3D micro-tomography, metallic foams, cellular materials, pore size calculation, mean density.
For the characterisation of the inner structure of cellular metals from 3D tomograms different methods were developed: evaluation of mean density in 3D, calculation of pore size and pore size distribution, separation of walls and nodes, detection of internal deformations of strength tested foams.
The aim of the investigation
For the characterisation of the cellular metals (foams) the knowledge of the inner structure is important. The mechanical properties of the foams depend on the structure of the material [1]. Porous materials most often are produced by foaming (not casting), therefore the quality over the larger areas has to be controlled. For a check at one glance the spatial density distribution should be represented in a 2D image. When the pores in the porous materials are closed, the distribution of the pore sizes can be determined and too big pores can be marked. For the open pore materials the connections between pores can be detected. For such materials thin wall areas can be separated from node areas (where several walls meet together). 3D image comparison before and after the compression yields the image of the partial shift and internal deformation zones. This allows a correlation with the other parameters.
3D micro-tomographs in BAM
Fig 1: 3D Tomographs for objects with diameter up to 200 mm (left) and up to 20 mm (right).
In the last years the interest in computed tomography investigations on new materials like fibre ceramics, metal ceramics and metallic cellular materials has increased. For these applications a fully three dimensional investigation of the objects with high spatial resolution in all directions is required. A common method to achieve high spatial resolution is using X-ray tubes with a very small focus and magnification technique.
For these purposes different 3D tomographs are used in BAM [2, 3]. A variety of objects from 200 mm diameter (with minimum resolution of 0.1 mm) down to small parts with 1mm diameter (with minimum resolution of 1.5 mm) can be investigated (fig.1).
Alluminium foams
In order to use metallic foams in a serial production (e.g. as crash absorbers), the parameters, which characterise the material, have to be known. At present the quality of the foams depends on the form of the produced object. Therefore the samples, which will be used to determine mechanical parameters, first have to be non-destructively tested. In figure 2 the image of a sample, which had to be used in a tension test, is presented. In the vertical slice, on the right near the top, a pore from one wall to the other can be seen. Here the size of the pores is not adapted to the thickness of the wall, therefore measured parameters would not be reliable.
Fig 2: Cylindrical sample for tension test, 12cm in height. Fig 3: Two dimensional representation of density distribution with marked faults.
Density evaluation
The requirements for foams are most often described using the parameter of mean density. Inside the probe this mean value can be reached in different ways and may be locally dependent. A foam with small pores and thin walls can have the same overall density as a foam with big pores and with only few walls. Furthermore, some big pores included in the probe cannot be detected using simple radiography due to the chaotic structure of the foam.
For the density evaluation a tool to describe the homogeneity of the probe was developed, using an idea of Degischer et al. [4]. First the region has to be defined within which all points should be averaged. The size of the averaging region should be set to the same size as the maximum pore which is still tolerable, and it should be at least three times bigger as the radius of the average pore. The averaging region is moved across the whole image in 3D. The resulting image shows density variations within the foam, without the foam structure. Then the areas, which have a too low density or too big pores, are highlighted. In order to get a 2D image the data set is x-rayed using the mean operation. Fig. 3 shows results for two cylindrical foam probes with 4 cm diameter. The probe on the left has several too big pores in the centre of the probe and an agglomeration of material at the bottom, whereas the density of the probe on the right is higher, but more homogenous, and there are only some too big pores found.
Investigation of the deformation
The failure mechanisms of strength tested foams can also be studied using 3D micro tomography. The samples were pressed in several steps and CT measurements were performed before the pressing of the foam and after each step of compression. The shift of the parts of strength tested samples is calculated comparing 3D images of the sample before and after the compression. This allows to link the internal deformation to the parameters, which are characteristic for this foam [5].
In figure 4 a vertical slice through a foam sample with closed pores is shown. From presented images it is possible to see, that this foam is deforming proportionally. The deformed walls are marked with arrows.
For the determination of the pore sizes first all volume outside the probe and every volume which is inside the probe, connected to the outside, is marked. Then a search algorithm is looking for non-marked voxels in a specified grey level range. 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 pore is filled with a different colour, in order to see which pores are interconnected one to another. The number of voxels in each pore is counted, the centre of gravity and the radius of an ideal sphere with same volume is calculated. From these data the pore size distribution is calculated.
Nodes and Walls
Beside the local density the ratio between the material content in the walls and in the nodes is an important feature for the characterisation of metallic foams. The nodes are described as areas, where more as two walls meet. For the separation of nodes and walls the image is first binarised and then eroded in 3D until all walls disappear. The number of necessary steps depends on the wall thickness. Then the same number of steps of "3D dilate" is performed. For the separation of nodes logical AND between binarised image and dilated image has to be performed. For the separation of walls the image of the nodes is subtracted from binarised image of the foam.
Fig 6: Separation of walls and nodes in metallic foams
High resolution 3D X-ray tomography enables detailed structural analysis of cellular metalls. Different features of the metallic foams can be characterised starting from high resolution 3D tomograms: deformation processes within the probe can be visualised; the mean density of the foam can be calculated; low and high density areas can be detected; pore sizes can be calculated; the pore size distribution can be found, the density of the selected structural elements can be determined.