1. Fracture of a thick-walled pressure vessel (10 points)

A thick-walled pressure vessel has inner radius >= 10 mm and outer radius R = 40 mm. A

flaw, depth a = 1 mm, is detected on the internal surface of the vessel. The vessel is made of

a steel with a yield strength or= 200 MPa and a fracture energy 10³ J/m². The Young's

modulus of the steel is 200 GPa. Estimate the pressure that the vessel can sustain.

Hint: The stress intensity factor for an internal crack in a thick-walled pressure vessel can

be estimated by the following expression (Underwood, J. H. (1972). Stress intensity factors for

internally pressurized thick-wall cylinders. ASTM International):