Self-Similar Regularities of Failure Staging and Power Laws of Fatigue-Crack Growth

An interpretation of the fracture mechanics approach that takes into account the ‘finiteness’ of the scale of the cohesive zone in the vicinity of the propagating crack tip (Finite Fracture Mechanics theory) is proposed, based on the outlined regularities of the criticality of damage stages and the transition to fracture. Multiscale regularities of transitions from fatigue damage to fracture and crack propagation kinetics are studied for a very-high-cycle fatigue regime from the standpoint of the duality of singularities that determine the development of the cohesive zone (Process Zone). The duality of singularities in crack propagation in damaged media is associated with the presence of two self-similar solutions: a self-similar solution for the stress field distribution at the crack tip (Irwin's solution) and intermediate asymptotic solutions. The stages of damage development in the "process zone" are described as a spatiotemporal singular dynamics of deformation localisation during the formation of autowave structures in a number of defects and localisation of damage in "modes with exacerbation" – collective modes of ensembles of defects. The spatial structural scales are determined from the data obtained through quantitative profilometry of the fracture surface and the calculation of scale invariants, which characterise the various stages of damage development in accordance with the established types of self-similar solutions. The dynamics of the stages of damage development correspond to a critical phenomenon, namely a nonequilibrium structural and scaling transition in defect ensembles, with the formation of collective degrees of freedom associated with the collective modes of defect ensembles. The laws of criticality permitted the formulation of an interpretation of the phenomenological laws of crack development kinetics under high- and very-high-cycle loading, which established a connection between the indices of the degree laws in the Paris and Paris-Hertzberg equations and the scale invariants of the relief of characteristic zones of fracture surfaces. The relevance of the study is confirmed by estimating the resources of materials and elements of designs of aircraft gas turbine engines in terms of flight cycle, with random dynamic effects and in dwell fatigue loads.