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# Strength of material using the Paris Law

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(See attached file for full problem description with equations and diagram)

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Practice problem for Fracture and Fatigue. Adapted from S. Suresh, Fatigue of Materials, second edition, Cambridge University Press Publishing.

Consider an aircraft fuselage, existing like a cylindrical pressure vessel. Every day, this aircraft takes 6 flights, and each time, the fuselage is pressurized to a  (This means the pressure DIFFERENCE between the inside and the outside.) The radius of the fuselage is . The fuselage skin is made of an aluminum alloy with thickness . Thus, you should all be able to calculate the hoop stresses in this system. Now assume that a crack of width exists in the fuselage, and that the plane of the crack is oriented radially outward (so that the hoop stresses apply mode I opening load to the crack.) The crack is disk-shaped, so a far field stress will cause the crack to propagate radially outward. However, obviously when the crack width is equal to the thickness of the fuselage, it will not travel any more in that direction, but will continue to propagate along the length of the fuselage.

Anyway, the Plane strain fracture toughness of the material is . Fatigue tests on the material revealed that for , the and for , the in the Paris Law regime. (). Providing that the fuselage pressure can be maintained even when the crack is 10 cm long, how many days will this aircraft be able to operate safely?