A cylindrical pressure vessel of radius 0.5 m is to be filled with pure water pressurized at 2 MPa and simultaneously subjected to a bending-moment of 128kN. m. The fracture toughness of the material is 35MPa. m1/2,and its yield strength is 800 MPa. Assume that all the cracks are aligned circumferentially and have a depth of a. The stress intensity factor is given as KI= σ(πa)1/2.

a) Find the minimum thickness of the vessel required to maintain a safety factor of at least 3.0 on the pressure, using the leak-before-break criterion for design against fracture.
b) Owing to a leakage in the piping system, the water in the supply gets mixed with NaOH (sodium hydroxide), resulting in stress-corrosion-cracking at the following rate,
da/dt =10^−11*KI^8 m/day
Using the thickness value obtained in part (a), design a proof test (stating the nature and magnitude of loads you choose) to ensure a minimum life-time of 8 hours in this environment.