Question 1

This question carries 50% of the marks for this assignment Your answer to
part (a) should be no more than about 250 words long. Show clearly each stage
of your working for parts (b) and (c).

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a.By considering a cylindrical pressure vessel subjected
to an internal pressureP, show in which
one of the three primary stress orientations a crack-like defect would be most
likely to cause failure when the internal pressure reaches a critical value.Support your answer
with sketches and explain your reasoning.

(10 marks)

·
b.A cylindrical pressure vessel that is used for
chemical processing is routinely pressurized to 28 MN m^–2. The vessel has a mean radius of 0.75 m and a wall
thickness of 0.11m, and is constructed from welded plates of material
with a UTS of 575 MN m^–2and a yield
strength of 450 MN m^–2.

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

(6 marks)

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

(4 marks)

·
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.

(5 marks)

·
iv.Following Question 1(b)(iii), you establish that the
fracture toughness is between 65MNm^–3/2and 110 MN m^–3/2. Use the Mathcad R6 Calculator to determine the safety factors for a flaw
that penetrates 4 mm into the wall section (i.e. a ‘crack length’ of 4 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.

(10 marks)

·
c.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 9 mm crack. Use both extremes of toughness given in Question 1(b)(iv).

(15 marks)