$6$ Consider applying the process known as auto$-$frettage to a thick walled steel cylinder

with the inner radius $50$ mm and the outer radius $150$ mm $.$ The cylinder is long and

has closed ends. Assuming linear elastic$-$perfectly plastic material with sigma$\_($y$)=552$MPa

and using Tresca failure criterion

i$.$ Find the internal pressure that causes first yielding.

ii$.$ Find the internal pressure that causes yield to reach the outer diameter.

iii. Load the cylinder to the average of the pressures in parts i$.$ and ii$.$ and then

unload. Determine the residual stress distribution. Plot radial and

circumferential stresses as a function of radius for loading and unloading.

Do the only part iii. average p$=395$mpa.