. 

An alternative method for examining the dynamic mechanical properties of liquids is to coat them onto an inert support (typically a glass fibre braid). This measurement is termed Torsional Braid Analysis and does not provide quantitative modulus measurements since it is difficult to decouple the response of the substrate from that of the sample. 

The static measurements of Hadley et al. using a grade of Rigidex polymer showed considerable differences compared with low density material. Apart from shallow minima in 0 and G at low draw ratios the behaviour at room temperature appeared rather straightforward (Fig. 11). With increase of draw ratio Eq increased steeply, the torsion modulus increased slightly and 90 varied only a little V12 and vjs were generally not inconsistent with a value of 0-50, and seemed insensitive to the... 

Modulus The ratio of stress to strain in a material over the range for which this value is constant. The type of modulus, which is measured, depends on the method of measurement, e.g., dynamic modulus, compressive modulus, elastic or tensile (Young s) modulus, shear modulus, torsion modulus, sonic modulus. 

Torsional modulus n. Shear modulus (G) as measured in a test in which the specimen is twisted. In ASTM D 1043, the test specimen is a flat rectangular bar with length about seven times its width of 6.35 mm and thickness 1/3 the width. The apparent shear modulus is given by... 

In general, the output of a TMA measurement is a plot of sample dimension or dimensional change versus temperature or time recorded in expansion, compression, tension, or flexure. Expansion, compression, and tension experiments are the most common measurements. Table 4.3 summarizes some key TMA applications in different measurement modes using different sample probes. Details of these measurements are discussed further in Sections 4.6 and 4.7 of this chapter. In addition to these basic types of measurement shear and torsional modulus of films, fibers, laminates, and adhesives can be measured using specially designed probes. 

Figure 5,55. Effect on modulus measured in DMA due to fiber orientation of a unidirectional fiber composite relative to sample clamping in three-point bending and torsion (from Gerrard, et al., 1990, reprinted with permisssion of the Society of Plastics Engineers).

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