If we apply a force to a copper rod that contains a small notch the rod plastically deforms and the notch does not decrease the force required to break the rod. The following images demonstrate the bending of the notched copper rod, with the energy of the force dissipating into the rod.
The fracture of a copper rod is an example of ductile fracture. In ductile fracture there is a lot of plastic deformation, and significant energy is absorbed before the fracture.