3 fatigue of a pressure vessel 10 points a cylindrical steel pressure
3. Fatigue of a pressure vessel (10 points)
A cylindrical steel pressure vessel of 7.5 m diameter and 40 mm wall thickness is to operate
at working pressure of 5.1 MPa. The fracture toughness for the steel is 200 MPa√m. The
growth of the crack by fatigue may be represented approximately by the equation
where A =2.44×10¹ (MPa) m¹. The design assumes that failure will take place by fast
fracture from a crack which has extended gradually along the length of the vessel by fatigue.
To prevent fast fracture, the total number of loading cycles from zero to full load and back
to zero again must not exceed 3000. Find the minimum pressure to which the vessel must be
tested before use to guarantee against failure in under the 3000 load cycles.
Hint: The stress intensity factor for a crack along the length of a thin-walled pressure vessel
can be estimated by the following expression (Tada, H., Paris, P. C., & Irwin, G. R. (1973). The
stress analysis of cracks. Handbook, Del Research Corporation, 34, 635):
K₁ = √na-F(2),
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