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Experimental study on the quasi-static compression behavior of multilayer aluminum foam sandwich structure
Journal of Alloys and Compounds 810 (2019) 151860
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Experimental study on the quasi-static compression behavior of multilayer aluminum foam sandwich structure Cheng-Xu Ren, Zheng-Fei Hu*, Cheng Yao, Fan Mo Laboratory for R&D and Application of Metallic Functional Materials, School of Materials Science and Engineering, Tongji University, Shanghai, 201804, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 June 2019 Received in revised form 6 August 2019 Accepted 12 August 2019 Available online 14 August 2019
The axial compression responses of multilayer aluminum foam panels (MLAF) and multilayer sandwich panels (MLAFS) with 5052 Al alloy interlayer plates were experimentally investigated under quasi-static compression condition. The influence of aluminum foam (AF) core density, stacking number and the interlayer plates in MLAFS structures were discussed extensively. Compared with bulk AF, the results indicate that the mechanical properties of MLAF structures are slightly decreased while the compressive resistance of MLAFS structures is obviously enhanced. The presence of Al alloy interlayer plates changes the deformation mode of MLAFS structures and induces collapse in sequence by layer. The effect of stacking number on the compressive behavior of MLAFS structures varies with AF core density and the optimum MLAFS structure was summarized in view of the energy absorption capacity and compressive deformation degree. © 2019 Elsevier B.V. All rights reserved.
Keywords: Aluminum foam Compression behavior Multilayer sandwich structure Energy absorption
1. Introduction Aluminum foam (AF) has received widespread attention due to its combination of excellent physical and mechanical properties [1,2]. Because of its unique structure characteristics, closed cell AF has achieved broad application in aerospace and automotive industry [3,4], such as cores for automobile impact beams, lightweight structure parts in transportation industry. A great deal of experimental studies on the response of monolithic AF, density graded AF and composite sandwich structures to different loading conditions have been undertaken throughout the world. Generally, the compression process of AF can be divided into three deformation stages: linear elastic deformation stage, plateau plastic deformation stage and densification stage. During the second compression stage, the special cellular structure of AF makes it maintain a stable value of stress while undergoing a large scale of deformation, which enables its excellent energy absorption capacity [5e8]. Extensive researches have been devoted to investigate the compressive properties [9,10], strain rate sensitivity [11,12] and deformation mechanism [13,14] of AF. Mu et al. [15] analyzed the
* Corresponding author. E-mail address: [email protected] (Z.-F. Hu). https://doi.org/10.1016/j.jallcom.2019.151860 0925-8388/© 2019 Elsevier B.V. All rights reserved.
effect of cell shape on the deformation behavior of closed-cell AF and proposed four failure modes at the cell/membrane level. Kadkhodapour and Raeisi [16] investigated the deformation behavior of closed-cell AF with regular cell shapes and emphasized the effect of topology structure. Xia et al. [17] fabricated closed-cell AF with different content of manganese and the results showed that Mncontaining foams exhibited much higher compressive properties than commercial pure AF. Recently, Jing et al. [18] investigated the compressive behavior of closed-cell AF with different densities under quasi-static and dynamic strain rate, and a multi-parameter dynamic constitutive model was proposed to describe the unique stress-strain response of AF. Raeisi et al. [19] studied the mechanical properties and energy absorption capacity of Z-pinned aluminum foam sandwich (AFS) both experimentally and numerically. The deformation characteristics were well identified at the cell level. Zhang et al. [20] explored the effect of samples size on the mechanical properties of closed-cell AF, it is proposed that there are different optimum sample sizes to characterize bulk material under different loading conditions. Generally, Previous studies [21,22] have demonstrated that there are relative weak zones and imperfections inside the AF structure, such as internal micro-pores, cracks and the inhomogeneity of cell structure, which might lead to the stress concentration locally and collapse starts from these regions. Stress in these weak regions increases quickly with the interaction between cells and transmits to surrounding cells,
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subsequently, collapse occurs at the next weakest region. So, the initiation and propagation of collapse bands can be observed at the macroscopic level [23e25]. Functionally graded aluminum foam (FGAF), with a structure of density graded AF, has also attracted widespread concerning for its potential mechanical properties of controlled deformation sequence and various plateau region desired [26e29]. Hangai et al. [30] fabricated FGAF with different pore structure and observed its deformation behavior during uniaxial compression test by X-ray computed tomography. The compression process of FGAF structure can be precisely controlled by changing its pore structure. The unique multiple plateau stages exhibited in the stress-strain curve demonstrate the significant effect of multilayer structure on the deformation and failure modes of these special designed structures. Besides, the aluminum foam is usually cladded with compact and stiff metal sheet covers in both sides to form AFS panel and enhance its mechanical performance. In the sandwich structure, the two stiff face sheets carry axial load and offer sandwich structure bending and stretching capability while the foam core bears shearing load and provides the ability to undergo large deformation at nearly constant stress. Apparently, this sandwich structure maintains the characteristics of aluminum foam of lightweight, improves flexural stiffness, impact performance and high-energy absorption capacity [31e33]. Following the review above, the combination of multilayer and sandwich structure has meaningful research significance for its potential excellent mechanical properties and novel deformation modes. An increasing number of investigations have been conducted on multilayer AF [34e36]. Cenk Kılıçaslan et al. [37] studied the compression properties of seven-layered aluminum corrugated sandwich with opposite core orientation both experimentally and numerically. Their investigation found that the presence of interlayer plates can induce the homogeneous collapse of individual layer. In this paper, different types of multilayer aluminum foam (MLAF) and multilayer aluminum foam sandwich (MLAFS) were fabricated. Each multilayer structure sample consists one AF core with relative density 0.11, 0.16 or 0.20. All of these samples were compressed under a constant strain rate of 102S1. In order to investigate the influence of multilayer structure and 5052 Al alloy interlayer plates, the compression tests of monolithic bulk AF with similar size and density were conducted under the same test condition for comparison. The objective of this investigation is to demonstrate the difference in compression characteristics between MLAF, MLAFS and monolithic bulk foams under identical strain rate. The optimum multilayer structure was summarized in view of energy absorption capacity for the potential applications. 2. Materials and methods Closed-cell aluminum foams at three different relative densities of 0.11, 0.16, and 0.20 were manufactured via melt foaming method using TiH2 as foaming agent. The relative density was defined by:
r ¼ r* =rm
alloy sheet of 1 mm thickness is also cut into 70 70 mm2 small pieces to serve as interlayer and face plates for MLAFS structure. Before fabricating the multilayer structure, the bonding surfaces of AF and 5052 Al alloy plates were polished with abrasive paper and then immersed in 10% NaOH solution 1min to clean oil, the pretreated samples should be rinsed in running water immediately for 2min to clear residual lye and then dried by air blower. The MLAF structures were fabricated in 3, 4 and 5 layers with 30 mm, 25 mm and 20 mm thickness AF core pieces respectively, which were bonded using epoxy resin of component A&B as glue. The MLAFS structures were fabricated in the same way, except that the 5052 Al alloy plates were used as extra interlayers and face plates. Added with the thickness of 5052 Al alloy plates, the overall height of MLAFS structures reaches to 94, 105 and 106 mm for three, four and five-layer structure respectively. The schematic diagrams of the MLAF and MLAFS structures are shown in Fig. 2. According to ISO 17340-2014 standard, the uniaxial compression tests were conducted on a computer controlled electronic universal testing machine (WDW/10e100), which has a function of automatic leveling to reduce the effect of imbalanced loading caused by surface irregularities. The tested sample was placed in the middle of the bottom compression platform, the upper compression plate with flat end was controlled to compress the sample at a constant velocity. The quasi-static compression tests for MLAF, MLAFS and monolithic bulk AF were performed at a constant strain rate of 102S1 (corresponding a platen velocity of 60 mm/min), at least three tests were conducted for the same samples to acquire the average values of compression parameters. During compression experiments, the load and displacement were recorded by computer connected to sensors and the deformation processes were also recorded using a digital camera. The experimental nominal stress is simply load divided by the contacting area of these samples (4900 mm2) and the nominal strain is displacement divided by the height of samples. 3. Results and discussions 3.1. Compression behavior of monolithic bulk aluminum foams The typical experimental compression stress-strain curves of monolithic bulk AF under a strain rate of 102S1 are shown in Fig. 3. It is evident that the compression process of AF can be divided into three stages, including a short linear elastic stage at the beginning, a long plateau stage and a final densification stage. Besides, the curve for AF in higher relative density of 0.20 exhibits significant strain hardening phenomenon at its second compression stage. This might be due to the different failure modes at the cell level. It is believed that for foams with lower density or thinner cell walls, the main failure mode is cell buckling and collapse continue under constant compression stress. However, for AF with higher density, the collapse of cells proceeds with the compression of entire cell walls and results in the more obvious strain hardening phenomenon [23].
(1)
where r* is the density of aluminum foam and rm is the density of the aluminum matrix. The appearances of the as-received aluminum foams at different densities are shown in Fig. 1. The average pore sizes of AF with relative density of 0.11, 0.16 and 0.20 are about 6.5 mm, 4.5 mm and 3.2 mm respectively. Four sizes of rectangular AF pieces in three densities were cut with a crosssection of 70 70 mm2 and heights of 100 mm, 30 mm, 25 mm and 20 mm. The pieces with 100 mm height are taken as monolithic bulk AF samples and the rest are ready to prepare the three, four and five-layer MLAF and MLAFS samples. A commercial 5052 Al
3.2. Compression behavior of MLAF and MLAFS structures The compression stress-strain curves for MLAF and MLAFS structures are shown in Fig. 4. Similar to the compression behavior of monolithic bulk AF, three deformation stages can also be recognized in Fig. 4. Compared to monolithic bulk AF at the same density, MLAF structures has a shorter plateau strain and the plateau stress at its second compression stage is even slightly lower than that of monolithic AF. However, the stress-strain curves of MLAFS structures show obvious stress oscillation at their second compression stage (oscillation stage) and the oscillation number is
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Fig. 1. Appearances of AF at different relative densities: (a) 0.11, (b) 0.16 and (c) 0.20.
Fig. 2. Schematic diagrams of MLAF and MLAFS samples.
accordant with the stacking number of AF core layers. More than all of that, the initial collapse stress and plateau stress of MLAFS are both higher than that of MLAF and monolithic AF, which indicates that the compression resistance of MLAFS structure is strengthened obviously for its unique structure. In order to display the failure pattern of MLAF structure under quasi-static compression detailly, the macro deformation sequence pictures of five-layer MLAF with AF core relative density of 0.20 are shown in Fig. 5. Fig. 5(aed) are captured at strains varied from 0.0 to 0.6 at a step of 0.2. The MLAF structure exhibits a shearing type non-progressive deformation characteristic. Deformation and collapse occurred at one specific interface among middle layers as shown in Fig. 5 (b). Previous studies have pointed out that the deformation and collapse of monolithic bulk foam began at the
weakest region and usually occurred at one end [23e25]. The extrusion between cellular pores was intensified and much more deformation bands were formed as compression process proceeds. The expansion of deformation bands in one AF core layer significantly propagated to neighbor layers through the bonding boundaries and the growth of deformation bands between layers induced the simultaneous deformation between AF layers. So, the stressstrain curve of MLAF structure is smoother at its second compression stage. The deformation process continued until the whole structure was compacted and stress increased with strain sharply. Compared to monolithic bulk AF, the shorter plateau stage of MLAF structure should be related to the less lateral expanding during compression. As to the slightly lower initial collapse stress and plateau stress of MLAF structure, this may be attributed to the
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Fig. 3. Stress-strain curves of monolithic bulk aluminum foam at three densities.
formation and extension of deformation bands between AF layers during compression [37], the multilayer interfaces induce more defects might be another reason. In contrast, the second compression stage of MLAFS structure exhibits obvious stress oscillation. In order to illustrate the deformation behavior of MLAFS structure and evaluate the effect of 5052 Al alloy interlayer plates, the complete compression process of fourlayer MLAFS sample with AF core relative density of 0.11 is shown in Fig. 6. The stress-strain curve in Fig. 7 shows peaks and troughs on its second stage, which are noted as point 1 to point 8 to illustrate the deformation sequence. It exhibits clearly in Fig. 6 (c and d) that a specific AF core layer marked with red box collapsed first while
other layers kept almost stable, and the deformation process of the first collapsed AF layer corresponds to the strain region from point 1 to point 3 on the curve in Fig. 7. After this specific layer was preliminary compacted, the next weakest AF core layer began to collapse as shown in Fig. 6 (e and f) marked with red box and its compression process corresponds to strain region from point 3 to 5. This deformation process continued layer by layer until all layers were preliminary densified. When the compression strain reached up to 0.55, the deformation proceeded with the compression of compacted aluminum foams and interlayer plates together, which led to the abrupt increase in stress values. According to ref.10 and 15, the cell structure plays a significant role in the AF deformation process. Collapse starts from the weakest interior parts of AF and stress in these regions are delivered to surrounding cells to form deformation bands. As the compression proceeding, the width and number of deformation bands continue to increase and large deformation is going on. Therefore, even though the nominal densities of AF core layers in one MLAFS sample are equal, their inner pore structures are different, so collapse begin at the weakest AF core layer as shown in Fig. 6 (c), stress increases with the collapse of this specific core layer and the next weakest layer begin to collapse when the stress reaches a certain value. The deformation of MLAFS structure is supposed to be sequential deformation by layer. From above observation, the macro deformation mode of MLAFS structures is obviously different with other AF structures. The compression characteristics of MLAF and MLAFS structures are shown in Fig. 8 and their deformation bands are marked in red boxes. For MLAF structure, as shown in Fig. 8 (a), deformation of AF structure develops in the form of deformation bands forming and propagating [13,23]. Generally, these deformation bands or shearing bands normal have a small angle deviation (about 15 ) to the planes of maximum shear stress, this result is consistent with
Fig. 4. Stress-strain curves of different AF, MLAFS and MLAF samples with the same AF core relative density: (a) 0.11, (b) 0.16, (c) 0.20.
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Fig. 5. The deformation steps of five-layer MLAF captured at strains varied from 0 to 0.6 at a step of 0.2.
some relevant reports in previous studies [15,16], which is believed to be caused by the heterogeneity of the AF structure at cell level. In fact, this angle will reduce obviously for samples with small thickness of the AF layers, so the constraint effect of the size also affects the angle of the deformation band. The discontinuity of the upper and lower AF layer leads to more defects at the interfaces, which causes the deformation of MLAF structure usually begins at the interface between layers as shown in Fig. 5. The MLAFS structure displays a totally different deformation characteristic, as shown in Fig. 8 (b), the AF core deformation starts when a layer of cells collapses which is almost parallel to the interlayer plates. No slant deformation bands are formed in the deformation process, which means more stress is needed to collapse cell structure. The presence of interlayer plates prevents deformation propagation through neighbor layers and enforces the distribution of compressive stress uniformly. They show a constraining effect and make it difficult to form slant deformation bands in AF core layer when the thickness of AF core layer is not enough to start collapse interiorly. So this deformation mode improves the compression resistance of MLAFS structure definitely. Meanwhile, this constraining effect obviously limits the lateral expanding during compression and this fact well explains the even shorter strain plateau stage of MLAFS structures. Compared the stress-strain curves for different samples shown in Fig. 4, the effects of interlayer plates in MLAFS structures can be summarized as follows: (i) the stress plateau rises obviously, which indicates the compression resistance of MLAFS structures are improved distinctly. (ii) the strain length of the plateau stage is shorter. The densification strain of MLAFS structure is approximately 0.55, while the corresponding end point of MLAF is about 0.65. (iii) failure mode of MLAFS is different with other structures. No visible deformation band present in compressive process. Each layer of AF core collapses homogeneously and the structure deforms progressively by layer. In order to compare the compression property and energy absorption capacity between monolithic bulk AF, MLAF and MLAFS structures under quasi-static compression process quantitatively,
the initial collapse stress (sc ) and plateau stress (spl ) in the second compression stage of these structures are calculated respectively. According to the standard ISO 17340-2014, sc is defined as the first maximum stress value on the stress-strain curve and the plateau stress of monolithic bulk AF and MLAF structures are defined as the average stress between 0.2 and 0.4 strain. Considering the stress oscillation exhibits in the second stage of MLAFS structures, the strain interval containing several complete oscillations are utilized to calculate plateau stress:
1 spl ¼ εL ε1
εðL
sðεÞ dε
(2)
ε1
Here ε1 and εL are strains correspond to the first and the last peak point on the oscillation stage of MLAFS structure respectively, such as point 1 and point 7 marked in Fig. 7. The four-layer MLAFS sample with AF core relative density of 0.11 is taken as an example. As shown in Fig. 7, the stain interval from point 1 to point 7, containing three complete oscillations, is chosen to calculate its plateau stress. The densification strain (εd ) is defined as the strain corresponding to the intersection of tangent drawn on the densification region and the plateau stress of the oscillation stage [22]. The schematic diagram of multiple parameters is shown in Fig. 7. The elaborate values of sc , spl and εd of MLAFS, MLAF and monolithic bulk foams are tabulated in Table 1. It indicates that the value of sc and spl for MLAFS structures are both higher than that of monolithic bulk AF and MLAF structures. The lower AF density, the greater the difference in compression parameters. Even though the plateau stage of MLAF structure is longer than MLAFS structure, the deformation resistance of MLAF structure is significantly weaker than MLAFS structure. Therefore, from the view of deformation resistance of multilayer structure, MLAFS structures are preferred. Further discussion will be presented about this kind of combination. The compression stress-strain curves of MLAFS structures with different AF core densities are plotted in Fig. 9. It is clearly noted
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Fig. 8. Compression characteristics of (a) MLAF structure, (b) MLAFS structure with AF core at relative density of 0.20.
Fig. 6. Compression process of four-layer MLAFS with AF core at relative density of 0.11 captured at (a) ε ¼ 0, (bei) from point 1 to point 8 and (j) ε ¼ 0.55.
that the number of peaks and troughs varies with stacking number. Based on the calculated results listed in Table 1, it can be concluded that with the increase of stacking number, the deformation resistance of MLAFS structures improves obviously. This should be related to the variation of thickness of single AF core layer when the stacking number increases. Generally, large number of irregular cells induces the inhomogeneity and vast hole-defects in aluminum foam structure. The number of defects increases with the thickness of specimen, which should result in weaker deformation resistance upon thickening [18]. Besides, the number of Al alloy interlayer plates in MLAFS structure increases with stacking number, this may also contribute to the higher strength of MLAFS structure with more stacking number. The densification strain become shorter with the increase of AF core density and stacking number. For AF core at relative density of 0.11, The densification strain of MLAFS structure is about 0.55, corresponding values for MLAF structure and monolithic bulk AF are about 0.65 and 0.75 respectively. The significantly decreased densification strain should be attributed to the multilayer structure and the presence of the interlayer plates in MLAFS structure as discussed above. In addition, with the same AF core density, the densification strain of MLAFS structures also decreases slightly with the increase of stacking number, which should be caused by the constraining effect of interlayer plates. The deformation resistance of MLAFS structures increases significantly with AF core density, as shown in Fig. 10. This is expected since with the increase of density, the wall thickness of AF cell increases while the cell size becomes smaller. Consequently, the deformation resistance of individual pore improved and the overall energy absorption capacity of AF enhanced either [18]. In order to evaluate the influence of AF core density on initial collapse stress and plateau stress of MLAFS structure quantitatively, the generally accepted relationship of the variation of sc and spl for cellular structure is defined as [1]:
sc ¼ Ac
b c
spl ¼ Apl
Fig. 7. Stress-strain curve of four-layer MLAFS with AF core at relative density of 0.11 and the schematic diagram of multiple compressive parameters.
rf rs
(3)
bpl
rf rs
(4)
Here Ac and Apl are strengthening coefficients, rf is the density of AF and rs is the density of solid metal. bc and bpl are constants related to cellular density. The variation of sc and spl as a function of AF core density for different MLAFS stacking structure are shown in
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Table 1 Collapse stress and plateau stress for different examined samples. Relative density
Stacking number
Collapse stress (MPa) MLAFS
0.11
0.16
0.20
bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer
3.78 4.34 4.66 4.62 8.15 8.93 9.37 9.69 9.73 12.23 13.13 13.72
Plateau stress (MPa) MLAF
MLAFS 3.37 3.96 4.09 3.99 8.30 8.79 9.16 9.58 11.70 11.93 13.16 13.69
2.62 2.41 2.79 6.60 7.24 7.56 11.75 11.06 12.29
Densification strain (%) MLAF 2.52 2.32 2.84 6.51 6.84 7.11 10.93 10.40 11.55
MLAFS 71 62 58 54 75 54 49 43 e 49 45 37
MLAF 67 66 64 66 65 69 63 66 60
Fig. 9. Stress-strain curves of MLAFS structures with AF core at relative density of (a) 0.11, (b) 0.16 and (c) 0.20.
Fig. 11. The experimental data for initial collapse stress and plateau stress as a function of AF core density are fitted by relationship y ¼ Arb . The value of ‘A’ and ‘b’ are listed in Table 2. The fitting parameters of ‘b’ are within the predicted range (from 1.5 to 2.5) reported in a previous study [1]. So, the equations (3) and (4) well describe the compressibility of AF multilayer sandwich structures. 3.3. Energy absorption capacity Aluminum foams have attracted extensive attention for its excellent energy absorption capacity while bearing load outside. Generally, the energy needed to deform structures up to a certain strain during compression is defined as the energy absorption capacity. Under uniaxial compression, the energy absorption per unit volume (Wv) is calculated as the area integrated under the stressstrain curve at a certain strain as follows:
εð0
Wv ¼
sdε
(5)
0
Another important parameter relevant to the energy absorption capability of AF is energy absorption efficiency, the energy absorption efficiency (EAE) is an important parameter to the characterization of AF, the equation can be expressed as below [6,18]:
1 hðεÞ ¼ sðεÞ
ðε
sðεÞdε
(6)
0
where h is the EAE, ε is nominal strain and sðεÞ is corresponding nominal stress. The energy absorption efficiency of different MLAFS samples with the same density were shown in Fig. 12. Unlike the
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Fig. 10. The stress-strain curves of (a) three-layer, (b) four-layer and (c) five-layer MLAFS structures with different AF core densities.
Fig. 11. (a) initial collapse stress and (b) plateau stress as a function of AF core density for multilayer MLAFS structures.
Table 2 Strengthening coefficients of “A” and “b” for MAFLS structures. Stacking number
Three-layer MLAFS Four-layer MLAFS Five-layer MLAFS
Initial collapse stress
Plateau stress
Ac
bc
Apl
bpl
178.7 198.2 233.5
1.66 1.68 1.76
195.3 267.1 308.4
1.73 1.86 1.93
smooth EAE-strain curve of monolithic bulk foam [19], the EAEstrain curves of MLAFS structure exhibits the unique characteristic of multiple steps. It shows that the energy absorption efficiency increases obviously with strain. Several protruding peaks
can be recognized on the EAE-strain curve and the location of these peaks corresponds to the troughs on the stress-strain curve, the number of these peaks is consistent with the layers in MLAFS structure. The vertical dashed lines in Fig. 12 show the positions of densification strain for different MLAFS structure, the densification strain of MLAFS structure decreases with the increase of stacking number. With the strain increases, for the same AF density, the value of EAE for the MLAFS structure reduces relatively with stacking number. These behaviors may be related to the constraining effect of interlayer plates as discussed above. The densification strain of most MLAFS structures investigated in this paper is about 0.55, as listed in Table 1. For comparison under the same deformation degree, the energy absorption for MLAFS structures as well as monolithic bulk foams and MLAF structures
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Fig. 12. The energy absorption efficiency of different layer MLAFS samples with the same AF core relative density: (a) 0.11, (b) 0.16 and (c) 0.20.
are calculated up to a strain of 0.45. The calculation results for MLAFS, MLAF structures and monolithic bulk AF are listed in Table 3 and the variation tendency is shown in Fig. 13. Generally, the MLAFS structure exhibits much higher energy absorption capacity compared with MLAF structure and monolithic bulk AF under the same deformation degree and its energy absorption capacity increases extremely with AF core density. In the view of energy absorption capacity, the stacking number has no evident effect on MLAFS structures when relative density of AF core is low, but when the relative density of AF core increases to 0.16 or 0.20, their energy absorption is obviously increased with the stacking number. Compared to monolithic AF, the energy absorption capacity of MLAFS structures is enhanced more than 20% when AF core at low relative density of 0.11, but only about 10% for AF core at high relative density of 0.20. The comparison results indicate a novel design guide for the application of aluminum foam structures, for
Table 3 Energy absorption capacity for different examined samples. Relative density
Stacking number
Energy absorption (MJ/ m3 )
0.11
bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer
1.44 1.84 1.85 1.84 3.43 3.83 4.13 4.44 5.04 5.19 5.66 6.35
MLAFS
0.16
0.20
Fig. 13. The variation tendency of energy absorption capacity for MLAFS structures and monolithic foams.
MLAF 1.06 1.01 1.19 2.81 3.13 3.11 4.72 4.40 4.99
the same degree of compressive deformation, MLAFS structures with more stacking number are preferred because of their improved ability of energy absorption capacity and high integrity and stiffness.
4. Conclusion The quasi-static compression behavior of monolithic bulk aluminum foams, multilayer aluminum foam (MLAF) and multilayer aluminum foam sandwich (MLAFS) with different density
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foam cores are investigated. All their compression processes can be divided into three stages but with an obvious difference in compression characteristics. MLAFS structures have much higher plateau stress and stress oscillates distinctly during the second deformation stage. The MLAF structure doesn't show any advantage over monolithic bulk foams, on the contrary, the deformation resistance of MLAFS structure with Al alloy interlayer plates is obviously improved. The presence of Al alloy interlayer plates distinctly changes the deformation mode and induces special compression characteristics for MLAFS structures, including enhanced deformation resistance, shorter oscillation stage and sequent deformation by layer. The effect of stacking number on the energy absorption capacity of MLAFS structures is gradually strengthened with the increase of AF core relative density and MLAFS structures with more stacking number are preferred at higher AF core density. Acknowledgement This work is supported by the National Key Research and Development Program of China (Project No. 2017YFB0103705, 2013BAG19B01). References [1] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, Cambridge University Press, UK, Cambridge, 1997. [2] R.E. Raj, B.S.S. Daniel, Structural and compressive property correlation of closed-cell aluminum foam, J. Alloy. Comp. 467 (2009) 550e556. [3] S.K. Nammi, P. Myler, G. Edwards, Finite element analysis of closed-cell aluminum foam under quasi-static loading, Mater. Des. 31 (2010) 712e722. [4] E. Andrews, W. Sanders, L.J. Gibson, Compressive and tensile behavior of aluminum foams, Mater. Sci. Eng. A 270 (1999) 113e124. [5] E. Linul, N. Movahedi, L. Marsavina, The temperature and anisotropy effect on compressive behavior of cylindrical closed-cell aluminum-alloy foams, J. Alloy. Comp. 740 (2018) 1172e1179. [6] Y. Sun, Q.M. Li, Dynamic compressive behavior of cellular materials: a review of phenomenon, mechanism and modelling, Int. J. Impact Eng. 112 (2018) 74e115. [7] Z. Zhang, J. Ding, X. Xia, Fabrication and characterization of closed-cell aluminum foams with different contents of multi-walled carbon nanotubes, Mater. Des. 88 (2015) 359e365. [8] Z. Wang, J. Shen, G. Lu, L. Zhao, Compressive behavior of closed-cell aluminum alloy foams at medium strain rates, Mater. Sci. Eng. A 528 (2011) 2326e2330. [9] Y. Li, Y. Wei, L. Hou, C. Guo, S. Yang, Fabrication and compressive behavior of an aluminum foam composite, J. Alloy. Comp. 649 (2015) 76e81. [10] I. Jeon, K. Katou, T. Sonoda, T. Asahina, K.J. Kang, Cell wall mechanical properties of closed-cell Al foam, Mech. Mater. 41 (2009) 60e73. [11] D.K. Rajak, L.A. Kumaraswamidhas, S. Das, S. Senthil Kumaran, Characterization and analysis of compression load behavior of aluminum alloy foam under the diverse strain rate, J. Alloy. Comp. 656 (2016) 218e225. [12] K.A. Dannemann, J. Lankford Jr., High strain rate compression of closed-cell aluminum foams, Mater. Sci. Eng. A 293 (2000) 157e164. [13] S. Pal, S. Maiti, G. Subhash, Effect of microscopic deformation mechanisms on the dynamic response of soft cellular materials, Mech. Mater. 42 (2010) 118e133. [14] M.A. Kader, M.A. Islam, M. Saadatfar, Macro and micro collapse mechanisms of closed-cell aluminum foams during quasi-static compression, Mater. Des. 118 (2017) 11e21.
[15] Y. Mu, G. Yao, L. Liang, H. Luo, G. Zu, Deformation mechanisms of closed-cell aluminum foam in compression, Scr. Mater. 63 (2010) 629e632. [16] J. Kadkhodapour, S. Raeisi, Microemacro investigation of deformation and failure in closed-cell aluminum foams, Comput. Mater. Sci. 83 (2014) 137e148. [17] X. Xia, H. Feng, X. Zhang, W. Zhao, The compressive properties of closed-cell aluminum foams with different Mn additions, Mater. Des. 51 (2013) 797e802. [18] L. Jing, X. Su, F. Yang, Compressive strain rate dependence and constitutive modeling of closed-cell aluminum foams with various relative densities, J. Mater. Sci. 53 (2018) 14739e14757. [19] S. Raeisi, J. Kadkhodapour, A. Tovar, Mechanical properties and energy absorbing capabilities of Z-pinned aluminum foam sandwich, Compos. Struct. 214 (2019) 34e46. [20] Y. Zhang, T. Jin, S. Li, D. Ruan, Sample size effect on the mechanical behavior of aluminum foam, Int. J. Mech. Sci. 151 (2019) 622e638. [21] I. Jeon, T. Asahina, The effect of structural defects on the compressive behavior of closed-cell Al foam, Acta Mater. 53 (2005) 3415e3423. [22] A. Aldoshan, S. Khanna, Effect of relative density on the dynamic compressive behavior of carbon nanotube reinforced aluminum foam, Mater. Sci. Eng. A 689 (2017) 17e24. [23] Y. Cheng, Y. Li, X. Chen, Compressive Properties and Energy Absorption of aluminum foams with a wide range of relative densities, J. Mater. Eng. Perform. 27 (2018) 4016e4024. [24] L. Zhu, K. Guo, Y. Li, T.X. Yu, Experimental study on the dynamic behavior of aluminum foam sandwich plates under single and repeated impacts at low temperature, Int. J. Impact Eng. 114 (2018) 123e132. [25] H.J. Chung, K.Y. Rhee, B.S. Han, Numerical study on the mechanical behavior of aluminum foam material using CT image, Adv. Mater. Res. 79e82 (2009) 1297e1300. [26] Y. Hangai, H. Ikeda, K. Amagai, Fabrication of two-layered aluminum foam having layers with closed-cell and open-cell pores, Metall. Mater. Trans. A 49 (2018) 4452e4455. [27] A. Pollien, Y. Conde, L. Pambaguian, Graded open-cell aluminum foam core sandwich beams, Mater. Sci. Eng. A 404 (2005) 9e18. [28] F. Xu, X. Zhang, H. Zhang, A review on functionally graded structures and materials for energy absorption, Eng. Struct. 171 (2018) 309e325. [29] X. Yu, Q. Qin, J. Zhang, Crushing and energy absorption of density-graded foam-filled square columns: experimental and theoretical investigations, Compos. Struct. 201 (2018) 423e433. [30] Y. Hangai, K. Takahashi, R. Yamaguchi, Nondestructive observation of pore structure deformation behavior of functionally graded aluminum foam by Xray computed tomography, Mater. Sci. Eng. A 556 (2012) 678e684. [31] X. Liang, H. Luo, Y. Mu, Experimental study on stress attenuation in aluminum foam core sandwich panels in high-velocity impact, Mater. Lett. 203 (2017) 100e102. [32] M. Saleh, V. Luzin, K. Toppler, Response of thin-skinned sandwich panels to contact loading with flat-ended cylindrical punches: experiments, numerical simulations and neutron diffraction measurements, Compos. Pt. B-Eng. 78 (2015) 415e430. [33] Q. Fang, J. Zhang, Y. Zhang, Mesoscopic investigation of closed-cell aluminum foams on energy absorption capability under impact, Compos. Struct. 124 (2015) 409e420. _ [34] I.K. Odacı, C. Kılıçaslan, A. Tas¸demirci, Projectile impact testing of glass fiberreinforced composite and layered corrugated aluminum and aluminum foam core sandwich panels: a comparative study, Int. J. Crashworthiness 17 (2012) 508e518. _ [35] C. Kılıçaslan, M. Güden, I.K. Odacı, The impact responses and the finite element modeling of layered trapezoidal corrugated aluminum core and aluminum sheet interlayer sandwich structures, Mater. Des. 46 (2013) 121e133. [36] Y.L. Lin, Z.F. Zhang, R. Chen, Cushioning and energy absorbing property of combined aluminum honeycomb, Adv. Eng. Mater. 17 (2015) 1434e1441. _ Odacı, Experimental and numerical studies on the [37] C. Kılıçaslan, M. Güden, I.K. quasi-static and dynamic crushing responses of multi-layer trapezoidal aluminum corrugated sandwiches, Thin-Walled Struct. 78 (2014) 70e78.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Experimental study on the quasi-static compression behavior of multilayer aluminum foam sandwich structure Cheng-Xu Ren, Zheng-Fei Hu*, Cheng Yao, Fan Mo Laboratory for R&D and Application of Metallic Functional Materials, School of Materials Science and Engineering, Tongji University, Shanghai, 201804, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 June 2019 Received in revised form 6 August 2019 Accepted 12 August 2019 Available online 14 August 2019
The axial compression responses of multilayer aluminum foam panels (MLAF) and multilayer sandwich panels (MLAFS) with 5052 Al alloy interlayer plates were experimentally investigated under quasi-static compression condition. The influence of aluminum foam (AF) core density, stacking number and the interlayer plates in MLAFS structures were discussed extensively. Compared with bulk AF, the results indicate that the mechanical properties of MLAF structures are slightly decreased while the compressive resistance of MLAFS structures is obviously enhanced. The presence of Al alloy interlayer plates changes the deformation mode of MLAFS structures and induces collapse in sequence by layer. The effect of stacking number on the compressive behavior of MLAFS structures varies with AF core density and the optimum MLAFS structure was summarized in view of the energy absorption capacity and compressive deformation degree. © 2019 Elsevier B.V. All rights reserved.
Keywords: Aluminum foam Compression behavior Multilayer sandwich structure Energy absorption
1. Introduction Aluminum foam (AF) has received widespread attention due to its combination of excellent physical and mechanical properties [1,2]. Because of its unique structure characteristics, closed cell AF has achieved broad application in aerospace and automotive industry [3,4], such as cores for automobile impact beams, lightweight structure parts in transportation industry. A great deal of experimental studies on the response of monolithic AF, density graded AF and composite sandwich structures to different loading conditions have been undertaken throughout the world. Generally, the compression process of AF can be divided into three deformation stages: linear elastic deformation stage, plateau plastic deformation stage and densification stage. During the second compression stage, the special cellular structure of AF makes it maintain a stable value of stress while undergoing a large scale of deformation, which enables its excellent energy absorption capacity [5e8]. Extensive researches have been devoted to investigate the compressive properties [9,10], strain rate sensitivity [11,12] and deformation mechanism [13,14] of AF. Mu et al. [15] analyzed the
* Corresponding author. E-mail address: [email protected] (Z.-F. Hu). https://doi.org/10.1016/j.jallcom.2019.151860 0925-8388/© 2019 Elsevier B.V. All rights reserved.
effect of cell shape on the deformation behavior of closed-cell AF and proposed four failure modes at the cell/membrane level. Kadkhodapour and Raeisi [16] investigated the deformation behavior of closed-cell AF with regular cell shapes and emphasized the effect of topology structure. Xia et al. [17] fabricated closed-cell AF with different content of manganese and the results showed that Mncontaining foams exhibited much higher compressive properties than commercial pure AF. Recently, Jing et al. [18] investigated the compressive behavior of closed-cell AF with different densities under quasi-static and dynamic strain rate, and a multi-parameter dynamic constitutive model was proposed to describe the unique stress-strain response of AF. Raeisi et al. [19] studied the mechanical properties and energy absorption capacity of Z-pinned aluminum foam sandwich (AFS) both experimentally and numerically. The deformation characteristics were well identified at the cell level. Zhang et al. [20] explored the effect of samples size on the mechanical properties of closed-cell AF, it is proposed that there are different optimum sample sizes to characterize bulk material under different loading conditions. Generally, Previous studies [21,22] have demonstrated that there are relative weak zones and imperfections inside the AF structure, such as internal micro-pores, cracks and the inhomogeneity of cell structure, which might lead to the stress concentration locally and collapse starts from these regions. Stress in these weak regions increases quickly with the interaction between cells and transmits to surrounding cells,
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subsequently, collapse occurs at the next weakest region. So, the initiation and propagation of collapse bands can be observed at the macroscopic level [23e25]. Functionally graded aluminum foam (FGAF), with a structure of density graded AF, has also attracted widespread concerning for its potential mechanical properties of controlled deformation sequence and various plateau region desired [26e29]. Hangai et al. [30] fabricated FGAF with different pore structure and observed its deformation behavior during uniaxial compression test by X-ray computed tomography. The compression process of FGAF structure can be precisely controlled by changing its pore structure. The unique multiple plateau stages exhibited in the stress-strain curve demonstrate the significant effect of multilayer structure on the deformation and failure modes of these special designed structures. Besides, the aluminum foam is usually cladded with compact and stiff metal sheet covers in both sides to form AFS panel and enhance its mechanical performance. In the sandwich structure, the two stiff face sheets carry axial load and offer sandwich structure bending and stretching capability while the foam core bears shearing load and provides the ability to undergo large deformation at nearly constant stress. Apparently, this sandwich structure maintains the characteristics of aluminum foam of lightweight, improves flexural stiffness, impact performance and high-energy absorption capacity [31e33]. Following the review above, the combination of multilayer and sandwich structure has meaningful research significance for its potential excellent mechanical properties and novel deformation modes. An increasing number of investigations have been conducted on multilayer AF [34e36]. Cenk Kılıçaslan et al. [37] studied the compression properties of seven-layered aluminum corrugated sandwich with opposite core orientation both experimentally and numerically. Their investigation found that the presence of interlayer plates can induce the homogeneous collapse of individual layer. In this paper, different types of multilayer aluminum foam (MLAF) and multilayer aluminum foam sandwich (MLAFS) were fabricated. Each multilayer structure sample consists one AF core with relative density 0.11, 0.16 or 0.20. All of these samples were compressed under a constant strain rate of 102S1. In order to investigate the influence of multilayer structure and 5052 Al alloy interlayer plates, the compression tests of monolithic bulk AF with similar size and density were conducted under the same test condition for comparison. The objective of this investigation is to demonstrate the difference in compression characteristics between MLAF, MLAFS and monolithic bulk foams under identical strain rate. The optimum multilayer structure was summarized in view of energy absorption capacity for the potential applications. 2. Materials and methods Closed-cell aluminum foams at three different relative densities of 0.11, 0.16, and 0.20 were manufactured via melt foaming method using TiH2 as foaming agent. The relative density was defined by:
r ¼ r* =rm
alloy sheet of 1 mm thickness is also cut into 70 70 mm2 small pieces to serve as interlayer and face plates for MLAFS structure. Before fabricating the multilayer structure, the bonding surfaces of AF and 5052 Al alloy plates were polished with abrasive paper and then immersed in 10% NaOH solution 1min to clean oil, the pretreated samples should be rinsed in running water immediately for 2min to clear residual lye and then dried by air blower. The MLAF structures were fabricated in 3, 4 and 5 layers with 30 mm, 25 mm and 20 mm thickness AF core pieces respectively, which were bonded using epoxy resin of component A&B as glue. The MLAFS structures were fabricated in the same way, except that the 5052 Al alloy plates were used as extra interlayers and face plates. Added with the thickness of 5052 Al alloy plates, the overall height of MLAFS structures reaches to 94, 105 and 106 mm for three, four and five-layer structure respectively. The schematic diagrams of the MLAF and MLAFS structures are shown in Fig. 2. According to ISO 17340-2014 standard, the uniaxial compression tests were conducted on a computer controlled electronic universal testing machine (WDW/10e100), which has a function of automatic leveling to reduce the effect of imbalanced loading caused by surface irregularities. The tested sample was placed in the middle of the bottom compression platform, the upper compression plate with flat end was controlled to compress the sample at a constant velocity. The quasi-static compression tests for MLAF, MLAFS and monolithic bulk AF were performed at a constant strain rate of 102S1 (corresponding a platen velocity of 60 mm/min), at least three tests were conducted for the same samples to acquire the average values of compression parameters. During compression experiments, the load and displacement were recorded by computer connected to sensors and the deformation processes were also recorded using a digital camera. The experimental nominal stress is simply load divided by the contacting area of these samples (4900 mm2) and the nominal strain is displacement divided by the height of samples. 3. Results and discussions 3.1. Compression behavior of monolithic bulk aluminum foams The typical experimental compression stress-strain curves of monolithic bulk AF under a strain rate of 102S1 are shown in Fig. 3. It is evident that the compression process of AF can be divided into three stages, including a short linear elastic stage at the beginning, a long plateau stage and a final densification stage. Besides, the curve for AF in higher relative density of 0.20 exhibits significant strain hardening phenomenon at its second compression stage. This might be due to the different failure modes at the cell level. It is believed that for foams with lower density or thinner cell walls, the main failure mode is cell buckling and collapse continue under constant compression stress. However, for AF with higher density, the collapse of cells proceeds with the compression of entire cell walls and results in the more obvious strain hardening phenomenon [23].
(1)
where r* is the density of aluminum foam and rm is the density of the aluminum matrix. The appearances of the as-received aluminum foams at different densities are shown in Fig. 1. The average pore sizes of AF with relative density of 0.11, 0.16 and 0.20 are about 6.5 mm, 4.5 mm and 3.2 mm respectively. Four sizes of rectangular AF pieces in three densities were cut with a crosssection of 70 70 mm2 and heights of 100 mm, 30 mm, 25 mm and 20 mm. The pieces with 100 mm height are taken as monolithic bulk AF samples and the rest are ready to prepare the three, four and five-layer MLAF and MLAFS samples. A commercial 5052 Al
3.2. Compression behavior of MLAF and MLAFS structures The compression stress-strain curves for MLAF and MLAFS structures are shown in Fig. 4. Similar to the compression behavior of monolithic bulk AF, three deformation stages can also be recognized in Fig. 4. Compared to monolithic bulk AF at the same density, MLAF structures has a shorter plateau strain and the plateau stress at its second compression stage is even slightly lower than that of monolithic AF. However, the stress-strain curves of MLAFS structures show obvious stress oscillation at their second compression stage (oscillation stage) and the oscillation number is
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Fig. 1. Appearances of AF at different relative densities: (a) 0.11, (b) 0.16 and (c) 0.20.
Fig. 2. Schematic diagrams of MLAF and MLAFS samples.
accordant with the stacking number of AF core layers. More than all of that, the initial collapse stress and plateau stress of MLAFS are both higher than that of MLAF and monolithic AF, which indicates that the compression resistance of MLAFS structure is strengthened obviously for its unique structure. In order to display the failure pattern of MLAF structure under quasi-static compression detailly, the macro deformation sequence pictures of five-layer MLAF with AF core relative density of 0.20 are shown in Fig. 5. Fig. 5(aed) are captured at strains varied from 0.0 to 0.6 at a step of 0.2. The MLAF structure exhibits a shearing type non-progressive deformation characteristic. Deformation and collapse occurred at one specific interface among middle layers as shown in Fig. 5 (b). Previous studies have pointed out that the deformation and collapse of monolithic bulk foam began at the
weakest region and usually occurred at one end [23e25]. The extrusion between cellular pores was intensified and much more deformation bands were formed as compression process proceeds. The expansion of deformation bands in one AF core layer significantly propagated to neighbor layers through the bonding boundaries and the growth of deformation bands between layers induced the simultaneous deformation between AF layers. So, the stressstrain curve of MLAF structure is smoother at its second compression stage. The deformation process continued until the whole structure was compacted and stress increased with strain sharply. Compared to monolithic bulk AF, the shorter plateau stage of MLAF structure should be related to the less lateral expanding during compression. As to the slightly lower initial collapse stress and plateau stress of MLAF structure, this may be attributed to the
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Fig. 3. Stress-strain curves of monolithic bulk aluminum foam at three densities.
formation and extension of deformation bands between AF layers during compression [37], the multilayer interfaces induce more defects might be another reason. In contrast, the second compression stage of MLAFS structure exhibits obvious stress oscillation. In order to illustrate the deformation behavior of MLAFS structure and evaluate the effect of 5052 Al alloy interlayer plates, the complete compression process of fourlayer MLAFS sample with AF core relative density of 0.11 is shown in Fig. 6. The stress-strain curve in Fig. 7 shows peaks and troughs on its second stage, which are noted as point 1 to point 8 to illustrate the deformation sequence. It exhibits clearly in Fig. 6 (c and d) that a specific AF core layer marked with red box collapsed first while
other layers kept almost stable, and the deformation process of the first collapsed AF layer corresponds to the strain region from point 1 to point 3 on the curve in Fig. 7. After this specific layer was preliminary compacted, the next weakest AF core layer began to collapse as shown in Fig. 6 (e and f) marked with red box and its compression process corresponds to strain region from point 3 to 5. This deformation process continued layer by layer until all layers were preliminary densified. When the compression strain reached up to 0.55, the deformation proceeded with the compression of compacted aluminum foams and interlayer plates together, which led to the abrupt increase in stress values. According to ref.10 and 15, the cell structure plays a significant role in the AF deformation process. Collapse starts from the weakest interior parts of AF and stress in these regions are delivered to surrounding cells to form deformation bands. As the compression proceeding, the width and number of deformation bands continue to increase and large deformation is going on. Therefore, even though the nominal densities of AF core layers in one MLAFS sample are equal, their inner pore structures are different, so collapse begin at the weakest AF core layer as shown in Fig. 6 (c), stress increases with the collapse of this specific core layer and the next weakest layer begin to collapse when the stress reaches a certain value. The deformation of MLAFS structure is supposed to be sequential deformation by layer. From above observation, the macro deformation mode of MLAFS structures is obviously different with other AF structures. The compression characteristics of MLAF and MLAFS structures are shown in Fig. 8 and their deformation bands are marked in red boxes. For MLAF structure, as shown in Fig. 8 (a), deformation of AF structure develops in the form of deformation bands forming and propagating [13,23]. Generally, these deformation bands or shearing bands normal have a small angle deviation (about 15 ) to the planes of maximum shear stress, this result is consistent with
Fig. 4. Stress-strain curves of different AF, MLAFS and MLAF samples with the same AF core relative density: (a) 0.11, (b) 0.16, (c) 0.20.
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Fig. 5. The deformation steps of five-layer MLAF captured at strains varied from 0 to 0.6 at a step of 0.2.
some relevant reports in previous studies [15,16], which is believed to be caused by the heterogeneity of the AF structure at cell level. In fact, this angle will reduce obviously for samples with small thickness of the AF layers, so the constraint effect of the size also affects the angle of the deformation band. The discontinuity of the upper and lower AF layer leads to more defects at the interfaces, which causes the deformation of MLAF structure usually begins at the interface between layers as shown in Fig. 5. The MLAFS structure displays a totally different deformation characteristic, as shown in Fig. 8 (b), the AF core deformation starts when a layer of cells collapses which is almost parallel to the interlayer plates. No slant deformation bands are formed in the deformation process, which means more stress is needed to collapse cell structure. The presence of interlayer plates prevents deformation propagation through neighbor layers and enforces the distribution of compressive stress uniformly. They show a constraining effect and make it difficult to form slant deformation bands in AF core layer when the thickness of AF core layer is not enough to start collapse interiorly. So this deformation mode improves the compression resistance of MLAFS structure definitely. Meanwhile, this constraining effect obviously limits the lateral expanding during compression and this fact well explains the even shorter strain plateau stage of MLAFS structures. Compared the stress-strain curves for different samples shown in Fig. 4, the effects of interlayer plates in MLAFS structures can be summarized as follows: (i) the stress plateau rises obviously, which indicates the compression resistance of MLAFS structures are improved distinctly. (ii) the strain length of the plateau stage is shorter. The densification strain of MLAFS structure is approximately 0.55, while the corresponding end point of MLAF is about 0.65. (iii) failure mode of MLAFS is different with other structures. No visible deformation band present in compressive process. Each layer of AF core collapses homogeneously and the structure deforms progressively by layer. In order to compare the compression property and energy absorption capacity between monolithic bulk AF, MLAF and MLAFS structures under quasi-static compression process quantitatively,
the initial collapse stress (sc ) and plateau stress (spl ) in the second compression stage of these structures are calculated respectively. According to the standard ISO 17340-2014, sc is defined as the first maximum stress value on the stress-strain curve and the plateau stress of monolithic bulk AF and MLAF structures are defined as the average stress between 0.2 and 0.4 strain. Considering the stress oscillation exhibits in the second stage of MLAFS structures, the strain interval containing several complete oscillations are utilized to calculate plateau stress:
1 spl ¼ εL ε1
εðL
sðεÞ dε
(2)
ε1
Here ε1 and εL are strains correspond to the first and the last peak point on the oscillation stage of MLAFS structure respectively, such as point 1 and point 7 marked in Fig. 7. The four-layer MLAFS sample with AF core relative density of 0.11 is taken as an example. As shown in Fig. 7, the stain interval from point 1 to point 7, containing three complete oscillations, is chosen to calculate its plateau stress. The densification strain (εd ) is defined as the strain corresponding to the intersection of tangent drawn on the densification region and the plateau stress of the oscillation stage [22]. The schematic diagram of multiple parameters is shown in Fig. 7. The elaborate values of sc , spl and εd of MLAFS, MLAF and monolithic bulk foams are tabulated in Table 1. It indicates that the value of sc and spl for MLAFS structures are both higher than that of monolithic bulk AF and MLAF structures. The lower AF density, the greater the difference in compression parameters. Even though the plateau stage of MLAF structure is longer than MLAFS structure, the deformation resistance of MLAF structure is significantly weaker than MLAFS structure. Therefore, from the view of deformation resistance of multilayer structure, MLAFS structures are preferred. Further discussion will be presented about this kind of combination. The compression stress-strain curves of MLAFS structures with different AF core densities are plotted in Fig. 9. It is clearly noted
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Fig. 8. Compression characteristics of (a) MLAF structure, (b) MLAFS structure with AF core at relative density of 0.20.
Fig. 6. Compression process of four-layer MLAFS with AF core at relative density of 0.11 captured at (a) ε ¼ 0, (bei) from point 1 to point 8 and (j) ε ¼ 0.55.
that the number of peaks and troughs varies with stacking number. Based on the calculated results listed in Table 1, it can be concluded that with the increase of stacking number, the deformation resistance of MLAFS structures improves obviously. This should be related to the variation of thickness of single AF core layer when the stacking number increases. Generally, large number of irregular cells induces the inhomogeneity and vast hole-defects in aluminum foam structure. The number of defects increases with the thickness of specimen, which should result in weaker deformation resistance upon thickening [18]. Besides, the number of Al alloy interlayer plates in MLAFS structure increases with stacking number, this may also contribute to the higher strength of MLAFS structure with more stacking number. The densification strain become shorter with the increase of AF core density and stacking number. For AF core at relative density of 0.11, The densification strain of MLAFS structure is about 0.55, corresponding values for MLAF structure and monolithic bulk AF are about 0.65 and 0.75 respectively. The significantly decreased densification strain should be attributed to the multilayer structure and the presence of the interlayer plates in MLAFS structure as discussed above. In addition, with the same AF core density, the densification strain of MLAFS structures also decreases slightly with the increase of stacking number, which should be caused by the constraining effect of interlayer plates. The deformation resistance of MLAFS structures increases significantly with AF core density, as shown in Fig. 10. This is expected since with the increase of density, the wall thickness of AF cell increases while the cell size becomes smaller. Consequently, the deformation resistance of individual pore improved and the overall energy absorption capacity of AF enhanced either [18]. In order to evaluate the influence of AF core density on initial collapse stress and plateau stress of MLAFS structure quantitatively, the generally accepted relationship of the variation of sc and spl for cellular structure is defined as [1]:
sc ¼ Ac
b c
spl ¼ Apl
Fig. 7. Stress-strain curve of four-layer MLAFS with AF core at relative density of 0.11 and the schematic diagram of multiple compressive parameters.
rf rs
(3)
bpl
rf rs
(4)
Here Ac and Apl are strengthening coefficients, rf is the density of AF and rs is the density of solid metal. bc and bpl are constants related to cellular density. The variation of sc and spl as a function of AF core density for different MLAFS stacking structure are shown in
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Table 1 Collapse stress and plateau stress for different examined samples. Relative density
Stacking number
Collapse stress (MPa) MLAFS
0.11
0.16
0.20
bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer
3.78 4.34 4.66 4.62 8.15 8.93 9.37 9.69 9.73 12.23 13.13 13.72
Plateau stress (MPa) MLAF
MLAFS 3.37 3.96 4.09 3.99 8.30 8.79 9.16 9.58 11.70 11.93 13.16 13.69
2.62 2.41 2.79 6.60 7.24 7.56 11.75 11.06 12.29
Densification strain (%) MLAF 2.52 2.32 2.84 6.51 6.84 7.11 10.93 10.40 11.55
MLAFS 71 62 58 54 75 54 49 43 e 49 45 37
MLAF 67 66 64 66 65 69 63 66 60
Fig. 9. Stress-strain curves of MLAFS structures with AF core at relative density of (a) 0.11, (b) 0.16 and (c) 0.20.
Fig. 11. The experimental data for initial collapse stress and plateau stress as a function of AF core density are fitted by relationship y ¼ Arb . The value of ‘A’ and ‘b’ are listed in Table 2. The fitting parameters of ‘b’ are within the predicted range (from 1.5 to 2.5) reported in a previous study [1]. So, the equations (3) and (4) well describe the compressibility of AF multilayer sandwich structures. 3.3. Energy absorption capacity Aluminum foams have attracted extensive attention for its excellent energy absorption capacity while bearing load outside. Generally, the energy needed to deform structures up to a certain strain during compression is defined as the energy absorption capacity. Under uniaxial compression, the energy absorption per unit volume (Wv) is calculated as the area integrated under the stressstrain curve at a certain strain as follows:
εð0
Wv ¼
sdε
(5)
0
Another important parameter relevant to the energy absorption capability of AF is energy absorption efficiency, the energy absorption efficiency (EAE) is an important parameter to the characterization of AF, the equation can be expressed as below [6,18]:
1 hðεÞ ¼ sðεÞ
ðε
sðεÞdε
(6)
0
where h is the EAE, ε is nominal strain and sðεÞ is corresponding nominal stress. The energy absorption efficiency of different MLAFS samples with the same density were shown in Fig. 12. Unlike the
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Fig. 10. The stress-strain curves of (a) three-layer, (b) four-layer and (c) five-layer MLAFS structures with different AF core densities.
Fig. 11. (a) initial collapse stress and (b) plateau stress as a function of AF core density for multilayer MLAFS structures.
Table 2 Strengthening coefficients of “A” and “b” for MAFLS structures. Stacking number
Three-layer MLAFS Four-layer MLAFS Five-layer MLAFS
Initial collapse stress
Plateau stress
Ac
bc
Apl
bpl
178.7 198.2 233.5
1.66 1.68 1.76
195.3 267.1 308.4
1.73 1.86 1.93
smooth EAE-strain curve of monolithic bulk foam [19], the EAEstrain curves of MLAFS structure exhibits the unique characteristic of multiple steps. It shows that the energy absorption efficiency increases obviously with strain. Several protruding peaks
can be recognized on the EAE-strain curve and the location of these peaks corresponds to the troughs on the stress-strain curve, the number of these peaks is consistent with the layers in MLAFS structure. The vertical dashed lines in Fig. 12 show the positions of densification strain for different MLAFS structure, the densification strain of MLAFS structure decreases with the increase of stacking number. With the strain increases, for the same AF density, the value of EAE for the MLAFS structure reduces relatively with stacking number. These behaviors may be related to the constraining effect of interlayer plates as discussed above. The densification strain of most MLAFS structures investigated in this paper is about 0.55, as listed in Table 1. For comparison under the same deformation degree, the energy absorption for MLAFS structures as well as monolithic bulk foams and MLAF structures
C.-X. Ren et al. / Journal of Alloys and Compounds 810 (2019) 151860
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Fig. 12. The energy absorption efficiency of different layer MLAFS samples with the same AF core relative density: (a) 0.11, (b) 0.16 and (c) 0.20.
are calculated up to a strain of 0.45. The calculation results for MLAFS, MLAF structures and monolithic bulk AF are listed in Table 3 and the variation tendency is shown in Fig. 13. Generally, the MLAFS structure exhibits much higher energy absorption capacity compared with MLAF structure and monolithic bulk AF under the same deformation degree and its energy absorption capacity increases extremely with AF core density. In the view of energy absorption capacity, the stacking number has no evident effect on MLAFS structures when relative density of AF core is low, but when the relative density of AF core increases to 0.16 or 0.20, their energy absorption is obviously increased with the stacking number. Compared to monolithic AF, the energy absorption capacity of MLAFS structures is enhanced more than 20% when AF core at low relative density of 0.11, but only about 10% for AF core at high relative density of 0.20. The comparison results indicate a novel design guide for the application of aluminum foam structures, for
Table 3 Energy absorption capacity for different examined samples. Relative density
Stacking number
Energy absorption (MJ/ m3 )
0.11
bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer bulk foam Three-layer Four-layer Five-layer
1.44 1.84 1.85 1.84 3.43 3.83 4.13 4.44 5.04 5.19 5.66 6.35
MLAFS
0.16
0.20
Fig. 13. The variation tendency of energy absorption capacity for MLAFS structures and monolithic foams.
MLAF 1.06 1.01 1.19 2.81 3.13 3.11 4.72 4.40 4.99
the same degree of compressive deformation, MLAFS structures with more stacking number are preferred because of their improved ability of energy absorption capacity and high integrity and stiffness.
4. Conclusion The quasi-static compression behavior of monolithic bulk aluminum foams, multilayer aluminum foam (MLAF) and multilayer aluminum foam sandwich (MLAFS) with different density
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foam cores are investigated. All their compression processes can be divided into three stages but with an obvious difference in compression characteristics. MLAFS structures have much higher plateau stress and stress oscillates distinctly during the second deformation stage. The MLAF structure doesn't show any advantage over monolithic bulk foams, on the contrary, the deformation resistance of MLAFS structure with Al alloy interlayer plates is obviously improved. The presence of Al alloy interlayer plates distinctly changes the deformation mode and induces special compression characteristics for MLAFS structures, including enhanced deformation resistance, shorter oscillation stage and sequent deformation by layer. The effect of stacking number on the energy absorption capacity of MLAFS structures is gradually strengthened with the increase of AF core relative density and MLAFS structures with more stacking number are preferred at higher AF core density. Acknowledgement This work is supported by the National Key Research and Development Program of China (Project No. 2017YFB0103705, 2013BAG19B01). References [1] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, Cambridge University Press, UK, Cambridge, 1997. [2] R.E. Raj, B.S.S. Daniel, Structural and compressive property correlation of closed-cell aluminum foam, J. Alloy. Comp. 467 (2009) 550e556. [3] S.K. Nammi, P. Myler, G. Edwards, Finite element analysis of closed-cell aluminum foam under quasi-static loading, Mater. Des. 31 (2010) 712e722. [4] E. Andrews, W. Sanders, L.J. Gibson, Compressive and tensile behavior of aluminum foams, Mater. Sci. Eng. A 270 (1999) 113e124. [5] E. Linul, N. Movahedi, L. Marsavina, The temperature and anisotropy effect on compressive behavior of cylindrical closed-cell aluminum-alloy foams, J. Alloy. Comp. 740 (2018) 1172e1179. [6] Y. Sun, Q.M. Li, Dynamic compressive behavior of cellular materials: a review of phenomenon, mechanism and modelling, Int. J. Impact Eng. 112 (2018) 74e115. [7] Z. Zhang, J. Ding, X. Xia, Fabrication and characterization of closed-cell aluminum foams with different contents of multi-walled carbon nanotubes, Mater. Des. 88 (2015) 359e365. [8] Z. Wang, J. Shen, G. Lu, L. Zhao, Compressive behavior of closed-cell aluminum alloy foams at medium strain rates, Mater. Sci. Eng. A 528 (2011) 2326e2330. [9] Y. Li, Y. Wei, L. Hou, C. Guo, S. Yang, Fabrication and compressive behavior of an aluminum foam composite, J. Alloy. Comp. 649 (2015) 76e81. [10] I. Jeon, K. Katou, T. Sonoda, T. Asahina, K.J. Kang, Cell wall mechanical properties of closed-cell Al foam, Mech. Mater. 41 (2009) 60e73. [11] D.K. Rajak, L.A. Kumaraswamidhas, S. Das, S. Senthil Kumaran, Characterization and analysis of compression load behavior of aluminum alloy foam under the diverse strain rate, J. Alloy. Comp. 656 (2016) 218e225. [12] K.A. Dannemann, J. Lankford Jr., High strain rate compression of closed-cell aluminum foams, Mater. Sci. Eng. A 293 (2000) 157e164. [13] S. Pal, S. Maiti, G. Subhash, Effect of microscopic deformation mechanisms on the dynamic response of soft cellular materials, Mech. Mater. 42 (2010) 118e133. [14] M.A. Kader, M.A. Islam, M. Saadatfar, Macro and micro collapse mechanisms of closed-cell aluminum foams during quasi-static compression, Mater. Des. 118 (2017) 11e21.
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