Catastrophic tearing

Rupture of a tensile test piece may be regarded as catastrophic tearing at the tip of a chance flaw. The success of the WLF reduction principle for fracture energy, G, in tearing thus implies that it will also hold for tensile rupture properties. Indeed, a/, and may be calculated from the appropriate value of G at each rate and temperature, using relations analogous to Eqs. (10.6) and (10.7). The rate of extension at the crack tip will, however, be much greater than the rate of extension of the whole test piece, and this discrepancy in rates must be taken into account (Bueche and Halpin, 1964). 

Using the principles outlined in Problem 5.16, calculate (1) the minimum value of A needed to cause crack growth over a long period in a wide sheet containing a 1 mm edge cut (take Y = 1.12 h and (2) the value of A at which a 10 mm central cut in a sheet of the same rubber causes catastrophic tearing. 

In TPE, the hard domains can act both as filler and intermolecular tie points thus, the toughness results from the inhibition of catastrophic failure from slow crack growth. Hard domains are effective fillers above a volume fraction of 0.2 and a size <100 nm [200]. The fracture energy of TPE is characteristic of the materials and independent of the test methods as observed for rubbers. It is, however, not a single-valued property and depends on the rate of tearing and test temperature [201]. The stress-strain properties of most TPEs have been described by the empirical Mooney-Rivlin equation... 

What is certain is that the initiation and propagation of a tear is a real and very important factor in the failure of rubber products, being involved in fatigue and abrasion processes as well as the catastrophic growth of a cut on the application of a stress. There is, therefore, considerable interest in the tearing resistance of rubbers. What is uncertain is how tear resistance should be measured and the results interpreted. 

If conditions of service are such that there is a probability of objects being present with sufficient force behind them to cause cutting even in high friction conditions, it might be argued that cuts are to be expected and it is resistance to catastrophic propagation of these cuts which is of importance and, hence, the appropriate test is one for tear strength. 

Scenarios— for each chenucal/mode of transport, three release sizes will be analyzed for a breach of the transportation container small hole (i.e., shearing of a valve coimection), tear (i.e., punctnre of the container), and catastrophic failure (i.e., large breach of the container), and are designated as small, medium, and large releases during the analysis... 

Distinction can be made between the force to initiate a tear and the force to propagate a tear. Both are important, as even when a tear has started, for example because of an accidental cut. the resistance to propagation will determine whether the damage becomes catastrophic. The discontinuity at which a stress concentration is produced is formed either by a cut, a sharp reentry angle, or both. Most. standard test pieces involve an artificially introduced cut, and only in a method with a sharp angle and no cut would any measure of tear initiation force be possible. 

Thick-layer elastic-bonded joints first yield before they tear when subjected to peeling forces, allowing the load to be distributed over a wider area. Consequently, the stresses within the bonded materials are kept at a relatively low level. The high tear propagation strength of polyurethanes - even after tear initiation - usually prevents sudden and catastrophic failure of the joint. This yielding behaviour means that damaged adhesive joints can often be identified and repaired before... 

Rivlin and Thomas [135] found that two characteristic tearing energies could be defined, one for very slow rates of tearing (r = 37kJm ) and one for catastrophic growth (T = 130 kJm ), and that both of these quantities were independent of the shape of the test piece. 

Extremely radioactive substances external to our bodies may also pose a threat. However, the danger is often overstated in the popular press, and most people are misinformed about the risks. Perhaps our inability to see radiation heightens our fears about it. The thought of an invisible ray of particles tearing away at our bodies without detection is frightful. However, barring catastrophic circumstances, such as detonation of a nuclear bomb or direct exposure to the core of a nuclear reactor, the dangers of low-level radioactive substances external to our bodies are minimal-unless they work their way into our bodies. 

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