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Internal microstructure evolution of aluminum foams under compression
Materials Research Bulletin 41 (2006) 1949–1958 www.elsevier.com/locate/matresbu
Internal microstructure evolution of aluminum foams under compression Min Wang, Xiao-Fang Hu *, Xiao-Ping Wu CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230026, PR China Received 25 October 2005; received in revised form 28 February 2006; accepted 3 March 2006 Available online 29 March 2006
Abstract In this paper, the internal microstructure deformation of open-cell and closed-cell aluminum foams under compression was investigated by using synchrotron radiation X-ray computed tomography (SR-CT) technique and digital image analysis method. The reconstructed images were obtained by using filtered back projection algorithm based on the original images taken from SR-CT experiments. Several important parameters including cross-section porosity, total porosity and cross-section deformation were computed from the reconstructed images. The variation of these parameters provided useful evolution information of internal microstructure of aluminum foams under compression. # 2006 Elsevier Ltd. All rights reserved. Keywords: Synchrotron radiation X-ray computed tomography; Aluminum foam; Microstructure
1. Introduction Aluminum foams with porous structure have many outstanding physical and mechanical properties such as energyabsorbing, sound-isolating, electromagnetism-shielding, etc. They have tremendous potential to be applied in many fields. They can be divided into two types of foams according to their pore structures, i.e., open-cell and closed-cell. The pores are isolated for closed-cell structures and conjoint for open-cell ones. The performance of aluminum foams depends mostly on the parameters such as porosity, shapes and distribution of pores [1–5]. Therefore, it is very important to study the mechanical behavior of their internal microstructures. One of most important characterization for the microstructural behavior is direct non-destructive three-dimensional microstructure investigation which can now be carried out by using X-ray computed tomography [6–10]. It can provide maps of the internal structure of a sample from the measurements of the attenuation of an X-ray beam passing through the sample at different incident angles. Because an image with high spatial resolution is generally obtained by using an X-ray source with a high photon flux, the use of synchrotron radiation (SR) is particularly attractive. The feasibility of using SR to obtain qualified images has already been demonstrated at several SR facilities around the world [10] especially at the Beijing synchrotron radiation facility (BSRF) in which a three dimensional SR-CT system has been installed. This SR-CT system allows the non-destructive acquisition of high-resolution images directly.
* Corresponding author. E-mail address: [email protected] (X.-F. Hu). 0025-5408/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.materresbull.2006.03.002
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Table 1 Open-cell and closed-cell aluminum foam specimens Specimen code
Cell structure
Cell size (mm)
Diameter (mm)
Height (mm)
Density (g/cm3)
OC CC
Open-cell Closed-cell
0.8–2.2 0.9–2
6 6
10 10
1.22 0.98
In order to investigate the microstructures evolution of materials, a set-up with precise rotation and uniaxial movement for samples has been developed in this system. In this paper, the images of internal microstructures of open-cell and closed-cell aluminum foams under compression were obtained by using this SR-CT system. The projection images were reconstructed by filtered back projection algorithm. Several important parameters such as cross-section porosity, total porosity and cross-section deformation were calculated based on the reconstructed images. Their variation with compressive displacement provided the evolution information of internal microstructure of aluminum foams. 2. Experiment 2.1. Specimen preparation Both open-cell and closed-cell aluminum foams, supplied by the Institute of Solid State Physics of Chinese Academy of Science, are considered in this study. The infiltration casting and powder metallurgy are the productive methods for open-cell and closed-cell aluminum foams, respectively. And their original materials both are 201AB aluminum alloy powder. All specimens are manufactured by wire-cutting technique and each specimen has a cylinder shape of a diameter of 6 mm and a height of 10 mm. The parameters of all specimens are listed in Table 1. 2.2. SR-CT method The experiment was carried out on the 4W1A beam-line at BSRF, Beijing, China. A schematic diagram of this SRCT projection imaging facility is given in Fig. 1. A wide collimated SR X-ray (up to 14 mm 10 mm) with energy range from 3 to 23 KeV is available. The X-ray with 20 KeV selected by silicon single-crystal monochromator was used in this test. The specimens were clipped in a specially designed loading platform that could be precisely operated with rotation and uniaxial movement. The synchrotron radiation X-ray passed through samples and reached an X-ray charge-coupled device (CCD) detector which recorded the intensity message of X-ray. The CCD including a 1300 1030 pixels chip with a unit pixel of 10.9 mm 10.9 mm, offered an 8 bits dynamic range. At every step of compression, a specimen was imaged in different projection angles (in the range of 0–1808). Typically, 200 shadow images of the specimen were acquired. The images were then processed by filtered back projection algorithm. A number of two-dimensional (2D) slides (in serial order) representing the effective attenuation coefficients of the specimen in terms of gray levels were obtained. These two-dimensional specimen slides can be stacked to provide a three-dimensional (3D) configuration scenery of the specimen.
Fig. 1. Schematic diagram of SR-CT projection imaging facility.
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Table 2 Compression displacements applied for specimens
OC Dl (mm) CC Dl (mm)
A
B
C
D
E
F
G
H
I
J
K
0 0
0.3 0.3
0.6 0.6
0.9 0.9
1.2 1.2
1.5 1.5
1.8 1.8
2.1 2.1
2.4 –
2.7 –
3.0 –
Fig. 2. Coordinate system for 3D imaging reconstruction.
2.3. Reconstruction of SR-CT images The experiment was displacement-controlled under compression. At each compressive displacement, the specimen was rotated and projection images were collected. The displacement, Dl, in each step of compression is shown in Table 2. Eleven and eight displacement steps were examined for open- and closed-cell specimens, respectively. A series of internal microstructure reconstructed images in different compression states were obtained by SR-CT technique. To ensure a uniform optical field through the specimen, only partial region is chosen to be reconstructed. In order to describe and compare these results easily, a Cartesian coordinate system is considered and shown in Fig. 2. The plane xoy is defined as the top cross section of the reconstructed part of the specimens. With the increase of the compressive displacement, the height of the reconstructed part decreases continuously. Consequently, the position of the bottom cross-section varies under different compressive states. Although the height of the observed region decreases during compression, the identical region in every state step can be found and reconstructed (see Section 4.2). To seek the identical region, a standard co-correlation calculation method has been used in this paper. The curve for the height of the reconstructed part (hrc) versus compressive displacement is shown in Fig. 3(a). The volume percentage ( p) of the reconstructed part to the whole specimen under different compression displacements is shown in Fig. 3(b). All images are reconstructed with binary processing to enhance the contrast of images. The black and white regions in the images of Figs. 4–7 represent matrix and pores, respectively. 3. Results 3.1. Reconstruction in original state (A) In the original state (A), both open and closed cell specimens were not compressed. The microstructures in state A show the real shapes, size and distribution of internal pores. Figs. 4 and 5 denote the internal structures for open- and closed-cell aluminum foams, respectively. Evidently the structures of open-cell are different from those of closed-cell. The internal pores in open-cell are mostly conjoint with each other, irregular in shapes and uneven in distribution. The internal pores in close-cell are mainly isolated with each other, simple geometric shapes like ellipsoid and non-uniform in distribution. 3.2. Evolution for open-cell foam The foam specimen will undergo deformation under compression. As a result, the sections (cross and vertical) will not only change positions, but also deform in their section planes. In order to find the same section before and after
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Fig. 3. (a) Reconstructed height vs. compression displacement and (b) volume percentage of the reconstructed part vs. compression displacement for open- and closed-cell aluminum foams.
deformation, a digital image correlation technique has been applied. The images illustrating deformation evolution in cross and vertical section for open-cell are given in Fig. 6 in which A, D, G and K represent different compression states, respectively (see Table 2). From the Fig. 6, it is observed that, with the increase of compressive displacement, the size of internal pores decreases continuously and their shapes change gradually. These changes lead to the variety of porosity directly. The porosity and deformation behavior are related to the difference in structures of cross sections (see Figs. 8(a) and 9(a) and Section 4).
Fig. 4. Reconstructed images of open-cell aluminum foam in original state; (a)–(c) illustrate the cross-section slice at z = 2502 mm; vertical section slice at x = 3106 mm and 3D image, respectively.
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3.3. Evolution for closed-cell foam Similarly, the images illustrating deformation evolution of internal microstructures for closed-cell are given in Fig. 7 in which A, C, E and H represent different compression states, respectively (see Table 2). Compared with open-cell foams, the deformation behavior of internal pores is much more complex for closed-cell foams. Because the pores of open-cell are conjoint, they will shrink instead of be crushed under compression.
Fig. 5. Reconstructed images for closed-cell aluminum foams in original state; (a)–(c) illustrate the cross-section slice at z = 3482 mm; verticalsection slice at x = 2976 mm and 3D image, respectively.
Fig. 6. (a) Evolution images at cross section z = 1341 mm for open-cell aluminum foam. (b) Evolution images at vertical-section x = 4742 mm for open-cell aluminum foam.
Fig. 7. (a) Evolution images at cross section z = 343 mm for closed-cell aluminum foam. (b) Evolution images at vertical-section x = 4382 mm for closed-cell aluminum foam.
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Fig. 8. (a) Cross-section porosity distribution along Z-axial in each compression state for open-cell aluminum foam. (b) Cross-section porosity distribution along z-axial in each compression state for closed-cell aluminum foam.
While the pores of closed-cell are isolated, some pores will be crushed under compression. The change in porosity and the deformation behavior are also related to the difference in structures of cross sections (see Figs. 8(b) and 9(b) and Section 4). 4. Discussion 4.1. Cross-section porosity and total porosity The cross-section porosity (Pcross-section) defines as the ratio of the area of pores in a cross section to the total crosssection area and the total porosity (Ptotal) is the ratio of the volume of pores to the total volume of the material. The reconstructed images show that the shapes, size and distribution of internal pores in each cross section are different. In order to illustrate such changes, the cross-section porosity and its variation with compression are analyzed to describe structures behavior. Fig. 8(a) and (b) show the cross-section porosity (Pcross-section) curves with its position (h) under different compression states for open- and closed-cell foams, respectively. Symbols A to K represent the different compression states (see Table 2). The curves in Fig. 8(a) and (b) indicate that the porosities in different cross section are not equal. Furthermore, the variation of the porosity of each cross section in compression for open-cell is clearly different from those of
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Table 3 Total porosity for open- and closed-cell aluminum foams
OC Ptotal (%) CC Ptotal (%)
A
B
C
D
E
F
G
H
I
J
K
50.2 57.8
48.4 57.4
47.3 56.1
45.7 54.1
43.9 51.0
41.9 47.8
40.5 44.1
39.7 40.9
33.7 –
30.3 –
26.2 –
closed-cell. For open-cell aluminum foam, as shown in Fig. 8(a), the cross-section porosity decreases continuously with the increase of compressive displacement, and the variation for each cross section is relatively uniform. This observation means that although porosity distribution along Z-axis is variable, the tendency and extent of its variation for each cross section are consistent. However, the situations are evidently different for closed-cell aluminum foam as shown in Fig. 8(b). The variation of cross-section porosity in the range from Z = 0 to 1600 mm is obviously higher than that in other range, which indicates that the deformation of closed-cell aluminum foam is non-uniform. The localized crushing seen on the left side of Fig. 8(b) has also been observed in a different material compression experiment done by Dunand group [11]. This phenomenon means that the porosity might not be a major factor to affect the deformation behavior for closed-cell foam. It is understood that deformation behavior for closed-cell aluminum foam is related not only to the porosity but also to its pore structures. The total porosity (Ptotal) reflects macro mechanical behavior of aluminum foams. It can be calculated for the reconstructed part in each state. The data in Table 3 show that the total porosity for open- and closed-cell aluminum foams are all decreased monotonously with compression.
Fig. 9. (a) Correlation coefficient for cross section between two compression states for open-cell aluminum foam. (b) Correlation coefficient for cross section between two compression states for closed-cell aluminum foam.
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4.2. Vertical displacement and deformation of cross sections To characterize the mechanical behavior effectively, besides the porosity, the deformation of aluminum foams should also be analyzed. For a simplified case of deformation, the displacement field of aluminum foams along Z-axis is assumed to be a plane deformation in this study. A standard co-correlation calculation, which can determine the vertical displacement of cross sections and illustrate the cross-section deformation indirectly, is applied. Let r represent the correlation coefficient for the same cross section between two conjoint compression states. When a cross section is chosen to be observed in a compression state, its position in Z-axis is known. In the following compression state, the position of the observed cross section in Z-axis can be determined by searching the cross section with the maximum correlation coefficient with the one in the previous step. Thus the vertical displacement can be obtained from the position difference between these two z-axes. When r = 1, it implies that the cross section has no deformation in its plane, i.e. the cross section is exactly the same as the last step. In other cases (r 6¼ 1), it indicates that the crosssection undergoes some deformation. The magnitude of r corresponds to the extent of deformation. The correlation coefficient curves versus cross sections in two consecutive compression steps are shown in Fig. 9. Although the foam is uniformly compressed, the deformation of each cross section shows inhomogeneity under compression for open-cell aluminum foams (Fig. 9(a)). However, the behavior for closed-cell aluminum foam is much different. The deformation in the upper cross section is significantly large compared to those in other cross sections, as illustrated in Fig. 9(b). The results are consistent with the analysis of porosity.
Fig. 10. (a) Displacement for each cross section along Z-axial in final state for open-cell aluminum foam. (b) Displacement for each cross section along z-axial in final state for closed-cell aluminum foam.
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The vertical displacements along Z-axis of cross sections are shown in Fig. 10. Obviously the distribution of displacements is nearly linear for open-cell and nonlinear for closed-cell, as depicted in Fig. 10(a) and (b), respectively. 4.3. Analysis of deformation mechanism Figs. 8 and 9 show the porosity and correlation coefficient evolution of each cross section under compression, respectively. In order to analyze their influence on deformation, the porosity curve in the original state A and correlation coefficient curve in the final state K are chosen, as shown in Fig. 11. Comparing curve A with curve K in Fig. 11(a), it can be observed that the two curves are nearly dissymmetric. The bigger the cross-section porosity is, the more deformation the cross-section undergoes. This phenomenon is termed as the deformation rule of open-cell aluminum foam (DROAF). Situation for closed-cell aluminum foams is more complex as shown in Fig. 11(b). The curves A and H can be divided into two parts (I and II). In part I, the mechanical behavior is similar to the case of open-cell aluminum foams, and its deformation follows the DROAF. The reason is that in part I the closed-cell structures are destroyed due to large deformation and they actually become open-cell. In part II, it does not follow the same rule. Generally, porosity is a major factor affecting the strength for open-cell aluminum foams. Large deformation always occurs in the region where local porosity is relatively large. The deformation process for open-cell aluminum foams is condensation. However, it is not the same case for closed-cell aluminum foams, in which the mechanical
Fig. 11. (a) Cross-section porosity curve in state A and cross-section correlation coefficient curve in state K for open-cell aluminum foam. (b) Crosssection porosity curve in state A and cross-section correlation coefficient curve in state H for closed-cell aluminum foam.
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behaviors are dominated by both porosity and pore structures. Some isolated pores in the weak region will be firstly crushed under compression. These isolated pores have become conjoint and the deformation will follow the DROAF. Large deformation takes place in this region continuously until some other pores are broken. This process will continue until whole foam is condensed. Consequently, there are two deformation processes for closed-cell aluminum foams under compression, i.e., the pores crush and the foam condensation. Actually the two processes occur alternately. 5. Conclusion Using the SR-CT technique, the open- and closed-cell aluminum foams were examined in situ under compression. A series of reconstruction images of internal microstructures were given. The porosity distribution was determined and the structural deformation evolution was analyzed based upon the experimental data. It was found that the mechanical behavior was much different between the open- and closed-cell foams under compression. For open-cell aluminum foam, the vertical displacements of each cross section were uniform, and the deformation in its cross-section plane mainly depended on the local porosity. For closed-cell foam, the vertical displacements of each cross-section became nonlinear along Z-axis, and cross-section deformation was dominated by porosity and pore structures. Unlike the condensation process for open-cell, closed-cell aluminum foams underwent the pore broken and condensation alternately under compression. Acknowledgements This work was supported by National Nature Science Foundation of China under Contract Nos. 10232030 and 10472113 and BSRF Foundation. The authors specially thank Dr. Daying Li and Prof. Yuanming Xia for their cooperation in the design of the loading platform. The authors also would like to thank Rui Jiang, Feng Xu, Fan Jiang, Bing Lu at USTC and Pei-ping Zhu, Qing-xi Yuan and Jun-yue Wang at BSRF for their valuable contribution to this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
O.B. Olurin, M. Arnold, C. Korner, R.F. Singer, Mater. Sci. Eng. A 328 (2002) 328–334. C. Motz, R. Pippan, Acta Mater. 49 (2001) 2463–2470. A.E. Makaki, T.W. Clyne, Acta Mater. 49 (2001) 1677–1686. O.B. Olurin, N.A. Fleck, M.F. Ashby, Mater. Sci. Eng. A 291 (2000) 136–146. I. Duarte, J. Banhart, Acta Mater. 48 (2000) 2349–2362. A. Pyzalla, B. Camin, T. Buslaps, M. Di Michiel, H. Kaminski, A. Kottar, A. Pernack, W. Reimers, Science 308 (2005) 92–95. X.-N. Jing, X.-F. Hu, J.-H. Zhao, Y.-O. Wang, Y.-L. Tian, J. Mater. Sci. Eng. 21 (2003) 327–330. E. Maire, L. Babout, J.-Y. Buffiere, R. Fougeres, Mater. Sci. Eng. A 319–321 (2001) 216–219. X.-F. Hu, Y.-O. Wang, X.-N. Jing, J.-H. Zhao, Y.-L. Tian, J. Exp. Mech. 18 (2003) 485–489. A. Elmoutaouakkil, G. Fuchs, P. Bergounhon, R. Peres, F. Peyrin, J. Phys. D: Appl. Phys. 36 (2003) A37–A43. D.K. Balch, J.G. O’Dwyer, G.R. Davis, C.M. Cady, G.T. Gray III, D.C. Dunand, Mater. Sci. Eng. A 391 (2005) 408–417.
Internal microstructure evolution of aluminum foams under compression Min Wang, Xiao-Fang Hu *, Xiao-Ping Wu CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230026, PR China Received 25 October 2005; received in revised form 28 February 2006; accepted 3 March 2006 Available online 29 March 2006
Abstract In this paper, the internal microstructure deformation of open-cell and closed-cell aluminum foams under compression was investigated by using synchrotron radiation X-ray computed tomography (SR-CT) technique and digital image analysis method. The reconstructed images were obtained by using filtered back projection algorithm based on the original images taken from SR-CT experiments. Several important parameters including cross-section porosity, total porosity and cross-section deformation were computed from the reconstructed images. The variation of these parameters provided useful evolution information of internal microstructure of aluminum foams under compression. # 2006 Elsevier Ltd. All rights reserved. Keywords: Synchrotron radiation X-ray computed tomography; Aluminum foam; Microstructure
1. Introduction Aluminum foams with porous structure have many outstanding physical and mechanical properties such as energyabsorbing, sound-isolating, electromagnetism-shielding, etc. They have tremendous potential to be applied in many fields. They can be divided into two types of foams according to their pore structures, i.e., open-cell and closed-cell. The pores are isolated for closed-cell structures and conjoint for open-cell ones. The performance of aluminum foams depends mostly on the parameters such as porosity, shapes and distribution of pores [1–5]. Therefore, it is very important to study the mechanical behavior of their internal microstructures. One of most important characterization for the microstructural behavior is direct non-destructive three-dimensional microstructure investigation which can now be carried out by using X-ray computed tomography [6–10]. It can provide maps of the internal structure of a sample from the measurements of the attenuation of an X-ray beam passing through the sample at different incident angles. Because an image with high spatial resolution is generally obtained by using an X-ray source with a high photon flux, the use of synchrotron radiation (SR) is particularly attractive. The feasibility of using SR to obtain qualified images has already been demonstrated at several SR facilities around the world [10] especially at the Beijing synchrotron radiation facility (BSRF) in which a three dimensional SR-CT system has been installed. This SR-CT system allows the non-destructive acquisition of high-resolution images directly.
* Corresponding author. E-mail address: [email protected] (X.-F. Hu). 0025-5408/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.materresbull.2006.03.002
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Table 1 Open-cell and closed-cell aluminum foam specimens Specimen code
Cell structure
Cell size (mm)
Diameter (mm)
Height (mm)
Density (g/cm3)
OC CC
Open-cell Closed-cell
0.8–2.2 0.9–2
6 6
10 10
1.22 0.98
In order to investigate the microstructures evolution of materials, a set-up with precise rotation and uniaxial movement for samples has been developed in this system. In this paper, the images of internal microstructures of open-cell and closed-cell aluminum foams under compression were obtained by using this SR-CT system. The projection images were reconstructed by filtered back projection algorithm. Several important parameters such as cross-section porosity, total porosity and cross-section deformation were calculated based on the reconstructed images. Their variation with compressive displacement provided the evolution information of internal microstructure of aluminum foams. 2. Experiment 2.1. Specimen preparation Both open-cell and closed-cell aluminum foams, supplied by the Institute of Solid State Physics of Chinese Academy of Science, are considered in this study. The infiltration casting and powder metallurgy are the productive methods for open-cell and closed-cell aluminum foams, respectively. And their original materials both are 201AB aluminum alloy powder. All specimens are manufactured by wire-cutting technique and each specimen has a cylinder shape of a diameter of 6 mm and a height of 10 mm. The parameters of all specimens are listed in Table 1. 2.2. SR-CT method The experiment was carried out on the 4W1A beam-line at BSRF, Beijing, China. A schematic diagram of this SRCT projection imaging facility is given in Fig. 1. A wide collimated SR X-ray (up to 14 mm 10 mm) with energy range from 3 to 23 KeV is available. The X-ray with 20 KeV selected by silicon single-crystal monochromator was used in this test. The specimens were clipped in a specially designed loading platform that could be precisely operated with rotation and uniaxial movement. The synchrotron radiation X-ray passed through samples and reached an X-ray charge-coupled device (CCD) detector which recorded the intensity message of X-ray. The CCD including a 1300 1030 pixels chip with a unit pixel of 10.9 mm 10.9 mm, offered an 8 bits dynamic range. At every step of compression, a specimen was imaged in different projection angles (in the range of 0–1808). Typically, 200 shadow images of the specimen were acquired. The images were then processed by filtered back projection algorithm. A number of two-dimensional (2D) slides (in serial order) representing the effective attenuation coefficients of the specimen in terms of gray levels were obtained. These two-dimensional specimen slides can be stacked to provide a three-dimensional (3D) configuration scenery of the specimen.
Fig. 1. Schematic diagram of SR-CT projection imaging facility.
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Table 2 Compression displacements applied for specimens
OC Dl (mm) CC Dl (mm)
A
B
C
D
E
F
G
H
I
J
K
0 0
0.3 0.3
0.6 0.6
0.9 0.9
1.2 1.2
1.5 1.5
1.8 1.8
2.1 2.1
2.4 –
2.7 –
3.0 –
Fig. 2. Coordinate system for 3D imaging reconstruction.
2.3. Reconstruction of SR-CT images The experiment was displacement-controlled under compression. At each compressive displacement, the specimen was rotated and projection images were collected. The displacement, Dl, in each step of compression is shown in Table 2. Eleven and eight displacement steps were examined for open- and closed-cell specimens, respectively. A series of internal microstructure reconstructed images in different compression states were obtained by SR-CT technique. To ensure a uniform optical field through the specimen, only partial region is chosen to be reconstructed. In order to describe and compare these results easily, a Cartesian coordinate system is considered and shown in Fig. 2. The plane xoy is defined as the top cross section of the reconstructed part of the specimens. With the increase of the compressive displacement, the height of the reconstructed part decreases continuously. Consequently, the position of the bottom cross-section varies under different compressive states. Although the height of the observed region decreases during compression, the identical region in every state step can be found and reconstructed (see Section 4.2). To seek the identical region, a standard co-correlation calculation method has been used in this paper. The curve for the height of the reconstructed part (hrc) versus compressive displacement is shown in Fig. 3(a). The volume percentage ( p) of the reconstructed part to the whole specimen under different compression displacements is shown in Fig. 3(b). All images are reconstructed with binary processing to enhance the contrast of images. The black and white regions in the images of Figs. 4–7 represent matrix and pores, respectively. 3. Results 3.1. Reconstruction in original state (A) In the original state (A), both open and closed cell specimens were not compressed. The microstructures in state A show the real shapes, size and distribution of internal pores. Figs. 4 and 5 denote the internal structures for open- and closed-cell aluminum foams, respectively. Evidently the structures of open-cell are different from those of closed-cell. The internal pores in open-cell are mostly conjoint with each other, irregular in shapes and uneven in distribution. The internal pores in close-cell are mainly isolated with each other, simple geometric shapes like ellipsoid and non-uniform in distribution. 3.2. Evolution for open-cell foam The foam specimen will undergo deformation under compression. As a result, the sections (cross and vertical) will not only change positions, but also deform in their section planes. In order to find the same section before and after
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Fig. 3. (a) Reconstructed height vs. compression displacement and (b) volume percentage of the reconstructed part vs. compression displacement for open- and closed-cell aluminum foams.
deformation, a digital image correlation technique has been applied. The images illustrating deformation evolution in cross and vertical section for open-cell are given in Fig. 6 in which A, D, G and K represent different compression states, respectively (see Table 2). From the Fig. 6, it is observed that, with the increase of compressive displacement, the size of internal pores decreases continuously and their shapes change gradually. These changes lead to the variety of porosity directly. The porosity and deformation behavior are related to the difference in structures of cross sections (see Figs. 8(a) and 9(a) and Section 4).
Fig. 4. Reconstructed images of open-cell aluminum foam in original state; (a)–(c) illustrate the cross-section slice at z = 2502 mm; vertical section slice at x = 3106 mm and 3D image, respectively.
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3.3. Evolution for closed-cell foam Similarly, the images illustrating deformation evolution of internal microstructures for closed-cell are given in Fig. 7 in which A, C, E and H represent different compression states, respectively (see Table 2). Compared with open-cell foams, the deformation behavior of internal pores is much more complex for closed-cell foams. Because the pores of open-cell are conjoint, they will shrink instead of be crushed under compression.
Fig. 5. Reconstructed images for closed-cell aluminum foams in original state; (a)–(c) illustrate the cross-section slice at z = 3482 mm; verticalsection slice at x = 2976 mm and 3D image, respectively.
Fig. 6. (a) Evolution images at cross section z = 1341 mm for open-cell aluminum foam. (b) Evolution images at vertical-section x = 4742 mm for open-cell aluminum foam.
Fig. 7. (a) Evolution images at cross section z = 343 mm for closed-cell aluminum foam. (b) Evolution images at vertical-section x = 4382 mm for closed-cell aluminum foam.
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Fig. 8. (a) Cross-section porosity distribution along Z-axial in each compression state for open-cell aluminum foam. (b) Cross-section porosity distribution along z-axial in each compression state for closed-cell aluminum foam.
While the pores of closed-cell are isolated, some pores will be crushed under compression. The change in porosity and the deformation behavior are also related to the difference in structures of cross sections (see Figs. 8(b) and 9(b) and Section 4). 4. Discussion 4.1. Cross-section porosity and total porosity The cross-section porosity (Pcross-section) defines as the ratio of the area of pores in a cross section to the total crosssection area and the total porosity (Ptotal) is the ratio of the volume of pores to the total volume of the material. The reconstructed images show that the shapes, size and distribution of internal pores in each cross section are different. In order to illustrate such changes, the cross-section porosity and its variation with compression are analyzed to describe structures behavior. Fig. 8(a) and (b) show the cross-section porosity (Pcross-section) curves with its position (h) under different compression states for open- and closed-cell foams, respectively. Symbols A to K represent the different compression states (see Table 2). The curves in Fig. 8(a) and (b) indicate that the porosities in different cross section are not equal. Furthermore, the variation of the porosity of each cross section in compression for open-cell is clearly different from those of
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Table 3 Total porosity for open- and closed-cell aluminum foams
OC Ptotal (%) CC Ptotal (%)
A
B
C
D
E
F
G
H
I
J
K
50.2 57.8
48.4 57.4
47.3 56.1
45.7 54.1
43.9 51.0
41.9 47.8
40.5 44.1
39.7 40.9
33.7 –
30.3 –
26.2 –
closed-cell. For open-cell aluminum foam, as shown in Fig. 8(a), the cross-section porosity decreases continuously with the increase of compressive displacement, and the variation for each cross section is relatively uniform. This observation means that although porosity distribution along Z-axis is variable, the tendency and extent of its variation for each cross section are consistent. However, the situations are evidently different for closed-cell aluminum foam as shown in Fig. 8(b). The variation of cross-section porosity in the range from Z = 0 to 1600 mm is obviously higher than that in other range, which indicates that the deformation of closed-cell aluminum foam is non-uniform. The localized crushing seen on the left side of Fig. 8(b) has also been observed in a different material compression experiment done by Dunand group [11]. This phenomenon means that the porosity might not be a major factor to affect the deformation behavior for closed-cell foam. It is understood that deformation behavior for closed-cell aluminum foam is related not only to the porosity but also to its pore structures. The total porosity (Ptotal) reflects macro mechanical behavior of aluminum foams. It can be calculated for the reconstructed part in each state. The data in Table 3 show that the total porosity for open- and closed-cell aluminum foams are all decreased monotonously with compression.
Fig. 9. (a) Correlation coefficient for cross section between two compression states for open-cell aluminum foam. (b) Correlation coefficient for cross section between two compression states for closed-cell aluminum foam.
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4.2. Vertical displacement and deformation of cross sections To characterize the mechanical behavior effectively, besides the porosity, the deformation of aluminum foams should also be analyzed. For a simplified case of deformation, the displacement field of aluminum foams along Z-axis is assumed to be a plane deformation in this study. A standard co-correlation calculation, which can determine the vertical displacement of cross sections and illustrate the cross-section deformation indirectly, is applied. Let r represent the correlation coefficient for the same cross section between two conjoint compression states. When a cross section is chosen to be observed in a compression state, its position in Z-axis is known. In the following compression state, the position of the observed cross section in Z-axis can be determined by searching the cross section with the maximum correlation coefficient with the one in the previous step. Thus the vertical displacement can be obtained from the position difference between these two z-axes. When r = 1, it implies that the cross section has no deformation in its plane, i.e. the cross section is exactly the same as the last step. In other cases (r 6¼ 1), it indicates that the crosssection undergoes some deformation. The magnitude of r corresponds to the extent of deformation. The correlation coefficient curves versus cross sections in two consecutive compression steps are shown in Fig. 9. Although the foam is uniformly compressed, the deformation of each cross section shows inhomogeneity under compression for open-cell aluminum foams (Fig. 9(a)). However, the behavior for closed-cell aluminum foam is much different. The deformation in the upper cross section is significantly large compared to those in other cross sections, as illustrated in Fig. 9(b). The results are consistent with the analysis of porosity.
Fig. 10. (a) Displacement for each cross section along Z-axial in final state for open-cell aluminum foam. (b) Displacement for each cross section along z-axial in final state for closed-cell aluminum foam.
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The vertical displacements along Z-axis of cross sections are shown in Fig. 10. Obviously the distribution of displacements is nearly linear for open-cell and nonlinear for closed-cell, as depicted in Fig. 10(a) and (b), respectively. 4.3. Analysis of deformation mechanism Figs. 8 and 9 show the porosity and correlation coefficient evolution of each cross section under compression, respectively. In order to analyze their influence on deformation, the porosity curve in the original state A and correlation coefficient curve in the final state K are chosen, as shown in Fig. 11. Comparing curve A with curve K in Fig. 11(a), it can be observed that the two curves are nearly dissymmetric. The bigger the cross-section porosity is, the more deformation the cross-section undergoes. This phenomenon is termed as the deformation rule of open-cell aluminum foam (DROAF). Situation for closed-cell aluminum foams is more complex as shown in Fig. 11(b). The curves A and H can be divided into two parts (I and II). In part I, the mechanical behavior is similar to the case of open-cell aluminum foams, and its deformation follows the DROAF. The reason is that in part I the closed-cell structures are destroyed due to large deformation and they actually become open-cell. In part II, it does not follow the same rule. Generally, porosity is a major factor affecting the strength for open-cell aluminum foams. Large deformation always occurs in the region where local porosity is relatively large. The deformation process for open-cell aluminum foams is condensation. However, it is not the same case for closed-cell aluminum foams, in which the mechanical
Fig. 11. (a) Cross-section porosity curve in state A and cross-section correlation coefficient curve in state K for open-cell aluminum foam. (b) Crosssection porosity curve in state A and cross-section correlation coefficient curve in state H for closed-cell aluminum foam.
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behaviors are dominated by both porosity and pore structures. Some isolated pores in the weak region will be firstly crushed under compression. These isolated pores have become conjoint and the deformation will follow the DROAF. Large deformation takes place in this region continuously until some other pores are broken. This process will continue until whole foam is condensed. Consequently, there are two deformation processes for closed-cell aluminum foams under compression, i.e., the pores crush and the foam condensation. Actually the two processes occur alternately. 5. Conclusion Using the SR-CT technique, the open- and closed-cell aluminum foams were examined in situ under compression. A series of reconstruction images of internal microstructures were given. The porosity distribution was determined and the structural deformation evolution was analyzed based upon the experimental data. It was found that the mechanical behavior was much different between the open- and closed-cell foams under compression. For open-cell aluminum foam, the vertical displacements of each cross section were uniform, and the deformation in its cross-section plane mainly depended on the local porosity. For closed-cell foam, the vertical displacements of each cross-section became nonlinear along Z-axis, and cross-section deformation was dominated by porosity and pore structures. Unlike the condensation process for open-cell, closed-cell aluminum foams underwent the pore broken and condensation alternately under compression. Acknowledgements This work was supported by National Nature Science Foundation of China under Contract Nos. 10232030 and 10472113 and BSRF Foundation. The authors specially thank Dr. Daying Li and Prof. Yuanming Xia for their cooperation in the design of the loading platform. The authors also would like to thank Rui Jiang, Feng Xu, Fan Jiang, Bing Lu at USTC and Pei-ping Zhu, Qing-xi Yuan and Jun-yue Wang at BSRF for their valuable contribution to this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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