An internal crack has been detected by means of X-rays in the shell of a large cylindrical pressure vessel. The stresses in the region of the crack area are a longitudinal tensile stress of sigma zz = 60000 psi, a circumferential tensile stress of sigma (theta theta) = 140000 psi, and a radial compressive stress of sigma rr = 5000 psi with sigma (r theta)= sigma rz = sigma (theta z)=0. The pressure vessel is so large tha there is no appreciable variation of stress over the region containing the crack. The crack is oriented so that its normal makes an angle of 40 degree with z- axis and 60 degree with y axis. what is the normal stress on the plane on the crack.
Laboratory test have shown that it is the tensile stress normal to the crack that causes it to propagte to failure. Assume that the tests indicated that a tensile stress of 120000 psi normal to the crack would cause a crack of the same size and shape to progagate. will the pressure vessel explode?