Shear modulus of the elastomer

In this equation G = NksT represents the shear modulus of the elastomer, as will be confirmed in Problem 3.1 solved at the end of this chapter. 

Since for an incompressible material E = 3G (see Chapter 4), it can be asserted that the quantity NkgT of Eq. (3.33) coincides with the shear modulus of the elastomer. 

Viscoelastics Certain silicone elastomers undergo changes in shear modulus under the influence of electric fields, which might be useful in active mechanical damping applications. 

The network from system 3 is distinct from the rest, being a glass at room temperature and also having a rubbery shear modulus near the value expected on the basis of G°. Possible reasons for this high value of G/G° follow those discussed previously with reference to Mc/Mc and Figure 9. The more flexible chains of the aliphatic systems give lower values of Tg, resulting in elastomers at room temperature. 

The equilibrium shear modulus of two similar polyurethane elastomers is shown to depend on both the concentration of elastically active chains, vc, and topological interactions between such chains (trapped entanglements). The elastomers were carefully prepared in different ways from the same amounts of toluene-2,4-diisocyanate, a polypropylene oxide) (PPO) triol, a dihydroxy-terminated PPO, and a monohydroxy PPO in small amount. Provided the network junctions do not fluctuate significantly, the modulus of both elastomers can be expressed as c( 1 + ve/vc)RT, the average value of vth>c being 0.61. The quantity vc equals TeG ax/RT, where TeG ax is the contribution of the topological interactions to the modulus. Both vc and Te were calculated from the sol fraction and the initial formulation. Discussed briefly is the dependence of the ultimate tensile properties on extension rate. 

Another important point is the question whether static offsets have an influence on strain amplitude sweeps. Shearing data show that this seems not to be the case as detailed studied in [26] where shear rates do not exceed 100 %.However, different tests with low dynamic amplitudes and for different carbon black filled rubbers show pronounced effects of tensile or compressive pre-strain [ 14,28,29]. Unfortunately, no analysis of the presence of harmonics has been performed. The tests indicate that the storage (low dynamic amplitude) modulus E of all filled vulcanizates decreases with increasing static deformation up to a certain value of stretch ratio A, say A, above which E increases rapidly with further increase of A. The amount of filler in the sample has a marked effect on the rate of initial decrease and on the steady increase in E at higher strain. The initial decrease in E with progressive increase in static strain can be attributed to the disruption of the filler network, whereas the steady increase in E at higher extensions (A 1.2. .. 2.0 depending on temperature, frequency, dynamic strain amplitude) has been explained from the limited extensibility of the elastomer chain [30]. 

The equilibrium small-strain elastic behavior of an "incompressible" rubbery network polymer can be specified by a single number—either the shear modulus or the Young s modulus (which for an incompressible elastomer is equal to 3. This modulus being known, the stress-strain behavior in uniaxial tension, biaxial tension, shear, or compression can be calculated in a simple manner. (If compressibility is taken into account, two moduli are required and the bulk modulus. ) The relation between elastic properties and molecular architecture becomes a simple relation between two numbers the shear modulus and the cross-link density (or the... 

The purpose of our study was a rheological evaluation of the effect of composition on the properties of ABS resins in the molten state. Steady-state viscosity was determined over a wide range of temperatures and shear rates. The shear modulus in the molten state was determined by measurement of the diameter of the extrudate. ABS resins in the molten state behaved as an amorphous homophase polymer. The effect of the elastomer phase on the viscoelastic properties which characterize the behavior of the continuous matrix, i.e. monomer friction coefficient and molecular weight between entanglements (Me), was calculated by the application of the molecular theories. The significance of these properties in heterophase systems is discussed. 

Mayer, B. P. Reimer, J. A. Maxwell, R. S., A Methodology for the Indirect Determination and Spatial Resolution of Shear Modulus of PDMS-SUica Elastomers. Macromolecules 2008,41,1323-1327. 

Jancar et al. (154) attempted to calculate the effect of a soft interphase on the stress field around and in the platelet shaped and fibrous inclusions of small aspect ratio. Because of the presence of a shear component of the stress in the interphase, a transfer of a portion of the load from the matrix to the core-shell inclusion is possible, even when the interphase layer has modulus of elasticity substantially lower than the matrix. At least five to six times thicker soft interphase compared with spherical inclusion is necessary to reduce the reinforcing efficiency of platelets with aspect ratio of 5 to a negligible value. Above the elastomer interphase volume fraction equal to about 12 vol% of the inclusions, the elastic modulus of the complex core-shell inclusion equals that of the PP matrix. 

Although constituent elastomer has historically been specified by durometer hardness, shear modulus is the most important physical property of the elastomer for purposes of bearing design. Research has concluded that shear modulus may vary significantly among compounds of the same hardness. Accordingly, shear modulus shall preferably be specified without reference to durometer hardness. 

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