In reply to norrisdan71:
Traditionally, it would be riveted.
I can see that a brittle glue might fracture, so a softer glue might be a better bet. You might also need to consider paint peel, and the effect of glue on the paint. It's all very well if the brooch sticks to the paint, but the whole lot comes away from the frame...
Some of the modern adhesive contact tapes are pretty damned good, provided surfaces are clean (grease-free) and smooth. A bent brooch might not meet that...