Mooney-Rivlin empirical relationship

The two network precursors and solvent (if present) were combined with 20 ppm catalyst and reacted under argon at 75°C to produce the desired networks. The sol fractions, ws, and equilibrium swelling ratio In benzene, V2m, of these networks were determined according to established procedures ( 1, 4. Equilibrium tensile stress-strain Isotherms were obtained at 25 C on dumbbell shaped specimens according to procedures described elsewhere (1, 4). The data were well correlated by linear regression to the empirical Mooney-Rivlin (6 ) relationship. The tensile behavior of the networks formed In solution was measured both on networks with the solvent present and on networks from which the oligomeric PEMS had been extracted. 

Overall cross-linking density data (t>t) of sulfur vulcanized (V)-EPTM and ENB-EPDM were obtained from stress-strain measurements performed under equilibrium conditions and using the Mooney-Rivlin and Guth-Einstein equations. Chemical cross-linking density data (pc) were obtained through the empirical relationship found by... 

Figure 2. The results of Figure 1 represented as suggested by the semi-empirical Mooney-Rivlin relationship (8,28-30) which usually gives a modulus Lf D decreasing linearly with decreasing a (28).

Considerably better agreement with the observed stress-strain relationships has been obtained through the use of empirical equations first proposed by Mooney and subsequently generalized by Rivlin. The latter showed, solely on the basis of required symmetry conditions and independently of any hypothesis as to the nature of the elastic body, that the stored energy associated with a deformation described by ax ay, az at constant volume (i.e., with axayaz l) must be a function of two quantities (q +q +q ) and (l/a +l/ay+l/ag). The simplest acceptable function of these two quantities can be written... 

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