If you had 100,000 psi chamber pressure and a 0.47" chamber diameter and steel that yield a 120 ksi, the thickness needed per thin wall hoop stress would be:
S = P [ID]/ 2[wall thickness]
I asked my father where he got that formula and he screamed at me, "From inspection!"
wall thickness = P[ID]/2S = 100kpsi [.47]/2 120ksi = 0.196" thick walls
OD = ID + 2 [ID] = .86" outside diameter of barrel around the chamber.
That is a skinny breech.
The gun will not blow up with 100 kpsi chamber pressure.
Clark: I don't know or what you were replying to in this post, but I am going to address it as a reply to my Bannerman Mosin Nagant conversion.
Bannerman conversions, those that have not blown yet, will, given enough load cycles. I am of the opinion that the steel is dangerously overstressed. I took some measurements from a M1891/30 Sniper that I own. My measurements have error, the dial caliper is likely out of calibration, and my measurements are crude. I measured the forward chamber shoulder on my Mosin and it is 1.80" in diameter. The barrel tapers aggressively forward of the chamber, and I measured the barrel diameter at the base of the rear sight, just in front of the sight blade. I was very lazy, I did not uncork the action from the stock and take more exact measurements. The 30-06 case is 2.494" long, I don't know just how much of the Nagant barrel was cut off in the conversion, so I did not try to estimate how much of the 30-06 case would be in the thin barrel section. I just made a SWAG that the case shoulder would be located at the rear sight base. The barrel actually tapers more, the taper slightly increasing towards the muzzle, so, if the barrel was cut back more, the chamber reamed deeper, the barrel only gets thinner. The diameter of my barrel at the rear sight base is 0.765". Plus or minus the inaccuracy of my caliper. The chamber dimension I have, the 30-06 reamer cuts the shoulder diameter to 0.443". I will use these numbers later, but I am going to address period materials.
It is a total mistake to assume vintage guns used contemporary materials. So many people who lack an understanding of history project back today's technologies and just assume the ancients had cell phones, satellite data, modern materials, CNC machines and grooved to Rock Music. This was not so. Millions of Mosin Nagants were made before vacuum tubes were invented. The material technology of the era was quite primitive. Plain carbon steels were state of the art and that is what was used in vintage rifles and pistols. These are data points I found about metal history, and they show the relative primitive state of metallurgy prior to WW1.
Silicon Steel patented in 1886
Manganese Steel licensed to use in US in 1890
Nickel Steel Armor adopted in by US Navy1891,
1910 Monnartz & Borchers patented Stainless Steel
Those steels and dates won't mean much to many, neither will the reference to vacuum tubes, infact, I expect the comparisons will be puzzling for many. So many people were born after vacuum tube technology ended, born after the era of six transistor radio's, in fact were born well after integrated circuit chip technology, that using vacuum tubes or transistors as examples of technological advancements won't make any impression at all. But I remember vacuum tube radios, and I remember the cat's eye tuner on the front of my Sears Silvertone vacuum tube shortwave radio.
I don't know what materials were used in Mosin Nagant barrels and receivers. I am going to make the assumption they used the same plain carbon steels the US Army used in the manufacture of the M1903 rifle. I have no reason to assume the Russians used alloy steels at any time during what has to be a century of manufacturing Mosin Nagants. If someone has metallurgical data contradicting this, please put it out in the public domain.
Source: July-Aug 1928 issue Army Ordnance,
“Heat Treatment and Finish of Small Arms at Springfield Armory"
Springfield Armory used steels they called "Class A, Class C", etc in the manufacture of the various components of the M1903 rifle. Class C steel was used for receivers and bolts, and Class A for barrels.
Code:
Carbon Manganese Max Phos Max Sulpher Component
Class C Steel .20-.30 1.0-1.30 . .050 .050 Receivers
Class A .45-.55 1.00-1.30 .050 .050 Barrels
This is from the article:
Barrels are rolled from the bar stock to a rough shape. After rolling, the barrel blanks are normalized at 1650 °F and annealed at 1600 °F for two hours. They are then hardened by heating in an open ifre to 1550 °F for one hour and then quenching in oil. They are tempered to meet the following physical specifications:
Yield Point, 75,000 lbs per sq. in.
Tensile Strength 110,000 lbs. per sq.in.
Elongation 20.0 per cent.
Contraction of Area, 50.0 per cent.
The standard .505 inch tensile test specimen is prepared from the breech end of the barrel blank. Each barrel blank is given a Brinell hardness test and must be between 228-269
The yield strength is 75,000 psia, you would expect an alloy steel to be around 90,000 lbs, if not more. Alloy steel yield varies considerable by what alloys are used, and what hardness is desired but it turns out that barrels are in fact fairly soft. Toughness is more desired than hardness and yield strength is traded for increases in toughness. Brittle is not a desired barrel material characteristic.
I used a thin walled pressure vessel calculator I found on the web to calculate hoop stresses. So based on these dimensions, the yeild strength of Class A materials, and assuming a 30-06 in the chamber, I get these numbers for hoop stress.
30-06 case shoulder at forward edge of Mosin Nagant chamber
Wall thickness (1.80"-0.443")/2 = 0.6785"
Cartridge Pressure =50,000
Material Yield = 75,000
Hoop stress= 66,273 psia.
30-06 case shoulder just at Mosin Nagant rear sight base
Wall thickness (0.765"-0.443")/2 = 0.161"
Cartridge pressure = 50,000 psia
Material Yield = 75,000 psia
Hoop stress= 118,788 psia.
There are known unknowns in this calculation. Pressures vary quite a bit, what we see given as a pressure in a reloading manual is an average. Maximum pressures are typically 20% higher than the average, sometimes higher than that. Material values have uncertainty, no metal will have an exact yield strength of 75,000 psia, or 100,000 psia, because metal strength varies. That is why margins are used in the design of mechanical items. Designing something with a calculated hoop stress of 75,000 psia and using a material with a yield of 75,000 is a guaranteed path to a catastrophic failure. There are rash, irresponsible people who would do this, and get away with it for a while, but metal fatigue will catch up with them. The calculated hoop stress of 118, 788 psia, which is based on the assumption that the 30-06 case shoulder is forward of the original Nagant chamber, with a material that stretches at 75,000 psia, ought to be a clue that Bannerman conversions were not structurally well thought out. I have not looked at a S/N curve to estimate the fatique life of any of these potential situations, and I really don't want to. I expect the best case stress situation would have a predicted fatique life in the hundreds of cycles, assuming good metal. Given that Imperial Russian steel was pre vacuum tube technology, and Soviet steel was awful (based on discussions with a West Point Metallurgical Teacher) I would not trust a Bannerman conversion, or a Bannerman conversion of a WW2 era Mosin.