Good stuff Stan.
Bruce Bowen’s H&R
https://www.trapshooters.com/threads/gun-blowups-past-thread.51234/ http://www.trapshooters.com/threads/h-r-detonation.146598/ Greener's (mostly unsuccessful) attempts in 1886
http://books.google.com/books?id=inQCAAAAYAAJ&pg=PA92Experts on Guns and Shooting, George Teasdale Teasdale-Buckell, 1900
https://books.google.com/books?id=4xRmHkr7Lp8C&pg=PA372 On the subject of steel v. Damascus, Mr Stephen Grant is very clear, and much prefers Damascus for hard working guns. He related an anecdote of one of his patrons, whose keeper stupidly put a 12-bore cartridge into his master’s gun without knowing that he had previously inserted a 20-case, which had stuffed up the barrel. Fortunately, no burst occurred, but a big bulge, which, however, Mr Grant hammered down, and the gun is now as good as ever.
A study by the Royal Military College of Science, sponsored by the Birmingham Proof House and the British Association for Shooting and Conservation, showed that an obstruction by 2 fibre wads (total weight of 4 grams) was sufficient to bulge or burst a 12 gauge barrel shooting a 28 gram (slightly less than 1 ounce) load. Peak pressure occurred 22mm (.866”) past the leading edge of the obstruction.
Bottom line is that an obstructional burst can not be predicted, and is dependent on (in the absence of a barrel defect) the combination of wall thickness at the point of obstruction, pressure at the point of obstruction, tensile strength of the steel, degree of obstruction, hoop stress, and likely some other stuff we don't fully understand.
All the burst formulae refer to a pipe capped at both ends with a static pressure (a pressure cylinder). Shotgun barrels are not designed to be pressure vessels as one end is open and the pressure rises and falls quickly.
Barlow's bursting formula P=2 S t / D
P=Bursting pressure in psi.
S=Tensile strength of material in tube wall.
t=Wall thickness in inches.
D=Outside diameter in inches.
Burrard used the Alger Burst Formula
Burst pressure = Ultimate tensile strength x 3(OD – ID) / OD + 2xID
The Hoop Stress Formula doesn't reliably predict shotgun barrel failure either
https://www.engineersedge.com/material_science/hoop-stress.htm Shotgun barrels are “thin wall cylinders”
stress = pr/t
p= pressure; r is the inside radius; t is the wall thickness
Barlow's (and the other formulae)
DO work with a totally obstructed barrel. When the "critical confluence" of variables meet, the barrel bulges or bursts.
Wallace H. Coxe, in "Smokeless Shotgun Powders: Their Development, Composition and Ballistic Characteristics" published by E.I. du Pont de Nemours & Co. in 1931 cites a study in which a fluid steel barrel was cut to 9” and capped, then a series of progressively increasing pressure loads fired. The barrel cap was blown off and barrel burst at
5,600 psi.
At least by the images I've accumulated, the point of the burst (not counting mud/snow in the muzzle) seems to be 6-12" from the breech


Modern 4140
