HIERARCHY OF CRACKS IN MECHANICS OF CYCLIC FRACTURE

The fatigue fracture of materials generally consists of three basic stages: (i) nucleation of a fatigue crack, (ii) propagation of this crack, and (iii) final fracture stage. If there are initial defects in the material, the fatigue fracture is mainly accounted for by the crack propagation process. The length of the initial cracks, depending on the nature of these defects, can range from thousandth and hundredth of millimeters (structural defects) to a few tens of a millimeter (technological defects and damage in operating). Depending on the level of stresses (nominal or local stresses in the concentrator zones) and also on the size of the cracks, the fracture process can occur with constrained (small-scale) or developed plasticity at the crack tip [1-3]. Plastic deformation plays an extremely important role in the process of fracture of metalline materials. On the one hand, plastic deformation leads to a substantial decrease in the peak local stresses at the crack tip. On the other hand, it leads to a microdamage of the material in the local zone, thereby favoring fracture. In the case of static loading, plastic effects accompany brittle fracture, while in the case of cyclic loading, local plastic strains changing in sign should be considered to be the basic factor determining the process of stable propagation of fatigue cracks. The fact that both initial cracks and plastic zones are characterized by a variety of line scales makes it necessary to use micro- and macromodels to describe different aspects of the fatigue fracture. Different nature of processes occurring on micro and macrolevels, as well as different approaches and methods used for modeling these processes, suggest a hierarchical consideration of cracks. The hierarchical models to some extent simplify the analysis of the propagation of cracks on each hierarchical level.