cyclic loading

This is low cycle behavior. What i would do is the following: Compute the principal stresses for all the possible configurations of pressure-temperature. Then pick the extreme stresses. That is, the lower minimum principal stress and the greater maximum principal stress. Then, define the mean and alternating stresses based on these two extreme stresses.This is a conservative criterion, though. If you are designing and don't matter about saving some steel, just assume that you have high cycle load and design for inifinite life, this would be simpler, but a very conservative design if you actually have a low cycle behavior.