13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- where sc l l l / = − . Introducing the parameter ( ) pz sc C L l β = , we can reduce the scaling relation (7) to the following form analogous to the Paris law: α ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ = − sc E l K dN d l C , (8) where α is a universal exponent. This form is similar to the equation proposed by Hertzberg for sc l b→ , where b is the Burgers vector. In the limit of small scales sc l b≈ the application of stress intensity factor conception is problematic and corresponding scaling laws can be introduced [2]. Using relation (8), which constructed based on the results experimental investigation of the fatigue crack growth kinetics with allowance for the calculated lsc values, it is possible to estimate the exponent as α ~2.3, which corresponds to the slope of the straight line in the rectifying coordinates (Fig. 3). Figure 3. Rectified plot of relation (8) A difference of the exponent α ~ 2.3 from values obtained in the regimes of multicycle fatigue testing suggests that there are certain specific features in the formation of fracture regions in the vicinity of crack tip under conditions of gigacycle loading. 3. Summary The constancy of the scaling index (Hurst exponent) in a broad interval of spatial scales, which includes the scales of evolution of the typical defect substructures, leads to a conclusion that the kinetics of crack propagation can be considered within the framework of a broad class of critical phenomena, namely, structure–scaling transitions [3, 4] that describe the evolution of defects on various scaling levels. Determination of the scaling index of deformation induced defect structures can provide a physical explanation of the universality of this class of physical phenomena with respect to the scenarios of fracture in materials of various classes and the influence of structural states (including those formed by accidental dynamic impacts) on the “threshold” characteristics of
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