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Metallic tube-reinforced aluminum honeycombs: Compressive and bending performances
Composites Part B 171 (2019) 192–203
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Metallic tube-reinforced aluminum honeycombs: Compressive and bending performances Yunwei Zhang a, d, 1, Leilei Yan b, c, *, 1, Wanbo Zhang d, Pengbo Su c, e, Bin Han f, Shuxiang Guo a, d a
Aeronautics Engineering College, Air Force Engineering University, Xi’an, 710051, China School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China c State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, China d Department of Basic Sciences, Air Force Engineering University, Xi’an, 710051, China e State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China f School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Honeycomb Hybrid Mechanical properties Finite element analysis (FEA) Buckling Energy absorption
Aluminum honeycombs are widely applied in weight sensitive applications, increasing their specific strength and energy absorption capacity are rather important. Thin-walled metallic tube was used to enhance the mechanical properties of aluminum honeycomb and formed a novel tube-reinforced honeycomb structure. Its compressive and three-point bending performances were studied experimentally and numerically. Due to tube filling, the specific compressive strength, elastic modulus and energy absorption have been increased by 16%, 26% and 73%, and the specific bending load and stiffness increased by 42% and 62% respectively. The strengthen mechanism study indicated that the sum of tube and honeycomb caused the increase of compressive properties, and aluminum tube filling changed the stress distribution and expanded the stress concentration region which led to a transformation of bending failure mode. The present reinforcement method will make honeycomb more competitive in light-weight structure applications.
1. Introduction Honeycomb and its sandwich structures have been widely used in weight sensitive applications, such as aircraft, high-speed trains and other light-weight vehicles [1–4]. The main advantages of such light-weight structures were high specific strength and high specific energy absorption (SEA) for honeycombs [5,6], and high flexural ri gidity and bending strength [7–11] for honeycomb core sandwich structures. Therefore, the mechanical properties of honeycomb-based light-weight structures have been widely designed and studied [12–15]. Kee et al. [5] experimentally studied the mechanical properties of honeycomb core sandwich structure in three-point bending, axial compression and lateral crushing loading conditions. Petras et al. [7] constructed a failure mode map for sandwich beam with GFRP laminate skins and Nomex honeycomb core under three-point bending, and the results showing that the failure mode was dependent on the ratio of skin thickness to span length and relative density of honeycomb. The effects of parameters on the mechanical properties of honeycomb were also
investigated by Sun et al. [8], such as the thickness of skins/face-sheets, hexagonal cell size, foil thickness and height of honeycomb core. Sun et al. [16] experimentally and numerically studied the dynamic response and failure mechanisms of honeycomb sandwich panels subjected to high-velocity impact. The discrete optimization method was used to generate an optimal design of a sandwich structure for achieving the highest specific energy absorption without perforation under certain impact energy. The discrete optimization method could be also used to optimize other practical engineering problems to find the optimal structure for a specific purpose [17–19]. For sandwich structure, when the weight of honeycomb core accounts for 50%–66.7%, it has been suggested have optimum mechanical properties [9]. Such studies showing that honeycombs have significant advantages in load carrying and energy absorption applications. Therefore, the rapid development of industrial technology, especially aerospace requires light-weight mate rials and structures (such as honeycomb) have much lower density, higher strength and energy absorption efficiency. For this purpose, several novel methods and structures were used to form composite
* Corresponding author. School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China. E-mail address: [email protected] (L. Yan). 1 These authors contributed equally to this work and should be considered co-first authors. https://doi.org/10.1016/j.compositesb.2019.04.044 Received 1 December 2018; Received in revised form 1 April 2019; Accepted 29 April 2019 Available online 1 May 2019 1359-8368/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic and parameter of empty and tube-reinforced honeycomb design.
plastic tubes into the aluminum honeycomb holes to increase the SEA capacity for compression tests. Such polypropylene foam could increase the mechanical behaviors of honeycombs dramatically, but also increase its density significantly [29]. Besides polypropylene foams, fiber rein forced honeycombs were also effective in impact resistance [31,32]. Tube structures have outstanding advantages in axial load carrying applications and are also used as a reinforced structure. Zhang et al. [33] investigated the square aluminum tube reinforced thin-walled beams under quasi-static and dynamic bending tests. The tube fillers consid erably improving the performance of thin-walled beams and outperform the aluminum foam filler. Wang et al. [34] experimentally studied the mechanical performances of energy absorption and deformation mode of honeycomb cells filled with circular tubes (HFCT) under axial loading, and showing evident promotion in energy absorption. Honey combs also have advantages in blast resistance [35,36]. Liu [36] investigated the blast resistance performances of the sandwich plate filled with HFCT core numerically. The results showing tube filling have advantages for honeycombs in energy absorption and blast resistance. Besides honeycomb, tube structures also used to reinforce foam struc tures. The energy-absorbing characteristics of polymer foams reinforced with small carbon fiber reinforced epoxy tubes were experimentally studied [37,38]. Yan et al. [39] recently reported a metallic tube enhanced aluminum foam, showing that metallic tube filling can significantly increase the compressive strength and energy absorption of aluminum foam. Further more, the aluminum tube and the carbon fiber reinforced plastic (CFRP) tube were used to reinforce each other under quasi-static axial compression [17] and three-point bending test [18]. To increase the mechanical properties of aluminum honeycomb and its sandwich structures, metallic tubes were used to form tubereinforced honeycomb in the present study. Compressive and three-
structures and anticipated to have higher specific strength and energy absorption (SEA) [20–28]. Methods were developed to form novel honeycomb structures to increase the mechanical performances of honeycomb, such as zero Poisson’s ratio [20], re-entrant anti-trichiral [21], double-V [22]and hierarchical [23–25] honeycombs. Especially for the hierarchical hon eycomb, compared with the regular one, the first- and second-order hierarchical honeycombs improved the SEA by 81.3% and 185.7%, respectively [25]. Besides these designs, Sun et al. [26] used periodical grids to reinforce soft honeycomb core of sandwich structures. The hybrid core sandwich specimens provided increased stiffness, specific stiffness, energy absorption and critical load, which were higher than the sum of honeycomb core sandwich specimens and grid core sandwich specimens. Du et al. [27] used paper-reinforced polymer (PRP) com posites as skin materials and resin-impregnated aramid paper as hon eycomb core to fabricate light-weight sandwich panel constructions. Such sandwich structure had comparable bending rigidity and flexural load bearing capability but lower areal weights when compared with some commercial products for automotive interior applications. Tao et al. [28] proposed a novel in-plane graded honeycomb and its dynamic behavior under out-of-plane compression was investigated using nu merical simulation and theoretical analysis. The crushing strength and energy absorption capacity were enhanced by positive gradient struc ture design. Foams and fibers were also used to reinforce honeycombs to increase its strength and energy absorption performances. Liu et al. [6,29] intensified the aluminum honeycomb by filling with expanded poly propylene foam. The peak strength, mean crushing strength and total energy absorption under the axial compression and the SEA under lateral crushing were increased. Antali et al. [30] embedded carbon fiber 193
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Fig. 2. Images of specimens for compression tests.
Fig. 3. Images of sandwich beam for three-point bending test. Careful treatments of specimens during fabrication can be seen on the left.
point bending loads were carried experimentally and numerically on tube-reinforced honeycomb, as well as empty honeycomb and aluminum tubes for comparison. The enhancement on specific compressive strength, elastic modulus and energy absorption under compressive load, and three-point bending load and stiffness were investigated. The failure mode and enhancement mechanisms were also studied. In addition, the specific strength and energy absorption per unit mass of the present tube-reinforced honeycomb were also compared with the competitive core designs.
Table 1 Parameters of the specimens for compression tests, where length (Lc), width (Wc), height (Hc) and density (ρc) of specimens are showing.
2. Experimental measurement
Specimens
Type
ρc (Kg/m3)
Lc (mm)
Wc (mm)
Hc (mm)
CE-1 CE-2 CT-1 CT-2
Empty Empty Tube-reinforced Tube-reinforced
70.63 71.03 99.38 98.75
40 40 40 40
40 40 40 40
20 20 20 20
surface cleaning was applied to aluminum honeycombs, tubes and facesheets. The prepared specimens for compressive test and three-point bending test were shown in Fig. 2 and Fig. 3 respectively.
2.1. Materials and fabrication Fig. 1 illustrated the geometry parameters of specimens for compressive and three-point bending test. Honeycomb (Fig. 1 (a)) and tube-reinforced honeycomb (Fig. 1 (b)) were prepared for compression tests, and which were also acted as the core of sandwich structure for three-point bending tests Fig. 1 (c) and Fig. 1 (d). The dimensions of hexagon side length (Lh ¼ 3 mm) and the wall thickness (Th ¼ 0.05 mm) of honeycomb; the outside diameter (Φt ¼ 10 mm), wall thickness (Tt ¼ 0.5 mm), height (Ht ¼ 20 mm) of metallic tubes and the thickness (Tf ¼ 1 mm) of face-sheets for sandwich beams were all fixed. The honeycomb and face-sheets were made of aluminum alloy 3003, and the tubes were made of aluminum alloy 6061. Specimens were cut from commercial honeycomb sheet by Electrical Discharge Machining (EDM) as well as aluminum tubes and face-sheets. For tube-reinforced honeycombs, through holes were perforated in the middle of honeycomb for tube filling firstly. And then it was fixed with aluminum tubes and face-sheets by epoxy glue. Before assembling,
2.2. Compressive test The detailed parameters and images of specimens for compression tests were shown in Table 1 and Fig. 2. Out-of-plane quasi-static compression tests were carried out by the electronic universal testing machine (INSTRON-3382) at ambient temperature as shown in Fig. 4, with a fixed loading rate of 1 mm/min. At least 80% compressive strain was achieved or each specimen to ensure complete deformation and energy absorption. Digital images of each sample were acquired by a video camera to study deformation modes and failure mechanisms (as well as three-point bending test). 2.3. Three-point bending test Specimens for three-point bending test consist of five unit-cells compared to compression test specimens (both empty and tube194
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Fig. 4. Experimental set-up for compression and three-point bending tests (Instron 3382). Table 2 Parameters of sandwich structures for three-point bending tests, where length (Ltb), width (Wtb), height (Htb) and average density (ρtb) of both empty (TB) and tube-reinforced (TB-T) sandwich beams are showing respectively. With fixed face-sheets thickness (Tf ¼ 1 mm). Specimens
Type
ρtb (Kg/
Ltb (mm)
Wtb (mm)
Htb (mm)
TB-1 TB-2 TB-T-1
Empty Empty Tubereinforced Tubereinforced
355 364 414
220 220 220
40 40 40
22 22 22
414
220
40
22
TB-T-2
m3)
reinforced sandwich structures). The detailed parameters and images of specimens for three-point bending test were summarized in Table 2 and Fig. 3. The three-point bending tests were also carried out by the electronic universal testing machine (model INSTRON-3382) with a fixed loading rate of 1 mm/min at ambient temperature, as illustrated in Fig. 4. The span length was set to be 160 mm. And the diameters of support and loading bars were 10 mm, according to ASTM: C393 standard [40].
Fig. 6. Nominal stress versus strain curves of empty honeycomb (CE-1), tubereinforced honeycomb (CT-1) and aluminum tube under uniaxial compression.
alloy 6061 with the density (ρAl 6061 ¼2700 kg/m3), Young’s modulus (EAl 6061 ¼69 GPa) and yield strength (σ Al 6061 ¼227.5 MPa) were used for the tubes.
3. Numerical investigation 3.1. Materials properties
3.2. Finite element model
The quasi-static compressive and three-point bending tests were numerically simulated by ABAQUS/Explicit, using same geometrical parameters with the experimental specimens. The density (ρAl 3003 ¼2730 kg/m3), Young’s modulus (EAl 3003 ¼69 GPa) and yield strength (σ Al 3003 ¼185 MPa) of aluminum alloy 3003 were used for facesheets and honeycomb in the finite element analysis. The aluminum
The finite element (FE) model for compression tests was shown in Fig. 5 (a), the honeycomb was compressed between two rigid plates. The bottom plate was fixed, and the top plate could only move for z-direc tion. And the FE model for three-point bending tests was shown in Fig. 5 (b), the sandwich structure was supported by two fixed rigid bars, and
Fig. 5. FE models for compression and three-point bending tests. 195
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Fig. 7. Experimental and simulated images illustrating the deformation history at the selected points marked in Fig. 6.
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Table 3 Summary of the experimental and numerical compressive strengthσ cpeak , elastic modulus E, energy absorption per unit volume Wv and per unit mass Wm of the specimens. The experimental results are the averaged measurements of specimens in Table 1. Compressive CE CE-FE CT CT-FE
ρc
σcpeak
ðKg=m3 Þ
ðMPaÞ
70.82 70.94 99.06 93.39
3.38 3.63 5.47 5.18
σcpeak ðσAl3003 ρc =ρAl 3003 Þ 0.70 0.76 0.81 0.82
E (MPa)
Wv (KJ/m3)
Wm (KJ/Kg)
509 1384 640 2196
618.29 751.74 1481.10 1534.93
8.66 10.60 14.95 16.44
4. Results and discussion 4.1. Compressive response 4.1.1. Experiment Under uniaxial compression tests, typical nominal stress versus strain curves of empty honeycomb (CE-1) and tube-reinforced honeycomb (CT-1) were shown in Fig. 6. For reference, the stress-strain curve of tube which used to reinforce the honeycomb under uniaxial compression tests was also included. Details of stress-strain curves as Fig. 6 shown can be seen as follows: ⅰ) For empty honeycomb (curve, CE-1), after a linear and nonlinear in crease the compressive stress reached its peak (3.38 MPa) and declined subsequently, and then present plateau region like foam structures (1.3 MPa) [42]. When the compress strain undergoes till 0.8, the densification occurred and caused a dramatic increase of compressive stress. ⅱ) For empty aluminum tube (curve, Tube), differs to aluminum honeycomb, its stress-strain curve showing multiple peaks and valleys before densification occurred due to layer by layer buckling of the empty tube (Fig. 7 (c)). ⅲ) The curve shape of tube-reinforced honeycomb (curve, CT-1) is similar to that of empty aluminum tube. For contrast, the sum of empty honeycomb (curve, CE-1) and empty aluminum tube (curve, Tube) which were tested separately also showing in Fig. 6 (curve, CE-1þTube), and agreed well with tube-reinforced honeycomb. In other words, the strength of novel designed tube-reinforced honey comb was just the sum of aluminum honeycomb and tube. Images in Fig. 7 showing the deformation history of empty honey comb, tube-reinforced honeycomb and empty tube at selected points ~ E in Fig. 6. When the first peak occurred, the compressive marked in A strain of tube-reinforced honeycomb increases from 0.008 to 0.032 compared to empty honeycomb, whereas, its densification strain declined from 0.809 to 0.704 which is similar to aluminum tube (0.709). The specimens all collapsed from one side layer by layer which causes the fluctuation of stress-strain curves, and each formation of folding for aluminum tube and tube-reinforced honeycomb related to one stress peak and valley marked in Fig. 6. The images after compression (Fig. 7, Final) indicated that the honeycomb and aluminum tube almost have no effect on each other. As summarized in Table 3, for tube-reinforced honeycomb (CT), the peak stress (σ cpeak ) increased from 3.38 MPa to 5.47 MPa, and elastic
Fig. 8. Energy absorption per unit volume (Wv) and per unit mass (Wm) of CE and CT specimens.
Fig. 9. Stress versus strain curves comparing with the experiment results under compression tests.
modulus E increased from 509 MPa to 640 MPa compared to empty honeycomb (CE), respectively. With consideration of weight alternation,
the top rigid bar compressed the structure from z-direction. Due to the thin thickness of the honeycomb, shell parts (S4R) were used for aluminum honeycomb. Solid element (C3D8R) was employed for aluminum tubes, and rigid element (R3D4) was used for the rigid part. Tie constraint was used to simulate the honeycomb adhesive connection between honeycomb and face-sheets as well as honeycomb and tubes. The friction coefficient was set to be 0.2 as the general contact between other surface pairs, and the quasi-static loading speed of simulation was set to 1 m/s. To verify the quasi-static progress, two principles need to be observed. Firstly, the total kinetic energy has to be very small compared to the total internal energy. Secondly, the crushing force-displacement response must be independent from the applied ve locity [5,41]. Mesh size sensitivity studies were also carried for all FE models.
σc
the normalized peak stress ðσAl 3003 ρpeak =ρ c
Al 3003 Þ
was also increased from 0.7 to
0.81, where ρAl 3003 ¼ 2730 kg/m3, σ Al 3003 ¼ 185 MPa was the density and yield stress of aluminum alloy 3003 respectively, and the average density ρc of specimens for compression tests was shown in Table 3. The energy absorption capacity was represented by energy absorp tion of per unit volume (Wv), which could be obtained through the integration of the stress-strain curves: Z ε Wv ¼ σ dε (1) 0
where the strain of specimens ε ¼ 0.5 was adopted here. In addition, the mass was an important factor for weight sensitive 197
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Fig. 10. Simulated images of specimens at cross section under compression at selected points (specific strain).
Fig. 11. FE simulated stress-strain curves with different tube thickness under compression tests.
Fig. 12. Load-displacement bending load.
application. Therefore, the specific energy absorption (SEA) was another important parameter, which could be defined as [42]:
4.1.2. FE analysis The FE analysis was used to study the strengthen mechanisms of tube-reinforced honeycombs. As shown in Fig. 9, the numerical simu lated stress-strain curves of empty (CE-FE) and tube-reinforced (CT-FE) honeycombs agree well with the experimental ones. In addition, the simulated deformation modes also matching the experimental ones well as showing in Fig. 7. As shown in Table 3, the simulated strength and energy absorption of both empty (CE-FE) and tube-reinforced (CT-FE) honeycombs are reasonable and fit well with the experimental ones. Note that for elastic modulus E, the numerical results were larger than the experimental ones. The inconsistency of E was suggested to be as follows: the compressive punch was treated as an ideal rigid plate in FE analysis,
Wm ¼
Wv
ρc
(2)
where theρc was the average density of the specimens. The energy absorption per unit volume (Wv) and per unit mass (Wm) of specimens were also summarized in Table 3. The results indicated that due to aluminum tube filling, the tube-reinforced honeycomb (CT) have a significant increase of Wv and Wm by 140% and 73% respectively. The benefits of metallic tube filling on energy absorption of aluminum honeycomb were shown obviously in Fig. 8.
198
curves
of
specimens
under
three-point
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Fig. 13. Photographs illustrating the deformation history at selected points marked in Fig. 12.
199
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however, in the experimental tests, the machine itself and punches all had its own rigidness which was neglected in FE analysis. Nevertheless, the experimental and numerical results are all indicated that the tubereinforced honeycombs have dramatically increased compressive strength, elastic modulus E, energy absorption (both Wv and Wm) compared to empty honeycombs. To better understanding the strengthen mechanism, the simulated section images of empty and tube-reinforced honeycombs were shown in Fig. 10. The deformation mode of tube-reinforced honeycomb (Fig. 10 (b)) have no distinct difference compared with empty honeycomb (Fig. 10 (a)), that means the deformation of aluminum tube and hon eycomb deforms individually. In other words, the present designed aluminum tube and honeycomb have no effect on each other. However, the aluminum foam-filled corrugated sandwich panel [42,43] and aluminum foam-filled tube [44,45] all showing a significant coupling effect. Therefore, the further study of tube-reinforced honeycombs by strength matching of tube and honeycomb may also have a coupling effect which may cause the strength and energy absorption further increased.
Fig. 14. Comparison of FE simulated load-displacement curves with experi ment results of specimens under three-point bending load.
4.1.3. Structure optimization Due to limitations of experimental conditions, only the honeycomb reinforced with the tube (Tt ¼ 0.5 mm) was experimentally studied. The compressive performance of the tube-reinforced honeycomb with different tube wall thickness (Tt ¼ 0.5 mm, 0.3 mm, and 0.1 mm) was studied by FE analysis. As shown in Fig. 11, the stress-strain curves of the tube-reinforced honeycomb (CT-FE) with different tube wall thickness have almost coincided with the curves (CE-FE þ Tube-FE) which were the sum of the empty honeycomb (CE-FE) and the corresponding tube (Tube), respectively. With the tube (Tt ¼ 0.5 mm, 0.3 mm, and 0.1 mm) filling, the Wm of the tube-reinforced honeycombs were increased by 57%, 24% and 15% respectively compared with the empty one. It indicated that the tube-reinforced honeycomb with thicker tube wall thickness had higher SEA.
collapse of the tube-reinforced sandwich beam was much more difficult to occur, which caused the increase of the peak bending load. The debonding of epoxy glue between its bottom face-sheet and honeycomb core led to the bending load decrease dramatically, and which was the dominant failure mode, as shown in Fig. 13 (b). Different to the empty one, the local failure of honeycomb in the tube-reinforced sandwich beam was transverse cracking instead of compression, and the reason was caused by the enhancement of compressive strength due to tube filling discussed before. The measured peak loading force (Fpeak) and its normalized form Fpeak ðρtb =ρAl 3003 Þ
of both empty (TB) and tube-reinforced sandwich beam (TB-T)
were summarized in Table 4. ρtb was the average density of the speci mens for three-point bending tests. The results showing that due to metallic tube reinforcement, the Fpeak of aluminum honeycomb sand wich beam increased by 64% compared with empty one. With consid
4.2. Bending response
eration of density increment, the normalized form
4.2.1. Experiment The load-displacement responses of both empty (TB-1 and TB-2) and tube-reinforced sandwich beam (TB-T-1 and TB-T-2) under three-point bending tests were compared in Fig. 12. And images of specimens under selected bending displacement δ marked in load-displacement curves (Fig. 12) were shown in Fig. 13. As shown in Fig. 12, for the empty sandwich beam, after a linear and nonlinear increase, the bending load decreased and then undergoes a plateau region. However, for the tube-reinforced sandwich beam, the bending load declined dramatically after its peak arrived, and the sus tained load is lower than that of the empty one. As the collapse history shown in Fig. 13 (a), for the empty sandwich beam, the top face-sheet deforms elastically and honeycomb collapses locally (below loading bar) which causes the decrease of bending load after its peak (point A). With the three-point bending progress, the local collapse of honeycomb continues and the plastic yielding of top face-sheet appears (point B and C). As the final image shown, no debonding occurred during the whole bending process, and local collapse and yielding of top face-sheet was the main deformation mode. For contrast, due to tube filling, the local
Fpeak ðρtb =ρAl 3003 Þ
still has a
significant increment (42%). What’s more, besides bending load resis tance, its bending stiffness (defined as the slope of the elastic region) also have a dramatical increase of 62%.
4.2.2. FE analysis To better understanding the bending behavior and enhancement mechanisms, FE simulation was carried. As shown in Fig. 14, the simulated load-displacement curve (TB-FE) of the honeycomb sandwich structure had a good agreement with the experimental measurement result (TB-1). But for the tube-reinforced beam, the simulated loaddisplacement curves (TB-T-FE) only had a good agreement with the experimental curve (TB-T-1) before the peak load point. After the peak load point, the FE result (TB-T-FE) was much larger than the experi mental result (TB-T-1). This is due to the debonding occurred at this stage between the honeycomb core and the below face-sheet. Compared Fig. 13 (b) with Fig. 15 (b), the debonding occurred can be obviously observed in the experiment specimen, while an ideal bonding surface was considered in the present FE model. For empty sandwich beam, the
Table 4 Summary of the experimental and numerical results of three-point bending. The experimental results are the averaged measurements of specimens in Table 2. The stiffness indicates the slope of load-displacement curve at elastic stage. Three-point bending TB (experimental) TB-FE (numerical) TB-T (experimental) TB-T-FE (numerical)
ρtb
ðKg=m3 Þ 360 311 414 329
Fpeak ðρtb =ρAl 3003 Þ
Fpeak (N) 1399 1471 2290 2437
10609 12903 15101 20221
200
δpeak (mm)
Stiffness (KN/mm)
0.90 0.88 0.99 1.08
2.03 3.56 3.28 3.61
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Fig. 15. Simulated cross section images of specimens during three-point bending process under different bending displacement.
dropped slowly with the ‘tie’ constraint. In addition, the simulated bending stiffness was larger than experimental ones, the cause of the inconsistency was similar to the compressive result discussed before. Fig. 15 showing the cross-section images of specimens during the three-point bending process with tubes in sandwich beam visible, and the distribution of Mises stress S can be seen clearly. For empty sandwich beam, the Mises stress S concentrated on top loading bar with a small region, and such stress concentration causing local collapse occurred (as Fig. 13 (a) shown). By contrast, the region of stress concentration was expanded for the tube-reinforced sandwich beam which led to a more complicated failure mode, along with transverse cracking. 4.2.3. Structure optimization As shown in Fig. 16, the tube-reinforced sandwich beam with different tube wall thickness (Tt ¼ 0.5 mm, 0.3 mm, and 0.1 mm) were also studied numerically. The load-displacement curve (TB-T-FE0.1 mm) almost coincided with the curve of the empty honeycomb sandwich beam (TB-FE). The loading of TB-T-FE-0.3 mm was higher than TB-FE but lower than TB-T-FE-0.5 mm. As discussed before, for the TB-T-FE-0.5 mm, the debonding occurred between the honeycomb and the below face-sheet in the experiment. This issue may be solved by using the thinner tubes, but loading will be lower corresponding.
Fig. 16. FE simulated load-displacement curves with different tube thickness under three-point bending load.
Mises stress S concentrated on top loading bar with a small region (as Fig. 15 (a) shown). For contrast, the region of stress concentration was expanded for the tube-reinforced sandwich beam (as Fig. 15 (b) shown). With the region of stress concentration expanded, the stress between the core and the below face-sheet increased rapidly, which lead to the debonding between the core and the below face-sheet. The loaddisplacement curve of TB-T-1 (in Fig. 14) dropped rapidly after the debonding occurrence at the peak load point, but the curve of TB-T-FE
4.3. Comparison with competitive core designs The uniaxial compressive strength (σcpeak ) and energy absorption
capacities per unit mass (Wm) of both empty and tube-reinforced hon eycombs were compared with several competitive core designs [43]. As shown in Fig. 17, the present newly developed tube-reinforced
Fig. 17. Compressive strength and energy absorption comparison of present honeycomb and tube-reinforced honeycomb with other competitive core designs [43]. 201
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honeycomb was competitive compared with empty honeycomb, espe cially energy absorption. Compared with other competitive cores, such as pyramidal which have been demonstrated have advantages in load carrying applications [46,47], the present result is more advantageous. With future geometric optimization design, the present tube-reinforced honeycomb structure is suggested to be more competitive.
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Theoretical, numerical and experimental analysis of three-dimensional double-V honeycomb. Mater Des 2018; 139:380–91. [23] Du B, Chen LM, Wu WJ, Liu HC, Zhao Y, Peng SW, Guo YG, Zhou H, Chen LL, Li WG, Fang D. A novel hierarchical thermoplastic composite honeycomb cylindrical structure: fabrication and axial compressive properties. Compos Sci Technol 2018;164:136–45. [24] Chen YY, Li TT, Jia Z, Scarpa F, Yao CW, Wang LF. 3D printed hierarchical honeycombs with shape integrity under large compressive deformations. Mater Des 2018;137:226–34. [25] Sun GY, Jiang H, Fang JG, Li GY, Li Q. Crashworthiness of vertex based hierarchical honeycombs in out-of-plane impact. Mater Des 2016;110:705–19. [26] Sun Z, Shi SS, Guo X, Hu XZ, Chen HR. On compressive properties of composite sandwich structures with grid reinforced honeycomb core. Compos B Eng 2016;94: 245–52. [27] Du Y, Yan N, Kortschot MT. Light-weight honeycomb core sandwich panels containing biofiber-reinforced thermoset polymer composite skins: fabrication and evaluation. Compos B Eng 2012;43(7):2875–82. [28] Tao Y, Duan SY, Wen WB, Pei YM, Fang DN. Enhanced out-of-plane crushing strength and energy absorption of in-plane graded honeycombs. Compos B Eng 2017;118:33–40. [29] Zhang YQ, Liu Q, He ZH, Zong ZJ, Fang JG. Dynamic impact response of aluminum honeycombs filled with Expanded Polypropylene foam. Compos B Eng 2019;156: 17–27. [30] Antali AA, Umer R, Zhou J, Cantwell WJ. The energy-absorbing properties of composite tube-reinforced aluminum honeycomb. Compos Struct 2017;176:630–9. [31] Liu LQ, Feng H, Tang HQ, Guan ZW. Impact resistance of Nomex honeycomb sandwich structures with thin fibre reinforced polymer facesheets. J Sandw Struct Mater 2018;20(5):531–52. [32] Crupi V, Kara E, Epasto G, Guglielmino E, Aykul H. Theoretical and experimental analysis for the impact response of glass fibre reinforced aluminium honeycomb sandwiches. J Sandw Struct Mater 2018;20(1):42–69. [33] Zhang X, Zhang H. Static and dynamic bending collapse of thin-walled square beams with tube filler. Int J Impact Eng 2018;112:165–79. [34] Wang ZJ, Qin QH, Chen SJ, Yu XH, Li HM, Wang YJ. Compressive crushing of novel aluminum hexagonal honeycombs with perforations: experimental and numerical investigations. Int J Solids Struct 2017;126–127:187–95. [35] Imbalzano G, Linforth S, Ngo TD, Lee PVS, Tran P. Blast resistance of auxetic and honeycomb sandwich panels: comparisons and parametric designs. Compos Struct 2018;183:242–61. [36] Liu J, Wang Z, Hui D. Blast resistance and parametric study of sandwich structure consisting of honeycomb core filled with circular metallic tubes. Compos B Eng 2018;145:261–9. [37] Alia RA, et al. The energy-absorbing characteristics of composite tube-reinforced foam structures. Compos B Eng 2014;61:127–35. [38] Zhou J, Guan Z, Cantwell WJ. The energy-absorbing behaviour of composite tubereinforced foams. Compos B Eng 2018;139:227–37. [39] Yan LL, Zhao ZY, Han B, Lu TJ, Lu BH. Tube enhanced foam: a novel way for aluminum foam enhancement. Mater Lett 2018;227:70–3. [40] ASTM C393/C393M-16. Standard test method for core shear properties of sandwich constructions by beam flexure. West Conshohocken, PA: ASTM International; 2016. www.astm.org. [41] Santosa SP, Wierzbicki T, Hanssen AG, Langseth M. Experimental and numerical studies of foam-filled sections. Int J Impact Eng 2000;24(5):509–34. [42] Yan LL, Yu B, Han B, Chen CQ, Zhang QC, Lu TJ. Compressive strength and energy absorption of sandwich panels with aluminum foam-filled corrugated cores. Compos Sci Technol 2013;86:143–8.
5. Conclusions Metallic tubes were used to increase the mechanical performances of aluminum honeycombs and its sandwich structures, and formed tubereinforced honeycomb. The compressive and three-point bending re sponses of the novel tube-reinforced honeycomb was studied experi mentally and numerically. The results are as follows: ⅰ) Compared with empty honeycomb, the normalized peak stress, elastic modulus E and energy absorption per unit mass (SEA) of tube-reinforced honeycomb can be increased by 16%, 26% and 73% respectively due to aluminum tube filling. The results almost equal to the sum of aluminum honeycomb and tube which were tested separately. ⅱ) The normalized peak bending load and stiffness of the tubereinforced sandwich beam were increased by 42% and 62% respectively compared with the empty sandwich beam. The nu merical results indicated that the tube filling changed the stress distribution and expanded the stress concentration region which resulted in the transformation of bending failure mode, from local to whole collapse accompany with transverse cracking. ⅲ) With the increase of compressive and bending resistance perfor mances, the novel tube-reinforced honeycomb is competitive in load carrying and energy absorption applications. Acknowledgment This work was supported by the National Natural Science Foundation of China (11702326, 11802221), Chinese Postdoctoral Science Foun dation (2018M633493), Postdoctoral Scientific Research Project of Shaanxi Province (2017BSHYDZZ74), Open Project Program of the State Key Laboratory for Strength and Vibration of Mechanical Structures (SV2016-KF-22), Xi’an Jiaotong University, Pre-research project of Department of Basic Sciences(YNJC19070602), Air Force Engineering University. References [1] Zhang QC, Yang XH, Li P, Huang GY, Feng SS, Shen C, Han B, Zhang XH, Jin F, Xu F, Lu TJ. Bioinspired engineering of honeycomb structure–Using nature to inspire human innovation. Prog Mater Sci 2015;74:332–400. [2] Prakobna K, Berthold F, Medina L, Berglund LA. Mechanical performance and architecture of biocomposite honeycombs and foams from core–shell holocellulose nanofibers. Compos Appl Sci Manuf 2016;88:116–22. [3] Hu DY, Wang YZ, Song B, Dang LW, Zhang ZQ. Energy-absorption characteristics of a bionic honeycomb tubular nested structure inspired by bamboo under axial crushing. Compos B Eng 2019;162:21–32. [4] Jiang W, Yan LL, Ma H, Fan Y, Wang JF, Feng MD, Qu SB. Electromagnetic wave absorption and compressive behavior of a three-dimensional metamaterial absorber based on 3D printed honeycomb. Sci Rep 2018;8(1):4817. [5] Kee PJ, Thayamballi AK, Kim G. The strength characteristics of aluminum honeycomb sandwich panels. Thin-Walled Struct 1999;35(3):205–31. [6] Liu Q, Fu J, Wang JS, Ma JB, Chen H, Li Q, Hui D. Axial and lateral crushing responses of aluminum honeycombs filled with EPP foam. Compos B Eng 2017; 130:236–47. [7] Petras A, Sutcliffe MPF. Failure mode maps for honeycomb sandwich panels. Compos Struct 1999;44(4):237–52. [8] Sun GY, Huo XT, Chen DD, Li Q. Experimental and numerical study on honeycomb sandwich panels under bending and in-panel compression. Mater Des 2017;133: 154–68. [9] He MF, Hu WB. A study on composite honeycomb sandwich panel structure. Mater Des 2008;29(3):709–13. [10] Wang ZG, Li ZD, Xiong W. Experimental investigation on bending behavior of honeycomb sandwich panel with ceramic tile face-sheet. Compos B Eng 2019;164: 280–6.
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[43] Yan LL, Han B, Yu B, Chen CQ, Zhang QC, Lu TJ. Three-point bending of sandwich beams with aluminum foam-filled corrugated cores. Mater Des 2014;60:510–9. [44] Movahedi N, Linul E. Quasi-static compressive behavior of the ex-situ aluminumalloy foam-filled tubes under elevated temperature conditions. Mater Lett 2017; 206:182–4. [45] Duarte I, Krstulovi�c-Opara L, Vesenjak M. Axial crush behaviour of the aluminium alloy in-situ foam filled tubes with very low wall thickness. Compos Struct 2018; 192:184–92.
[46] Zok FW, Waltner SA, Wei Z, Rathbun HJ, McMeeking RM, Evans AG. A protocol for characterizing the structural performance of metallic sandwich panels: application to pyramidal truss cores. Int J Solids Struct 2004;41(22):6249–71. [47] Zhang QC, Han YJ, Chen CQ, Lu TJ. Ultralight X-type lattice sandwich structure (I): concept, fabrication and experimental characterization. Sci China E 2009;52(8): 2147–54.
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Contents lists available at ScienceDirect
Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Metallic tube-reinforced aluminum honeycombs: Compressive and bending performances Yunwei Zhang a, d, 1, Leilei Yan b, c, *, 1, Wanbo Zhang d, Pengbo Su c, e, Bin Han f, Shuxiang Guo a, d a
Aeronautics Engineering College, Air Force Engineering University, Xi’an, 710051, China School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China c State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, China d Department of Basic Sciences, Air Force Engineering University, Xi’an, 710051, China e State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China f School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Honeycomb Hybrid Mechanical properties Finite element analysis (FEA) Buckling Energy absorption
Aluminum honeycombs are widely applied in weight sensitive applications, increasing their specific strength and energy absorption capacity are rather important. Thin-walled metallic tube was used to enhance the mechanical properties of aluminum honeycomb and formed a novel tube-reinforced honeycomb structure. Its compressive and three-point bending performances were studied experimentally and numerically. Due to tube filling, the specific compressive strength, elastic modulus and energy absorption have been increased by 16%, 26% and 73%, and the specific bending load and stiffness increased by 42% and 62% respectively. The strengthen mechanism study indicated that the sum of tube and honeycomb caused the increase of compressive properties, and aluminum tube filling changed the stress distribution and expanded the stress concentration region which led to a transformation of bending failure mode. The present reinforcement method will make honeycomb more competitive in light-weight structure applications.
1. Introduction Honeycomb and its sandwich structures have been widely used in weight sensitive applications, such as aircraft, high-speed trains and other light-weight vehicles [1–4]. The main advantages of such light-weight structures were high specific strength and high specific energy absorption (SEA) for honeycombs [5,6], and high flexural ri gidity and bending strength [7–11] for honeycomb core sandwich structures. Therefore, the mechanical properties of honeycomb-based light-weight structures have been widely designed and studied [12–15]. Kee et al. [5] experimentally studied the mechanical properties of honeycomb core sandwich structure in three-point bending, axial compression and lateral crushing loading conditions. Petras et al. [7] constructed a failure mode map for sandwich beam with GFRP laminate skins and Nomex honeycomb core under three-point bending, and the results showing that the failure mode was dependent on the ratio of skin thickness to span length and relative density of honeycomb. The effects of parameters on the mechanical properties of honeycomb were also
investigated by Sun et al. [8], such as the thickness of skins/face-sheets, hexagonal cell size, foil thickness and height of honeycomb core. Sun et al. [16] experimentally and numerically studied the dynamic response and failure mechanisms of honeycomb sandwich panels subjected to high-velocity impact. The discrete optimization method was used to generate an optimal design of a sandwich structure for achieving the highest specific energy absorption without perforation under certain impact energy. The discrete optimization method could be also used to optimize other practical engineering problems to find the optimal structure for a specific purpose [17–19]. For sandwich structure, when the weight of honeycomb core accounts for 50%–66.7%, it has been suggested have optimum mechanical properties [9]. Such studies showing that honeycombs have significant advantages in load carrying and energy absorption applications. Therefore, the rapid development of industrial technology, especially aerospace requires light-weight mate rials and structures (such as honeycomb) have much lower density, higher strength and energy absorption efficiency. For this purpose, several novel methods and structures were used to form composite
* Corresponding author. School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China. E-mail address: [email protected] (L. Yan). 1 These authors contributed equally to this work and should be considered co-first authors. https://doi.org/10.1016/j.compositesb.2019.04.044 Received 1 December 2018; Received in revised form 1 April 2019; Accepted 29 April 2019 Available online 1 May 2019 1359-8368/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic and parameter of empty and tube-reinforced honeycomb design.
plastic tubes into the aluminum honeycomb holes to increase the SEA capacity for compression tests. Such polypropylene foam could increase the mechanical behaviors of honeycombs dramatically, but also increase its density significantly [29]. Besides polypropylene foams, fiber rein forced honeycombs were also effective in impact resistance [31,32]. Tube structures have outstanding advantages in axial load carrying applications and are also used as a reinforced structure. Zhang et al. [33] investigated the square aluminum tube reinforced thin-walled beams under quasi-static and dynamic bending tests. The tube fillers consid erably improving the performance of thin-walled beams and outperform the aluminum foam filler. Wang et al. [34] experimentally studied the mechanical performances of energy absorption and deformation mode of honeycomb cells filled with circular tubes (HFCT) under axial loading, and showing evident promotion in energy absorption. Honey combs also have advantages in blast resistance [35,36]. Liu [36] investigated the blast resistance performances of the sandwich plate filled with HFCT core numerically. The results showing tube filling have advantages for honeycombs in energy absorption and blast resistance. Besides honeycomb, tube structures also used to reinforce foam struc tures. The energy-absorbing characteristics of polymer foams reinforced with small carbon fiber reinforced epoxy tubes were experimentally studied [37,38]. Yan et al. [39] recently reported a metallic tube enhanced aluminum foam, showing that metallic tube filling can significantly increase the compressive strength and energy absorption of aluminum foam. Further more, the aluminum tube and the carbon fiber reinforced plastic (CFRP) tube were used to reinforce each other under quasi-static axial compression [17] and three-point bending test [18]. To increase the mechanical properties of aluminum honeycomb and its sandwich structures, metallic tubes were used to form tubereinforced honeycomb in the present study. Compressive and three-
structures and anticipated to have higher specific strength and energy absorption (SEA) [20–28]. Methods were developed to form novel honeycomb structures to increase the mechanical performances of honeycomb, such as zero Poisson’s ratio [20], re-entrant anti-trichiral [21], double-V [22]and hierarchical [23–25] honeycombs. Especially for the hierarchical hon eycomb, compared with the regular one, the first- and second-order hierarchical honeycombs improved the SEA by 81.3% and 185.7%, respectively [25]. Besides these designs, Sun et al. [26] used periodical grids to reinforce soft honeycomb core of sandwich structures. The hybrid core sandwich specimens provided increased stiffness, specific stiffness, energy absorption and critical load, which were higher than the sum of honeycomb core sandwich specimens and grid core sandwich specimens. Du et al. [27] used paper-reinforced polymer (PRP) com posites as skin materials and resin-impregnated aramid paper as hon eycomb core to fabricate light-weight sandwich panel constructions. Such sandwich structure had comparable bending rigidity and flexural load bearing capability but lower areal weights when compared with some commercial products for automotive interior applications. Tao et al. [28] proposed a novel in-plane graded honeycomb and its dynamic behavior under out-of-plane compression was investigated using nu merical simulation and theoretical analysis. The crushing strength and energy absorption capacity were enhanced by positive gradient struc ture design. Foams and fibers were also used to reinforce honeycombs to increase its strength and energy absorption performances. Liu et al. [6,29] intensified the aluminum honeycomb by filling with expanded poly propylene foam. The peak strength, mean crushing strength and total energy absorption under the axial compression and the SEA under lateral crushing were increased. Antali et al. [30] embedded carbon fiber 193
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Fig. 2. Images of specimens for compression tests.
Fig. 3. Images of sandwich beam for three-point bending test. Careful treatments of specimens during fabrication can be seen on the left.
point bending loads were carried experimentally and numerically on tube-reinforced honeycomb, as well as empty honeycomb and aluminum tubes for comparison. The enhancement on specific compressive strength, elastic modulus and energy absorption under compressive load, and three-point bending load and stiffness were investigated. The failure mode and enhancement mechanisms were also studied. In addition, the specific strength and energy absorption per unit mass of the present tube-reinforced honeycomb were also compared with the competitive core designs.
Table 1 Parameters of the specimens for compression tests, where length (Lc), width (Wc), height (Hc) and density (ρc) of specimens are showing.
2. Experimental measurement
Specimens
Type
ρc (Kg/m3)
Lc (mm)
Wc (mm)
Hc (mm)
CE-1 CE-2 CT-1 CT-2
Empty Empty Tube-reinforced Tube-reinforced
70.63 71.03 99.38 98.75
40 40 40 40
40 40 40 40
20 20 20 20
surface cleaning was applied to aluminum honeycombs, tubes and facesheets. The prepared specimens for compressive test and three-point bending test were shown in Fig. 2 and Fig. 3 respectively.
2.1. Materials and fabrication Fig. 1 illustrated the geometry parameters of specimens for compressive and three-point bending test. Honeycomb (Fig. 1 (a)) and tube-reinforced honeycomb (Fig. 1 (b)) were prepared for compression tests, and which were also acted as the core of sandwich structure for three-point bending tests Fig. 1 (c) and Fig. 1 (d). The dimensions of hexagon side length (Lh ¼ 3 mm) and the wall thickness (Th ¼ 0.05 mm) of honeycomb; the outside diameter (Φt ¼ 10 mm), wall thickness (Tt ¼ 0.5 mm), height (Ht ¼ 20 mm) of metallic tubes and the thickness (Tf ¼ 1 mm) of face-sheets for sandwich beams were all fixed. The honeycomb and face-sheets were made of aluminum alloy 3003, and the tubes were made of aluminum alloy 6061. Specimens were cut from commercial honeycomb sheet by Electrical Discharge Machining (EDM) as well as aluminum tubes and face-sheets. For tube-reinforced honeycombs, through holes were perforated in the middle of honeycomb for tube filling firstly. And then it was fixed with aluminum tubes and face-sheets by epoxy glue. Before assembling,
2.2. Compressive test The detailed parameters and images of specimens for compression tests were shown in Table 1 and Fig. 2. Out-of-plane quasi-static compression tests were carried out by the electronic universal testing machine (INSTRON-3382) at ambient temperature as shown in Fig. 4, with a fixed loading rate of 1 mm/min. At least 80% compressive strain was achieved or each specimen to ensure complete deformation and energy absorption. Digital images of each sample were acquired by a video camera to study deformation modes and failure mechanisms (as well as three-point bending test). 2.3. Three-point bending test Specimens for three-point bending test consist of five unit-cells compared to compression test specimens (both empty and tube194
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Fig. 4. Experimental set-up for compression and three-point bending tests (Instron 3382). Table 2 Parameters of sandwich structures for three-point bending tests, where length (Ltb), width (Wtb), height (Htb) and average density (ρtb) of both empty (TB) and tube-reinforced (TB-T) sandwich beams are showing respectively. With fixed face-sheets thickness (Tf ¼ 1 mm). Specimens
Type
ρtb (Kg/
Ltb (mm)
Wtb (mm)
Htb (mm)
TB-1 TB-2 TB-T-1
Empty Empty Tubereinforced Tubereinforced
355 364 414
220 220 220
40 40 40
22 22 22
414
220
40
22
TB-T-2
m3)
reinforced sandwich structures). The detailed parameters and images of specimens for three-point bending test were summarized in Table 2 and Fig. 3. The three-point bending tests were also carried out by the electronic universal testing machine (model INSTRON-3382) with a fixed loading rate of 1 mm/min at ambient temperature, as illustrated in Fig. 4. The span length was set to be 160 mm. And the diameters of support and loading bars were 10 mm, according to ASTM: C393 standard [40].
Fig. 6. Nominal stress versus strain curves of empty honeycomb (CE-1), tubereinforced honeycomb (CT-1) and aluminum tube under uniaxial compression.
alloy 6061 with the density (ρAl 6061 ¼2700 kg/m3), Young’s modulus (EAl 6061 ¼69 GPa) and yield strength (σ Al 6061 ¼227.5 MPa) were used for the tubes.
3. Numerical investigation 3.1. Materials properties
3.2. Finite element model
The quasi-static compressive and three-point bending tests were numerically simulated by ABAQUS/Explicit, using same geometrical parameters with the experimental specimens. The density (ρAl 3003 ¼2730 kg/m3), Young’s modulus (EAl 3003 ¼69 GPa) and yield strength (σ Al 3003 ¼185 MPa) of aluminum alloy 3003 were used for facesheets and honeycomb in the finite element analysis. The aluminum
The finite element (FE) model for compression tests was shown in Fig. 5 (a), the honeycomb was compressed between two rigid plates. The bottom plate was fixed, and the top plate could only move for z-direc tion. And the FE model for three-point bending tests was shown in Fig. 5 (b), the sandwich structure was supported by two fixed rigid bars, and
Fig. 5. FE models for compression and three-point bending tests. 195
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Fig. 7. Experimental and simulated images illustrating the deformation history at the selected points marked in Fig. 6.
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Table 3 Summary of the experimental and numerical compressive strengthσ cpeak , elastic modulus E, energy absorption per unit volume Wv and per unit mass Wm of the specimens. The experimental results are the averaged measurements of specimens in Table 1. Compressive CE CE-FE CT CT-FE
ρc
σcpeak
ðKg=m3 Þ
ðMPaÞ
70.82 70.94 99.06 93.39
3.38 3.63 5.47 5.18
σcpeak ðσAl3003 ρc =ρAl 3003 Þ 0.70 0.76 0.81 0.82
E (MPa)
Wv (KJ/m3)
Wm (KJ/Kg)
509 1384 640 2196
618.29 751.74 1481.10 1534.93
8.66 10.60 14.95 16.44
4. Results and discussion 4.1. Compressive response 4.1.1. Experiment Under uniaxial compression tests, typical nominal stress versus strain curves of empty honeycomb (CE-1) and tube-reinforced honeycomb (CT-1) were shown in Fig. 6. For reference, the stress-strain curve of tube which used to reinforce the honeycomb under uniaxial compression tests was also included. Details of stress-strain curves as Fig. 6 shown can be seen as follows: ⅰ) For empty honeycomb (curve, CE-1), after a linear and nonlinear in crease the compressive stress reached its peak (3.38 MPa) and declined subsequently, and then present plateau region like foam structures (1.3 MPa) [42]. When the compress strain undergoes till 0.8, the densification occurred and caused a dramatic increase of compressive stress. ⅱ) For empty aluminum tube (curve, Tube), differs to aluminum honeycomb, its stress-strain curve showing multiple peaks and valleys before densification occurred due to layer by layer buckling of the empty tube (Fig. 7 (c)). ⅲ) The curve shape of tube-reinforced honeycomb (curve, CT-1) is similar to that of empty aluminum tube. For contrast, the sum of empty honeycomb (curve, CE-1) and empty aluminum tube (curve, Tube) which were tested separately also showing in Fig. 6 (curve, CE-1þTube), and agreed well with tube-reinforced honeycomb. In other words, the strength of novel designed tube-reinforced honey comb was just the sum of aluminum honeycomb and tube. Images in Fig. 7 showing the deformation history of empty honey comb, tube-reinforced honeycomb and empty tube at selected points ~ E in Fig. 6. When the first peak occurred, the compressive marked in A strain of tube-reinforced honeycomb increases from 0.008 to 0.032 compared to empty honeycomb, whereas, its densification strain declined from 0.809 to 0.704 which is similar to aluminum tube (0.709). The specimens all collapsed from one side layer by layer which causes the fluctuation of stress-strain curves, and each formation of folding for aluminum tube and tube-reinforced honeycomb related to one stress peak and valley marked in Fig. 6. The images after compression (Fig. 7, Final) indicated that the honeycomb and aluminum tube almost have no effect on each other. As summarized in Table 3, for tube-reinforced honeycomb (CT), the peak stress (σ cpeak ) increased from 3.38 MPa to 5.47 MPa, and elastic
Fig. 8. Energy absorption per unit volume (Wv) and per unit mass (Wm) of CE and CT specimens.
Fig. 9. Stress versus strain curves comparing with the experiment results under compression tests.
modulus E increased from 509 MPa to 640 MPa compared to empty honeycomb (CE), respectively. With consideration of weight alternation,
the top rigid bar compressed the structure from z-direction. Due to the thin thickness of the honeycomb, shell parts (S4R) were used for aluminum honeycomb. Solid element (C3D8R) was employed for aluminum tubes, and rigid element (R3D4) was used for the rigid part. Tie constraint was used to simulate the honeycomb adhesive connection between honeycomb and face-sheets as well as honeycomb and tubes. The friction coefficient was set to be 0.2 as the general contact between other surface pairs, and the quasi-static loading speed of simulation was set to 1 m/s. To verify the quasi-static progress, two principles need to be observed. Firstly, the total kinetic energy has to be very small compared to the total internal energy. Secondly, the crushing force-displacement response must be independent from the applied ve locity [5,41]. Mesh size sensitivity studies were also carried for all FE models.
σc
the normalized peak stress ðσAl 3003 ρpeak =ρ c
Al 3003 Þ
was also increased from 0.7 to
0.81, where ρAl 3003 ¼ 2730 kg/m3, σ Al 3003 ¼ 185 MPa was the density and yield stress of aluminum alloy 3003 respectively, and the average density ρc of specimens for compression tests was shown in Table 3. The energy absorption capacity was represented by energy absorp tion of per unit volume (Wv), which could be obtained through the integration of the stress-strain curves: Z ε Wv ¼ σ dε (1) 0
where the strain of specimens ε ¼ 0.5 was adopted here. In addition, the mass was an important factor for weight sensitive 197
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Fig. 10. Simulated images of specimens at cross section under compression at selected points (specific strain).
Fig. 11. FE simulated stress-strain curves with different tube thickness under compression tests.
Fig. 12. Load-displacement bending load.
application. Therefore, the specific energy absorption (SEA) was another important parameter, which could be defined as [42]:
4.1.2. FE analysis The FE analysis was used to study the strengthen mechanisms of tube-reinforced honeycombs. As shown in Fig. 9, the numerical simu lated stress-strain curves of empty (CE-FE) and tube-reinforced (CT-FE) honeycombs agree well with the experimental ones. In addition, the simulated deformation modes also matching the experimental ones well as showing in Fig. 7. As shown in Table 3, the simulated strength and energy absorption of both empty (CE-FE) and tube-reinforced (CT-FE) honeycombs are reasonable and fit well with the experimental ones. Note that for elastic modulus E, the numerical results were larger than the experimental ones. The inconsistency of E was suggested to be as follows: the compressive punch was treated as an ideal rigid plate in FE analysis,
Wm ¼
Wv
ρc
(2)
where theρc was the average density of the specimens. The energy absorption per unit volume (Wv) and per unit mass (Wm) of specimens were also summarized in Table 3. The results indicated that due to aluminum tube filling, the tube-reinforced honeycomb (CT) have a significant increase of Wv and Wm by 140% and 73% respectively. The benefits of metallic tube filling on energy absorption of aluminum honeycomb were shown obviously in Fig. 8.
198
curves
of
specimens
under
three-point
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Fig. 13. Photographs illustrating the deformation history at selected points marked in Fig. 12.
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however, in the experimental tests, the machine itself and punches all had its own rigidness which was neglected in FE analysis. Nevertheless, the experimental and numerical results are all indicated that the tubereinforced honeycombs have dramatically increased compressive strength, elastic modulus E, energy absorption (both Wv and Wm) compared to empty honeycombs. To better understanding the strengthen mechanism, the simulated section images of empty and tube-reinforced honeycombs were shown in Fig. 10. The deformation mode of tube-reinforced honeycomb (Fig. 10 (b)) have no distinct difference compared with empty honeycomb (Fig. 10 (a)), that means the deformation of aluminum tube and hon eycomb deforms individually. In other words, the present designed aluminum tube and honeycomb have no effect on each other. However, the aluminum foam-filled corrugated sandwich panel [42,43] and aluminum foam-filled tube [44,45] all showing a significant coupling effect. Therefore, the further study of tube-reinforced honeycombs by strength matching of tube and honeycomb may also have a coupling effect which may cause the strength and energy absorption further increased.
Fig. 14. Comparison of FE simulated load-displacement curves with experi ment results of specimens under three-point bending load.
4.1.3. Structure optimization Due to limitations of experimental conditions, only the honeycomb reinforced with the tube (Tt ¼ 0.5 mm) was experimentally studied. The compressive performance of the tube-reinforced honeycomb with different tube wall thickness (Tt ¼ 0.5 mm, 0.3 mm, and 0.1 mm) was studied by FE analysis. As shown in Fig. 11, the stress-strain curves of the tube-reinforced honeycomb (CT-FE) with different tube wall thickness have almost coincided with the curves (CE-FE þ Tube-FE) which were the sum of the empty honeycomb (CE-FE) and the corresponding tube (Tube), respectively. With the tube (Tt ¼ 0.5 mm, 0.3 mm, and 0.1 mm) filling, the Wm of the tube-reinforced honeycombs were increased by 57%, 24% and 15% respectively compared with the empty one. It indicated that the tube-reinforced honeycomb with thicker tube wall thickness had higher SEA.
collapse of the tube-reinforced sandwich beam was much more difficult to occur, which caused the increase of the peak bending load. The debonding of epoxy glue between its bottom face-sheet and honeycomb core led to the bending load decrease dramatically, and which was the dominant failure mode, as shown in Fig. 13 (b). Different to the empty one, the local failure of honeycomb in the tube-reinforced sandwich beam was transverse cracking instead of compression, and the reason was caused by the enhancement of compressive strength due to tube filling discussed before. The measured peak loading force (Fpeak) and its normalized form Fpeak ðρtb =ρAl 3003 Þ
of both empty (TB) and tube-reinforced sandwich beam (TB-T)
were summarized in Table 4. ρtb was the average density of the speci mens for three-point bending tests. The results showing that due to metallic tube reinforcement, the Fpeak of aluminum honeycomb sand wich beam increased by 64% compared with empty one. With consid
4.2. Bending response
eration of density increment, the normalized form
4.2.1. Experiment The load-displacement responses of both empty (TB-1 and TB-2) and tube-reinforced sandwich beam (TB-T-1 and TB-T-2) under three-point bending tests were compared in Fig. 12. And images of specimens under selected bending displacement δ marked in load-displacement curves (Fig. 12) were shown in Fig. 13. As shown in Fig. 12, for the empty sandwich beam, after a linear and nonlinear increase, the bending load decreased and then undergoes a plateau region. However, for the tube-reinforced sandwich beam, the bending load declined dramatically after its peak arrived, and the sus tained load is lower than that of the empty one. As the collapse history shown in Fig. 13 (a), for the empty sandwich beam, the top face-sheet deforms elastically and honeycomb collapses locally (below loading bar) which causes the decrease of bending load after its peak (point A). With the three-point bending progress, the local collapse of honeycomb continues and the plastic yielding of top face-sheet appears (point B and C). As the final image shown, no debonding occurred during the whole bending process, and local collapse and yielding of top face-sheet was the main deformation mode. For contrast, due to tube filling, the local
Fpeak ðρtb =ρAl 3003 Þ
still has a
significant increment (42%). What’s more, besides bending load resis tance, its bending stiffness (defined as the slope of the elastic region) also have a dramatical increase of 62%.
4.2.2. FE analysis To better understanding the bending behavior and enhancement mechanisms, FE simulation was carried. As shown in Fig. 14, the simulated load-displacement curve (TB-FE) of the honeycomb sandwich structure had a good agreement with the experimental measurement result (TB-1). But for the tube-reinforced beam, the simulated loaddisplacement curves (TB-T-FE) only had a good agreement with the experimental curve (TB-T-1) before the peak load point. After the peak load point, the FE result (TB-T-FE) was much larger than the experi mental result (TB-T-1). This is due to the debonding occurred at this stage between the honeycomb core and the below face-sheet. Compared Fig. 13 (b) with Fig. 15 (b), the debonding occurred can be obviously observed in the experiment specimen, while an ideal bonding surface was considered in the present FE model. For empty sandwich beam, the
Table 4 Summary of the experimental and numerical results of three-point bending. The experimental results are the averaged measurements of specimens in Table 2. The stiffness indicates the slope of load-displacement curve at elastic stage. Three-point bending TB (experimental) TB-FE (numerical) TB-T (experimental) TB-T-FE (numerical)
ρtb
ðKg=m3 Þ 360 311 414 329
Fpeak ðρtb =ρAl 3003 Þ
Fpeak (N) 1399 1471 2290 2437
10609 12903 15101 20221
200
δpeak (mm)
Stiffness (KN/mm)
0.90 0.88 0.99 1.08
2.03 3.56 3.28 3.61
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Fig. 15. Simulated cross section images of specimens during three-point bending process under different bending displacement.
dropped slowly with the ‘tie’ constraint. In addition, the simulated bending stiffness was larger than experimental ones, the cause of the inconsistency was similar to the compressive result discussed before. Fig. 15 showing the cross-section images of specimens during the three-point bending process with tubes in sandwich beam visible, and the distribution of Mises stress S can be seen clearly. For empty sandwich beam, the Mises stress S concentrated on top loading bar with a small region, and such stress concentration causing local collapse occurred (as Fig. 13 (a) shown). By contrast, the region of stress concentration was expanded for the tube-reinforced sandwich beam which led to a more complicated failure mode, along with transverse cracking. 4.2.3. Structure optimization As shown in Fig. 16, the tube-reinforced sandwich beam with different tube wall thickness (Tt ¼ 0.5 mm, 0.3 mm, and 0.1 mm) were also studied numerically. The load-displacement curve (TB-T-FE0.1 mm) almost coincided with the curve of the empty honeycomb sandwich beam (TB-FE). The loading of TB-T-FE-0.3 mm was higher than TB-FE but lower than TB-T-FE-0.5 mm. As discussed before, for the TB-T-FE-0.5 mm, the debonding occurred between the honeycomb and the below face-sheet in the experiment. This issue may be solved by using the thinner tubes, but loading will be lower corresponding.
Fig. 16. FE simulated load-displacement curves with different tube thickness under three-point bending load.
Mises stress S concentrated on top loading bar with a small region (as Fig. 15 (a) shown). For contrast, the region of stress concentration was expanded for the tube-reinforced sandwich beam (as Fig. 15 (b) shown). With the region of stress concentration expanded, the stress between the core and the below face-sheet increased rapidly, which lead to the debonding between the core and the below face-sheet. The loaddisplacement curve of TB-T-1 (in Fig. 14) dropped rapidly after the debonding occurrence at the peak load point, but the curve of TB-T-FE
4.3. Comparison with competitive core designs The uniaxial compressive strength (σcpeak ) and energy absorption
capacities per unit mass (Wm) of both empty and tube-reinforced hon eycombs were compared with several competitive core designs [43]. As shown in Fig. 17, the present newly developed tube-reinforced
Fig. 17. Compressive strength and energy absorption comparison of present honeycomb and tube-reinforced honeycomb with other competitive core designs [43]. 201
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honeycomb was competitive compared with empty honeycomb, espe cially energy absorption. Compared with other competitive cores, such as pyramidal which have been demonstrated have advantages in load carrying applications [46,47], the present result is more advantageous. With future geometric optimization design, the present tube-reinforced honeycomb structure is suggested to be more competitive.
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5. Conclusions Metallic tubes were used to increase the mechanical performances of aluminum honeycombs and its sandwich structures, and formed tubereinforced honeycomb. The compressive and three-point bending re sponses of the novel tube-reinforced honeycomb was studied experi mentally and numerically. The results are as follows: ⅰ) Compared with empty honeycomb, the normalized peak stress, elastic modulus E and energy absorption per unit mass (SEA) of tube-reinforced honeycomb can be increased by 16%, 26% and 73% respectively due to aluminum tube filling. The results almost equal to the sum of aluminum honeycomb and tube which were tested separately. ⅱ) The normalized peak bending load and stiffness of the tubereinforced sandwich beam were increased by 42% and 62% respectively compared with the empty sandwich beam. The nu merical results indicated that the tube filling changed the stress distribution and expanded the stress concentration region which resulted in the transformation of bending failure mode, from local to whole collapse accompany with transverse cracking. ⅲ) With the increase of compressive and bending resistance perfor mances, the novel tube-reinforced honeycomb is competitive in load carrying and energy absorption applications. Acknowledgment This work was supported by the National Natural Science Foundation of China (11702326, 11802221), Chinese Postdoctoral Science Foun dation (2018M633493), Postdoctoral Scientific Research Project of Shaanxi Province (2017BSHYDZZ74), Open Project Program of the State Key Laboratory for Strength and Vibration of Mechanical Structures (SV2016-KF-22), Xi’an Jiaotong University, Pre-research project of Department of Basic Sciences(YNJC19070602), Air Force Engineering University. References [1] Zhang QC, Yang XH, Li P, Huang GY, Feng SS, Shen C, Han B, Zhang XH, Jin F, Xu F, Lu TJ. Bioinspired engineering of honeycomb structure–Using nature to inspire human innovation. Prog Mater Sci 2015;74:332–400. [2] Prakobna K, Berthold F, Medina L, Berglund LA. Mechanical performance and architecture of biocomposite honeycombs and foams from core–shell holocellulose nanofibers. Compos Appl Sci Manuf 2016;88:116–22. [3] Hu DY, Wang YZ, Song B, Dang LW, Zhang ZQ. Energy-absorption characteristics of a bionic honeycomb tubular nested structure inspired by bamboo under axial crushing. Compos B Eng 2019;162:21–32. [4] Jiang W, Yan LL, Ma H, Fan Y, Wang JF, Feng MD, Qu SB. Electromagnetic wave absorption and compressive behavior of a three-dimensional metamaterial absorber based on 3D printed honeycomb. Sci Rep 2018;8(1):4817. [5] Kee PJ, Thayamballi AK, Kim G. The strength characteristics of aluminum honeycomb sandwich panels. Thin-Walled Struct 1999;35(3):205–31. [6] Liu Q, Fu J, Wang JS, Ma JB, Chen H, Li Q, Hui D. Axial and lateral crushing responses of aluminum honeycombs filled with EPP foam. Compos B Eng 2017; 130:236–47. [7] Petras A, Sutcliffe MPF. Failure mode maps for honeycomb sandwich panels. Compos Struct 1999;44(4):237–52. [8] Sun GY, Huo XT, Chen DD, Li Q. Experimental and numerical study on honeycomb sandwich panels under bending and in-panel compression. Mater Des 2017;133: 154–68. [9] He MF, Hu WB. A study on composite honeycomb sandwich panel structure. Mater Des 2008;29(3):709–13. [10] Wang ZG, Li ZD, Xiong W. Experimental investigation on bending behavior of honeycomb sandwich panel with ceramic tile face-sheet. Compos B Eng 2019;164: 280–6.
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