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
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.
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.At least by the images I've accumulated, the point of the
obstructional burst (not counting mud/snow in the muzzle) seems to be 6-12" from the breech
jOe's indestructible 4140
Thin barrel splits seem to be mostly 14-18"
And over-pressure loads blow out the breech
