Long version
https://docs.google.com/document/d/1dnRLZgcuHfx7uFOHvHCUGnGFiLiset-DTTEK8OtPYVA/edit

Short version; turn-of-the-century barrels did not have the corrosion resistance of chrome moly 4140 which was developed in the 20s for automotive axles.
The vast majority of utility grade single and double barrels were likely Decarbonized Steel, possibly rephosphorized and “cold rolled” for greater strength. “Mild” Low Carbon and Low Alloy “Plain” Steels were in general industrial use by the 1870s. Barrels, and especially frames were also AISI 1018 or 1020, both of which are easily “Carburized” or Color Case Hardened.

Actual barrel analysis:
1. 1898 Hunter Arms “Armor Steel” was similar to AISI 1211 Rephosphorized Resulfurized Low Alloy Steel / 1045 Carbon Steel.
2. c. 1900 Crescent “Wilson’s Welded Steel” = Bessemer Rephosphorized Carbon Steel similar to AISI 1017
3. c. 1910 Meriden Fire Arms “Armory Steel” was Bessemer Rephosphorized Carbon Steel similar to AISI 1211 / 1016 Steel.
4. A pre - WWI Parker “Titanic” barrel (courtesy of Dave Suponski) was AISI 1030 with low concentrations of nickel and chromium.
5. A pre - WWI Parker “Trojan” barrel (courtesy of Dave Suponski) was AISI 1035.
6. A pre - WWI Parker “Vulcan” (courtesy of Ron Graham) was AISI 1015.
Higher grade guns had higher grade steel; AISI 1030 - 1045 (possibly rephosphorized), Nickel Steel, Vickers, Delcour-Dupont, Cockerill Acier Universel or Acier Special, Siemens-Martin, Krupp Fluss Stahl, Wittener Excelsior Stahl.

Immediately post-WWI “Fluid Steel” barrels appear to be primarily AISI 1030 or 1040 Carbon Steel, possibly rephosphorized, with alloy steels appearing on higher grade guns; Krupp and Winchester Nickel Steel, Poldi Antikorro, Böhler Antinit.