Acylindrical pressure vessel is made from cast iron. the pressure vessel has an average radius of 250 mm, and a wall thickness of 4.5 mm. semi-circular cracks of length 2a, and depth a, may exist in the wall of the cylinder. for these cracks the stress-intensity factor is given by k_i = sigma squareroot pi a, where sigma is the stress normal to the crack. the pressure vessel is proof tested at an internal pressure of 5.0 mpa, before service. during service, there is a constant pressure of 1.0 mpa in the cylinder, but the cylinder also supports an oscillating axial load that varies between -200 kn and + 100kn (i) will the pressure vessel fail by brittle fracture, or by leaking when the crack depth equals the wall thickness? discuss both during proof test, and during services. (ii) what is the minimum number of cycles it will take for the cylinder to fail by this mechanism. (~8400 cycles) given that the fracture toughness of the cast iron is 10 mpa squareroot m, and the yield stress is 400 mpa. under the service conditions described above, it may be assumed that crack growth follows a paris law of da/dn = 1.50 times 10^-9 lambda k^4_i m/cycle, where the stress-intensity factor range, lambda k_i, is in mpa squareroot m. (when calculating lambda k, ignore any contribution from k_i < 0).