Mooney Rivlin plot for

Figure 8. Mooney-Rivlin plots for strain dependent measurements at 298 K. Key A, PDMS-BI , PDMS-B2 X, PDMS-B3 O, PDMS-B5 , PDMS-B6 , PDMS-B7 V, PDMS-B8 A, PDMS-B9 PDMS-B10.

Figure 28 41 depicts the isochronal Mooney-Rivlin plots for SBR-1, where the extrapolated values of bW/bli and X lbW/bI2 are represented by solid lines and the sum of them by broken lines. As above, these sums are equivalent to the Mooney-Rivlin plot of uniaxial data. We again find that the slope of the sum curves depends mainly on the Xj dependence of bW/dli and therefore the slope is not equal to... 

Fig. 7.2 Mooney-Rivlin plot for the Slip-Link model...

Figure 12.10. Mooney-Rivlin plots for pureNR and 1 phr MWNTs/NR composite.

Figure 7.19. Mooney-Rivlin plot for 7S and IIS soy fractions at 30% moisture content (Copyright 1998 from Understanding phase transitions and ehemieal complexing reactions in 7S and 1 IS soy protein fractions by Morales-Diaz and Kokini (In Phase/State Transitions in Foods, Rao and Hartel (Eds.)). Reproduced by permission of Routledge/Taylor Francis Group, LLC.)...

Figure 3.12 Mooney-Rivlin plots for various rubbers in uniaxial extension (8). (From Ref. 2.)...

Mooney-Rivlin plots for uniaxial tension data on three networks prepared from radiation-crosslinking a linear polybutadiene melt with------------------... 

Figure 9.18 Mooney-Rivlin plot for sulfur-vulcanized natural rubber. Solid line, equation (9.48) dotted line, equation (9.63).

Figure 11. Mooney-Rivlin plot of stress-strain data (32) for three triol-based polyester networks prepared from sebacoyl chloride and LHT240 at various initial dilutions in diglyme as solvent. Conditions P100 is 0% solvent P130 is 30% solvent PI 65 is 65% solvent.

Fig. 49 Mooney-Rivlin plots of reduced stress ((7red) against deformation ( ) for (a) CR gum and PTFEokGy—CR at 10, 20, and 30 phr loading and (b) comparison of PTFE500kGy-CR with PTFEokGy CR and PTEE20kGy-CR. C is the contribution to ared arising from chemical crosslinking...

Fig. 27. Mooney-Rivlin plot of uniaxial extension data for NR (A) compared with the sum of dWIdli and 3W/3/2, where bW/blf were extrapolated for uniaxial extension from biaxial data. The contributions of bW/bli and l dW/bI2 to their sum are also shown...

Fig. 21. Mooney-Rivlin plots (Eq. IV-1) for a chemically crosslinked polyurethane rubber (from polyoxypropyleneglycol, toluene diisocyanate and trimethylol propane). Note the differences in Cx and C2 values in extension and compression...

Figyre 3.16 Mooney-Rivlin plots [Eq. (3.38)] showing the effect of the temperature on stress-strain isotherms for model PDMS networks (15,16). The filled circles represent the reversibility of the elastic measurements, and the vertical lines locate the fracture points. (From Ref. 15.)... 

For classical models, the Mooney-Rivlin coefficients are 2Ci=G and 2 = 0. However, experimental data plotted in Fig. 7.13, in the form suggested by Eq. (7.59), show that C2>0. In this Mooney-Rivlin plot, the stress divided by the prediction of the classical models is plotted as a function of the reciprocal deformation 1/A. The predictions of the affine, phantom, and Edwards tube network models correspond to horizontal lines on the Mooney-Rivlin plot (C2 = 0). Experimental data on uniaxial... 

Figure 6-6. Simulated Mooney-Rivlin plot, equation (6-82), for C2/C = 2. Solid line is the undistorted response of the material "data" are the results with a 1% (standard deviation) random error incorporated into both the force and length "measurements."...

The data for this figure are provided above and in the CD in file NR-Mod.TXT. Using a spreadsheet, generate a Mooney-Rivlin plot and calculate C, and C2. In addition, fit the data to the equivalent multivariant linear form... 

Figure 5. Mooney-Rivlin plots of stress-strain data(lO) for two tetrol-based polyurethane networks from system 5 of Figures 2 and 4, prepared at various dilutions in nitrobenzene as solvent. Networks swollen in nitrobenzene at 4QOC...

Equation (29.7) makes obvious the reasons for the representation of experimental data in the so-called Mooney-Rivlin plot. If the material has a Mooney-Rivlin strain energy density function then a plot of (cn — straight line with the slope and intercept at A = 1 determining 2C2 and (2Ci -I- 2C2), respectively. 

FIGURE 29.2. Comparison of typical stress-strain data for PDMS rubber [39] in a Mooney-Rivlin plot with Neo-Hookean and Mooney-Rivlin strain energy function descriptions. (See text for discussion). 

An alternative model which also describes stress-strain data for larger deformation is presented by the Mooney-Rivlin equation [40, 41], The equation describes the rubber elasticity of a polymer network on the basis that the elastomeric sample is incompressible and isotropic in its unstrained state and that the sample behaves as Hookean solid in simple shear. In a Mooney-Rivlin plot of a uniaxial deformation, the experimental measured stress cr, divided by a factor derived from classical models, is plotted as function of the reciprocal deformation 1/A ... 

The predictions of the classical models of rubber elasticity correspond to horizontal lines in a Mooney-Rivlin plot (C2 = 0). Plots for experimental data show a positive slope (C2 > 0). This indicates a stress softening with increasing deformation (as the reciprocal deformation 1 /X decreases). A comparison of (4) and (6) shows that, for the classical models, the Mooney-Rivlin coefficient 2Ci, corresponds to the shear modulus G given by (5), and the Mooney-Rivlin plot presents another method to determine crosslink density Vc or the average molecular mass of a network chain Me ... 

The copolymers listed in Table V were cured in the form of 0.01" thick films. The cured polymer was cut into strips one inch wide, and these strips were used for subsequent testing, direct measurement was made of the crosslink density of these polymers, but a relative value could be inferred from Mooney-Rivlin plots of the stress-strain data. 

Values of Ye calculated from the modified Ploiy-Buhner equation were in good agreement with those from the ultimate property data and with values obtained by compressive stress-strain measurements in the swollen state, as measured in several solvents. Table III gives the results and the solubility parameter for the solvents used. These values are apparent values if C2 in the Mooney-Rivlin plot is not zero or close to it. However, if C 0, then Ye will be independent of V2 (actually, of V2 V3) and an appropriate plot of the data confirms the near zero value, in agreenent with Figure 13. 

---