that the anisotropic grain structure might have on the self-affine character of the crack paths. As it is shown in Fig. 7, the grains are elongated in the rolling direction, it is known that this causes anisotropic behavior of mechanical properties so one can expect an analogous effect on the self-affine parameters. Rolling direction Rolling direction 20µm Fig. 6 Scheme showing the orientation of the tension specimen with respect to the rolling direction. Fig. 7 Microstructure of the aluminum foil showing grains elongated in the rolling direction. // // // // ⊥ ⊥ ⊥ 101 102 103 100 101 102 parallel perpendicular ζ = 0.67 Zmax(µm) r(µm) Fig. 8 Samples of the recorded crack paths in the rolling direction (//) and the perpendicular direction (⊥). Fig. 9 Self-affines curves for the profiles in the parallel and perpendicular direction respectively, both curves reveal that the roughness exponent ζ has a value of 0.67 The crack paths obtained as a results of the tension test were recorded at various magnifications using SEM, optical microscopy and a conventional document scanner. Samples of the recorded self-affine paths are shown in Fig. 8 where paths belonging to cracks propagating in the rolling direction are “wider” and clearly distinguishable from those propagating in the perpendicular direction. The self-affine plot shown in Fig. 9 reveals that the roughness exponent has about the same value for both directions, ζ = 0.67, this value is in good agreement with the results predicted by the random fuse model and a 2D simulation of crack propagation reported in reference [16]. It is not possible to estimate with good precision the correlation lengths but Fig. 9 suggest that this parameter is larger for the parallel direction compared to that of the perpendicular direction, one can speculate that this can be interpreted as an effect of the elongation of the grains caused by the rolling process.
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