Storage modulus strain dependence

Storage modulus MPa Depends on compounding ingredients, temperature, strain rate 0.3 (14, 23, ... 

Figure 6. Dependence of storage modulus for PMMA and EPDM on temperature at a frequency of 1Hz and a strain of 0.1%.

Now these expressions describe the frequency dependence of the stress with respect to the strain. It is normal to represent these as two moduli which determine the component of stress in phase with the applied strain (storage modulus) and the component out of phase by 90°. The functions have some identifying features. As the frequency increases, the loss modulus at first increases from zero to G/2 and then reduces to zero giving the bell-shaped curve in Figure 4.7. The maximum in the curve and crossover point between storage and loss moduli occurs at im. 

The strain dependence of the elastic storage modulus of clay-filled NBR has been measured and the results compared with those of unfilled vulcanizates. The corresponding data are shown in Fig. 19. From this figure it is revealed that there is no Payne effect, because the G values do not decrease with the increase in strain... 

Figure H3.2.4 Linear viscoelastic region as determined by the strain dependence of G (storage modulus) and G (loss modulus).

FIGURE 15. Panel a shows the strain amplitude sweep experiment on the 2D film of Ag nanopartides. The storage modulus, C p), is higher than the loss modulus, C" (O) at low strain amplitudes. Panel b shows the frequency dependence of interfacial storage, C ( ), and loss, C" (o), moduli of the film. Reproduced from ref 33. Copyright 2007 American Chemical Society. 

Fig. 32 a Time development of the small strain storage modulus of uncross-linked S-SBR composites with 50 phr N234 during heat treatment at 160 °C for various molar masses, as indicated (0.28% strain, 1 Hz), b Strain dependency of the storage modulus of the samples depicted in a after heat treatment for 60 min at 160 °C... 

Accordingly, we expect a power law behavior G,0 (O/Op)3 5 of the small strain elastic modulus for 0>0. Thereby, the exponent (3+df [j)/(3—df)w3.5 reflects the characteristic structure of the fractal heterogeneity of the filler network, i.e., the CCA-clusters. The strong dependency of G 0 on the solid fraction Op of primary aggregates reflects the effect of structure on the storage modulus. 

Fig. 42 Strain dependency of the storage modulus at 20 °C of cross-linked S-SBR- and EPDM composites filled with 50 phr N220 and graphitized N220g, respectively...

Wu et al. (73) studied the viscoelastic properties, viz. storage modulus (GO and complex viscosity (r 0 with respect to frequency (co) of PLA-carboxylic-acid-functionalized MWCNTs nanocomposites using a rheometer (HAAKE RS600, Thermo Electron Co., USA). The dynamic frequency sweep measurements were carried out at the pre-strain level of 1%. They observed that the addition of carboxylic-acid-functionalized MWCNTs weakened the dependence of G on go, especially at higher loading levels (Figure 9.12). This indicates... 

Fig. 1 a,b. Strain amplitude dependence of the complex dynamic modulus E E l i E" in the uniaxial compression mode for natural rubber samples filled with 50 phr carbon black of different grades a storage modulus E b loss modulus E". The N numbers denote various commercial blacks, EB denotes non-commercial experimental blacks. The different blacks vary in specific surface and structure. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 1 Hz, and static pre-deformation of -10 %. The x-axis is the double strain amplitude 2eo... 

Changes in mechanical properties are recorded by a piezoforce transducer which measures the power amplitude of the plates in the gaps (width = 1.45 mm) at a given frequency. The strain and frequency can be controlled in a wide range by a piezo translator. Depending on the frequency, storage modulus, loss modulus and complex viscosity can be calculated from the values of force obtained as a function of strain, frequency, and phase displacement (Eq. 2). 

The strain response can be broken down into its elemental components of stress, which are in phase or out of phase, to derive the values for G and G". The storage modulus G is the ratio of the applied stress that is in phase with the strain (8 = 0°). This means that G is an expression of the magnitude of the energy stored in the material, recoverable per deformation cycle (68). The loss modulus G" is the ratio of the applied stress that is out of phase with the strain (8 = 90°), meaning that it is a measurement of the energy lost as viscous dissipation per deformation cycle (66-68). These two moduli are dependent on the phase angle of the system and are... 

The response of unvulcanized black-filled polymers (in the rubbery zone) to oscillating shear strains (151) is characterized by a strong dependence of the dynamic storage modulus, G, on the strain amplitude or the strain work (product of stress and strain amplitudes). The same behavior is observed in cross-linked rubbers and will be discussed in more detail in connection with the dynamic response of filled networks. It is clearly established that the manyfold drop of G, which occurs between double strain amplitudes of ca. 0.001 and 0.5, is due to the breakdown of secondary (Van der Waals) filler aggregation. In fact, as Payne (102) has shown, in the limit of low strain amplitudes a storage modulus of the order of 10 dynes/cm2 is obtained with concentrated (30 parts by volume and higher) carbon black dispersions made up from low molecular liquids or polymers alike. Carbon black pastes from low molecular liquids also show a very similar functional relationship between G and the strain amplitude. At lower black concentrations the contribution due to secondary aggregation becomes much smaller and, in polymers, it is always sensitive to the state of filler dispersion. 

Fig. 14. Dependence of the storage modulus of carbon black filled butyl rubber on strain amplitude. Figures on curves are volume percentages of HAF black.

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