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

 

[_coyote_]

,Residual stresses can be determined by using the equation:σ_res = σ_1 - P Where σ_res is the residual stress, σ_1 is the initial stress from your calculation, and P is the autofrettage pressure. Therefore, you can calculate the residual stresses at the cylinder bore when the autofrettage pressure is removed as σ_res = σ_1 – 580 To determine the new factor of safety, you need to calculate the total stress at the cylinder bore when the working pressure of 240 MN/m squared is applied. The total stress is given by the equation:σ_tot = σ_res + 240 The factor of safety is then calculated as the ratio of yield stress to total stress: FOS = 850/σ_tot. Once you have calculated the residual stress and the total stress, you can then use these values to calculate the new factor of safety.