I read Mr. Stallones reply with great interest- when you weld with the SMAW (stick rod) process, either a chipping hammer or an air driven chipper not only removes surface slag, but stress relieves the metal in the HAZ areas- But the metal still is fairly warm from the Arc heat input-
To peen a rounded barrel "in situ" might be a challange- both top and bottom ribs prevent a full 360 degree impingment of the hammer face, to chase the stresses into a circle--
Did you use a fitted mandrel inside the barrel- most folks I know aren't aware of the reason why the back face of a machinists and or peening hammer is rounded- you strike a portion of a metal arced surface such as a gun barrel with the flat face of your hammer- Not Good--