Effective moduli, non-linear deformation and strength of a cracked elastic solid

Abstract Utilizing the principles of Linear Elastic Fracture Mechanics (LEFM), the effective elastic moduli, the stability, and the strength of a solid containing a random distribution of interacting cracks is calculated. In order to account for the effects of interacting cracks, the “external crack” model is introduced, as a high crack density complement to non-interacting crack models. The behaviour of rock may be seen as progressing from the non-interacting crack models to the external crack model as cracks extend, interact, and coalesce. In rock mechanics, it is more common to encounter boundary conditions other than pure load controlled, and therefore we utilize the Griffith locus, which can determine the onset of fracture and the manner in which fractures extend, under any combination of load-controlled and displacement-controlled boundary conditions. Stress intensity factors are also calculated for random distributions of interacting cracks under displacement-controlled boundary conditions. The external crack model is found to exhibit sub-critical strain softening behaviour, and this gives a mechanism, not found in the non-interacting crack models, for the ultimate failure of brittle rock.