Modulus reduction factor

The effect of polymer-filler interaction on solvent swelling and dynamic mechanical properties of the sol-gel-derived acrylic rubber (ACM)/silica, epoxi-dized natural rubber (ENR)/silica, and polyvinyl alcohol (PVA)/silica hybrid nanocomposites was described by Bandyopadhyay et al. [27]. Theoretical delineation of the reinforcing mechanism of polymer-layered silicate nanocomposites has been attempted by some authors while studying the micromechanics of the intercalated or exfoliated PNCs [28-31]. Wu et al. [32] verified the modulus reinforcement of rubber/clay nanocomposites using composite theories based on Guth, Halpin-Tsai, and the modified Halpin-Tsai equations. On introduction of a modulus reduction factor (MRF) for the platelet-like fillers, the predicted moduli were found to be closer to the experimental measurements. 

As a matter of fact, 2-D disk-like clay platelets can make less contribution to modulus than 1-D fiber-like inclusion. A modulus reduction factor (MRF) [51] is introduced to modify the Halpiii-Tsai model as... 

Dow and Rosen s results are plotted in another form, composite material strain at buckling versus fiber-volume fraction, in Figure 3-62. These results are Equation (3.137) for two values of the ratio of fiber Young s moduius to matrix shear modulus (Ef/Gm) at a matrix Poisson s ratio of. 25. As in the previous form of Dow and Rosen s results, the shear mode governs the composite material behavior for a wide range of fiber-volume fractions. Moreover, note that a factor of 2 change in the ratio Ef/G causes a factor of 2 change in the maximum composite material compressive strain. Thus, the importance of the matrix shear modulus reduction due to inelastic deformation is quite evident. 

In this work, we have investigated one aspect of this problem i.e. the effects of adding two types of particulate elastomeric additives and of filler content on two recognized stress factors (coefficient of thermal expansion and modulus) of a model molding compound. From this work, we have concluded that particulate elastomer additives can not only lower stress by modulus reduction but also by CTE reduction and possibly by reduced dimensional changes when the part cools from the molding temperature. 

Figure 9.12 Stress reduction factor as a function of non-dimensional time for various values of Biot s modulus, /3.

For the geotextile to provide an effective reinforcement function, it should have not only a high tensile strength, but also a high tensile modulus so that its resistance to tensile loads generated within the soil occurs at sufficiently small strains to prevent excessive movement of the reinforced soil structure. It is self-evident that decreases in these properties with time (i.e. creep behaviour) must be low, and that the polymers used should have resistance to degradation by the soil. An estimate of the anticipated reduction in strength can be determined from an analysis of creep strain versus time plots for various stress levels and a suitable reduction factor applied. 

Table 1.33 Reduction factors for strength, stiffness (Young s modulus) and ultimate strain under media contact for GF-UP and GF-VE...

In describing measurements of complex modulus (or viscosity) at different temperatures, and in some cases at different polymer concentrations, the variables were separated to provide the modulus as an unspecified function of reduced frequency and a frequency reduction factor as an unspecified function of temperature or concentration. This principle, discussed earlier by H, Leaderman... 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

The effect of strain amplitude is most pronounced in compounds containing reinforcing fillers and can result in a reduction in shear modulus of as much as a factor of 4 when going from a very small strain to about 10%. This is due to breakdown of filler structure which is associated with energy losses that cause a peak in the tan8 value. It was because of this that earlier British and international standards called for tests to be made at 2 and 10% shear strain, a sensible recommendation that has been overlooked in the present version. Turner6 produces an interesting model based on frictional elements to explain this behaviour. 

The effectiveness factor versus the Weisz modulus according to Kao and Satterfield [61] is shown in Fig. 21 for C = 0.5 and different values of B. From this diagram, a similar behavior is seen as in the case of a simple, first order, reversible reaction (see Fig. 18) with decreasing value of B, the effectiveness factor is reduced. A decline of the effectiveness factor is also observed for a rise of the parameter C, which corresponds to a shift towards the chemical equilibrium, and hence to a reduction of the net reaction rate [91]. 

Figure 2. Viscoelastic master curves represented on reduced temperature nomograph. Key solid symbols, modulus values and open symbols, loss tangent values. Insert at upper left shows the shift factor function, aT, used for data reduction.

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