Anybody Rockwell tested shotgun barrels? Any idea what range of hardness is the target?

Rifle barrels seem to range from Rc 26-32. And at Trinidad, we checked to make sure thickness 18" from the barrel was at least .022". German proof house specifies .0906 min thickness at end of chamber and .032 18" from breech.

But all this should be relative to a hoop stress calculation compared to yield strength of the steel used at the hardness it is, right?

Not to hard they cut easy with a hacksaw.

I know a shotgun smith that makes custom barrels from 4140 tube steel

They are a bit softer than rifle barrels, which, as you know, are very soft; and most shotgun barrels aren't made from chrome moly of any alloy. Some after market ones are. For rifles, even annealed 4140 has a hoop strength at least 3 times above working pressures. Remember about 20 years ago, Remington got sued about their 1100 barrel steel due to idiots blowing them up, likely by plugging the muzzle with mud. Anyway, they changed their steel. The use of steel shot has led to thicker and harder barrels as well for shotguns. The old barrels seem to be in the RC 20 or even below; being made from low carbon steel like 1117 or so. More modern shotgun barrels are a bit harder but not much. Doesn't take much to hold a shotgun shell; it has been done with iron water pipe.

Thanks, all.

1117 ? that's a very easy to machine [no other properties] steel I'd rather have something better for my gun !!

It's better than Damascus twist iron and "steel", or just welded wrought iron. Remember, all Civil War Rifle-Muskets were made from a flat piece of wrought iron, welded at the seam and drawn out to 40 inches. They never blow up with the correct loads.

And you'd rather it be soft enough to bulge rather than shatter if there was ever an overload.