So Chuck, what you are saying is that a bulge repair if done very precisely should be at least as strong as the original metal prior to the bulging incident? I'm not a physicist or an engineer and this is a little over my head. ...
The metal (at the repair site) would be at least as strong (as the original metal), BUT the thickness of the metal (almost certainly) would not be as thick as the original. Thus, even though the metal was stronger, the place of the repair would be weaker because there was less metal there.
... Also, where would a bulge lie on the stress deformation axis? Right at yield or could it be way far to the right?
Following the stress-strain diagram starting from zero, the part of the diagram going from zero to the yield point is the area where the metal behaves "elastically", i.e., the metal deforms under the stress to a degree described by the curve but, when the stress is removed, the metal returns to its original shape/size. The stress-strain relationship in the elastic range is usually linear. Ideally, the gunbarrel will never exceed the yield point (leave the elastic range) ever.
Once the stress applied to the metal reaches the yield point, the metal will move from elastic deformation into plastic deformation. Any stress in excess of the yield point will result in a permanent "plastic" deformation of the metal. A bulge, a bend, a dent - these are all plastic deformation. Plastic deformation results in permanent deformation and thus damage to the metal. While, as described above, the stress and deformation can be relieved by annealing, the shape has been permanently changed. Banging out the dent or bulge can reshape the metal to the original, desired shape, but it does not restore the strength.
There is a point on the stress-strain diagram immediately following the elastic limit where the amount of stress needed to create a certain amount of strain (movement) decreases. Thus, the little dip. Following that point, the amount of stress needed to create a certain amount of strain (movement) increases. That increase is work hardening. The stress-strain relationship in the plastic range is usually non-linear.
Plastic deformation and work hardening will continue until the metal reaches the plastic limit, where it fractures. Which is what we're worried about.
