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Fracture Mechanics
 
Problem 12
Failure analysis often requires a check that defects of the size found are the cause of fracture. Hence their criticality has to checked under the appropriate conditions of stress and fracture toughness. This example illustrates such a procedure for the case of pressurised cylinder. This is a typical example of the application of the 'triangle of integrity' concept (see Problem 11 theory card), but also introduces the concept of superposition of K values arising from two load types (hoop stress and internal pressure). It should take around 15 minutes to complete. A small aluminium alloy beer barrel of diameter 380 mm (D) and wall thickness 3.2 mm (t), exploded when a pressure reduction valve malfunctioned and the barrel experienced the full 42 bar gauge pressure (p) of the CO2 cylinder supplying it with gas. Failure analysis indicated that cracks had been present on the inside surface of the barrel, orientated perpendicular to the hoop stress, which had lengths (2c) in the range 75 - 125 mm and depths (a) between 1.5 - 2.5 mm. It was not recorded in the report which particular lengths related to the various crack depths, i.e. 75 mm cracks could have depths from 1.5 - 2.5 mm, as could the longer cracks. Subsequently, when litigation is under consideration for a compensation claim against the barrel/regulator manufacturers, you are requested to show that such cracks would be critical under the applied stress. Fracture toughness testing has indicated that KC = 56 MPam1/2 for this aluminium alloy. Present your findings in the form of a table for various crack depths, showing calculated geometry correction factors, actual a/t ratios and, hence, possible a/c ratios. Suitable geometry correction curves are shown below and you may take hoop stress as pD/2t. 
The stress intensity factor is found from: 
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Failure Analysis - Fracture Mechanics - Failure As A Design Criterion |