PSI - Issue 2_B

6

Vladimir Oborin et al. / Procedia Structural Integrity 2 (2016) 1063–1070 Author name / Structural Integrity Procedia 00 (2016) 000–000

1068

A minimum (critical) scale l sc that corresponds to beginning of multiscale long-range correlation in defect ensembles is determined by the computing of the Hurst exponent. The function K(r) is calculated for one dimensional profiles of fracture surface relief according to the formula by Bouchaud (1997), Froustey (2010):   H x r z x r z x K r     2 1 / 2 ) ( )) ( ( , (6) where K(r) is the averaged difference between the values of 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 allowed one to evaluate the lower boundary of the scaling range l sc , and the value of upper boundary considering one as the characteristic scale of the process zone L pz , i.e. the area of correlated behavior of multiscale defect structures (Fig.4).

(a) (b) Fig.4. Characteristic one-dimensional profiles for zone 1 (a), plot lnK(r) vs. ln(r) for zone 1 (b). The values of the Hurst exponent H and the scales L pz and l sc for different loading conditions are given in Table 1. Table 1. The values of the Hurst exponent H and scales L pz and l sc at various levels of fatigue longevity.

Elongation (mm)

Striker velocity (m/s)

Sample number

 , MPa

  , cycles 

Zone number

l sc , mkm

L pz , mkm

H

1 2

0.89 1.77

28.41 40.30

130 120

7,33·10 +6 7,82·10 +8

2 2 3 2 2 2 2

1.4 0.5 0.8 1.0 1.0 1.1 0.7

20.6 10.9 21.4 18.2 14.2 23.1 12.4

0.57 0.63 0.62 0.60 0.46 0.59 0.48

3 4 5 6

1.27 2.21

32.10 40.30

120 105 154 150

5,72·10 +7 5,83·10 +6 1,60·10 +6 1,28·10 +6

QS QS

1.5 2.5

The comparative analysis of the scaling characteristics of samples loaded under conditions of high - and gigacycle fatigue shows a significant decrease in the range of spatial scales, where the Hurst exponent remains constant for dynamically loaded samples in the «fish-eye» (0.5-10.9 mkm) zone.