Having discussed this with a mechanical and metallurgical engineer there is no good answer.
There are of course several bursting formula including Barlow's 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 formula (including American Standard, Alger, Lame & others) refer to a pipe capped at both ends with a static pressure (a pressure cylinder). Barlow's refers to a thick wall pressure vessel (wall thickness greater than 1/10 – 1/20 ID).
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”
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.
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.
re grease:
Tom Roster
“One test European shotgun manufacturers use to fast-proof barrels if standard proofing methodologies and loads are not available, is to liberally oil the bore and then fire a standard service load in it. The well-oiled bore interior will cause the pressure to rise some 6,000 to 7,000 pounds per square inch (PSI) above the Maximum Average Pressure (MAP) for service loads. And grease inside the bore can cause the pressure levels produced by shotshell service loads to easily double."
OTOH there are many studies documenting how difficult is can be to burst a barrel, including Greener's attempts in 1886
http://books.google.com/books?id=inQCAAAAYAAJ&pg=PA92and of course
The Double Gun & Single Shot Journal“Finding Out For Myself” series by Sherman Bell with technical assistance from Tom Armbrust esp.
Vol 18, Issue 1, Spring 2007 -
Destructive testing on a Damascus barrel with thinned walls; calculated by O.D. - I.D. and not measured.
Destructive testing using various obstructions, including a 20g shell.
Destructive testing using a shell loaded with 3 1/4 Drams by volume or 56 grains of Unique (similar to “Infallible”) with 1 1/4 oz. shot. The chamber burst with the first shot. The 3 1/4 Dram Equivalent load is 24 grains of “Infallible”, and 56 grains estimated pressure was 50,000 psi.
In this regard, a Parker fella friend Mechanical Engineer who lives in Vegas was investigating hydraulic pressure testing using some of the tubes I've accumulated; unfortunately life and marriage have gotten in the way.
I've had no contact with Zircon/Ron Graham (a metallurgical engineer) who had collected about 40 barrels for testing, including the Parker barrels destroyed by Bell, for several years.
I'll bet a military ordnance engineer might have an answer. Don't you have any PhD buddies up in Huntsville who could help?
