I'm not a metallurgical or mechanical engineer, and only know what those that are tell me, and what I've learned from reading.

The non-deep thinkin' non-expert version:
Cleavage occurs when the pressure exceeds the ultimate (tensile) strength of the steel.
Low cycle fatigue occurs when the pressure exceeds the yield strength (or elastic limit; the stress which gives a permanent deformation of 0.2%) and it has a characteristic micrographic appearance described as "wave in the sand" or "beach marks".
The barrel wall stretches (elastic deformation) with each pressure event (shot) until cleavage occurs. The number of cycles required for cleavage depend on the pressure, steel yield strength and ductility (% elongation), and wall thickness...and no doubt a lot of other things I don't understand.
The wall of a barrel that ruptures from an obstruction will of course "stretch" until cleavage (with a characteristic "ring bulge"), and this is not low cycle fatigue.

600X Scanning Electron Micrograph

[Linked Image from photos.smugmug.com]