This question should take about 15 minutes to complete. It illustrates the difference between design for 'failure' using the traditional solid mechanics approach of yield criteria, and the fracture mechanics criterion of energetically favourable fast fracture.
A cylindrical pressure vessel, with a diameter of 6.1 m and a
wall thickness of 25.4 mm, underwent catastrophic fracture when the internal pressure reached 17.5 MPa.
The steel of the pressure vessel had E = 210 GPa, a yield strength of 2450 MPa a value of GC = 131 kJ/m2.
a) Show that failure would not have been expected if the von Mises yield criterion had served for design purposes:
b) Based on Griffith's analysis determine the size of crack that might have caused this failure, stating assumptions that you have made.