Application of a physically consistent theory of brittle fracture

摘要

This paper examines the profile and associated stress field of an equilibrium slit crack in a brittle solid using a mesoscopic fracture model. The model is based on a physically consistent description of crack profiles in solids, developed from an analysis by Chan et al. in which the forms of intersurface cohesive forces are used explicitly. The mesoscopic nature of the problem arises from the embedding of the nonlinear and non-monotonic atomic-scale intersurface cohesive forces and length scales into a classical formulation of the elastic fracture problem. The analysis is used to calculate the full crack profile, encompassing three asymptotic limits: the near-tip Barenblatt zone, a transition zone in which the cohesive forces are still active and the far-field elastic classical zone. The analysis is also used to calculate the stress field surrounding the crack, revealing a finite maximum at the crack tip associated with the interatomic bond strength. A result of the analysis is that very small cracks (such as might occur in microelectronic circuits) have suppressed stress fields that cannot be related to the equilibrium condition of Griffith thermodynamics by the Irwin crack extension exercise and that vary with crack size. The Griffith equilibrium condition itself is unaffected by the modified stress fields and is uniquely defined by the integral of the cohesive forces acting across the faces of the crack. [References: 13]