There are a number of bursting pressure formula; Burrard used the Alger Burst Formula:
Burst pressure = Ultimate tensile strength x 3(OD – ID) / OD + 2xID
There is also Lame, Boardman & Lame, American Standard, and (most commonly used) Barlow's:
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.
Barlow’s refers 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. I've discussed this issue with a mechanical and a metallurgical engineer, and there is essentially NO formula that can be used for shotgun barrels.
Nor can the Hoop Stress Formula be reliably applied
http://www.engineersedge.com/material_science/hoop-stress.htm http://lassengunsmithing.com/html/CylinderStress.htm Shotgun barrels are “thin wall cylinders”
Hoop stress = pr/t
p= pressure; r is the inside radius; t is the wall thickness
Every burst formula requires knowledge of the tensile strength of the metal and the wall thickness. The average tensile strength in one (soon to be published) study for Crolle Damascus was 54,700 psi. That is a bit more than 1/2 of the standard for hot rolled AISI 1040 and Chrome Moly 4140; both of which may be "cold rolled" to higher strength, and heat treated to MUCH higher strength.
