For a long time, the development of our ideas about the fracture process was hampered by the incomplete mathematical description of the conditions near the crack end. In recent years, this subject has attracted considerable research attention, which has led to some important results. However, these theories are also unable to describe the crack growth pattern with sufficient completeness. In this paper, attention is focused on the investigation of equilibrium and non-equilibrium crack propagation conditions at a given location and the prediction of the pattern of its further propagation, as well as on the mechanical and mathematical substantiation of the fractality of the fracture surface.
