Heatup Stress Profile:

In During heatup, it could be seen which while the pressure stresses are always tensile, at the 1/4 thickness (1/4 T), the temperature stresses are compressive. Therefore, the stresses at the 1/4 T location tend to cancel in during system heatup.  At the 3/4 T location, therefore, the stresses from both temperature and pressure are tensile and therefore, reinforce each other during system heatup. For this purpose the 3/4 T location is limiting in during system heatup.

Figure: Heatup Stress Profile

At the time of system cooldown, the stress profile of Figure is acquired.  During cooldown, the outer wall lags the temperature drop of the inner wall and is at a higher temperature. It could be seen which during cooldown, the stresses at the 3/4 T location are tensile because of system pressure and compressive because of the temperature gradient. Therefore during cooldown, the stresses at the 3/4 T location tend to cancel. At the 1/4 T location, therefore, the pressure and temperature stresses are both tensile and reinforce each other.  Therefore, the 1/4 T location is limiting in during system cooldown.