Size Effect and Multiscale Fracture

We study fracture of notched samples made of quasi-brittle, polyphase materials like rock, concrete or ceramics. The fracture demonstrates the size effect during loading. This means that a full-size sample made of such a material exhibits different fracture behaviour than a laboratory-size sample. The effect is explained by the existence of an extended zone of distributed defects and cracks (process zone) that surrounds the tip of the propagating fracture. The growth mechanisms of the process zone is scale-dependent: in an unbounded sample or a full-size structure, the zone develops until its maximum width and then it remains of the same width, while in a bounded sample that is less than some critical size, the process zone cannot be fully developed. Various similarity and scaling approaches to mechanics of multiple fracture are discussed. The growing process zone is modelled as a pattern of fractures having fractal properties on the intermediate stage of the development of the pattern. A formula is derived for the critical tensile stress that depends on both the sample size and the size of the process zone.