Atomistic Aspects of Brittle Fracture

Abstract

The mechanical properties of materials are ultimately determined by events occurring on the atomic scale. In the case of brittle fracture, this connection is obvious, since the crack in a perfectly brittle material must be atomically sharp at its tip. The crack moves by breaking individual bonds between atoms and can therefore be regarded as a macroscopic probe for the atomic bonding. Nevertheless, traditional analysis of brittle-fracture processes resorts to the treatment of Griffith,1 which implies thermodynamic equilibrium. The Griffith criterion for the mechanical stability of a crack can be formulated as a balance of the crack driving force, the energyrelease rate G, and the surface energy ɣs of the two freshly exposed fracture surfaces: G = 2ɣs. The crack driving force can be obtained from elasticity theory. Within linear elasticity, the crack is characterized by a singularity in the stress field that decays as the inverse square root of the distance R from the crack. The strength of the singularity is characterized by the stressintensity factor K, the square of which directly gives access to the energy-release rate (G = K2/E′, where E′ is an appropriate elastic modulus). While this linear elastic description of the material is not disputed for brittle materials, except for a few atomic bonds around the crack, the assumption that the resistance of the material to crack propagation will only be characterized by the surface energy of the fracture surfaces is certainly worth some further consideration. Such considerations should range from examining atomic details at the tip of a single brittle crack to the relevance of more complex fracture events involving additional irreversible processes and complex crack geometries.