The experimental details and results for the two cases considered in our work are presented below. 3D case, A319-type Aluminum alloy The cast aluminum alloy employed for this part of our work is an A319-type alloy, which is commonly used in the automotive industry. The typical chemical compositon is as follows (wt %): Si:7.147, Cu:3.261, Fe:0.612, Zn:0.664, Mn:0.0374, Ni:0.041, Ti:0.154, Mg:0.313, Sr:0.014, Al: balance. Fig.1 shows the microstructure of this alloy as observed by optical microscopy, the dendrites of alpha aluminum-rich phase is observed along with a numbre of different phases in the interdendritic regions. There is also a grain structure which was revealed using a special preparation. Image analysis measurements showed that the largest heterogeneities were the dendrites and the grains, with characteristic lengths identified as the primary dendrite arm length (800 µm) and the grain size (950 µm). Samples of this material were broken in Charpy impact tests according to ASTM standard E-23-93. The resulting fracture surfaces were examined by Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM) and an stylus profilometer. These three techniques were used to obtain topometric profiles both in the perpendicular and parallel direction with respect to the crack propagation direction, see Fig. 2. Profiles of the arrested crack front were also recorded using a different procedure which is described later in this section. Using these profiles we were able to determine the perpendicular out-of-plane roughness exponent ζ⊥, the parallel out-of-plane roughness exponent ζ//, and the roughness exponent of the crack front ζf, Fig. 2. Fig.1 Optical micrography showing the microstructure of the A319-type alloy. Fig. 2 Scheme illustrating the height profiles in the parallel and perpendicular directions with respect to the propagation direction, the crack front and the three roughness exponents are also included. The SEM topometric profiles in the parallel and perpendicular directions were obtained by sectioning the surfaces previously plated with nickel, then SEM images are recorded using backscattered electrons and the profile is extracted by image analysis procedures. More details of these technique can be found in references [6, 15-17]. SEM profiles of 1024 points were obtained at magnifications ranging from 100X to 4000X. The AFM profiles are directly recorded by scanning the uncoated surfaces, we have used the contact mode in air. Profiles of 512 points with scan sizes ranging from 0.5 to a maximum of 6 µm were obtained. The stylus profilometer provided us with profiles of a maximum length of around one centimeter, a typical profile consisted of around 10,000 points with resolution of 0.25 µm.
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