Mechanisms and measures for the ductility of materials failure

An operational definition for the ductility of failure is given. Many examples illustrate the procedure for specific applications. The ductile/brittle transition is an integral part of the formalism. Further applications are made to the solids forming elements in the Periodic Table. The cases of graphene and diamond are used to verify the procedure. Bond bending and bond stretching are shown to provide an atomic scale criterion for ductile versus brittle failure behaviours.