A long version is here
https://docs.google.com/document/d/1dnRLZgcuHfx7uFOHvHCUGnGFiLiset-DTTEK8OtPYVA/edit Summary of “Cold rolled” barrel steel tensile strengths. All can be heat treated for different applications (rifle receivers) to much higher strength, and yield strength matters also.
AISI 1005: 40,000 psi
Twist and Crolle Damascus: about 55,000 psi
Winchester Standard Ordnance and other "cold rolled" Bessemer/Decarbonized steels and AISI 1020: 60,000 psi
c. 1900 “Fluid Steel” (Siemens-Martin & Krupp Open Hearth Steel AISI 1021-1034): 75,000 – 85,000 psi
AISI 1140: 85,000
Krupp Fluss Stahl (Homogeneous Fluid Steel) was introduced about 1890 and by reported composition was similar to AISI 1045: 85,000 psi.
AISI 1040 (and modified), Bohler “Blitz”, 4140 Chrome Moly (not used until after 1930s): 95,000 – 100,000 psi
Winchester Nickel Steel and Marlin “Special Smokeless Steel”: 100,000 – 105,000 psi
Remington Ordnance Steel: 110,000 psi
Krupp “Nirosta” (1912 patent NIchtROstender STAhl 21% Chromium / 7% Nickel Stainless Steel introduced in 1913): 114,000 psi
Winchester Proof Steel (probably AISI 4340) introduced in 1931 for the Model 21: 115,000 - 120,000 psi
Krupp Spezial Gewehr Lauf Stahl / 1895 “Special Gun Barrel Steel”): 138,000 psi
Bohler “Antinit” (Rostfrei Laufstahl chrome-molybdenum-vanadium introduced 1912): 138,000 psi
Phosphorus increases strength and machinability, but can embrittle steel, esp. if cold (ie The Titanic).
Sulfur increases machinability, but if high Sulfur/Manganese ratio leads to Manganese Sulfide inclusions.
Nickel & Chromium increase corrosion resistance and hardenability.
I think we have good data that the Belgian produced "rough forged tubes" used by U.S. double gun makers prior to WWI were mostly AISI 1018 - 1030, possibly rephosphorized, with Decarbonized Steel on lower grades.
Modern alloy steels are harder with greater corrosion resistance.
Turn-of-the-century U.S. maker barrels were proved at 15,500 - 17,500 psi and were designed for shells with pressures similar (and the 1 1/4 oz. 3 1/2 Dr. Eq. Smokeless Powder greater) to today's loads.