9. Spherical pressure vessels with a radius of 1.0 m and thickness of 25 mm were built to store 5.0 wt% brine at 70 C at 5.0 MPa for chemical plants. The pressure vessels were improperly designed using an aluminum alloy that is susceptible to stress-corrosion cracking in the presence of brine. The stress-corrosion cracking characteristics of this alloy are given in the figure below. The pressure vessels continually failed during service. The yield stress of this alloy is 400 MPa, the ultimate tensile strength is 550 MPa. Any cracks in the pressure vessel are semi-circular with a radius of a. The stress- intensity factor acting on these cracks can be assumed to be given by K = a, where is the stress acting normal to the cracks. (a) (b) Did failure occur by fast fracture, yield, or leaking during service? When you were hired to replace the engineer, you started a program of proof testing all the pressure vessels to ensure that failure by stress-corrosion cracking does not occur during service. What is the pressure you used for proof testing? (Justify your choice.) (16 MPa) Crack growth rate, da/dt (mm/day) 10 0.1 0.01 0.001 5 Crack growth in an aluminum alloy in 5 wt% brine at 70 6 40 50 7 8 9 10 20 30 Applied stress-intensity factor, K, (MPam /2)