# -For the situation of Prob. 11

-For the situation of Prob. 11.42, use numerical integration to estimate Ni f , allowing K to vary with crack length according to the exact K2 from Fig. 8.23(b). A spherical pressure vessel has an inner radius of 0.6 m and a wall thickness of 50 mm. The material is an austenitic stainless steel with a fracture toughness of at least 200 MPa√m. Nondestructive inspection revealed a surface crack in the inner wall of length 2c = 8 mm and depth a = 2 mm. Although the crack will change its a/c = 0.5 proportions somewhat if it grows, a reasonable approximation for preliminary analysis is to assume that a/c remains constant as the crack increases its depth a. In this case, FD for Fig. 8.19(b) varies with the relative crack depth a/t, as given by Eq. 8.23. (a) How many times can the vessel be pressurized to 20 MPa and depressurized before failure occurs? (b) Does failure occur by leaking of the vessel or by brittle fracture? If the former, what is the safety factor against brittle fracture when the vessel leaks?

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