13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- long-range correlation interactions in the ensembles of defects formed in a process zone scale Lpz (Fig. 2). The values of the critical scale lsc for various stages of crack propagation are presented in the Table 1. Table 1. Values of parameters at various stages of fatigue crack development KΔ , MPa m l,m Δ NΔ ,cycle dl/dN, m/cycle sc l , μm H 6,200 6,80·10-4 1,01·10+6 6,73·10-10 2,6±0,2 0,57±0,02 5,890 2,00·10-4 2,82·10+5 7,09·10-10 2,5±0,1 0,56±0,03 5,596 3,20·10-4 4,74·10+5 6,75·10-10 3,4±0,1 0,54±0,03 5,316 2,20·10-4 4,22·10+5 5,21·10-10 1,7±0,3 0,52±0,02 5,050 2,60·10-4 7,37·10+5 3,53·10-10 3,7±0,2 0,49±0,03 4,797 1,60·10-4 2,75·10+5 5,82·10-10 2,2±0,2 0,47±0,05 4,558 3,20·10-4 7,13·10+5 4,48·10-10 4,1±0,3 0,59±0,03 4,330 4,93·10-4 2,03·10+6 2,42·10-10 3,6±0,2 0,49±0,03 Manifestations of the self-similar nature of the fatigue crack growth were studied using methods of the theory of similarity and dimensionality [6, 7]. The crack growth rate was defined as a = dl/dN (where l is the crack length and N is the number of cycles) and studied as for correlation with the following parameters: a1 = ΔK, stress intensity coefficient; a2 = E, Young’s modulus; a3 = lsc, correlation scale in the ensemble of defects; a4 = Lpz, the scale related to the process zone. 3D New View high resolution data of roughness in the crack process zone (Fig.1) revealed the existence of two characteristic scales: the scale of process zone Lpz and correlation length lsc that is the scale when correlated behavior of defect induced roughness has started [1]. Using the Π-theorem and taking into account the dimensionality of variables [dl/dN] = L, [ΔK] =FLۛ 3/2, [l sc] = [Lpz] = L, and [E] = FL –2, the kinetic equation for the crack growth: , , , ) (Ф pz sc K E l L dl dN = Δ , (5) can be rewritten as follows: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ =Φ sc pz sc sc l L E l K dN l dl , 1 . (6) Estimation of the values ( ) 1 << Δ sc K E l and / 1 >> pz sc L l suggest an intermediate-asymptotic character of the crack growth kinetics for Eq. (6) in the following form: β α ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ = sc pz l L E l K dN dl sc , (7)
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