Self-limiting in stresses

A primary stress (internal pressure) can be analogous to a cantilever beam with a weight on the end. If you put too much weight on it, the beam will continue to bend until it breaks.

A secondary, self-limiting stress (thermal expansion) would be the same cantilever beam, but instead of imposing an over load - you would impose a set displacement/deflection. Such as - the end of the beam is to deflect 0.25". This would be analogous to a cantilever with a support under the opposite end with a 0.25" gap. The difference between the two is that the secondary, self-limiting stress will not "continue on" until failure - it will yield until the distance is taken up and then stop.

The attached link discusses the difference between primary and secondary stress in connection with pressure vessel design.