A theoretical and experimental evaluation of the Griffith theory of brittle fracture

The stress model used in the derivation of the Griffith theory of brittle fracture has been examined analytically and experimentally for compressive loading. Stress distribution around open elliptical and circular voids has been calculated and compared with implications of the Griffith theory. In the experimental study plaster of Paris models, each containing a single open elliptical or circular void of varying size and orientation, have been loaded under uniaxial compression. The first event of the fracture history for single voids and cracks of any shape and orientation was the appearance of tensile fractures which originated at points of maximum tension and propagated into a direction parallel with the applied uniaxial load. The orientation of the “critical crack” (i.e., for which the fracture initiation stress is the lowest), has been found to be different however from the one predicted by the Griffith theory. For all elliptical shapes the major axis of the “critical crack” was perpendicular to the direction of the uniaxial load. In addition, fracture initiation depended greatly on the size of the crack, particularly at smaller sizes. For every critically oriented crack there appeared to be a “critical size”. Critically oriented open cracks that were greater than the critical size initiated first fractures when the applied uniaxial compressive stress reached the tensile strength of the material surrounding the crack. Voids and cracks smaller than the “critically oriented and sized crack” initiated fractures at higher stresses. The first-formed tension fractures did not lead to collapse of the test models. On further increases of stress, shear fractures appeared starting from the points of high compressive stress concentration around the crack periphery. The shearing initiated new tension fractures and eventually the test specimen collapsed. The importance of a shear mechanism in loading brittle materials to ultimate rupture was emphasized further through observations of the fracture history of solid test models (without cracks) loaded under polyaxial compression. These tests demonstrated that the development of the large-scale, through-going shear zone is preceded by a long history of fracture development, including several stages of tensile and shear fracturing and that the formation of such shear zone represents the last stage of the fracture history.