Crack tying stress

Figure 8.2 5. (a) Interface crack with strings tying the faces together (b) stress required to break the tied joint is Griffith stress plus the tying stress. 

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... 

The overload mechanism of failure was confirmed by field measurement of stress on cargo ships, which showed cracking. A typical residual stress pattern obtained on the tie-down sockets installed on the ships is shown in Figure 2.28. 

Polymers having broad MW distributions not only exhibit improved polymer molding, but the MW breadth can also increase some of the polymer physical characteristics, including impact and tear resistance, toughness, creep and hoop stress resistance in pipe, and especially resistance to chemical attack, or stress crack (ESCR). These improved properties result because a broad MW distribution usually contains more of the long chains that can act as tie molecules to connect the crystalline lamellae (Figure 42). 

The report of the inquiry [111] criticised the design and fabrication of the alterations made to the original pontoon. The actual cause of the accident was the failure of some tie bars in the detail around the jacking points. The failure was due to brittle fracture which initiated from severe notches such as a small radius curve at the fillet between the spade end and the shank of the tie bar. Weld defects and fatigue cracks were also present in tie bars subsequently recovered from the sea bed. The tie bars had been flame cut to shape and had weld repairs visible to the eye. There had been no post welding heat treatment of the steel. The steel complied with the original specification but tests showed low Charpy V notch impact values. Photo elastic tests indicated a stress concentration factor of 7 at the fillet between the spade end and the shank. The fracture was initiated in the opinion of the inquiry tribunal by the low ambient temperature of around 3°C. 

The stress through most of the craze has a constant value acrazeJ this crazing stress is essentially a material constant for a given type of polymer. This stress is carried primarily by the main craze fibrils which run perpendicular to the craze/bulk interface. However, there are in addition to the main craze fibrils cross-tie fibrils, which connect the main craze fibrils laterally. These permit some transfer of stress in the lateral direction (see figure 7.7), with the result that there is a stress concentration at the crack tip. It is this stress concentration that causes the breakdown of the last load-bearing fibril and the growth of the crack. At the crudest level we can model the craze as an elastic continuum and write the stress as a function of the distance x from the end of the crack as... 

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