Torsional modulus

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). 

T and are the glass-transition temperatures in K of the homopolymers and are the weight fractions of the comonomers (49). Because the glass-transition temperature is directly related to many other material properties, changes in T by copolymerization cause changes in other properties too. Polymer properties that depend on the glass-transition temperature include physical state, rate of thermal expansion, thermal properties, torsional modulus, refractive index, dissipation factor, brittle impact resistance, flow and heat distortion properties, and minimum film-forming temperature of polymer latex... 

Young s modulus Torsion modulus Poisson s ratio Compressibility (dv/Vf dp) ... 

The constant G, called the shear modulus, the modulus of rigidity, or the torsion modulus, is directly comparable to the modulus of elasticity used in direct-stress applications. Only two material constants are required to characterize a material if one assumes the material to be linearly elastic, homogeneous, and isotropic. However, three material constants exist the tensile modulus of elasticity (E), Poisson s ratio (v), and the shear modulus (G). An equation relating these three constants, based on engineering s elasticity principles, follows ... 

Pure crystalline silicon is a brittle material with a gray metallic appearance. Its mechanical properties, such as Knoop hardness (950-1150 kg mm-2), Young s modulus (190 GPa for (111), 170 GPa for (110), 130 GPa for (100)), torsion modulus (4050 kg mm-2) and compression breaking strength (5000 kg cm-2) vary slightly with crystal orientation. Silicon has a low thermal expansion coefficient (2.33x 1(T6 K-1) and a high thermal conductivity (148 W K-1m-1). Crystalline silicon melts at 1413 °C (1686 K). 

These tests are based on the evolution of the static or dynamic torsion modulus when the temperature decreases. Results can be ... 

The elastic modulus is the slope of the tangent at the origin of the stress/strain curve. The tensile or compression modulus is often called Young s modulus whereas the torsion modulus is often called shear modulus or Coulomb s modulus. 

Hence, the elastic modulus corresponds in principle to the force per square millimeter that is necessary to extend a rod by its own length. Materials with low elastic modulus experience a large extension at quite low stress (e.g., rubber, = 1 N/mm ). On the other hand, materials with high elastic modulus (e.g., polyoxymethylene, s 3500 N/mm ) are only slightly deformed under stress. Different kinds of elastic modulus are distinguished according to the nature of the stress applied. For tension, compression, and bending, one speaks of the intrinsic elastic modulus ( modulus). For shear stress (torsion), a torsion modulus (G modulus) can be similarly defined, whose relationship to the modulus is described in the literature. 

The Clash-Berg temperature (ASTM Dl043-6IT) is the temperature at which the torsional modulus of a 0.075-inch sample equals 135,000 p.s.i. A constant torque of 0.5 inch-pound was applied and five-second readings were taken on a Tinius-Olsen instrument. 

The relative modulus at any temperature is the ratio of the torsional modulus at that temperature to the torsional modulus at 23°C and the results can be expressed as the temperatures at which the relative moduli are 2, 5, 10 and 100 respectively. A table is given in the standard to save calculation. Alternatively, the apparent torsional moduli can be calculated from ... 

This is the same relationship, but different symbols have been used, as given in Chapter 8, Section 7.3 for torsional modulus tests and in Chapter... 

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.

In a study of internal friction in polytetrafiuoroethylene, McCrum (1959a) investigated samples varying from 48% to 92% crystallinity. The dependence of the logarithmic decrement and the torsion modulus... 

Fig. 9. The torsion modulus of four samples of polytetrafluoroethylene of various crystallinities from 4.2 to...

The Thermoelastic 125 (30% by weight of polystyrene) has been studied by Canter132 as a function of temperature using a specimen moulded at 150 °C. Differential scanning calorimetry has revealed the presence of two transitions. The lower transition temperature corresponds to Tg of polybutadiene chains and the upper transition temperature corresponds to Tg of styrene chains. The upper transition has also been studied by temperature dependence of the torsional modulus. 

The expansion coefficient is also similar to that of polycarbonate, and the same is true for the torsional modulus vs. temperature as shown in Figure 2. Trogamid T has a good tensile strength (ca. 500 kg.) even at temperatures as high as 100 °C. 

In addition to the characterization of polymers and liquid crystals, AW devices have been used in the characterization of layered metal films, especially superlattices [237-239]. Metal superlattice structures are of interest because they display interesting characteristics including, in some cases, superconductive properties. Superlattice metal films can exhibit a supermodulus effect (i.e., an increase in the Young s and torsional modulus) or an anomalous softening ( 35%)... 

Silverman, from Maxwell s equation ( 6.VIII E), rj=nr, where =torsional modulus and r=relaxation time (which Silverman identified with the average time of existence of an associated group of molecules), found ... 

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