Anisotropic Compressive Behavior of Functionally Density ... - MDPI

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Anisotropic Compressive Behavior of Functionally Density Graded Aluminum Foam Prepared by Controlled Melt Foaming Process Bingbing Zhang 1 , Shuangqi Hu 1, * and Zhiqiang Fan 2 1 2

*

School of Environment and Safety Engineering, North University of China, Taiyuan 030051, China; [email protected] School of Science, North University of China, Taiyuan 030051, China; [email protected] Correspondence: [email protected]; Tel.: +86-0351-3922150

Received: 19 November 2018; Accepted: 3 December 2018; Published: 5 December 2018







Abstract: Aluminum foams with a functionally graded density have exhibited better impact resistance and a better energy absorbing performance than aluminum foams with a uniform density. Nevertheless, the anisotropic compression behavior caused by the graded density has scarcely been studied. In this paper, a density graded aluminum foam (FG) was prepared by a controlled foaming process. The effect of density anisotropy on the mechanical behavior of FGs was investigated under quasi-static compression and a low-velocity impact. Digital image correlation (DIC) and numerical simulation techniques were used to identify deformation mechanisms at both macro and cell levels. Results show that transverse compression on FGs lead to a higher collapse strength but also to a lower energy absorption, due to the significant decrease in densification strain and plateau stress. The deformation behavior of FGs under longitudinal compression was dominated by the progressive extension of the deformation bands. For FGs under transverse compression, the failure mode of specimens was characterized by multiple randomly distributed deformation bands. Moreover, the transverse compression caused more deformation on cells, through tearing and lateral stretching, because of the high lateral strain level in the specimens. It was concluded that the transverse compression of FGs lead to a lower plateau stress and a lower cell usage, thus resulting in a poorer energy absorption efficient; this constitutes a key factor which should be taken into consideration in structural design. Keywords: density graded aluminum foams; anisotropy; mechanical behavior; deformation mechanism; digital image correlation

1. Introduction Aluminum foams have found many potential applications in efficient constructions, lightweight structures, heat insulation and acoustic insulation. The energy absorption of aluminum foams is mostly dominated by the long stress plateau stage, leading to a low loading transmission to the protected structures. In order to more efficiently deal with more complicated requirements, functionally graded aluminum foams (FGs) have been suggested in recent decades [1]. Great efforts have been conducted to prepare FGs through metallurgy, casting, and melt foaming processes [2–6]. The gradient can be acquired by adjusting the cell size or fabricating different material layers [7–9]. FG aluminum foams have pronounced better impact dissipation performance than those with a uniform density [10,11]. Among all methods, direct foaming is more feasible and less costly to get considerable dimensions of density graded aluminum foam. As a consequence, the mechanical behavior of FGs have been experimentally and theoretically investigated [12–14]. The typical response of FGs was characterized the gradual or stepwise increased plateau stress which can help to tailor special structural response. Materials 2018, 11, 2470; doi:10.3390/ma11122470

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response of FGs was characterized the gradual or stepwise increased plateau stress which can help to tailor special structural response. However, However, this this research research largely largely focused focused on on the the FGs’ FGs’ longitudinal longitudinal compression compression in in the the density density gradient direction. Investigations on the transverse compression of FGs is scarce. Clearly, gradient direction. Investigations on the transverse compression of FGs is scarce. Clearly, it it is is crucial crucial to examine the extensive loading conditions for these materials, because the impact could be laterally to examine the extensive loading conditions for these materials, because the impact could be laterally carried past decades, decades, the the anisotropic anisotropic compressive carried out out on on the the structure. structure. In In past compressive behavior behavior of of both both closed closed and and open cell aluminum foams has been widely specified [15–20]. Results show that the collapse open cell aluminum foams has been widely specified [15–20]. Results show that the collapse strength strength of under transverse transverse compression compression reduced reduced as as compared compared to to longitudinal longitudinal compression, compression, of aluminum aluminum foam foam under and that the reduction was directly in relation to the cell aspect ratio. However, the reported and that the reduction was directly in relation to the cell aspect ratio. However, theanisotropy reported was substantially attributed toattributed the elliptical cellelliptical shape along the foaming direction. anisotropy anisotropy was substantially to the cell shape along the foamingThis direction. This could in fact be avoided by controlling both the preparation technology and the preferred selection in anisotropy could in fact be avoided by controlling both the preparation technology and the preferred productions with uniform cell structures. selection in productions with uniform cell structures. As for the the transverse transversecompression compressionofofFGs, FGs,the themechanical mechanical response is inevitably influenced As for response is inevitably influenced by by the varied density in the lateral direction, exhibiting different deformation mechanisms. While the varied density in the lateral direction, exhibiting different deformation mechanisms. While the the longitudinal compression FGs have beenstudied, studied,the themechanical mechanical behaviors behaviors under under transverse longitudinal compression of of FGs have been transverse compression are yet to be adequately identified. To the best of our knowledge, available studies compression are yet to be adequately identified. To the best of our knowledge, available studies do do not this paper, paper, FGs not provide provide abundant abundant information information for for this this problem. problem. In In this FGs were were prepared prepared via via aa controlled controlled foaming foaming process process by by dispersing dispersing different different foaming foaming agent agent contents contents in in different different depths depths of of matrixes. matrixes. The The anisotropy of mechanical properties and deformation mechanisms were also identified, which should anisotropy of mechanical properties and deformation mechanisms were also identified, which should help help provide provide suggestions suggestions in in structural structural design. design.

2. Materials and Methods 2. Materials and Methods Density graded aluminum foam was produced by controlling the contents of a foaming agent, Density graded aluminum foam was produced by controlling the contents of a foaming agent, and a subsequent cooling procedure, as suggested in [8]. Firstly, pure aluminum was melted at ~680 and a subsequent cooling procedure, as suggested in [8]. Firstly, pure aluminum was melted at ◦ C. Secondly, 2 wt.% calcium was introduced as thickening agent. Thirdly, the 370 ◦ C pre-heated TiH 2 ~680 °C. Secondly, 2 wt.% calcium was introduced as thickening agent. Thirdly, the 370 °C pre-heated powders with different contents (1.0, 1.5 and 2.0 wt.%) were dispersed from bottom to the top of the TiH2 powders with different contents (1.0, 1.5 and 2.0 wt.%) were dispersed from bottom to the top molten body, acting as foaming agent. At last, a cooling procedure was implemented by spraying water of the molten body, acting as foaming agent. At last, a cooling procedure was implemented by at the bottom of the mold before the melt grown up. The growth process of cells was simultaneously spraying water at the bottom of the mold before the melt grown up. The growth process of cells was influenced by the gravity of andofthe reducing temperature, resulting in gradually simultaneously influenced bythe themelt gravity therapidly melt and the rapidly reducing temperature, resulting varied cell sizes in the vertical direction. All uniaxial compression specimens were cut from blocks in gradually varied cell sizes in the vertical direction. All uniaxial compression specimens were cut 3 (200 200 × (200 160 mm the cellular is quite homogeneous at specific density levels 3) wherestructure from×blocks × 200) where × 160 mm the cellular structure is quite homogeneous at specific (see Figure 1a). To acquire the density gradient, series of cuboid sections in different depths from the density levels (see Figure 1a). To acquire the density gradient, series of cuboid sections in different top werefrom cut out, densities were The relative density was ρr = ρfwas /ρm , depths the and top the were cut out, andcalculated. the densities were calculated. Theexpressed relative as density where ρ and ρ are the densities of the foam and the aluminum matrix, respectively. The density f as ρm expressed r = ρf/ρm, where ρf and ρm are the densities of the foam and the aluminum matrix, nearly increased depth, as shown in Figure The variation cell structure with the respectively. Thelinearly densitywith nearly increased linearly with1b. depth, as shownofinthe Figure 1b. The variation depth is illustrated in Figure 1c. of the cell structure with the depth is illustrated in Figure 1c.

Figure Variation trend trend Figure 1. 1. Variation aluminum aluminum foam foam and and (d), (d), compression (LC). compression (LC).

of (a–c) (a–c) cell of cell structure structure and and density density the illustration for the transverse the illustration for the transverse

of of functionally functionally density density compression (TC) compression (TC) and and

graded graded (FG) (FG) longitudinal longitudinal

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Specimens uniform density density (UF) (UF) had had aa nominal nominal dimension dimension of of40 40×× 40 40 × × 40 40 mm mm33.. Five Specimens with with aa uniform Five 3 density density levels levels (0.39–0.65g/cm (0.39–0.65g/cm)3 )were weretested testedto toacquire acquirethe themechanical mechanical properties properties of of UFs. UFs. The The results results reported here were wereaveraged averagedfrom fromthree three repeated tests each case. three of samples reported here repeated tests forfor each case. ForFor FGs,FGs, three sets sets of samples with 3 were tested, all with a dimension of 50 × 60 × 80 with a nominal density of 0.45, 0.57 and 0.62 g/cm 3 a nominal density of 0.45, 0.57 and 0.62 g/cm were tested, all with a dimension of 50 × 60 × 80 mm3 . 3. The longitudinal and transverse compressions were respectively marked as LC and TC, as mm The longitudinal and transverse compressions were respectively marked as LC and TC, as illustrated illustrated in Figure 1d. Low-velocity tests were carried at room temperature by using a in Figure 1d. Low-velocity impact testsimpact were carried out at room out temperature by using a drop-weight drop-weight impact testing system, as illustrated in Figure 2. impact testing system, as illustrated in Figure 2.

Figure 2. Sketch map of drop-weight tests. Figure 2. Sketch map of drop-weight tests.

The force–time and displacement–time histories in drop-weight tests were acquired by recording The force–time and displacement–time histories in drop-weight tests were acquired by the acceleration of the drop hammer. The engineering strain and stress of specimens were obtained recording the acceleration of the drop hammer. The engineering strain and stress of specimens were through the following calculation method: obtained through the following calculation method: Z Z τ (1) 1 τ 1  [v0 − ε(t) = a(t)dt]dt (1)  (t )  L [0v0  a (0t )dt ]dt

L 0



0

Ma(t) σ(t) = Ma (tA )

 (t ) 

(2)(2)

where L and A is height and sectional area of the specimens, respectively. M is the weight of the drop A hammer, a(t) is the acceleration signal, v0 is the impact velocity of the drop-weight upon the specimens, where anddetermined A is height by andthe sectional of the specimens, respectively. is the weight ofwas the drop which Lwas freefallarea height of the weight. A large drop M hammer of 70 kg used hammer, a(t) is the acceleration signal, v 0 is the impact velocity of the drop-weight upon the to reduce high frequency oscillation of the acceleration signal. The impact velocity of drop-weight specimens, which determined bym the freefall height of the A large hammer of 70 kg under freefall fromwas a height of 1.8–2.0 onto the specimens wasweight. 5.94–6.26 m/s. drop A load cell comprising was used to reduce high frequency oscillation of the acceleration signal. The impact velocity of a set of semiconductor strain gauges was used to measure the impact force transmitted at thedropback weight under freefall from a height of 1.8–2.0 m onto the specimens was 5.94–6.26 m/s. A load cell surface of specimen (see Figure 2). In addition, the deformation processes of specimens were captured comprising a set camera of semiconductor strain by a high-speed with a frame rate gauges of 5000 was fps. used to measure the impact force transmitted at theInback surface of specimen (see Figure 2). In addition, the deformation processes of specimens order to acquire an insight view on the deformation and densification mechanisms of FGs, were captured by a high-speed camera with a frame rate of 5000 fps. a two-dimensional numerical model was established by using a surface scanning method. At first, In order onelectric the deformation and densification mechanisms of FGs, a the surface (80to×acquire 48 mm2an ) ofinsight the FGview cut by discharge machine (EDM) was well polished. Then two-dimensional numerical model was established by using a surface scanning method. At first, the the surface morphology was scanned. Contour lines of each cell were extracted to be an IGES model. 2) of the FG cut by electric discharge machine (EDM) was well polished. Then the surface 48 mm Finally, (80 the ×IGES model was imported into commercial software ANSYS/LS-DYNA to create the finite surface was scanned. Contour linesplate of each cell were to be history an IGESextracted model. elementmorphology model. The model was loaded by a rigid moving with aextracted velocity–time Finally, the IGES model was imported into commercial software ANSYS/LS-DYNA to create the from the experiments. The support at the other side was modelled by a stationary rigid platefinite (see element model. Theline model was loaded by atrend rigid plate a velocity–time historyspecify extracted Figure 3). The red shows the variation of themoving materialwith porosity. The red squares the from experiments. support at the other was four modelled finite the mesh elements ofThe a single connection point side between cells. by a stationary rigid plate (see Figure 3). The red line shows the variation trend of the material porosity. The red squares specify the finite mesh elements of a single connection point between four cells.

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Figure 3. Numerical simulation model of FG thespecimen FG specimen andvariation the variation trend of material Figure 3. Numerical simulation model of the and the trend of material porosity. porosity.

3. Results

3. Results

3.1. Quasi-Static Compression Behavior 3.1. Quasi-Static Compression Behavior curves of UFs with different densities. All curves exhibited three Figure 4a shows a set of stress-strain

compression including flat stress plateau which accounts All for curves energyexhibited absorption. Figurestages, 4a shows a set ofastress-strain curvesstage of UFs with primarily different densities. A distinct stress drop stages, was observed after thestress yield stage which attributed to the for onsets of the three compression including a flat plateau stageshould which be primarily accounts energy absorption. distinct stress drop was yield stage which should be attributed to of cell’s collapse. ACompressive strength andobserved plateau after stressthe both increase with the density. The results of the cell’s collapse. strength and plateau stress both the LCthe andonsets TC specimens are shown in Compressive Figure 4b. Typical stress–strain responses of UFincrease and FG with specimens Theinresults LCAs and specimens are shown in Figure 4b. Typical stress–strain responses aredensity. compared Figureof4c. weTC can see, LC exhibits progressively increased plateau stress and lower of UF and FGthose specimens in Figure 4c. As weplateau can see, LC are exhibits progressively stress drop than of UFs.are Thecompared increase trend of stress at the stage demonstrated by the increased plateau stress and lower stress drop than those of UFs. The increase trend of stress atcan thebe dashed lines. As compared with TC specimens, three obvious characteristics of LC specimens Materials 2018, 11, x FOR PEER REVIEW 5 of 14 plateau stage are demonstrated by the dashed lines. As compared with TC specimens, three obvious found: lower compressive strength, higher plateau stress, and larger densification strain. characteristics of LC specimens can be found: lower compressive strength, higher plateau stress, and larger densification strain.

(a)

(b)

(c) Figure 4. Mechanical response of (a) UFs and (b) FGs under quasi-static compression and 4. Mechanical response of (a)between UFs andUF (b)and FGs quasi-static compression and (c) (c) Figure comparison of stress-strain response FGunder specimens. comparison of stress-strain response between UF and FG specimens.

3.2. Drop-Weight Impact Tests Figure 5a,b shows typical drop-weight test results performed on FGs with nominal density of ~0.56 g/cm3 under longitudinal and transverse compression, respectively. The stress at the impact

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3.2. Drop-Weight Impact Tests Figure 5a,b shows typical drop-weight test results performed on FGs with nominal density of ~0.56 g/cm3 under longitudinal and transverse compression, respectively. The stress at the impact surface and the back surface of the specimen were both compared with the stress under quasi-static compression. As observed, at the elastic stage, the elasticity modulus under impact tests was smaller because of the data smoothing process. Also, it can be seen that the first peak force at the rear surface is higher than that at the front surface, which should be attributed to the impact effect at the interface between the load cell and the rigid support. However, after the failure strain, the stress profile of the back surface agrees well with that of the front surface. In this case, the macro deformation of the specimen could be assumed to be homogenous. As a result, the stress profiles of the front surface were Materials 2018, 2018, 11, 11, xx FOR FOR PEER PEER REVIEW REVIEW of 14 14 Materials 66 of adopted to characterize the dynamic compression behavior of FGs in the following contexts.

(a) (a)

(b) (b)

Figure 5. Validation of stress equilibrium for specimens under (a) LC and (b) TC. Figure 5. 5. Validation Validation of of stress stress equilibrium equilibrium for for specimens specimens under under (a) (a) LC LC and and (b) (b) TC. TC. Figure

Typical dynamic test results of FGs with different densities under LC and TC were indicated in Typical dynamic test results ofLC FGsand with different densities under LC LC and and TC were were indicated in dynamic results of FGs with different densities under TC indicated in Figure Typical 6. As we can see,test FGs under TC show similar compressive behavior with that under Figure 6. 6. As As we we can can see, see, FGs FGs under under LC LC and and TC TC show show similar similar compressive compressive behavior behavior with with that that under under Figure static compression. FGs under TC exhibit higher strength and lower plateau stress. Also, dynamic static compression. compression. FGs FGs under TC TC exhibit exhibit higher higher strength strength and and lower lower plateau plateau stress. stress. Also, Also, dynamic dynamic static strength and plateau stressunder of both LC and TC specimens agree well with the quasi-static compression strength and and plateau plateau stress stress of of both both LC LC and and TC TC specimens specimens agree agree well well with with the the quasi-static quasi-static compression compression strength values, indicating that the strain rate have no obvious effect on the mechanical properties of FGs in values, indicating indicating that that the the strain strain rate rate have have no no obvious obvious effect effect on on the the mechanical mechanical properties properties of of FGs FGs in in values, the present impact velocity range. For LC and TC specimens subjected to the same impact energy, the present present impact impact velocity velocity range. range. For For LC LC and and TC TC specimens specimens subjected subjected to to the the same same impact impact energy, energy, the TC specimens produce larger compression strain (see Figure 6). One can conclude that FGs under TC specimens specimens produce produce larger larger compression compression strain strain (see (see Figure Figure 6). 6). One One can can conclude conclude that that FGs FGs under under aa TC a longitudinal show better betterenergy energywhen whenabsorbing absorbing performance in the present velocity range. longitudinal impact impact show performance in the present velocity range. longitudinal impact show better energy when absorbing performance in the present velocity range.

(a) (a)

(b) (b)

Figure 6. Mechanical response of (a) UFs and (b) FGs under impact compression. Figure 6. 6. Mechanical Mechanical response response of of (a) (a) UFs UFs and and (b) (b) FGs FGs under under impact impact compression. compression. Figure

3.3. Mechanical Mechanical Properties Properties and and Energy Energy Absorption Absorption 3.3. The compressive compressive strength strength σσcc of of aluminum aluminum foam foam under under both both longitudinal longitudinal and and transverse transverse The compression can can be be directly directly determined determined by by the the relative relative density density [21,22]: [21,22]: compression (3) (3) 

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3.3. Mechanical Properties and Energy Absorption The compressive strength σc of aluminum foam under both longitudinal and transverse compression can be directly determined by the relative density [21,22]: σc = Aρr α

(3)

where A and α are fitting parameters. Therefore, the variation of average strengths with the density of all specimens (UF, LC and TC) was scattered in Figure 7a. The strength can be well fitted by the relation. Clearly, the strength of TC specimens is higher than that of UF and LC specimens. However, Materials 2018, 11, x FOR PEER REVIEW 7 of 14 the strength of the LC specimen was slightly lower than that of UF. This can be attributed to the fact that that the the damage damage resistance resistance of of the the LC LC specimen specimen was was dominated dominated by by the the weakest weakest part part of of material material with with the lowest density. the lowest density.

(a)

(b)

Figure 7. (a) Compressive strength of UF and FG aluminum foams and (b) anisotropy parameter. Figure 7. (a) Compressive strength of UF and FG aluminum foams and (b) anisotropy parameter.

In the case of TC, materials with different densities experienced the same deformation rate. In the case TC, materialsby with differentthe densities experienced the same deformation rate. The The The strength canofbe calculated averaging load sharing of each section in the specimen. strength can be calculated by averaging the load sharing of each section in the specimen. The transverse compression strength of aluminum foams can be predicted by taking cell shape anisotropy transverse compression strength of aluminum foams can beshape predicted by taking cell shape anisotropy into consideration [17,19]. For three groups of FGs, the cell anisotropy parameter R at different into consideration [17,19]. Formeasured three groups FGs, the cell shape anisotropy R atcell different depths of the specimen was andofillustrated in Figure 7b. As weparameter can see, the shape depths of the specimen was measured and illustrated Figure 7b. As parameter we can see,was theset cellasshape anisotropy slightly increased with cell size. Therefore,inthe anisotropy 1.22, anisotropy slightly increased Therefore, the anisotropy parameter as 1.22, 1.18, 1.18, and 1.13 for three sets ofwith FGs.cell Assize. a consequence, the nominal strength ofwas TC set specimens was and 1.13 for three sets of FGs. As a consequence, the nominal strength of TC specimens was predicted predicted as: Z α 1 + 1/R A L x as: σTC = ∗ [ρr1 + (ρr2 − ρr1 )] dx (4) 2R L 0 L

11/ R

A



L

x

 TC density at two ends [  rof  r 2   r1 )] (4) where ρr1 and ρr2 are the relative specimen, L isdx the sample length in density 1 the ( 0 2 RshapeLanisotropy, Land A and α are fitting parameters for UFs varied direction, R represents the cell as specified inρFigure 7a.relative The predicted are indicated in Figure slightly lower where ρr1 and r2 are the density atvalues two ends of the specimen, L is7a, thewhich sampleare length in density than thedirection, experiment results. This probably to the change deformation mechanism: transverse varied R represents theiscell shapedue anisotropy, and Aofand α are fitting parameters for UFs compression may not only change the loadvalues sharing but also form the laterally constrained as specified in Figure 7a. The predicted aremechanism, indicated in Figure 7a, which are slightly lower structure [23]. than the experiment results. This is probably due to the change of deformation mechanism: transverse Figure 8amay shows a comparison of σthe σpl between and TC specimens, and compression not only change load sharing LC mechanism, but also where form strength the laterally c and plateau stressstructure of UFs were constrained [23].also scattered. It can be seen that all FGs exhibited higher plateau stress than UF foams. LC specimens exhibited the highest plateau stress and lowest strength, as compared with UF and TC specimens. For aluminum foam, energy absorption was influenced by both the plateau stress σpl and the densification strain εD . Therefore, the variation of εD and energy absorption Eabs were 

depths of the specimen was measured and illustrated in Figure 7b. As we can see, the cell shape anisotropy slightly increased with cell size. Therefore, the anisotropy parameter was set as 1.22, 1.18, and 1.13 for three sets of FGs. As a consequence, the nominal strength of TC specimens was predicted as: Materials 2018, 11, 2470

 TC 

11/ R A L x   [  r1  (  r 2   r1 )] dx 2R L 0 L

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(4)

also examined 8b). As we canatsee, densification strain LofisLC is approximate where ρr1 and ρ(see r2 areFigure the relative density twothe ends of the specimen, thespecimens sample length in density to that of UFs. However, LC exhibited better energy absorption because of their higher plateau varied direction, R represents the cell shape anisotropy, and A and α are fitting parameters forstress. UFs Although TCinpresented plateau stress, the energy absorption was7a, still inferior UFs because as specified Figure 7a.higher The predicted values are indicated in Figure which areto slightly lower of thethe distinctly reduced densification strain.due Thattois, transverse the benefit than experiment results. This is probably the change ofcompression deformationcounteracted mechanism: transverse of graded density in energy absorption, though it improved the collapse resistance of materials. This compression may not only change the load sharing mechanism, but also form the laterally should be taken into account constrained structure [23]. in light-weight structural design involving FGs. Materials 2018, 11, x FOR PEER REVIEW

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Figure 8a shows a comparison of σc and σpl between LC and TC specimens, where strength and plateau stress of UFs were also scattered. It can be seen that all FGs exhibited higher plateau stress than UF foams. LC specimens exhibited the highest plateau stress and lowest strength, as compared with UF and TC specimens. For aluminum foam, energy absorption was influenced by both the plateau stress σpl and the densification strain εD. Therefore, the variation of εD and energy absorption Eabs were also examined (see Figure 8b). As we can see, the densification strain of LC specimens is approximate to that of UFs. However, LC exhibited better energy absorption because of their higher plateau stress. Although TC presented higher plateau stress, the energy absorption was still inferior to UFs because of the distinctly reduced densification strain. That is, transverse compression counteracted the benefit of graded density in energy absorption, though it improved the collapse resistance of materials.(a) This should be taken into account in light-weight (b) structural design involving FGs. Figure 8. (a) Mechanical properties and (b) energy absorption of UF and FG foams. Figure 8. (a) Mechanical properties and (b) energy absorption of UF and FG foams.

4. 4. Discussion Discussion

4.1. Quasi-Static Quasi-Static Deformation Deformation Mechanisms Mechanisms 4.1. Deformation images at areare shown in Figure 9. When the Deformation at different differentstages stagesofofLC LCand andTC TCspecimens specimens shown in Figure 9. When LC specimen was compressed over the failure strain, cell collapse first arose at the top side because of the LC specimen was compressed over the failure strain, cell collapse first arose at the top side the lowest Thedensity. corresponding compressioncompression strain map was acquired by using digital because of density. the lowest The corresponding strain map was acquired by image using correlation analysis [24], analysis see Figure 9a2. With further the crushed zone progressively digital image correlation [24], see Figure 9a2. compression, With further compression, the crushed zone extended downstream to the part with denser material. A gradual collapse behavior of the material is progressively extended downstream to the part with denser material. A gradual collapse behavior of advantageous special structural design. In the case of TC,Indeformation randomly formed the material is to advantageous to special structural design. the case of bands TC, deformation bands in the whole region, see Figure 9b1,b2. see As Figure a consequence, thea failure mode of the TC specimen randomly formed in the whole region, 9b1,b2. As consequence, the failure mode of was the dominated by the overall shear bands, which is in accordance with UFs [25–27]. TC specimen was dominated by the overall shear bands, which is in accordance with UFs [25–27].

Figure deformation behavior behaviorofofFG FGfoam foamunder under and sketch of Mode C Figure 9. 9. Typical Typical deformation (a)(a) LCLC and (b)(b) TC,TC, (c) (c) sketch of Mode C and Mode D and (d) typical deformation cells.cells. and Mode D and (d) typical deformation

It was was reported reported that relation to to failure mechanism on It that energy energyabsorption absorptionofofaluminum aluminumfoams foamsisisinin relation failure mechanism cell/membrane scales [28–32]. At the cell cell level,level, threethree deformation mechanisms were concluded, that is, on cell/membrane scales [28–32]. At the deformation mechanisms were concluded, that is, (I) large compressive deformation without rotation, (II) large deformation incorporating with obvious rotation, (III) distortion involving in-plane shear failure of cell walls [25,33]. The three mechanisms can also be specified in FGs as indicated in Figure 9a1. However, the crushed cells in LC specimens tended to localize around the moving band, while in TC specimens, the initially collapsed cells randomly distributed in the whole specimen as the red arrows indicated in Figure 9b1.

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(I) large compressive deformation without rotation, (II) large deformation incorporating with obvious rotation, (III) distortion involving in-plane shear failure of cell walls [25,33]. The three mechanisms can also be specified in FGs as indicated in Figure 9a1. However, the crushed cells in LC specimens tended to localize around the moving band, while in TC specimens, the initially collapsed cells randomly distributed in the whole specimen as the red arrows indicated in Figure 9b1. At the membrane level, four failure patterns can be identified: bending, shearing, tearing, and a combined lateral stretching and buckling of the cell membranes, named as Mode A–D [34]. These failure patterns were also observed in FGs. Bending and shearing of membranes were observed at the initial collapse stage in both LC and TC. Conversely, tearing and lateral stretching, illustrated in Figure 9c, mostly arose at the later period of deformation for LC specimens. It means that Mode C Materials 2018, 11, x FOR PEER REVIEW 9 of 14 and D mainly took place at higher nominal strain level [33] (see Figure 9a4). The typical cells were indicated in Figure 9d1,d2. However, in transverse compression, tearing and lateral stretching can be D mainly took place at higher nominal strain level [33] (see Figure 9a4). The typical cells were apparently identified even at the initial collapse stage (see Figure 9b1). The typical cells were specially indicated in Figure 9d1,d2. However, in transverse compression, tearing and lateral stretching can be indicated in Figure 9d3,d4. This can be primarily attributed to the density variation at the orientation apparently identified even at the initial collapse stage (see Figure 9b1). The typical cells were specially perpendicular to the 9d3,d4. loadingThis direction. Differenceattributed in mechanical performance of neighbouring cells indicated in Figure can be primarily to the density variation at the orientation lead to mismatches in deformation behavior, resulting in a larger extent of lateral strain concentration. perpendicular to the loading direction. Difference in mechanical performance of neighbouring cells In lead this case, higher strain level derived in some local regions, thus causing stretching and tearing to mismatches in deformation behavior, resulting in a larger extent of lateral strain of cellconcentration. membranes. In TC specimens were more likelyin tosome produce cracking the whole In fact, this case, higher strain level derived locallongitudinal regions, thus causingon stretching specimen, as illustrated in Figure 9b3. and tearing of cell membranes. In fact, TC specimens were more likely to produce longitudinal cracking on the whole specimen, as illustrated in Figure 9b3.

4.2. Axial Deformation Under Drop-Weight Impact

4.2.High Axialspeed Deformation Impact impact tests to identify the anisotropic compression imagesUnder wereDrop-Weight captured during

behavior of FGs. representative set ofduring imagesimpact corresponding to an LC specimen iscompression illustrated in High speedAimages were captured tests to identify the anisotropic behavior of FGs. representative setfrom of images an LCand specimen is illustrated in Figure 10. The localAdensity increased the topcorresponding to the bottom.toAxial lateral strain maps were Figure 10. The local density increased from the top to the bottom. Axial and lateral strain maps were obtained using the digital image correlation (DIC) technique. As shown, the collapse of cells and obtained using the digital image correlation technique. As shown, collapse of Afterwards, cells and localized deformation bands was observed at the(DIC) top side of the specimen (seethe Figure 10b2). deformation bands was spread observed at the top to side the specimen (seedensity. Figure It 10b2). thelocalized deformation band progressively downstream theofregion with higher can be Afterwards, the deformation band progressively spread downstream to the region with higher concluded that a failure pattern of LC specimen under low-velocity impact was also characterized by can be concluded a failurewhen pattern LC specimen low-velocity impact was also thedensity. gradualIt collapse of cells. that However, theofspecimen wasunder compressed to some extent, a new characterized by the gradual collapse of cells. However, when the specimen was compressed to some deformation band formed before the front end of the crushed zone (see Figure 10a4). This should a new deformation band formed before the front end of the crushed zone (see Figure 10a4). be extent, attributed to the fact that cells in the crushed zone may not be fully compressed during the front This should be attributed to the fact that cells in the crushed zone may not be fully compressed during end moving forward. Cells in this zone were partially deformed, obtaining s comparable loading the front end moving forward. Cells in this zone were partially deformed, obtaining s comparable capacity with uncrushed ones in the downstream. Therefore, the weakest part in the current deformed loading capacity with uncrushed ones in the downstream. Therefore, the weakest part in the current specimen may be involved in the deformation at the region outside of the crushed zone. deformed specimen may be involved in the deformation at the region outside of the crushed zone.

(a) Typical deformation behavior (b–c) strain fields LCspecimen specimenunder underdrop-weight drop-weight tests. FigureFigure 10. (a)10. Typical deformation behavior andand (b–c) strain fields ofof LC tests.

For TC specimens, multiple deformation bands randomly arose in the whole region of the specimen after the initial collapse stage (see Figure 11). Just like UFs, the weakest cells randomly were distributed into the specimen. When the specimen was compressed to the failure strain, the collapse of these cells first occurred, bringing adjacent cells into deformation and then randomly forming

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For TC specimens, multiple deformation bands randomly arose in the whole region of the specimen after the initial collapse stage (see Figure 11). Just like UFs, the weakest cells randomly were distributed into the specimen. When the specimen was compressed to the failure strain, the collapse of these cells first occurred, bringing adjacent cells into deformation and then randomly forming multiple localized regions (see Figure 11b2). Materials 2018, 11, x FOR PEER REVIEW 10 of 14

Figure 11. (a) Typical deformation behavior and (b–c) strain fields of TC specimen under Figure 11. (a) Typical deformation behavior and (b–c) strain fields of TC specimen under drop-weight drop-weight tests. tests.

4.3. Lateral Deformation Under Drop-Weight Impact 4.3. Lateral Deformation Under Drop-Weight Impact For all LC and TC specimens, intense lateral strain simultaneously arose in the fields containing For all LCas and TC specimens, lateral strain simultaneously arose in the fields containing crushed cells, shown in Figuresintense 10c1 –c4 and 11c1–c3. Moreover, at the same compression extent, crushed cells, as shown in Figures 10c1–c4 and 11c1–c3. Moreover, at the same compression extent, the specimen under TC exhibited higher lateral strain than the LC specimen. As a result, the TC the specimen TC exhibited higher lateral strainfailure than the LC specimen. result, In the TC specimen was under more likely to produce lateral stretching on both macro andAs cella scales. order specimen was more likelydeformation to produce lateral stretching failure on both macro andfive cellsubsections scales. In order to investigate the lateral of FGs, the strain map was divided into (see to investigate the lateral deformation of FGs, the strain map was divided into five subsections (see Figure 12a). Five simulated extensometers were created at the mid-position of each subsection. After Figure 12a). Five deformation simulated extensometers were created at the mid-position each subsection. After that, the lateral of each subsection was characterized by theofhorizontal strain of the that, the lateral deformation of each subsection was characterized by the horizontal strain of the corresponding simulated gauge. The variation trend of lateral strain with the global compression corresponding simulated gauge.are The variation trend12b. of lateral strainmentioning with the global compression strain of LC and TC specimens shown in Figure It is worth that the simulated strain of LC and TC specimens are shown in Figure 12b. It is worth mentioning that the simulated gauge failed once aluminum foam cells covered by the grids were severely crushed. Additionally, gauge failed once aluminum foam cells covered bysubsection, the grids were severely crushed. Additionally, when the localized deformation band spread to the the lateral strain curve would rapidly when the localized deformation band spread to the subsection, the lateral strain curve would rapidly rise up to some extent and then break off. rise up some in extent and then off. Astoshown Figure 12c, forbreak the LC specimen, lateral strain at different positions of the specimen As shown in Figure 12c, for the LC specimen, strainshow at different positions of the specimen exhibited regular distribution and variation trend.lateral All curves a plateau-like deformation stage, exhibited regular distribution and variation trend. All curves show a plateau-like deformation stage, which corresponds to the strain state before the deformation band arrives. The red arrows in Figure 12c which corresponds to the strain state before the deformation band arrives. The red arrows in Figure indicate the arrival time of deformation band. Clearly, the deformation band gradually spread from 12c arrivalwhich time is of in deformation Clearly, the deformation band 10. gradually spread the indicate top to thethe bottom, accordance band. with the sequential images in Figure from By thecontrast, top to thethe bottom, which is in accordance with the sequential images in Figure 10. We can distribution of lateral deformation in the TC specimen was irregular. By contrast, distribution of lateral in the TC specimen was irregular. Wematerial can see see that strain ofthe TSG1 maintained a verydeformation low level (~0.4%) during the compression. The that strain of TSG1 maintained a very low level (~0.4%) during the compression. The material in the in the top subsection retained intact cell morphology quite well, indicating that cells in this region top subsection retained intact cell morphology quiteinwell, indicating thatfailure cells inpattern this region mostly mostly produced axial compression, as illustrated Figure 11a3. The of these cell produced axial compression, as illustrated in Figure 11a3. The failure pattern of these cell membranes membranes was dominated by Mode A and B. Conversely, TSG3~TSG5 passed through the onset region was dominated by Modeband, A and B. Conversely, TSG3~TSG5 passed through the gauges. onset region of of localized deformation demonstrating higher lateral strain than the other two Crushed localized deformation higher in lateral than the other two gauges. Crushed cells concentrated intoband, these demonstrating subsections, resulting morestrain failure patterns of cell membranes. cells concentrated into these subsections, resulting in more failure patterns of cell membranes. Moreover, TSG obviously demonstrated higher lateral strain than LSG at the same relative position Moreover, obviously lateraltransverse strain than LSG at theproduced same relative of the specimenTSG (see Figure 12). demonstrated It revealed thathigher FGs under compression more position of the specimen (see Figure 12). It revealed that FGs under transverse compression produced lateral stretching deformation on cell/membrane scales. more lateral stretching deformation on cell/membrane scales.

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Figure 12.Schematic (a,b) Schematic diagram simulated extensometers extensometers and (c) (c) lateral strainstrain curvescurves of LC and Figure 12. (a,b) diagram of of simulated and lateral of LC and TC specimens. TC specimens.

4.4. Anisotropic Compression Behavior Numerical Simulation Simulation 4.4. Anisotropic Compression Behavior in in Numerical Figure 13 shows deformation images of FGs under longitudinal and transverse compression

Figure 13 shows deformation images of FGs under longitudinal and transverse compression from from the numerical simulation. As we can see, this compression behavior agrees well with the the numerical simulation. As we can see,gradually this compression agrees well the experiments; experiments; the deformation band extended tobehavior the downstream in LCwith specimen and the deformation gradually extended to the downstream in band LC specimen and randomly randomly band occured in TC specimen. Strikingly, the deformation more likely arose from theoccured corner because of the stress state band in the rectangular specimen, as indicated in Figure 13b2. of the in TC specimen. Strikingly, thedistribution deformation more likely arose from the corner because However, when the LC specimen was compressed by 28%, the other localized deformation band stress distribution state in the rectangular specimen, as indicated in Figure 13b2. However, when the formed in a position far away from the front end of the crushed zone (see Figure 13a3). It revealed LC specimen was compressed by 28%, the other localized deformation band formed in a position far that localized defects and mechanical inhomogeneity of cells in the LC specimen was still the primary away from the front end of the crushed zone (see Figure 13a3). It revealed that localized defects and factor in determining the formation and evolution pattern of the deformation band. The onset of cell mechanical inhomogeneity of cells in the LC specimen was strength still the of primary factorIninthe determining collapse at the initial failure stage dominated the nominal the material. LC the formation and pattern the all deformation band. The onset of cell collapse the initial specimen, theevolution initial collapse cellsof were localized in the low-density region, leading to a at weak resistance to failurethe of the material (see Figure 13a1). Conversely, in LC the specimen, TC specimen, initialcollapse failure stage dominated nominal strength of the material. In the thethe initial collapse cells wereinwidely distributed inregion, the specimen, therefore exhibiting a higher thematerial cells were all localized the low-density leading to a weak resistance tostrength failure than of the larger-sized cells in the LC specimen (see Figure 13b1). (see Figure 13a1). Conversely, in the TC specimen, the initial collapse cells were widely distributed in In addition, when the TC specimen was compressed by 55%, materials in the high-density zone the specimen, therefore exhibitingwhile a higher strength the larger-sized cells in the LCporosity specimen (see have tended to densification, materials in thethan low-density zone still maintained high Figure 13b1). (see Figure 13b6). The compacted zone, marked by the black circle, provided a quickly increased carrying capacity lead to a densification behavior by on stress-strain curve.inAs a consequence, In addition, whenand the thus TC specimen was compressed 55%, materials the high-density zone the densification strain of the TC specimens was distinctly decreased. In other words, materials underporosity have tended to densification, while materials in the low-density zone still maintained high transverse compression were not adequately used to absorb enough energy until the densification (see Figure 13b6). The compacted zone, marked by the black circle, provided a quickly increased occurred. In summary, a lower utilization of cells and plateau stress in FG specimens under carryingtransverse capacitycompression and thus lead to a densification behavior on stress-strain curve. As a consequence, lead to poorer energy absorption, making it more efficient than LC specimen. the densification strain of the TC specimens was distinctly decreased. In other words, materials under transverse compression were not adequately used to absorb enough energy until the densification occurred. In summary, a lower utilization of cells and plateau stress in FG specimens under transverse compression lead11,tox FOR poorer Materials 2018, PEERenergy REVIEWabsorption, making it more efficient than LC specimen.12 of 14

Figure 13. Numerical deformation under(a) (a)LC LCand and Figure 13. Numerical deformationbehavior behavior of of FGs FGs under (b)(b) TC.TC. 5. Conclusions Functionally density graded aluminum foam (FG) was prepared through a controlled foaming process by dispersing different content of foaming agent at different depths. An anisotropic mechanical behavior was identified under both longitudinal and transverse compression. The

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5. Conclusions Functionally density graded aluminum foam (FG) was prepared through a controlled foaming process by dispersing different content of foaming agent at different depths. An anisotropic mechanical behavior was identified under both longitudinal and transverse compression. The conclusions are summarized as follows: 1. 2. 3. 4. 5.

The transverse compression of FGs lead to higher collapse strength but significantly reduced energy absorption, which was attributed to the decrease in plateau stress and densification strain. The deformation behavior of FGs under longitudinal and transverse compression was respectively dominated by the progressively extended and randomly distributed deformation bands. The high strength of transverse compressed specimen was primarily due to the density anisotropy and transition in deformation mechanisms at both macro and cell levels. The decrease in densification strain of FGs under transverse compression was caused by lower utilization of cells in the high porosity zone. Transverse compression caused more tearing and lateral stretching deformation on cells because of the high lateral strain level in the specimens.

Author Contributions: Conceptualization, S.Q.H. and Z.Q.F.; methodology, B.B.Z.; validation, B.B.Z. investigation, B.B.Z. and Z.Q.F.; writing—original draft preparation, B.B.Z.; writing—review and editing, S.Q.H.; project administration, Z.Q.F.; funding acquisition, Z.Q.F. Funding: This research was funded by the National Natural Science Foundation of China (No. 11602233), the Science Foundation for Young Scholars of Shanxi Province (No. 201701D221018), and the Science Foundation of National Defense Key Discipline Laboratory for Target Damage Technology (No. DXMBJJ2017-01) Conflicts of Interest: The authors declare no conflict of interest.

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