Strengths and extensibilities, threshold

Nevertheless, they are much larger than would be expected on the basis of C-C bond strengths alone. For example, about 2 x 10 molecules cross a randomly chosen fracture plane having an area of 1 m, and the dissociation energy of the C-C bond is about 5 x 10 J. Thus, a fracture energy of only about 1 J/m would be expected on this basis, instead of the observed value of about 50 J/m. This large discrepancy has been attributed by Lake and Thomas 

Tearing under shear stresses (schematic). (From Knauss (1970) and Ahagon et al. 

FIGURE 10.7 Expansion of a cavity under a triaxial tension. 

FIGURE 10.10 Cavitation near a rigid inclusion (schematic). 

Two other features of molecular networks can be taken into account, at least in an approximate way the presence of physical entanglements between chains, at a characteristic spacing along each chain of molecular weight, M, and the 

Low values of fracture energy, only about one order of magnitude greater than the threshold level, have been obtained by measuring the resistance of rubber to cutting with a sharp knife, a razor blade. Frictional effects were 

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The strength and extensibility of a noncrystallizable elastomer depend on its viscoelastic properties (28,29), even when the stress remains in equilibrium with the strain until macroscopic fracture occurs. In theory, such elastomers have a time- or rate-independent strength and ultimate elongation, but such threshold quantities apparently have not been measured, though rough estimates have been made (28,30). 

The threshold tear strength of elastomeric molecular networks does not appear to depend strongly, if at all, upon the uniformify of network strand lengths. It is found to be proportional to Mc where Mc is the mean molecular weight of the strands, in accordance with the theory of Lake and Thomas (3). However, it is considerably smaller for Si-0 networks than for C-C networks at equal Mc values. This is attributed to differences in strand length and extensibility. 

Data are presented which illustrate that the tensile strength and elongation-at-break depend significantly on the extension rate even when the stress remains in equilibrium with the strain prior to fracture. A crude estimate was made of the threshold (lowest possible) values of the true stress-at-break and the elongation-at-break for the TIPA elastomer. The estimated quantities are about 26% less than those found at an extension rate of about 0.01 min-1 at 30°C. 

The scaling behaviour of the most probable fracture strength (jf, expressed by the fracture exponent Tf near the percolation threshold, has been investigated extensively. The theoretical results compare well with those observed experimentally, and in computer simulations. Although considerable progress has been made here, experimental results for continuum percolation are scarce, and more investigations are clearly necessary. 

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