Tear energy

To make the flaw grow, say by 1 mm, we have to tear the rubber to create 1 mm of new crack surface, and this consumes energy the tear energy of the rubber per unit area X the area of surface torn. If the work done by the gas pressure inside the balloon, plus the release of elastic energy from the membrane itself, is less than this energy the tearing simply cannot take place - it would infringe the laws of thermodynamics. 

All sorts of accidents (the sudden collapsing of bridges, sudden explosion of steam boilers) have occurred - and still do - due to this effect. In all cases, the critical stress - above which enough energy is available to provide the tearing energy needed to... 

Figure 12 Three-dimensional plot of the tear energy of a viscoelastic composite as a function of temp, and strain rate. Source Ref. 39.

Effect of Tear Rate and Test Temperature on Tear Energy Gc. 13... 

Values of tear energy obtained in this way for some simple mbbery solids are discussed in Section 1.4.4, and compared with theoretical estimates for a network of long dexible molecules with C-C... 

Measurements of tear energy Gc as a function of tear rate at various temperatures are plotted in Figure... 

FIGURE 1.11 Tear energy Gc versus rate R of tear propagation for a cross-linked sheet of a high-styrene copolymer of butadiene and styrene (48% styrene Tg = —30°C). (From Gent, A.N. and Lai, S.-M., J. Polymer Sci., Part B Polymer Phys., 32, 1543, 1994. With permission.)... 

This behavior is similar to the cut growth and fatigue behavior of rubber compounds. The rate of the growth of a cut is a function of the tearing energy [38,39] which itself is proportional to the stored elastic energy density in the test piece. The exact value depends on the shape of the test piece. 

Above To there is a small region for which the cut growth rate dc/dn is proportional to the tearing energy T... 

FIGURE 26.45 Rate of cut growth dcjdn as function of the tearing energy T for a natural mbber (NR) gum compound. (From Lake, G.J. and Lindley, P.B., Rubber 146, 10, 1964.)... 

Figure 26.46 shows the cut growth rate for six polymers as gum rubbers and filled with two levels of reinforcing carbon black [40]. They aU can be represented by a power function over a considerable range of tearing energies. 

If these large energy concentrations meet a flaw in the rubber, the resulting tearing energy will increase the flaw at each pass until a rubber particle is detached. This is essentially the mechanical basis of the abrasion process. 

FIGURE 26.56 Log Abrasion loss by a blade (solid lines) and log cut growth rate (dashed hnes) of noncrystallizing rubber compounds as function of log frictional and log tearing energy, respectively isomerized natural rubber (NR), 2 styrene-butadiene rubber (SBR), and 3 acrylate-butadiene rubber (ABR). (From Champ, D.H., Southern, E., and Thomas, A.G., Advances in Polymer Friction and Wear, Lieng Huang Lee (ed.), Plenum, New York/London, 1974, p. 134.)... 

By using different loads, different tearing energies are produced. Figure 26.56 shows the results of their experiments for three gum rubbers. The solid hnes represent the abrasion per cycle and the dashed lines the rate of cut growth. 

In general, economic inefficiency in resource allocation would be the result of a divergence between private benefits or costs and social benefits or costs, i.e. the result of externalities. Private costs (or internal costs) are directly taken by the buyer. Private costs for a transport user would, for example, include expenses for wear and tear, energy cost of vehicle use, transport fares, taxes and charges, as well as welfare effects such as own time costs. 

Figure 3. Threshold tear energy T . Key O, A, , PDMS networks , A. PB networks , PI networks versus molecular weight Mc between cross-links calculated from Ct. O, , , random cross-linking A, A. trifunctional end-linking , tetrafunctional end-linking.

When the tearing (fracture) energy is measured under conditions at which energy is not dissipated in viscous processes, its value is termed the threshold tearing energy, T0 (30,31,32). If T0 for the TIPA elastomer is the same as that for a hydrocarbon elastomer whose 2Cj equals that for the... 

The tearing energy for the trouser test piece is given by ... 

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