I agree with Chuck that the metal is work "strengthened" (hardened) by the plastic deformation. If the exact cause of the bulges was to be repeated in exactly the same location, the bulges might be enlarged or reappear if the barrel had been "hammered down." However, the exact replication of the conditions is very, very unlikely.
Bulges are dents in reverse. I see a lot of dents removed from barrels at the major SXS meets. I am unaware of any problems steming from dent repair. Dents are usually caused by mechanical force whereas bulges are usually caused by force from pressure. The metal neither knows nor cares where the force comes from. So, why would bulges be different from dents? In this case, it is not clear what caused the bulges - whether pressure or mechanical in origin. I don't think it matters. At issue is whether a crafsman can knock them back into place.
craigd, I'd think the barrel metal has plenty of room for further deformation before necking and fracturing. I do agree that the wall thickness should be measured in and around the bulges as accurately as possible to preclude the possibility of previously thinned walls. If the bulge is properly "shrunk" back into place, there should be no particular permanent wall thinning - this depends on a skilled craftsman with knowledge of working sheet metal. In deference to the experience of the gunmakers, I agree that the price of this set should discount the second barrels and that repair should be undertaken only if the repair cost is considered a "sunk cost."
Riveling! I have hypothesized that the root cause of riveling is shot bridging. Any size shot can form a bridge, but the following illustrates the three sizes of shot that appear to me to be most prone to "strong" bridging.
If the shot forms a "strong" (sufficiently strong to resist force from the ambient gas stream) bridge, it can support shear force and act as a barel obstruction until sufficient force is generated by gas hammer pressure to collapse it. I think the judder (a repeated stick-slip event) refered to by Thomas would occur if the shot bridge failed to collapse and the wad repeatedly stuck and then slipped under gas hammer pressure. The gas hammer overpressure may be capable of bulging the barrels slightly in a ring pattern, slipping to releave the pressure, sticking and causing a second gas hammer with a second ring bulge, and repeat. This is theory, not fact. I have been challenged to work out the likely gas hammer overpressure range and plan to work on this question in the near future. I'd be happy for any technical critique of the above theory.
