Threshold Fracture of Networks
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THRESHOLD FRACTURE OF NETWORKS
K. A. Mazich and C. A. Smith Ford Motor Co., PO Box 2053 Drop 3198, Dearborn, HI 48121
ABSTRACT We discuss the threshold fracture energy, CO, of networks over a wide range of cross-link density. C, for networks with an average number of main chain steps, rc, that compare favorably with the entanglement spacing, rc, follow the 1/2 power law, Co - rIf. Two views of molecular fracture, one a chain-breaking mechanism and the other a suction process, produce the 1/2 power law. For lightly cross-linked networks (rc >> re), Go appears to decrease with increasing rc. Trapped entanglements limit the extensibility and fracture energy of these networks. Consideration of rupture of trapped entangled chains gives Go -rc1fl; this form agrees reasonably well with data at high rc.
INTRODUCTION Cohesive failure of elastomers represents a class of polymer-polymer junctions that has steadily attracted much theoretical and experimental interest. Failure forms an important subject with broad technical significance and many interesting features. These features include the comparatively large strains at the junction and the imminent viscoelastic processes around the junction. These processes are comparable to linear viscoelastic properties evident at small strains, and the rationing of energy among these mechanisms depends on the crack velocity and temperature (1,2). Non-linear stress in strain and viscous processes in elastomers render local stress and strain fields intractable with linear elastic fracture mechanics. Consequently, failure in elastomers is almost always treated with energy balance methods, where the fracture energy, G, provides a quantitative measure of toughness (3). Fracture energy is attributable to the energy needed to rupture some fraction of the covalent bonds in the network and the energy dissipated through viscous processes in the crack tip region. These energy requirements exceed the weak secondary forces of the thermodynamic surface energy in Griffith's original theory (4) by several orders of magnitude. In principle, energy methods allow us to relate observations of crack growth to C without any specific information of failure processes at the crack tip. At fracture initiation, the net release of stored energy in the bulk material (expressed by G) is countered by the resistance, R (see reference 5, for example). R depends on local processes of dissipation. Frictional resistance of network imperfections (such as dangling ends and sol fraction, on a large scale) or monomeric units (at small scale) generally provides the majority of resistance in the crack tip region. This situation is shown in Figure 1, where several network imperfections are being pulled through the surrounding mesh of network chains in front of the crack and others are unloaded behind the crack tip. The energy dissipated by these processes and the size of the crack tip region depends on the crack velocity and the temperature (6); the temperature dependence may follow typical superposition arguments (2).
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