Correlation regimes in fluctuations of fatigue crack growth

This paper investigates correlation properties of fluctuations in fatigue crack growth of polycrystalline materials, such as ductile alloys, that are commonly encountered in structures and machinery components of complex electromechanical systems. The model of crack damage measure indicates that the fluctuations of fatigue crack growth are characterized by strong correlation patterns within short-time scales and are uncorrelated for larger time scales. The two correlation regimes suggest that the 7075-T6 aluminum alloy, analyzed in this paper, is characterized by a micro-structure which is responsible for an intermittent correlated dynamics of fatigue crack growth within a certain scale. The constitutive equations of the damage measure are built upon the physics of fracture mechanics and are substantiated by Karhunen–Loève decomposition of fatigue test data. Statistical orthogonality of the estimated damage measure and the resulting estimation error are demonstrated in a Hilbert space setting.