wrote:

If the defect is very small, or the
material is brittle, proof loading may form a crack. There will be
some residual compression at the crack tip, but not enough to make the
part stronger than it was before it was cracked.

If you take the trouble to read the text I cited, you'll see the
specific case of gun barrels is described, where overloading serves 2
purposes -- either it will improve the fatigue life, or if the crack is
already severe it will cause a complete failure then and there. This is
exactly the principle Jobst Brandt describes in stress relieving spokes
that have already been in service.