Spherical pressure vessel is constructed with the diameter of d = 45 cm. Vessel is to be capable of withstanding the internal pressure of p = 7 MPa, and the wall thickness is such as to keep nominal circumferential wall stress under 17.5 MPa. However, the vessel bursts at an internal pressure of only 3.5 MPa, and a micrographic investigation reveals the fracture to have been initiated by an internal radial crack 2.5 mm in length.
a) Estimate the fracture toughness (KIc) of the material.
b) Determine the internal pressure that causes the leak-before-break.