A unified and universal Griffith based criterion for brittle fracture
Abstract Within the framework of continuum fracture mechanics, brittle fracture of a notch is conventionally distinguished from that of a crack due to the absence of stress singularity near the notch root. It is revealed that the fracture stress, which is equal to the ideal strength, effectively describes the brittle fracture from the root of a nano notch; however, it fails below a critical dimensional limit (i.e. an extremely confined stress concentration field of 5 nm) due to the continuum assumption for the discrete atomic systems. On the basis of atomic fracture mechanics accounting for atomic discreteness, surprisingly, the Griffith based criterion which is originally proposed for cracks describes brittle fracture well in non crack systems (notches) even below the critical size. We further demonstrate an ultimate unification of the proposed Griffith based criterion for brittle fracture in both non crack and crack systems even with different shapes for all scales. These results provide an in depth understanding of the inherent nature of brittle fracture, and greatly benefit the safety evaluation and design of brittle failure in wide range of engineering applications.