·Table of Contents
·Materials Characterization and testing
3D Investigations of Metallic Foams by mikrotomography (µCT)E. Jasiūnienė, B. Illerhaus, J. Goebbels
BAM, Berlin, Germany
Also the definition of underlying principles of foaming and of material strength, the generation of simple models, or the calculation of complex structures, needs the geometrical description of foams. No other method beside 3D-CT is able to give a complete test of the inner integrity of these objects.
||Fig 1: 13D-CT for objects with diameter of up to 200 mm left and up to 20 mm right|
The CT results shown here were obtained using a X-ray microfocus tube at 120 kV and 200 mA. A 0.5 mm copper filter was inserted. The voxel side length, used for the density calculations, was 250 µm, for the porosity calculations - 70 µm respectively. For the reconstruction of the 3D image of the investigated object from the collected data the Feldkamp algorithm  was used.
The investigation of metallic foams is very specific. Here on the one hand the highest possible resolution is required for the investigation of the formation of walls, their thickness and integrity. Especially the investigations on strength tested probes need high resolution to visualise the beginning of deformation within the probe in comparison to the undeformed probe. On the other hand a general characterisation of the metallic foam probe is needed: is there a conjunction between mean density and stiffness?
|Fig 2: A vertical slice through the cube with 20 mm side length: |
a) before the compression; b)after 5% compression
For the density evaluation the probe has to be measured with the resolution which is high enough to visualise the walls. If the resolution is lower than the wall thickness, the calculated mean density will be lower (due to exponential attenuation) than the true one. But the comparison between similar probes will still be valid.
The tool to describe the homogeneity of probe on the basis of an idea by Kottar et al.  was developed. First the region has to be defined within which all points should be averaged. The averaging region is moved across the whole probe in 3D. The resulting image has the same size but allows to inspect density variations within the foam. By now the information is still in 3D, this means, all information is not visible at one glance. Therefore a software tool, which x-rays the data using the 'mean' operation, was used. The result is a two dimensional representation of the density distribution. Fig. 3 shows two cylindrical foam probes. The probe in fig.3, a) has an agglomeration of material at the top, whereas the density distribution in the probe in fig.3, b) is more homogenous.
|Fig 3: Two dimensional representation of the density distribution of cylindrical foam probes: |
a) image had max grey value of 180, which was scaled to 255,
b)image had max grey value of 100, which was scaled to 255
If there would be a bigger bubble inside, this would not be clearly visible by now. So all areas with a too low density over a certain region where highlighted. At this point the size of the averaging region becomes important. It should be set to the same size as the maximum pore which is still tolerable. Highlighting of these regions before the X-ray process will show up both by now: the low and high density areas. In fig. 3 these low density areas (the big bubbles) are visible as a kind of fleck on the image. Due to the use of 'mean' filter the image is independent of the form of the object.
To test the results of our measurements we used a special kind of porous material . This porous material consisted of metallic spheres with a known diameter, which where sintered together under slight pressure.
In a first step all volume outside the probe and every volume which is inside the probe, but outside the spheres, and therefore connected to the outside, was marked. For that a search algorithm in 3D was used, which expands the marked area as long as voxels in a given range of grey values, adjacent to a marked voxel, are found. (For results see ).
As long as the spatial resolution is good enough, the border of a material is defined as half the grey value of bulk material. If some walls get thinner than the spatial resolution, their apparent grey level may be lowered. In these cases the true value can be regained by first setting a lower level for the binarisation of the image and then using a 3D erode algorithm. The level of eroding is determined by the point spread function of the source detector system.
In the next step a search algorithm is looking for non-marked voxels in a specified range, which should be smaller than the first to avoid picking up voxel outside the spheres. From this starting point it expands its field of search marking voxel as 'inside' as long as new voxels in the grey level range adjacent to the marked one are found. Each bubble is filled with a different colour, so it is possible to see which bubbles are interconnected one to another. The number of voxels in each bubble is counted and the coordinates are summed. When one bubble is filled, the radius of an ideal sphere with same volume and the centre of gravity is calculated. These data can be used for theoretical calculations. In fig. 4, a) an example of the program output is shown, and fig. 4, b) shows the pore size distribution.
|Fig 4: a) an example of the program output; b) the pore size distribution|
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