PSI - Issue 41

Aleksandr Inozemtsev et al. / Procedia Structural Integrity 41 (2022) 510–517 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 5. (a) Characteristic surface relief of a fatigue fracture zone; (b) 3D morphology.

The minimum (critical) scale l sc corresponding to the occurrence of multiscale long-range correlations in the defect ensembles is determined by calculating the Hurst exponent. The function K(r) for one-dimensional profiles of the fracture surface relief is calculated using the Bouchaud (1997) formulas: ( ) H x r z x r z x K r  = + − 2 1 / 2 ) ( )) ( ( , (2) where K(r) is the average difference between the surface relief heights z(x+r) and z(x) in the window of size r , and H is the Hurst exponent (surface roughness index). Representation of the function K(r) in logarithmic coordinates made it possible to evaluate the lower boundary of the scaling range l sc , and the value of upper boundary considering it as the characteristic scale of the process zone L pz , i.e. the area of correlated behavior of multiscale defect structures (Fig.6b).

(a) (b) Fig.6. (a) Characteristic one-dimensional profile; (b) plot Log 2 K(r) vs. Log 2 (r) . The values of the Hurst exponent H and the scales L pz and l sc for different loading conditions are given in Table 3.