PSI - Issue 47

Aleksandr Inozemtsev et al. / Procedia Structural Integrity 47 (2023) 705–710 Author name / Structural Integrity Procedia 00 (2019) 000–000

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critical phenomena in the context of fracture scenarios for different classes of materials and explain the influence of structure peculiarities (including structures formed under fatigue and dwell fatigue loading). The surface topography of deformed specimens after fatigue tests were scanned using a New-View high-resolution interferometer-profiler (at x1000 magnification) and then analyzed by the fractal analysis methods to determine the conditions for the correlated behavior of multiscale defect structures (Fig. 2).

a) b) Fig. 2. (a) Characteristic surface relief of a fatigue fracture zone; (b) 3D morphology.

To provide representative data on the defect-induced relief structure, we analyzed from 10 to 12 one-dimensional "slices" within each "window" with a vertical resolution of ~0.1 nm and a horizontal resolution of ~0.1 μm. The minimum (critical) scale l sc , corresponding to the establishment of long-correlation interactions in the ensembles of defects, was determined using the method for calculating the Hurst exponent. The K(r) function was calculated based on the one-dimensional profiles of the fracture surface relief using the formula by Bouchaud (1997), Bannikov (2016), Oborin (2016):   2 1/2 ( ( ) ( )) H x K r z x r z x r     (1) where K(r) is the average difference between the surface relief elevations z(x+r) and z(x) in a window of size r , H is the Hurst exponent (roughness index). The representation of the function K(r) in logarithmic coordinates in accordance with relation (1) allows us to estimate the critical scale l sc . The lower bound was taken as the value of the critical scale l sc , the upper bound was taken as the value of the scale associated with the process zone L pz , which is the region of the correlated behavior of defect structures (Fig. 3).