2D Model Material


Experimental Procedure

Various hole geometries were created in aluminum sheets using a femtosecond laser (see here for details) to study the effect of holes arrangement on fracture and to obtain quantitative information for comparison with model in the literature. The samples were then tested in-situ in a Scanning Electron Microscope.

Experimental Results

First, 2 holes were drilled in the middle of aluminum sheets at different angles with respect to the tensile axis (vertical). One can see in Figure 1 the growth and linkage of voids leading to 2 types of coalescence mode:
  • Coalescence by internal necking when the voids are at 90° to the tensile axis
  • Coalescence by shear when the voids are at 45° to the tensile axis



Figure 1.: In situ SEM images of the deformation sequence of aluminum alloy 5052 containing various hole configurations and taken at various far field true strains. Two holes oriented at 90° with respect to the tensile direction (vertical): (a) 0, (b) 0.204, (c) 0.213, (d) 0.220, (e) 0.223. Two holes oriented at 45° with respect to the tensile direction (vertical): (f) 0, (g) 0.233, (h) 0.234, (i) 0.235, (j) 0.237

Optical micrographs using Nomarski contrast (DIC) were taken after deformation and show spreading of the plasticity between the void when they are at 90° and a localized plasticty when they are at 45° (Figure 2).


Figure 2.: Optical images in Normaski contrast showing the thickness deformation patterns in an array of holes oriented at (a) 90° and (b) 45° with respect to the vertical tensile axis.

The fracture surfaces of samples containing arrays of holes at 90° and 45° to the tensile axis are shown in Figure 3.


Figure 3.: SEM images of the fracture surface of a cample containing arrays of laser holes oriented at (a) 90° and (b) 45° to the tensile axis. The electron beam was perpendicular to the tensile axis in figures (a) and (b). A close up of the ligament between two holes from the array at 45° is shown in (c). The black arrows indicate the laser holes.

Detail of the shearing process is shown in Figure 4. Due to constraining effects of the hole-free material on either side of the holes, the fracture contains both shearing and internal necking modes.


Figure 4.: (a) Schematic drawing explaining the failure process of holes oriented at 45° with respect to the tensile axis (vertical). The shearing at 45° is followed by a normal type of failure due to constraining effects and the high-stress triaxiality ahead of the crack. The arrows indicate the direction of local material flow. (b) Close up of two holes from an array of holes oriented at 45° to the tensile axis (vertical).

Quantitative information on the holes dimension is easily extracted from the SEM images and is used for comparison with models in the literature (Figures 5 and 6).


Figure 5.: Schematic drawing showing how the various void dimension parameters are extracted.

Figure 6. Normalized diameter of the holes vs. true far field strain for 2 holes at 90° to the tensile axis and for different hole spacings 2W.

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