Mooney-Rivlin representation

Number-average molecular weights are Mn = 660 and 18,500 g/ mol, respectively (15,). Measurements were carried out on the unswollen networks, in elongation at 25°C. Data plotted as suggested by Mooney-Rivlin representation of reduced stress or modulus (Eq. 2). Short extensions of the linear portions of the isotherms locate the values of a at which upturn in [/ ] first becomes discernible. Linear portions of the isotherms were located by least-squares analysis. Each curve is labelled with mol percent of short chains in network structure. Vertical dotted lines indicate rupture points. Key O, results obtained using a series of increasing values of elongation 0, results obtained out of sequence to test for reversibility. 

The stress-strain curve for unfilled NR exhibits a large increase in stress at higher deformations. NR displays, due to its uniform microstructure, a very unique important characteristic, that is, the ability to crystallise under strain, a phenomenon known as strain-induced crystallization. This phenomenon is responsible for the large and abrupt increase in the reduced stress observed at higher deformation corresponding, in fact, to a self-toughening of the elastomer because the crystallites act as additional cross-links in the network. This process can be better visualized by using a Mooney-Rivlin representation, based on the so-called Mooney-Rivlin equation ... 

In order to characterize the deviation from the ideal phantom network behavior, the Mooney-Rivlin representation is often used ... 

Fig. 12 Result of mechanical measurement performed on a magnetoelast filled with randomly distributed carbonyl iron. The concentrations of the filler particles are indicated on the figure. The cross-linker content was 3 wt % in each case. Neo-Hookean (left figure) and Mooney-Rivlin representations (rightfigure) are plotted...

Schematic stress-strain isotherms in elongation for a unimodal elastomer in the Mooney-Rivlin representation of modulus against reciprocal elongation. The isotherms are represented as the dependence of the reduced stress ([f ] = f /(a - on reciprocal elongation. (f = f/A, f = elastic force, A = undeformed area, a = elongation). The top three are for a crystallizable network curve A for a relatively low temperature, B for an increased temperature, and C for the introduction of a swelling diluent. Isotherm D is for an unswollen unimodal network that is inherently noncrystallizable.

Fig. 7.21. (a) Force against relative extension for a crosslinked elastomer, (b) Mooney-Rivlin representation... 

In order to test the applicability of Equations [5.1] and [5.5] for gels filled with magnetic particles, a Mooney-Rivlin representation of experimental data obtained in the absence of external magnetic field is shown in Fig. 5.11. 

Stress-strain measurements for PDMS samples filled with randomly distributed carbonyl iron particles, (a) On the basis of statistical theory of rubber elasticity and (b) Mooney-Rivlin representation of experimental data. Symbols represent different amounts of iron particles as indicated in the figure. 

Fig. 32. Stress-strain and birefringence-strain data of a chemically crosslinked polyurethane rubber in Mooney-Rivlin type representations (Eq. IV-26a and Eq. IV-29). Data reported by Blokland (14)...

Fig. 22.13 Reduced stress representation of the stress-strain curves for the four adhesives. The broken line is an illustrative fit of the data with the Mooney-Rivlin model.

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 3.410. Graphical representation of Mooney-Rivlin equation (244) for the unreinforced and reinforced with 30% black carbon ethylene-propylene rubber at 30°C (o in dyne/om ) [1198].

Figure 3.411. Graphical representation of the Mooney-Rivlin equation for the ethylene-propylene rubber swollen in benzene [1198].

Comparison with values of and of the NAST model described earlier supports this hypothesis [36]. However, unlike the NAST model, the Mooney-Rivlin model fails to predict compression data as the linearity shown in Figure 9.21 continues for a > 1, whereas the experimental data show a maximum and a decrease in the function plotted in Figure 9.21. There have been many other constitutive relations for rubbers based on different representation of the strain energy function... 

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