13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- of which was controlled by varying the amplitude of oscillations. The corresponding stress intensity coefficient ΔK was calculated by the following formula: ( / ) 1 0 2 U Y l w l E K π ν − Δ = , (2) where E is the Young’s modulus, ν is the Poisson ratio, U0 is the amplitude of oscillations, Y is the polynomial factor, and w is the sample width. For a given sample geometry (Fig. 1) the polynomial factor was as follows: 4 3 2 ( / ) 0.635( / ) 1.731( / ) 3.979( / ) 1.963( / ) l w l w l w l w Y l w + − + = . (3) Figure 2 shows the typical surface relief observed on a sample, which was obtained using a high-resolution NewView interferometer. This profilometer ensured a vertical resolution of 0.1 nm and a lateral resolution of 0.5 μm. These patterns were analyzed using the methods of correlation analysis for determining the conditions of scaling invariance in the ensembles of structures, which were assumed to govern the subsequent stage of crack development. Figure 2. Schematic diagram showing a region at the crack tip and typical image of the surface relief The structure scaling parameter of the measured surface profiles was determined based on the average difference K(r) in relief heights z(x) on the fracture surface, which was defined and represented as follows: ( ) ( ) H x r K r z x r z x ∝ = + − 2 1/ 2 ) ( ) ( , (4) where H is the index of surface roughness (Hurst exponent). By representing these data in logarithmic coordinates according to Eqs. (4), it is possible allows to evaluate the roughness index as a spatial invariant, which corresponds to a constant slope of the plot of lnK(r) versus ln(r) for a definite scale on which it is observed. The linearity of lnK(r) versus ln(r) plots allowed the roughness parameter to be evaluated as invariant in the given interval of scales r. The resolving power of the interferometer employed ensures determination of the upper and lower boundaries of scaling between K and r. The minimal value of the scales r was assumed to determine the critical scale lsc for establishing
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