1. Spherical pressure vessels with a radius of 1.0 m and thickness of 25 mm are made of a type of steel with the yield strength of 1600 MPa and fracture toughness of 100 MPam. The cyclic crack growth characteristics of this alloy are shown below. 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 = 0.8 where is the stress acting normal to the cracks. It is required that the vessels should function properly under a varying pressure condition from 10 MPa to 20 MPa. AK, kivin 10 10 10 5 10 20 10 (a) 20 50 50 100 103 100 10 (c) 10 10 10 107 da/cN, inches/cycle AK, Stress Intensity Range, MPa/m a) Does failure occur by fast fracture, yield, or leaking during service? Show work. b) Can you do a proof test before service to ensure that failure by cyclic crack growth does not occur during service? If so, what is the pressure used for proof testing? (125 MPa; be careful!)