  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-Lo\`{e}ve
decomposition of fatigue test data. Statistical orthogonality of the estimated
damage measure and the resulting estimation error is demonstrated in a Hilbert
space setting.
