Torsional modulus of elasticity

The apparent torsional modulus of elasticity is given by the expression... 

Torsional modulus of elasticity Also called modulus of rigidity. It is approximately equal to the shear modulus. 

Flexibility Stresses Bending and torsional stresses shall be computed using the as-instaUed modulus of elasticity E and then combined in accordance with Eq. (10-100) to determine the computed displacement stress range Sg, which shah not exceed the allowable stress range [Eqs. (10-93) and (10-94).]... 

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 ... 

The hardness of a polymer can also be estimated from the modulus of elasticity E (high E modulus indicates high hardness). The advantage here is that every region of elasticity and every degree of hardness can be detected with a single kind of measurement (determination of stress-strain-behavior or torsional oscillation). 

For an ideal solid, Hooke s law holds the stress, cr, applied is proportional to the deformation, e, and the proportionality constant is the modulus of elasticity E, so a = E e. Besides E also other quantities play a role, such as the shear modulus, G, in a shearing deformation or torsion, which is related to E. For the sake of simplicity we shall mainly use as a representative quantity for the elastic stiffness in any geometry of loading. 

Under conditions of small damping, the elastic (storage) modulus (G ) equals the torsional modulus of the rod (G) and thus the equation for simple harmonic motion may be rewritten ... 

Elastomers are cross-linked macromolecules above the glass transition temperature. The cross-link density is the fundamental engineering quantity which, for instance, determines the modulus of elasticity. Usually, it is measured during vulcanization of well-defined rubber samples in a vulcameter by the moment necessary to perform a given torsional shear of the test sample. Swelling experiments can be performed alternatively, but are problematic for filled elastomers. Such measurements are based on the assumption that the measured quantity does not vary over the sample volume. Inhomogeneous cross-link densities can be determined from the surface hardness, but volumetric resolution is achieved by conventional methods only after cutting the sample. 

The Shear Modulus of Elasticity is derived from the torsion of a cylindrical test piece. Its symbol is G. 

The workhorse of the RTS industry is TS polyester (also called polyester-TS) with glass fiber. The fiber reinforcement may be in the form of chopped fibers, porous nonwoven mats, woven fabrics, or continuous fibers. The combination of plastics and reinforcements results in versatile materials with unusual characteristics. The reinforcement adds strength and toughness to inherent weather resistance, moldability, and colorability. Thus RTSs are used because of their increased tensile, flexural, torsional, and impact strengths increased modulus of elasticity increased creep resistance reduced coefficient of thermal expansion increased thermal conductivity and, in many cases, lower costs. 

In the swelled state, the physical properties of the polymers are altered. For example, their volume increases, the cooling rate is increased, transition intervals are reduced (plasticization), and the modulus of elasticity and modulus of torsion are changed. 

Modulus of elasticity Shear modulus, torsional modulus Torsional modulus... 

Modulus of elasticity, tension, psi X 10. Modulus of rigidity, torsion, psi X 10. . Dielectric strength, step-hy-step, volts/mil... 

AST FAAR supplies a torsion test instrument for the measurement of the apparent modulus of elasticity versus temperature of plastics and elastomers (Table 18.2), according to the following specifications ASTM D1043 [21], DIN 53477 [22], ISO 498 [55], and BS 2782 Method 156 [3]. 

It is thus possible to measure accurately the apparent modulus of elasticity of specimens obtained from a wide range of materials (the modulus is, in this case, defined as apparent as it is obtained by measuring the angular torsion of the specimens under test). 

An adhesive is often subjected to a rupture test, in which the stress response of the material is measured in order to determine the utility of the adhesive. In such a test, one or a combination of several different modes of deformation—shear, extension, compression, torsion, or flexure—can be important. While one of these modes may resemble the application of interest more closely than the other modes, the knowledge obtained regarding material behavior from the different tests is similar in some cases, the information is the same. In other words, the information gathered in one experiment can often be predicted from the results of the other experiments. Although this is a gross simplification, one can, for purposes of illustration, cite the behavior of linearly elastic solids and purely viscous Newtonian liquids. While the former material is characterized by its elastic modulus, the behavior of the latter is determined by the (shear) viscosity. In the case of incompressible Hookean solids, the modulus of elasticity is three times the shear modulus. (See also Chapter 2 by Krieger.)... 

Elasticity, modulus of The modulus of elasticity is the ratio of stress to strain when a material is deformed elastically. Young s modulus applies to tensile forces. Compression, torsion strains, etc. also have elastic moduli. 

The above measurement approach illustrates the influence of heterogeneity and anisotropy on moduli but is not very practical. A sonic method of measuring properties, though not as precise as tensile or torsion tests, is often used and is based upon the fact that the speed of sound, v, in a medium is related to its modulus of elasticity, E, and density, p, such that (Kolsky, 1963),... 

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