A research laboratory receives delivery of a new custom-made cylindrical thin-wall pressure vessel. The pressure vessel has inner radius R = 300 mm, and wall thickness t = 10 mm. The vessel is made of 7075-T6 aluminum (toughness Kc = 29 MPam, ultimate tensile strength ou 570 MPa, and yield strength % = 505 MPa) The vessel is used to hold a gas at various pressure p. The inside of the vessel has a polymer lining to shield the metallic surface from direct contact with the gas. The polymer lining does not affect the mechanical behavior of the metallic pressure vessel. (a) The laboratory seeks to avoid yielding failure that shows up on the outside surface of the pressure vessel. Determine the allowable pressure p that the vessel can hold to give a safety factor of X = 3 against yielding on the outside surface of the pressure vessel. Use the Octahedral Shear Stress Yield Criterion (von Mises Yield Criterion). PR 0=T =-P R , = 0 (b) After repeated use, a longitudinal crack of size 2a (a = 3 mm) shows up in the vessel wall (see Figure). Luckily, the polymer lining prevents gas leak. A PR 0x = 21 The laboratory seeks to avoid fracture of the cracked pressure vessel. For the cracked pressure vessel, determine the allowable pressure p that the vessel can hold to give a safety factor of XK = 3 against fracture. 20 (inside) (outside) The stress intensity factor K, is given below (Tada, Paris, Irwin, 1985): o = P x = a/fRt K = Ta-F(x) F(X) = (1+1.25x) /2