A cylindrical pressure vessel that is used for chemical processing is routinely pressurized to 26 MN m-2. The vessel has a mean diameter of 1.6 m and a wall thickness of 0.095 m, and is constructed from welded plates of material with a UTS of 565 MN m-2 and a yield strength of 460 MN m-2.

i. Calculate the maximum stress at full pressure that could drive the growth of a crack.

ii. State, with justification, whether or not the service condition represents a high load on the structure.

iii. To determine the safety of the vessel, you need to know the fracture toughness of the steel. Suggest how you could obtain this value.

iv. Following part (iii), you establish that the fracture toughness is between 75 MN m-3/2 and 115 MN m-3/2. Use the Mathcad R6 Calculator to determine the safety factors for a flaw that penetrates 6 mm into the wall section (i.e. a ‘crack length' of 6 mm on the Mathcad R6 Calculator) with zero secondary stress. For each case state what type of failure is likely to occur if the vessel is overloaded.

v. The vessel is welded, so conservative procedures demand that you assume that any flaws are in the welded zones. Use the Mathcad R6 Calculator to predict the maximum residual (secondary) stress, introduced during welding, that the vessel can withstand without failing when it contains a 8 mm crack. Use both extremes of toughness given in (Q1- iv).