Leonard,
Yes, the vac-arc-remelt process was toyed with in the late 50's and eventually Latrobe came on-line with a vac-arc-remelt plant in the mid 60's. This process allows for producing much cleaner metals with less probability of inclusions and elements not disolved into solution. Most aircraft grade steels are made this way today. I believe, but could be mistaken, that round bar 4140 used in barrels is commonly produced with the benefit of this process in the U.S..
Still, inclusions do occur as we discovered when tungsten inclusions were found widespread in titanium aircraft bolts that were made from recycled Soviet submarine scrap, even after the vac-arc-remelts and slag removal (saw) of the ends of the ingots, common to Ti recycling. The tungsten inclusions were from hand-welding with TIG where the tungstens had been 'dipped' and broken off in the solidified weld.
So, there's always some probability of an inclusion in metals, even using the best available processes. That's why critical airplane structures "assume a flaw" and we calculate crack growth from there and insert multiple inspections before the crack gets to critical length.
With barrels, I suspect engineers today, assume a flaw and mitigate the possibility it will grow by lowering stresses (make it thicker). At least I hope they do.
