A pressure vessel is to be treated to generate compressive residual stresses on it inner surface. This involves increasing the pressure until taking 75% of the wall thickness goes into the plastic range. The external diameter of the vessel is 250mm and the internal diameter is 120mm, so that it must be regarded as a thick cylinder. The yield stress of the material is approximately 400MPa.

(a) Calculate the internal pressure required

(i) to cause first yield

(ii) to cause yield one third of the way through the wall thickness

(iii) to cause yield all the way across the wall

(b) Using your answers from part (a), sketch a curve of internal pressure versus radius of yielded zone boundary for the cylinder. Comment on the factor of safety against plastic collapse associated with the target amount of yield, taking into account the assumptions inherent in the calculations.