Self-similarity of damage-failure transition and the power laws of fatigue crack advance

Abstract

We propose the interpretation of the Finite Fracture Mechanics based on the criticality of damage-failure transition due to specific metastability of free energy release. Multiscale mechanisms of fatigue damage-failure transitions in metals are studied for Very High Cycle Fatigue and analyzed as duality of inherently linked two types of singularities related to the collective modes of defects and singularity of stress field as the classical framework of fracture mechanics. Development of collective modes of defects (solitary waves of plastic strain localization and blow-up dissipative structures of damage localization) with the nature of intermediate self-similar solutions are considered for the interpretation of the incomplete self-similarity and mechanism of small crack nucleation (“fish-eye” area in VHCF) and growth up to the Paris crack size. Spatial structural scales corresponding to different stages of damage-failure transition were identified due to the analysis of roughness correlation and estimating of the power (the Hurst) exponent and corresponding structural lengths of characteristic fracture surface areas These lengths and power exponents were used in the constitutive laws as the structure sensitive parameters for characteristic damage-failure transition stages (small crack initiation and growth, the Paris crack advance).