there are 2 types of overload failure. brittle and ductile.

ductile failure is when the material gradually stretches and tears away from itself (like bending a paper clip). this is the way that the steel and aluminum in bike frames should fail. it is preferable because the deformation that comes before the actual separation absorbs very large amounts of energy, which will in a sense soften the eventual failure.

in brittle failure (like snapping a dry stick) the material will deform and store energy like in ductile failure. however, the deformation is not permanent so when the 2 halves separate they will spring back to appear like the piece was cleaved clean in 1/2 and they could go right back together. in essence the part will "spring apart" releasing energy instead of storing it, leading to a potentially more catastrophic failure.

a single carbon fiber strand will fail this way, but when mixed with epoxy in a composite the sequential tearing of hundreds of individual strands will make the part as a whole fall somewhere in between the two modes.

but i think you have bigger problems to worry about if you and the bike are under enough force to cause either of these failures.