In many industrial fields, such as aviation, aerospace,

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1 August 2012 Research & Development Compressive properties of aluminum foams by gas injection method *Zhang Huiming 1, Chen Xiang 1, 2, Fan Xueliu 1, and Li Yanxiang 1,2 (1. Department of Mechanical Engineering, Tsinghua University, Beijing , China; 2. Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Tsinghua University, Beijing , China) Abstract: The compressive properties of aluminum foams by gas injection method are investigated under both quasi-static and dynamic compressive loads in this paper. The experimental results indicate that the deformation of the aluminum foams goes through three stages: elastic deforming, plastic deforming and densification stage, during both the quasi-static and dynamic compressions. The aluminum foams with small average cell size or low porosity have high yield strength. An increase in strain rate can lead to an increase of yield strength. The yield strength of the aluminum foams under the dynamic loading condition is much greater than that under the quasi-static loading condition. Dynamic compressive tests show that a higher strain rate can give rise to a higher energy absorption capacity, which demonstrates that the aluminum foams have remarkable strain rate sensitivity on the loading rate. Key words: aluminum foam; strain rate; porosity; energy absorption CLC numbers: TG Document code: A Article ID: (2012) In many industrial fields, such as aviation, aerospace, construction and automotive, the needs of high quality, energy-absorbing structural parts are increasing. With increasing car speeds and the potential impact energy, the demands for improvement of the crash-worthiness of the car are a pressing issue. By converting the impact energy into plastic deformation energy and keeping the peak force acting on the protected objects below the level could cause damage, closed-cell aluminum foams with their large amount of cavities could be used as shock absorption structures, such as bumpers, door pillars, etc., for their high strength and stiffness [1]. The research on the relationship between the strain and stress at low and high strain rates and the energy absorption capability of the closed-cell aluminum foams has been a worldwide research interest [2-9]. The mechanical properties of the closed-cell aluminum foams are mainly determined by the size of the pores and the morphology characterization, such as relative density, average pore size, anisotropy and defects in the foam structure [2, 10]. A lot of research has been done to compare the compressive process of different kinds of metallic foams. Some studies on both open-cell and closed-cell metallic foams [3, 11-13] show that the plateau stress is almost insensitive to strain rate for the given strain rates but other research [14-17] has shown that *Zhang Huiming Male, master degree candidate at the Department of Mechanical Engineering, Tsinghua University. He obtained his B.S. degree from Huazhong University of Science and Technology in His research interests mainly focus on fabrication and mechanical properties of aluminum foams. xchen@tsinghua.edu.cn (corresponding author: Chen Xiang) Received: ; Accepted: the metallic foams have remarkable strain rate sensitivity to the loading rate. Gibson and Ashby have pointed out that the strain rate dependence of the mechanical properties of foams is caused in two ways, which are the inherent dependence of the cell-wall material itself and the dependence caused by the presence of a gas or liquid inside the pores [13]. It is believed that aluminum foam of different structures may lead to different experimental results. The aluminum foams fabricated by the gas injection method have a uniform pore size distribution and a thin cell wall. In this paper the quasi-static and dynamic compressive tests were performed to investigate the deformation mode of the aluminum foam in the low and high strain rates. The deformation mechanism of the aluminum foam during the compressive process was discussed. 1 Experimental procedure A356 aluminum alloy was used as the base material and was melted and held at 680 in a crucible heated by a resistance furnace. Compressed air was injected into the aluminum melt to produce the aluminum foams through an orifice submerged at the bottom of the crucible and the initial temperature of the compressed air was kept at 15 to 20. The 10 volume percent of 9 μm sized Al 2 O 3 particles were added into the A356 aluminum alloy melt and then dispersed by mechanical stirring at the rate of 1,300 r min -1. As the air was injected into the melt, the bubble would form, detach and flow to the surface of the melt and then the foams were collected at the melt surface. Cylindrical specimens with the size of Φ 8 cm and length 12 cm were cut from the collected foams using electro-discharge machining. The section observation method was applied to determine the average pore diameter. Ten parallel lines in the 215

2 CHINA FOUNDRY X, Y, and Z directions were measured and pore number was counted on each line (Fig. 1(a)). Chord length was gotten by dividing length by pore number in three orthogonal directions. Lastly, average pore diameter was calculated using equation (1). Figure 1(b) showed the chord length versus number of measurements. Figure 1(b) shows that the chord length would be constant when the number of measurements was greater than 8 or 9. Thus a total of 10 measurements were made on each specimen. The chord length of a specimen is the average value for the 10 measurements. where, D is the average chord length, t is the average chord length in three directions. (a) Chord length (cm) Number of measurements Fig.1: Schematic diagram of (a) measuring the average pore size and (b) relationship between chord length and the number of measurements The quasi-static compressive testing was carried out at room temperature using a WDW-100 computer-controlled test machine. The compressive rate was 5 mm min -1 (strain rate: s -1 ) and the load-displacement curves were recorded. The stress-strain (σ-ε) curves were obtained after data processing. The dynamic compressive testing was conducted at room temperature using a drop hammer testing machine (developed here) at the Automobile Collision Laboratory of Tsinghua University (Fig. 2). All aluminum foam specimens were fixed on the center of a steel tray with a diameter of 12 cm to prevent them from moving off center during the drop testing. The weight of the drop hammer is 2.7 kg and the drop height of the Fig. 2: Schematic diagram of the drop hammer test apparatus (1) (b) Vol.9 No.3 hammer could be adjusted to get different impact velocities and impact energies. A force sensor with a sensitivity of 4.53 pc/n and a maximum range of 60 kn was mounted below the tray. The experimental parameters, such as compressive load, impact time, impact speed, could be recorded through an intelligent data acquisition and processing system at the data acquisition frequency of 5,000 fps. A high-speed camera was used to record the process of compressive deformation of the aluminum foam specimens. The images of the compressive process were treated by a non-contact strain measurement system (VIC-2D and VIC-3D) to calculate the strain rate of the aluminum foams. 2 Results and discussion 2.1 Quasi-static compressive properties of aluminum foam Quasi-static compressive deformation stress-strain (σ-ε) curves for the specimens prepared by the gas injection method, having porosities from 94% to 97%, are shown in Fig. 3. It has been shown that the compression of the aluminum foams experienced is in the typical deformation process of the metallic foams [13] and the curves comprise three regions, namely elastic deformation, plastic deformation and densification regions. A very small, linear, elastic deformation is displayed and the stress increases rapidly when the pressure head acts on the surface of the aluminum foam where partially reversible cell-wall bending occurs. The plastic deformation of aluminum foam occurs after the first maximum; and an extended plateau region appears where the foam cell walls buckle, yield and fracture. Mostly deformation is localized in the defect (or weak links) regions in the foams when the specimen is crushed. Then the region in the middle of the sample begins to crush. As the crushing proceeds, the deformation and the stress passes to the un-deformed region layer by layer; the failure subsequently develops along the clusters of defects and thereafter the cell wall material itself becomes pressed together and the whole sample is crushed (densification region). The sharp increase of the stress at the end of the curves corresponds to densification in the foam. It also can be seen from Fig. 3 that the extended plateau fluctuates due to the pores in the foam being not exactly regular and the abrupt and repeatable failure of successive pore layers. For the aluminum foam with the same average pore size, the plateau stress decreases (Fig. 3(a)) with an increase in the porosity from 94% to 97%. The densification stage starts at 50% strain for the aluminum foams with smaller porosity; and at 65% strain for the aluminum foams with larger porosity. For foams having similar pore size, the smaller the porosity, the thicker the pore cell wall; so the foam can bear a higher load giving a higher yield plateau. For foams having similar density, the larger the pore size, the lower the yield strength. The plateau stress is about 0.29 MPa and the densification strain is 62% when the pore size is about 0.97 cm; while the plateau stress is only about 0.19 MPa and the densification 216

3 August 2012 Research & Development Fig. 3: Quasi-static stress-strain curves of aluminum foam specimens: (a) different nominal porosities of 94% and 97% at average pore size of 1.27 cm and (b) different average pore sizes of 0.97 cm and 1.27 cm at nominal porosity of 96% strain is up to 65% when the pore size is about 1.27 cm (Fig. 3b). Figure 4 shows the quasi-static deformation process of the aluminum foams prepared by the gas injection method. As an energy-absorbing material, aluminum foams have the characteristics that higher strain could be obtained at lower stress levels. According to the formula of energy absorption capacity (Eq. 2) of closed-cell foam given by Gibson and Ashby [10], the extended plateau is particularly important for the foam application, and the higher the yield stress of aluminum foams, the greater the energy absorbed. ε ε pl where, W is the energy absorption capacity of aluminum foam, σ pl is the plateau stress at the strain of ε. (2) Figure 5 shows stress versus strain curves (σ-ε) of aluminum foam samples with and without a skin subjected to quasi-static compressive loads. By the gas injection fabrication method, the skin of the aluminum foam is as thin as the cell wall thickness, which is about 50 μm. It is easy to estimate the weight fraction of skin in the total weight of the samples. The result turns out that the fraction of skin in weight is less than 5% of the total weight of the sample and therefore the weight of skin is ignored. The yield stress of the aluminum foam with a skin is at about 0.4 MPa and the plateau strain ranges from 2% to 70%. Compared with the samples without a skin, the specimens with a skin can withstand a greater load in the deformation process, giving rise to a higher plateau stress and thus can absorb more energy before the densification stage. Fig. 4: Photographs of aluminum foam taken during quasi-static deformation process 217

4 CHINA FOUNDRY Vol.9 No.3 Fig. 5: Stress versus strain curves of quasi-static compression of aluminum foams with a nominal porosity of 96% and a pore size of 1.42 cm 2.2 Effect of pore morphology on quasistatic compressive properties of aluminum foams Gibson and Ashby [13] developed a formula to calculate the static plateau stress for the compression of plastic foams, which is: pl ys s s where, σ * pl is the plateau stress of the aluminum foam, σ ys and r s are the yield stress and density of the solid aluminum alloy that the foam cell wall is made of, r * is the density of the aluminum foam, and f is the fraction of solid in the cell edges of foam. According to Eq. 3, in the ideal model, the plateau stress of foam depends only on the porosity, the greater the porosity, the smaller proportion of aluminum foam cell wall and the smaller load the foam can bear. However, there are many defects in the actual (3) aluminum foams: (1) the pores are not in the form of regular tetrakaidecahedra, that is, the pores are not regular hexagons in the cross section of the foam; (2) there are a variety of the pore sizes and the thickness of cell wall; (3) there is severe deformation of the foams. Although the aluminum foams have some different aspects compared with regular tetrakaidecahedra, this model is accepted as the standard model in theoretical analysis, because it is very simple and matches the experiment results [2]. Figure 6 shows the defects such as coalescence and elongation of pores in the aluminum foam after binary image processing. These defects seriously affect the compressive properties of aluminum foam. Figure 7 illustrates the compressive stress-strain curves of A356 alloy and the compressive yield strength of aluminum foam having different porosities. According to Eq. 2, the average yield stress of the aluminum foam with porosity of 96% is 0.35 MPa, while with porosity of 93% it is 0.93 MPa. Comparing the quasi-static compressive results with theoretical calculated values at the given porosity, the calculated yield strength is higher than the experimental result. According to the deformation characteristics of aluminum foam, compressed foam collapses layer by layer because the distribution of defects is not uniform and thus results in the fluctuation of the stress-strain curves. Hence, the yield strength will be close to the theoretical value when the morphology of the pores is in the form of a uniform honeycomb. Fig. 6: Morphology of foam defects: (a) coalescence of pores and (b) elongation of pores Yield strength (MPa) º Yield strength of base material: 91.5 MPa MPA Fig. 7: Yield strength of aluminum base material and foam: (a) A356 aluminum alloy and (b) aluminum foam 218

5 August 2012 Research & Development 2.3 Dynamic compressive properties of aluminum foam Dynamic compressive deformation process and the stressstrain (σ-ε) curves for the specimens prepared by gas injection method are shown in Figs. 8 and 9, respectively. It can be seen that the dynamic compression of the aluminum foams experienced also is in the typical deformation process of metallic foams and the deformation of the aluminum foams will go through three stages: elastic deforming, plastic deforming and densification stage. According to the highspeed camera, the crushing of the foam was started in the regions having the lowest density or clusters of defects (or weak links) for the specimen at the beginning of deformation. 0% 11% 22% 34% 45% 56% 66% 77% Fig. 8: Photographs of aluminum foam in dynamic deformation process taken by a high-speed camera Fig. 9: Stress versus strain curves of dynamic compression of aluminum specimens with a nominal porosity of 94% and pore size of 0.93 cm s -1 Strain rate: 40 s -1, 68-1 Average pore diameter: 0.93 cm Porosity: 94% The failure subsequently develops along the clusters of defects until the deformation covers the entire specimen and the foam becomes pressed together. It also can be seen from Fig. 9 that, compared with the opencell aluminum foams [3], the closed-cell aluminum foams are more sensitive to the strain rate during the compression. The explanation of such behavior lies in the increase in the gas pressure in the pores of the closed-cell aluminum foam during the compressive process, which gives rise to the resistance to the deformation. The deformation rate of the pores is different at various strain rates. Therfore the speed of increase in the gas pressure in the pores is different, resulting in the changes in the yield strength [13]. According to Eq. 2 developed by Gibson and Ashby, for the closedcell aluminum foam with a porosity of 94%, the plateau stress is about 0.37 MPa at the strain rate of s -1 ; the plateau stress is 6.06 MPa at the strain rate of 40 s -1 ; and the plateau stress is MPa at the strain rate of 68 s -1. Compared with the quasistatic deformation, the higher impact velocity allows the rapid rupture and collapse of the pores of the aluminum f o a m i n t h e d y n a m i c compressive process. At the same time, the rise of the gas pressure in the pores has the tendency to prevent the foam collapse; and to compensate for the decrease of stress caused by the foam collapse. So the yield strength under dynamic compression is significantly higher than that under quasi-static compression. It must be pointed out that the densification strain is still at 60% to 70% whether under dynamic or quasi-static compression. According to Eq. 2, the energy absorbed per unit volume is proportional to the yield stress of the aluminum foam and more impact energy could be absorbed with an increase in the compressive strain. Figure 10 shows the energy absorption capability of aluminum foam at different strain rates. It can be seen from Fig. 10 that the higher the strain rate, the higher the plateau stress of the aluminum foam; and the higher the impact energy absorbed. Conpared with the quasi-static compression, the dynamic compression of aluminum foam shows a similar deformation process, and the yield strength of aluminum foam with small porosity and pore size is higher. The increase in plateau stress and the associated increase in the energy absorption capacity at higher strain rate are of benefit to the use of aluminum foams in high-impact energy-absorption 219

6 CHINA FOUNDRY Fig. 10: Energy absorption capability of aluminum foam at different strain rates applications. The higher strain rate can give rise to a higher energy absorption capacity under dynamic compression, which demonstrates that the aluminum foams have remarkable strain rate sensitivity to the loading rate. 3 Conclusions : 0.37 MPa : s -1 : 6.06 MPa : 40 s -1 : MPa : 68 s -1 (1) The compression of the aluminum foams experienced is typical of the deformation process of metallic foams under both quasi-static and dynamic compressive loads and will go through three stages: elastic deformation, plastic deformation and densification stage. In the elastic deformation stage, the aluminum foam will deform with the increase in the load and partially reversible cell wall bending will occur. The plastic deformation of aluminum foam occurs after the first maximum and an extended plateau region appears where the foam cell walls buckle, yield and fracture. The crushing of the foam starts in the regions having the lowest density or clusters of defects (or weak links) of the specimen and then the failure subsequently develops along the clusters of defects until the deformation covers the entire specimen and the foam becomes pressed together. (2) Under quasi-static compressive load, the smaller the porosity of the foam, the thicker the cell wall, the greater load the foam can bear, and the higher plateau stress for the aluminum foam with the same average pore size. The smaller the average pore size, the higher the load the foam can bear, and the higher the yield strength. (3) Compared with the specimens without a skin, the samples with a skin can withstand a greater load during the deformation process, giving rise to a higher plateau stress and thus can absorb more energy before the densification stage. (4) The closed-cell aluminum foams have remarkable strain rate sensitivity to the loading rate. The greater the strain rate, the higher the yield strength and the higher the impact energy Vol.9 No.3 absorbed. The yield strength under dynamic compression is significantly higher than the yield strength under quasi-static compression. References [1] Fuganti A, Lorenzi L, Arve Gronsund H, and Magnus L. Aluminum foam for automotive applications. Advanced Engineering Materials, 2000, 2(4): [2] Ashby M F, Evans A G, Fleck N A, et al. Metal foams: a design guide, Oxford, UK: Butterworth-Heinemann, [3] Deshpande V S and Fleck N A. High strain rate compressive behaviour of aluminum alloy foams. International Journal of Impact Engineering, (3): [4] Andrews E, Sanders W, and Gibson L J. Compressive and tensile behaviour of aluminum foams. Materials Science and Engineering A, 1999, 270(2): [5] Ruan D, Lu G, Chen F L, and Siores E. Compressive behaviour of aluminium foams at low and medium strain rates. Composite Structures, 2002, 57: [6] Shen Jianhu, Lu Guoxing, and Ruan Dong. Compressive behaviour of closed-cell aluminium foams at high strain rates. Composites, Part B: Engineering, 2010, 41: [7] Markaki A E and Clyne T W. The effect of cell wall microstructure on the deformation and fracture of aluminiumbased foams. Acta Materialia, 2001, 49: [8] Koza E, Leonowicza M, Wojciechowskia S, et al. Compressive strength of aluminium foams. Materials Letters, 2003, 58: [9] Hanssen A G, Langseth M, and Hopperstad O S. Crash behavior of foam-based components: validation of numerical simulations. Advanced Engineering Materials, 2002, 4: [10] Gibson L J, and Ashby M F. Cellular solids: structures and properties. 2nd ed., Cambridge, UK: Cambridge University Press, [11] Kenny L D. Mechanical properties of particle stabilised aluminum foams. Materials Science Forum, 1996, : [12] Dannemann K A, Jr. and Lankford J. High strain rate compression of closed-cell aluminium foams. Materials Science and Engineering A, 2000, 293(1-2): [13] Hall I W, Guden M, and Yu C J. Crushing of aluminum closed cell foams: density and strain rate effects. Scripta Materialia, 2000, 43: [14] Mukai T, Kanahashi H, Miyoshi T, et al. Experimental study of energy absorption in a closed-celled aluminium foam under dynamic loading. Scripta Materialia, 1999, 40(8): [15] Kanahashi H, Mukai T, Yamada Y, et al. Dynamic compression of an ultra-low density aluminium foam. Materials Science and Engineering A, 2000, 280(2): [16] Liu J, Yu S, Song Y, et al. Dynamic compressive strength of Zn-22Al foams. Journal of Alloys and Compounds, 2009, 476(1-2): [17] Wang Z, Shen J, Lu G, and Zhao L. Compressive behavior of closed-cell aluminum alloy foams at medium strain rate. Materials Science and Engineering A, 2010, 528(6): The work was financially supported by the Scientific Research Program of Zhejiang Province, China (No. 2009C31049). 220