Residual stresses in thick cylinders (Autofrettage)

MechEngStu

Hello,

I have been working on a question regarding thick cylinders and determining the factor of safety (FOS).

I have attached the main part of the question that I was able to solve.

However, the question now asks that due to the low FOS, the cylinder is subjected to an autofrettage pressure of 580MN/m squared. Determine the residual stresses produced at the cylinder bore when the autofrettage pressure is removed and determine the new factor of safety when the working pressure of 240 MN/m squared is applied.
The material yield stress is given as 850 MN/m squared and axial stresses can be ignored.

What I have done to solve this was to simply sub 580 in for the value of P in the attached file. This gave me sigma 1 and sigma 3. I then followed the same steps as before but I got a factor of safety of 0.65 which is lower than the previous.

If anyone could point me in the right direction with regard to finding the residual stresses at least, it would be much appreciated.

Thanks

Attached Thumbnails