Looks like we've got it down to the late 30s
http://parkerguns.org/forums/archive/index.php?t-2719.html Researcher stated early 30s
"IMHO those Damascus barrel warnings that began appearing on shotshell boxes by the early 1930s were more a thinly veiled attempt to coerce shooters into buying new guns, though they probably did have some relevance to all those cheap Belgian imports that came into North America from 1880 to WW-I. All the major U.S. manufacturers guaranteed their Twist and Damascus barrel guns for nitro powders. Most U.S. manufacturers dropped their composite iron and steel barrels when the sources of the rough tubes dried up with the outbreak of WW-I, but at least Parker Bros. continued to offer them into the late 1920s. There is at least one late Parker Bros. double with Bernard barrels, vent rib, beavertail forearm and single selective trigger known."
