Deformation Behavior Estimation of Aluminum Foam by X-ray CT Image-based Finite Element Analysis
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- Hangai, Y., Yamaguchi, R., Takahashi, S. et al. Metall and Mat Trans A (2013) 44: 1880. doi:10.1007/s11661-012-1532-7
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Aluminum foam is a lightweight material owing to the existence of a large number of internal pores. The compressive properties and deformation behavior of aluminum foam are considered to be directly affected by the shape and distribution of these pores. In this study, we performed image-based finite element (FE) analyses of aluminum foam using X-ray computed tomography (CT) images and investigated the possibility of predicting its deformation behavior by comparing the results of FE analyses with those of actual compressive tests. We found that it was possible to create an analytic model reflecting the three-dimensional (3D) pore structure using image-based modeling based on X-ray CT images. The stress distribution obtained from image-based FE analysis correctly indicates the layer where deformation first occurs as observed in actual compressive tests. Also, by calculating the mean stress of each plane perpendicular to the direction of compression based on the stress distribution obtained from image-based FE analysis, it was found that deformation begins in the layer containing the plane with maximum stress. It was thus possible to estimate the layer where deformation begins during the compression of aluminum foam.
Metal foams are lightweight materials with excellent impact-energy-absorbing properties, and their use in automobile components is expected to improve fuel consumption and safety. So far, a variety of methods has been proposed for the preparation of metal foams, and the compressive properties and impact-energy-absorbing properties of metal foams have been examined in many studies.[1–6] The compressive properties are thought to be greatly affected by the internal pore structure, but the current understanding of the relation between compressive properties and internal pore structure is limited to discussion based on scant information about the porosity (density) and externally observed changes in the pore structure during compressive deformation.[6–11] It is hoped that a more detailed consideration of information pertaining to the internal pore structure will reveal its effect on the compressive properties of foams and thus enable the production of metal foams with superior compressive properties as well as the prediction of their properties.
Image-based modeling is a technique that is capable of building analytic models that closely reflect information about a material’s three-dimensional (3D) shape. Modeling methods include serial sectioning and X-ray computed tomography (CT), which have been applied to numerous materials such as porous ceramics, skeletal structures,[13,14] and pore defects in aluminum alloy die castings.[15,16] Such techniques are also being applied to metal foams. For example, analyses using image-based finite element (FE) analysis have been used to model the actual 3D pore structure of metal foams to predict their stress–strain curves.[17–20] Moreover, studies have elucidated how micropores in cell walls affect the stress distribution in the walls. However, because the morphological information used in these analyses was obtained using serial sectioning and synchrotron radiation X-ray micro tomography over a limited region of observation, almost all of these analyses focused on test specimens with relatively few macro size pores, and the effect of the interaction between pores has therefore not been considered. Moreover, almost no research is currently being conducted on the behavior of successive layer deformation observed during the compression of aluminum foam.
In this study, we attempted the image-based FE analysis of aluminum foam using general-purpose X-ray CT on compressive test specimens with at least seven pores on each side. When applied to actual products, it is preferred that such analysis targets large regions and that compressive properties, including the site where deformation begins, the types of pores that weaken metal foams, and the magnitudes of the plateau stress and absorption energy, can be predicted by nondestructive means without performing an actual compressive test. Among these properties, the aim of our research is to establish a method for predicting the layer where deformation first occurs. To this end, we first performed X-ray CT imaging of aluminum foam and created an analytic model reproducing in detail the pore structure based on the image data obtained. We then simulated a compressive test by applying image-based FE analysis to the model. We also performed an actual compressive test on the aluminum foam imaged by X-ray CT and observed its deformation behavior. We then compared the results of both tests to investigate the possibility of predicting the layer in which deformation in aluminum foam begins.
2 Experimental and Analytical Methods
2.1 Test Specimens
2.2 X-Ray CT Imaging Method
X-ray CT imaging was performed using an SMX-225CT microfocus X-ray CT system (Shimadzu Corporation). Cone-beam CT was used to obtain 3D images. The image size was 512 × 512 × 480 voxels, with each voxel forming a cube of side 74.6 μm. The X-ray tube voltage was 80 kV, and the X-ray tube current was 30 μA. Figure 1(b) shows an example of a tomographic image obtained by X-ray CT imaging. The white areas are aluminum (cell walls), and the black areas are pores or external air.
2.3 Compressive Test Method
After X-ray CT imaging, the specimens were subjected to compressive testing at a cross-head speed of 5 mm/minutes using an Autograph AG-100kNG universal testing machine (Shimadzu Corporation). At the same time, the deformation behavior of the compressive test specimen undergoing compression was observed by video imaging from a single direction.
2.4 Image-Based FE Analysis Method
An FE analysis model was created by voxel modeling based on the acquired X-ray CT images. VOXELCON 2011 image-based structural analysis software (Quint Corporation) was used for 3D image processing and FE analysis. After layering of the tomographic images to obtain 3D images, a suitable threshold value was selected from a pixel value histogram so that aluminum and pores were distinguished, and image voxels were classified into material voxels and space voxels. X-ray CT image noise was eliminated at this stage by means of a mean filter. The material voxels were then converted into cubic FEs, with one voxel corresponding to one element, to obtain a 3D voxel model such as that shown in Figure 1(c). Figure 1(d) shows a 3D voxel model of the area around pores, which has been extracted and enlarged. It is apparent that each pore is separated by sufficiently fine voxels.
Next, in addition to the voxel models above, the material surface (pore surface) was extracted as an isosurface by means of the threshold value employed for voxel modeling based on the X-ray CT image, and a 3D STL model was created. Individual pore volumes were calculated from this STL model. At this stage, noise was eliminated by a mean filter, after which the pore walls were thickened by two more passes of the maximum filter to prevent the loss of walls thinner than one voxel. Pore volumes were slightly underestimated as a result.
A completely fixed base surface and 1 mm (4 pct) compression of the upper surface of the test specimen were assumed in the FE model via displacement boundary conditions. A linear elasticity analysis was performed on the cell walls on the assumption that they were pure aluminum with Young’s modulus E = 69 GPa and Poisson’s ratio ν = 0.3.
The resultant stress was evaluated on the basis of the average element stress, but to eliminate the effect of the stress concentration (excessive stress) due to surface irregularities in the voxel model, the stress on each voxel of interest was taken to be the arithmetic mean of the stress of the voxel of interest and those of the 26 surrounding adjacent voxels in 3D space, that is, a total of 27 voxels. However, at areas such as pore surfaces, where voxels were not surrounded by 26 voxels, the mean value only included material voxels. In addition, to alleviate the excessive stress at boundaries generated as a result of the absence of more than half of the adjacent material voxels, a fine one-voxel layer was inserted above and below the compressive surface.
3 Experimental and Analytical Results and Discussion
3.1 Evaluation of Deformation Layers Based on Stress Distribution
Similarly to in Figure 3, the layer where deformation begins is indicated by a red frame in Figure 4(b). Voxels with comparatively high stress are abundantly distributed in the red-framed region, whereas high stress is almost absent from the upper part of the test specimen, where no change was observed under a compression of ε = 12 pct. Namely, it appears that the layer where deformation begins and the high-stress region correspond with each other.
3.2 Evaluation of Deformation Layer From the Mean Stress in Planes Perpendicular to the Direction of Compression
3.3 Evaluation of Deformation Layer Obliquely Inclined to the Direction of Compression
It is anticipated that these methods of predicting the layer where deformation first occurs can be extended to aluminum foams for which control of the order of deformation is essential, for example, functionally graded aluminum foams,[26–30] fabrication of which has been attempted in recent years. In functionally graded aluminum foams, deformation is controlled by optimizing the type of alloy and the arrangement of characteristics of the pore structure, such as porosity and pore size. However, in practice, it is difficult to experimentally test all combinations of these characteristics. If some assumptions are made on the deformation behavior of such foams, then analysis should make it possible to evaluate the properties of functionally graded aluminum foam for use as a structural component.
It was possible to create an analytic model reflecting the 3D pore structure using image-based modeling based on X-ray CT images.
The stress distribution obtained from image-based FE analysis and the layer where deformation first begins observed in actual compressive tests corresponds with each other. It was thus possible to predict the layer where deformation first occurs during the compression of aluminum foam.
By calculating the mean stress of each plane perpendicular to the direction of compression from the stress distribution obtained from image-based FE analysis, it was found that deformation begins in the layer containing the plane of maximum stress. It was thus possible to estimate the layer where deformation begins during the compression of aluminum foam.
In some cases, aluminum foam deformed obliquely under compression. However, an approximate evaluation should be possible under the assumption that deformation occurs in a layer perpendicular to the direction of compression.
This study was partly financially supported by the Industrial Technology Research Grant Program in 2009 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan and JKA promotion funds from AUTORACE. The authors thank Professor K. Saito, Gunma University, for his helpful advice on conducting the experiments, and T. Miyoshi, Shinko Wire Company, Ltd., for providing ALPORAS.