Shear modulus/strength

Property Density kgm Shear Shear modulus strength Resistance to smoke and flame LOI Water absorption % Form Ability Maximum Temperature of use °C... 

Young s Modulus Transverse Rupture Vickers Hardness of Elasticity Shear Modulus Strength... 

Superabsorbents. Water-sweUable polymers are used extensively in consumer articles and for industrial appUcations. Most of these polymers are cross-linked acryUc copolymers of metal salts of acryUc acid and acrylamide or other monomers such as 2-acrylamido-2-methylpropanesulfonic acid. These hydrogel forming systems can have high gel strength as measured by the shear modulus (134). Sometimes inorganic water-insoluble powder is blended with the polymer to increase gel strength (135). Patents describe processes for making cross-linked polyurethane foams which contain superabsorbent polymers (136,137). 

Accordingly, we have supposedly found the shear modulus G.,2. However, a relationship such as Equation (2.107) does not exist for strengths because strengths do not transform like stiffnesses. Thus, this experiment cannot be relied upon to determine S, the ultimate shear stress (shear strength), because a pure shear deformation mode has not been excited with accompanying failure in shear. Accordingly, other approaches to obtain S must be used. 

The continuing search to determine the shear modulus and shear strength consists of a collection of tests. Several tests are discussed because each has faults, as will be seen, and because, to some extent, there is no universal agreement on the best way to measure the shear properties. 

Another test used to determine the shear modulus and shear strength of a composite material is the sandwich cross-beam test due to Shockey and described by Waddoups [2-17]. The composite lamina... 

The shear modulus of a material can be determined by a static torsion test or by a dynamic test employing a torsional pendulum or an oscillatory rheometer. The maximum short-term shear stress (strength) of a material can also be determined from a punch shear test. 

Unlike the methods for tensile, flexural, or compressive testing, the typical procedure used for determining shear properties is intended only to determine the shear strength. It is not the shear modulus of a material that will be subjected to the usual type of... 

TDI isomers, 210 Tear strength tests, 242-243 TEDA. See Triethylene diamine (TEDA) Telechelic oligomers, 456, 457 copolymerization of, 453-454 Telechelics, from polybutadiene, 456-459 TEM technique, 163-164 Temperature, polyamide shear modulus and, 138. See also /3-transition temperature (7)>) Brill temperature Deblocking temperatures //-transition temperature (Ty) Glass transition temperature (7) ) Heat deflection temperature (HDT) Heat distortion temperature (HDT) High-temperature entries Low-temperature entries Melting temperature (Fm) Modulu s - temperature relationship Thermal entries Tensile strength, 3, 242 TEOS. See Tetraethoxysilane (TEOS)... 

Young s Modulus of Elasticity 620-720 GPa Shear Modulus 262 GPa Poisson s Ratio 0.18 Transverse Rupture Strength 550 MPa... 

In case of copper some rheological experiments carried out at a given polymer concentration and increasing amoimt of cations indicates that copper/pectin systems in the one-phase domain behave as a viscoelastic liquid rather than a viscoelastic solid referred to as true gel (G (co) = G, when to—>0 with Gg the equilibrium shear modulus)[35]. Despite the lack of experimental data the range in cation and polymer concentration in which true gels may be observed seemed very limited. These results corroborate the strength of the binding of copper by pectins evidenced by the properties of the phase separation curves. 

A measure of shear strength is the shear modulus. For covalent crystals this correlates quite well with hardness (Gilman, 1973). It also correlates with the hardnesses of metals (Pugh, 1954), as well as with ionic crystals (Chin, 1975). Chin has pointed out that the proportionality number (VHN/C44) depends on the bonding type. This parameter has become known as the Chin-Gilman parameter. 

Since hardness and the shear modulus are usually proportional, the factors that determine the shear moduli need to be understood. The shear moduli are functions of the local polarizability and this depends on the valence electron density, as well as the energy needed to promote a valence electron to its first excited state. The latter depends on the strength of the chemical bond between two atoms. This will be discussed in more detail in Chapter 3. 

It is very difficult to obtain values for the intrinsic hardnesses of silicate and related types of glass. Therefore, no attempts at quantitative analyses will be made here. A semi-empirical method has been proposed by Yamane and Mackenzie (1974) based on the geometric mean of bond strength relative to silica, shear modulus, and bulk modulus. For 50 silicate glasses it yields estimates within ten percent of measured values, and for a few non-silicate glasses it is quite successful, as Figure 14.2 indicates. 

Yoon assumed a constant shear modulus, r0=gyb=2g/J thus the corresponding fracture energy is, according to Eq. 21, WQ=r02/(2g). This results in the following value of the ultimate strength... 

Estimates of the ultimate shear strength r0 can be obtained from molecular mechanics calculations that are applied to perfect polymer crystals, employing accurate force fields for the secondary bonds between the chains. When the crystal structure of the polymer is known, the increase in the energy can be calculated as a function of the shear displacement of a chain. The derivative of this function is the attracting force between the chains. Its maximum value represents the breaking force, and the corresponding displacement allows the calculation of the maximum allowable shear strain. In Sect. 4 we will present a model for the dependence of the strength on time and temperature. In this model a constant shear modulus g is used, thus r0=gyb. 

Estimates of the Shear Modulus, Shear Strength and Ultimate Strength of Cellulose II, PpPTA and PIPD-HT Fibres... 

In the macrocomposite model it is assumed that the load transfer between the rod and the matrix is brought about by shear stresses in the matrix-fibre interface [35]. When the interfacial shear stress exceeds a critical value r0, the rod debonds from the matrix and the composite fails under tension. The important parameters in this model are the aspect ratio of the rod, the ratio between the shear modulus of the matrix and the tensile modulus of the rod, the volume fraction of rods, and the critical shear stress. As the chains are assumed to have an infinite tensile strength, the tensile fracture of the fibres is not caused by the breaking of the chains, but only by exceeding a critical shear stress. Furthermore, it should be realised that the theory is approximate, because the stress transfer across the chain ends and the stress concentrations are neglected. These effects will be unimportant for an aspect ratio of the rod Lld> 10 [35]. 

Equation 116 was also derived in Sect. 2. It shows that the fibre strength according to the shear failure criterion increases with improved alignment of the chains, and that it is proportional to the shear modulus g. 

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