Energy jump during bond breaking

Abstract

In current fracture theory, the fracture stress is related to the surface energy on the basis of linear elastic theory. However, the fracture stress does not necessarily exceed the stress required to break atomic bonds. Here, we show that a jump in the inelastic separation energy is generated by fracture, where the inelastic separation energy is the energy between the separation planes measured by excluding the contribution of elastic relaxation, and the stress at the onset of the energy jump is the fracture stress. Analysis of the electronic states of β- SiC (cubic SiC), Ge, and Cu by first-principles tensile tests shows that the electrons redistribute during surface formation in the transition from the onset to the end of the energy jump. Therefore, it is suggested that the inelastic separation energy at the end of the energy jump can be identified with the fracture energy. Also, first-principles shear tests show that an energy jump occurs during shearing for β- SiC, but not for Ge and Cu. Thus, an energy jump is a sign of fracture (bond breaking), and an energy jump during shearing is a good indicator estimating the ductile and brittle character. These principles can hold for any solid and will therefore be beneficial for the fundamental understanding of the mechanical properties of solids and for their industrial applications.