SECTION B-Structural Analysis

5. A thin-walled cylindrical pressure vessel with a diameter, D = 8 m, and an operational pressure 5 MPa made from a steel with a yield strength of σys = 1250 MPa and Kic=126 MPa√m.

Failure of the pressure vessel can be assumed to occur from embedded elliptical defects orientated perpendicular to the hoop stress. The largest crack found by NDT in the wall of the vessel is an elliptical defect in the welding zone with size of 2a = 8 mm and 2c = 40 mm.

(a) For a factor of safety of 2 based on yielding find the thickness of the thin-walled pressure vessel t.
(b) In this case how much is stress intensity factor and what is the factor of safety against the brittle fracture?
(c) What is the maximum flaw length that can be tolerated before the stress in the casing reach to design stress. Assume the crack aspect ratio a/2c remain unchanged.
(d) Find the plastic zone size for pane strain condition and determine whether the use of LEFM, based on Kic, is likely to be conservative or not for the given dimensions of defects and motor case, i.e. whether plane strain conditions exist.

The stress intensity factor for an embedded crack, at the semi-minor axis position (crack depth a), can be found from 

Where a is crack length and t is the vessel thickness. The flow shape parameter Q can be found from Figure Q5 on the next page.

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