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Dynamic response of sandwich panel with hierarchical honeycomb cores subject to blast loading
Thin-Walled Structures 142 (2019) 499–515
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Full length article
Dynamic response of sandwich panel with hierarchical honeycomb cores subject to blast loading
T
Guangyong Suna,b,∗, Jingtao Zhanga, Shiqiang Lia,c, Jianguang Fangb, Erdong Wanga, Qing Lib a
State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, China School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia c Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China b
ARTICLE INFO
ABSTRACT
Keywords: Sandwich panel Hierarchical structure Blast resistance Energy absorption Impulse loadings Explosion-proof structure
This paper introduces a novel hierarchical core structure to sandwich panel for bearing the blast loading, in which each vertex of a regular hexagonal cell was replaced with a smaller hexagonal unit. The finite element (FE) models of such hierarchical honeycomb sandwich panels were established and validated with the experiments under different impulse loads. The hierarchical honeycomb cores were compared with the regular honeycomb counterpart in terms of the peak deflection on the back facesheet, compression and specific energy absorption (SEA) of the core. The results showed that the maximum deflection at the back facesheet of the hierarchical honeycomb sandwich panels were smaller than the regular honeycomb counterpart for a higher level of blast load (specifically, the dimensionless impulse higher than 0.06). It was found that the structural hierarchical parameter (i.e. the ratio of the newly-introduced smaller hexagonal edge length (L1) to the regular hexagon edge length (L0)), had limited influence on the maximum deflection of back facesheet of the sandwich panel, but had a significant effect on the SEA of the cores.
1. Introduction Blast is a major threat to structural safety and public security, which has drawn extensive attention all over the world recently. To address this issue, numerous studies have been conducted to improve the blast resistance of vehicles and buildings. In this regard, explosion-proof structures have proven to be effective in reducing blast impact, thereby protecting vehicles and buildings from devastating damage. As a class of explosion-proof structures which are able to dissipate sizable explosive energy through large plastic deformation under impact/blast loading [1–6], sandwich panels have been extensively used in a broad range of areas, such as aerospace, automotive, marine, defense and railway industry [7–10]. They have exhibited compelling advantages, such as high strength-to-weight ratio, high stiffness-to-weight ratio, high thermal isolation capacity, and excellent energy absorption and structural protection characteristics [11–15].
∗
To date, polymeric foams, honeycombs, metallic foams and functionally graded materials have been used as the core fillers of sandwich structures for explosion-proof applications, attributable to their lightweight, energy absorption efficiency, and high specific stiffness [16–21]. In these candidate materials, the aluminum honeycomb has exhibited superior performance in the compressive modulus and shear strength [22]. From the mechanical point of view, it is very similar to the I-beam with enhanced overall structural stiffness, stability, compressive capacity and bending characteristics. There have been substantial studies on the blast resistance of regular honeycomb sandwich plates based upon experiment, simulation and analysis [23–30]. For example, Chi et al. [23] studied a circular sandwich panel with an aluminum honeycomb core subjected to blast loadings by analyzing the influence of core height and facesheet thickness experimentally. Zhu et al. [24] performed the FE simulations to investigate the effects of blast loading and responses of honeycomb
Corresponding author. State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, China. E-mail address: [email protected] (G. Sun).
https://doi.org/10.1016/j.tws.2019.04.029 Received 17 October 2018; Received in revised form 1 April 2019; Accepted 15 April 2019 Available online 05 July 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
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sandwich panels in terms of deformation/failure modes and the deflection in the back facesheet. Yamashita and Gotoh [26] investigated the effects of the cell shape and foil thickness on the crush behavior; and showed that the crush strength was higher for a smaller branch angle and a greater thickness. Dharmasena et al. [27] compared the energy absorption of sandwich panels with the solid plates that have the same areal density under three levels of impulse loads; and they found that the cellular wall buckling and core densification increased with the impulse loading. From these abovementioned studies, the mechanical characteristics of the regular honeycomb sandwich panels have been explored extensively for their broad applications in engineering practice [31,32], but the investigation into a hierarchical honeycomb core is rare. The hierarchical honeycomb structures have been studied for its appealing lightweight potential and superior mechanical characteristics [33–36]. For example, Fang et al. [33] systematically studied the hierarchical honeycomb for outof-plane crash using the experimental, analytical and numerical
approaches; further showing the crashworthiness features and benefits of multi-level structural hierarchy. Ajdari et al. [34] investigated the hierarchical honeycomb structures using the analytical, numerical and experimental methods; and they found that the first- and second-order hierarchical honeycombs can be 2.0 and 3.5 times stiffer than a regular honeycomb with the same mass. Zhang et al. [35] modeled hierarchical honeycombs (the 1st and 2nd order hierarchies) under an impact loading. The results exhibited that the hierarchical honeycomb could improve the crushing strength and crushing force of the honeycomb sandwiches effectively. To enhance the crashing characteristics of the hierarchical honeycombs, Sun et al. [36] investigated the first- and second-order hierarchical configurations under an “out-of-plane” loading. The results demonstrated that the specific energy absorptions (SEA) of the first- and second-order hierarchical honeycombs could be enhanced by 81.3% and 185.7%, respectively. These preliminary studies demonstrated that the hierarchical honeycombs have substantially better crashworthiness behaviors.
Fig. 1. (a) Top view of honeycombs (b) Single unit-cell of regular honeycomb and hierarchical honeycomb (c) 3D view of regular honeycomb and hierarchical honeycomb.
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Fig. 2. Symmetric model of the sandwich panel for blast loading.
While the hierarchical honeycomb structures have exhibited superior mechanical characteristics, to the authors’ best knowledge, their resistance to blast loading has not been explored to date. The present study aimed to fill this knowledge gap by scrutinizing the resistance of sandwich panels with a novel hierarchical honeycomb core to the impulse loadings. The 3D finite element (FE) model of the honeycomb sandwich panel was first created and validated against the experimental results. The effects of the loading intensity and hierarchical core configuration on the back-panel deflection and energy absorption were quantified. It showed that the blast resistance of the hierarchical honeycomb sandwich panel is superior to the regular honeycomb core. This new core structure is expected to substantially enhance the sandwich capacity of explosion proof for various applications.
0
Note that = 0 downgrades to a regular honeycomb. The sandwich panel to be investigated here consists of steel front facesheet, steel back facesheet and aluminum honeycomb core, as shown in Fig. 2(a). In this study, all the parameters of the honeycomb sandwich panels are summarized in Table 1. And all the honeycomb sandwich panels were of a square shape and had the same overall area of W × W and the same effective area of W1 × W1, which was exposed to the impulsive load as illustrated in Fig. 2(b). 2.2. Finite element model The numerical simulations were conducted by using explicit nonlinear FE code LS-DYNA 971. The FE model comprised two facesheets and a core layer with either a regular honeycomb or a hierarchical honeycomb structure. Due to the symmetry of the sandwich panel and blast loading, only 1/2 of the sandwich panels were modeled to reduce the computational cost. Thus a symmetric boundary condition about the y-z plane was imposed, as shown in Fig. 2 (a). Further, the boundaries of all the sandwich components were fully clamped through the nodal constraints without deformation, and the area of boundary conditions are shown in Fig. 2 (b). In FE modeling, the Belytschko-Tasy shell elements were used for both the honeycomb cell foils and facesheets. A convergence test was conducted, and the deflection history of the central point on the front facesheet was selected to be a criterion as suggested in Refs. [1,37]. Five different mesh sizes, specifically 0.6, 0.8, 1.0, 1.2 and 1.4 mm, were employed, respectively. Fig. 3 shows the histories of the deflection at the central point of the front facesheet, which indicated that 1 mm mesh size was sufficient to balance the simulation accuracy and computational efficiency.
2. Structural configurations and finite element model 2.1. Geometric description According to Ajdari et al.'s work [34], we proposed to replace each three-edge vertex of a regular hexagonal lattice with a smaller hexagon to obtain the hierarchical honeycombs, as illustrated in Fig. 1. A specific structural organization parameter ( ) that defines the hierarchical honeycomb in relation to the regular configuration was introduced in terms of the ratio of newly proposed hierarchical hexagonal side length (L1) to the original side length (L0 = 10mm ) of the regular hexagon, i.e., = L1/ L 0 , as illustrated in Fig. 1. To avoid overlapping with the original edges, some geometric constraints must be imposed as,
0
L1
(1)
L 0 /2
(2)
0.5
which leads to Table 1 The parameters of the sandwich panels. Parameters
Thicknesses of front facesheet (tf) 1.6 mm
Thicknesses of back facesheet (tb) 1.6 mm
Core height (H) 30 mm
501
wall thickness (t) 0.1 mm
Overall area (W × W) 300 × 300 mm
2
Effective area (W1× W1) 250 × 250 mm2
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Automatic surface-to-surface contact was defined in between the honeycomb core and the facesheets. The automatic single surface contact was adopted for modeling the self-contact of honeycomb foil surfaces. The static and dynamic friction coefficients were set to be 0.3 and 0.2, respectively [1]. In the FE simulations, the facesheets and honeycomb were modeled in LS-DYNA material Type 3. The material properties of the steel facesheets and aluminum core were taken from the literature [20,24], respectively. Herein, we assume that those materials are sufficiently plastic to resist the failure under blast loading. The facesheets were made of the mild steel, whose strain rate effect was accounted using the Cowper and Symonds model [18]. Thus, the yield stress was calculated mathematically as: 0 0
=1+
1/
C
(3)
where 0 is the dynamic flow stress; 0 is the initial yield stress, is the equivalent strain rate. The material properties of the mild steel facesheet material include the density st = 7800kg/m3, Poisson's ratio
Fig. 3. Mesh size sensitivity for the deflection at the central front facesheet.
Fig. 4. Comparison of the FE simulation with the experimental results [29].
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G. Sun, et al. st = 0.3, Young's modulus Est = 210GPa , and yield stress st = 300MPa [20]. The rate parameters of mild steel, i.e. C = 40.4 s−1 and α = 5 [37], were adopted to simulate the strain-rate effect of the facesheet materials in the blast simulations. The honeycombs were made of aluminum alloy and the strain rate is neglected for its insensitivity in general [24,38] in this study. The density of the honeycomb core material (aluminum alloy A5052) is 3 Poisson's ratio Young's modulus Al = 0.33 , Al = 2680kg/m , EAl = 70GPa , and yield stress Al = 265MPa [24]. In this study, a uniformly distributed blast loading, as reported in literature [30], was applied to be a pressure pulse on the front facesheet of the sandwich panel. The pressure is described in terms of time as follows:
p (t ) = p0 e
with the experiments of regular honeycomb core under the blast loads as reported in literature e.g. Refs. [29,30]. A regular honeycomb can be considered as a zeroth order hierarchy with = L1/ L 0 = 0 . The dimension of the experimental honeycomb specimens was 244 × 244 × 1.6 mm, whose facesheets were also made of mild steel square plates and core was made of aluminum alloy. Since the facesheets were not adhered to the honeycomb surfaces in the experiments, the energy absorption due to debonding was neglected. All the specimens had a circular explosive area of diameter 106 mm. The impulse was obtained using the measured swing of the pendulum. A uniformly distributed blast loading was applied as a pressure pulse on the frontal facesheet of the sandwich panel. The pressure was depicted in Eq. (4). The pressure pulses were defined in terms of the
(4)
t/t 0
where p0 is the initial pressure, and obviously, the pressure decays exponentially with a decay period of t 0 = 50µs . The impulse was defined as follows
I0 = W12
0
p (t ) dt
(5)
where W1 is the characteristic length of effective area of the sandwich panel, and the unit of the impulse is N⋅s. 2.3. Validation of the FE model As no in-house experimental tests have been conducted for the sandwich panel with a hierarchical aluminum honeycomb core under the blast loading, the FE model was validated through a comparison Table 2 The mass of hierarchical honeycomb core for different hierarchical parameters. Label
Hierarchical parameter
Mass of the core (g)
0 1–0.1 1–0.2 1–0.3 1–0.4 1–0.5
0 0.1 0.2 0.3 0.4 0.5
40.99 48.97 57.24 65.50 72.86 80.49
Fig. 6. Comparison of the maximum back facesheet deflections of the regular ( = 0 ) and hierarchical ( > 0 ) honeycomb sandwiches under different actual impulse loadings (a) and dimensionless impulses (b).
Fig. 5. Plot of the maximum and residual deflection at different time points.
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momentum conservation, as
I0 = R2
0
p (t ) dt
(6)
where R is the radius of the explosive area, and R = 53mm here. The impulses used in the validation varied from 4.4 N⋅s to 30.3 N s. A comparison between the experimental results [29] and the numerical simulations is shown in Fig. 4 (a), which graphed the maximum deflections ( max ) in the back facesheet of sandwich panels under different impulse loadings (I0 ). It is clear that the predicted FE results matched with the experimental results fairly well. Further, the deformation modes of sandwich core were compared in Fig. 4(b) for the experimental and numerical results, which agreed with one another very well. Thus, it was confident that the material model, contact algorithms, element type and size, boundary conditions, etc. adopted in the finite element model were sufficiently suitable for predicting the blasting responses of sandwich panels with hierarchical honeycomb cores. The validated numerical model could be extended to explore the blast resistance of sandwich panels under the relative large impulse range (100–300 N s) because they adopted the same modeling method.
Fig. 7. Comparison of the energy absorption in the back facesheet of the regular ( = 0 ) and hierarchical honeycomb with = 0.2 sandwich panels under a low impulse ( I = 0.04 ).
3. Results and discussion 3.1. Effects of structural hierarchical parameter In order to investigate the effects of hierarchical parameter on the blast resistance of the sandwich panel, was varied from 0.1 to 0.5 with an increment of 0.1 for the hierarchical honeycomb core. The corresponding mass of hierarchical honeycomb core was given in Table 2. The dynamic responses of the sandwich panel were quantified in terms of the maximum deflection, residual deflection, energy absorption in the back facesheet, as well as the deformation mode and energy absorption of the core here. The difference between the maximum deflection and residual deflection is illustrated in Fig. 5. Generally, the terrorist bombing in real life are often occurred under in a relatively large impulse. To explore the blast resistance of the regular and hierarchical honeycomb core sandwich structures under a relatively large impulse, the impulses in the following parametric analysis will be varied from 100 N s to 300 N s. 3.1.1. Dynamic responses of the back facesheet As a protective structure, sandwich panel is expected to assure and/ or maximize the safety of the targets behind the back facesheet. Thus, the maximum deflection of the center point of the back facesheet was
Fig. 9. Comparison of the energy absorption in the back facesheet of the regular ( = 0 ) and hierarchical honeycomb with = 0.2 sandwich panels under a high impulse (I = 0.07 ).
Fig. 8. Maximum core compression at the center point of back facesheet under different actual impulse loadings (a) and dimensionless impulses (b). 504
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Fig. 10. Comparison of the energy absorption by the back facesheet under different actual impulse loadings (a) and dimensionless impulses (b). Fig. 11. Comparison of the residual deflections of the back facesheet under different actual impulse loadings (a) and dimensionless impulses (b).
selected as a key indicator for assessing the structural resistance to the blast loading. The impulses and the deflections in the FE simulations were presented in a dimensionless form herein, similarly to Ref. [39], as,
I =
=
maximum deflection of the center point in the back facesheet, and W 1 is the characteristic length of the sandwich structure in the effective explosion area. To characterize the deformation of sandwich panels, Nurick and Shave [40] first identified three failure modes observed in the blastloaded plates, namely, Mode I: large ductile deformation; Mode II: tensile-tearing and deformation; and Mode III: transverse shear failure. In this present study, the back facesheet showed a typical Mode I response with substantial ductile deformation. The maximum deflections at the center point of the back facesheet of the regular and hierarchical
I0 m max
W1
y/
(7) (8)
where m is the mass per unit area of the sandwich, y is the yield stress of the core aluminum, is the density of core aluminum, max is the
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Fig. 12. Deflections (a) and deformation (b) process of hierarchical honeycomb cores under different impulse loadings.
honeycomb panel were graphed in Fig. 6 for the different impulse loadings considered here. When the dimensionless impulse I was less than 0.05, the maximum deflection of the back facesheet of the regular honeycomb panel was much smaller than that of the hierarchical honeycomb sandwich panels. This is because the core of the regular honeycomb has less number of cell-walls and is more deformable in comparison with the hierarchical counterparts; as a result, the regular honeycomb panel yielded a greater front facesheet deflection and more severe deformation in the core, making these two components absorb more energy. Consequently, this led to a smaller deflection and less energy absorption in the back facesheet of the regular honeycomb panel, as shown in Fig. 7. When the impulse is large (e.g. I = 0.07 ), the compression ratio of core (defined as the ratio of core compression to core original height) of
the regular honeycomb sandwich panel is greater than the compression ratios of hierarchical honeycomb cores, as shown in Fig. 8. In such loading levels, the regular honeycomb panel absorbed the blast energy mainly by plastic deformation in the front and back facesheets. In contrast, the cores of the hierarchical honeycomb were able to absorb considerable energy in addition to the front and back facesheets. This contributed on relatively less energy absorption in the back facesheet as shown in Fig. 9. Thus, the back facesheet deflections of the hierarchical honeycomb sandwich panels were smaller than that of the regular honeycomb panel. Figs. 10 and 11 show the energy absorption and residual deflections, also known as plastic deflections of the back facesheets, under several different impulses, respectively. The residual deflection is an important indicator for measuring the protection of the target objects behind the
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Fig. 13. Deformation process of hierarchical core at different time points.
Fig. 14. The typical deformation mode of the hierarchical honeycomb core.
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increased with the impulse. The regular core sandwich panel had a less residual deflection in comparison with all these hierarchical counterparts when the dimensionless impulse was less than 0.05; however it intersected the hierarchical curves when the impulse was in between 0.05 and 0.06 as shown. Further, the regular honeycomb panel had a greater residual deflection than all the hierarchical counterparts when the impulse was higher than 0.06. Note that the residual deflections of the back facesheet in all these hierarchical panels tended to be nearly the same, whereas the difference of deflections between the regular and hierarchical panels became wider with increase in the impulse loading. The underlying mechanism is fairly similar to that for elucidating the maximum deflection at the center point of the back facesheet. To illustrate the influence on the deflection mode of the back facesheet, the deflections and deformation patterns in the back facesheet of the hierarchical honeycomb core ( = 0.2 ) are shown for different impulses in Fig. 12. It can be seen from Fig. 12 (a) that the maximum residual deflection on the back facesheet of the hierarchical honeycomb mainly occurred around its central area. From Fig. 12 (b), it is also clear that the deformation of the front and back facesheets mainly exhibited a global mode under different impulses. As can be seen from this figure, when the load was small, the deformation of the sandwich plate mainly occurred in the front panel and core, and no separation took place between the core and back facesheet. When the load increased, the core became densified and the back facesheet experienced larger deformation. At the same time, the back facesheet began to separate from the core. When the core layer was densified, the back facesheet started playing a main role in further energy absorption. Therefore, when the level of blast load was high, increasing energy absorption capacity of the core would be beneficial to reduce the deformation of the back facesheet. 3.1.2. Dynamic responses of the core layer The difference of these abovementioned sandwich panels was due to the different configurations of the honeycomb core, which considerably influenced the structural resistance to blast loading. This subsection will analyze the dynamic responses of the core layer in terms of the deformation mode, core compression and energy absorption. From this study, all the deformation processes of the cores were fairly similar; and Fig. 13 illustrates a typical process of core compression response, which depicts the core of hierarchical honeycomb with = 0.2 loaded by impulse of I = 0.059 . It can be seen that the core deformed at t = 159µs for a uniform blast; and the center region of the core deformed faster than the edge area. At about t = 479µs the core had been densified and the compression in the center region was most severe. A typical deformation mode of the core as reported in Ref. [1] is shown in Fig. 14. It can be seen that there were three characteristic regions that can be observed in the simulations. (1) Fully-folded region, which appeared in the center of the panel and transmitted high blast loading from the front facesheet to the back facesheet. In this region, the maximum deflection on the back facesheet appeared at the center; (2) Partially-folded region, where the curvatures of the top and bottom surfaces of the core were different, led to certain shear, in which the core would deform with both compression and shearing; (3) Clamped region, whose degree of freedoms were completely constrained to simulate the clamped frame; and thus there was actually no deformation in this region (as seen on the sides in Fig. 14). As shown in Fig. 8, it was noted that the core compression ratio of the regular honeycomb was always severe under the same impulse
Fig. 15. Comparison of energy absorption of the regular ( =0) and hierarchical ( >0) honeycomb cores under different actual impulse loadings (a) and dimensionless impulses (b).
sandwich panel [16]. A smaller residual deflection on the back facesheet is commonly regarded to be beneficial for structural safety under blast loading. As shown in Fig. 10, with increase in impulse loading, the energy absorbed by the back facesheet increased gradually. It is observed that when the impulse was less than 0.045, the energy absorbed by the back facesheet of the regular honeycomb sandwich panel was lower than those of all the hierarchical counterparts. However, when the impulse was greater than 0.055, the back facesheet in the regular honeycomb core absorbed more energy than those of the hierarchical counterparts. Interestingly, it is observed that all the back facesheet with the hierarchical cores absorbed nearly the same energy. As shown in Fig. 11, the residual deflections of the back facesheet
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Fig. 16. Comparison of structure deformation of the regular ( = 0 ) and hierarchical ( = 0.2 ) honeycomb cores.
loading. This was because the regular honeycomb core had a smaller number of cell-walls and corners, and thus it was more deformable than the hierarchical counterparts. Moreover, the core compression ratio of the regular honeycomb to hierarchical honeycomb ( = 0.1) were much higher than the others when the impulse loading is relatively small (e.g. I = 0.04 ). When the impulse reached I = 0.065, the difference of core compression ratios between the regular and hierarchical honeycombs was around 2.7–6.1%. In addition, the core compressions ratio of the hierarchical honeycomb with = 0.2, 0.3, 0.4 and 0.5 were fairly similar when the impulse varied from I = 0.035 to I = 0.065, indicating that the structural hierarchical parameter had a relatively small influence on the core compression ratio of the honeycomb sandwich panel when the blast load I < 0.065. Fig. 15 compares the energy absorption of the different core components in the honeycomb sandwich panels. It is clear that the hierarchical honeycomb core was able to absorb more energy through plastic deformation than the regular counterpart under the same impulse loading. This is because the hierarchical honeycomb core has more corners in the cross-section and a smaller folding wavelength [33], leading to more folds for absorbing energy as shown in Fig. 16. Therefore, the hierarchical honeycomb cores are able to absorb more impact energy [36] and generate much better resistance against blast loading. In order to take into account the mass of the core, the specific energy absorption (SEA) was adopted here to describe the energy absorption efficiency of the core, as,
SEA =
EA M
= 0.1, the hierarchical core yielded the highest SEA . When > 0.1, the SEA decreased with increasing . The regular honeycomb achieved a lower SEA than the hierarchical cores for = 0.1, 0.2 and 0.3, but a higher SEA for = 0.4 and 0.5 when the impulse was smaller than 0.045. When the impulse was higher than 0.06, the SEA of the regular honeycomb was higher than those of the hierarchical honeycombs except for the case of = 0.1. The SEA of the hierarchical core with = 0.1 was the highest of all the configurations simulated, which confirmed that the design region might need to be in a range of 0.06 0.2 [36]. The literature [36] stated that the honeycombs with the first- and second-order hierarchy can improve SEA in comparison with the regular honeycomb that had the same density, leading to better crashworthiness. More specifically, SEA of the hierarchical 0.2 [36]. core reached its maximum in the region of 0.06 3.2. Influence of wall thickness To explore the effects of the wall thickness, four honeycomb sandwich panels with different cell-wall thicknesses were compared for the same hierarchical parameter ( = 0.2) in this section, as seen in Table 3. 3.2.1. Dynamic responses of the back facesheets The maximum deflections at the center point of back facesheet with different wall thicknesses of hierarchical core are shown in Fig. 18 (a) for different impulses. When the impulse was less than 0.06, the thinner the wall thickness, the lower the maximum deflection. This is because that the core with a low relative density was easy to deform; and thus the core compression was greater than those with a high relative density. From Fig. 18 (b), it can be seen that at impulse I = 0.04 , the energy absorbed by the core and back facesheet of Mul0.2-H30-t0.12 (t = 0.12) is higher than that of Mul0.2-H30-t0.06 (t = 0.06) (referring the labeling system in Table 3), implying that the back facesheet of Mul0.2-H30-t0.06 generated a smaller deflection. When the impulse was greater than 0.07, the core with a low
(9)
where EA is the energy absorbed by the core and M is the mass of the core. Fig. 17 compares the SEA s of the different core configurations under different impulses. It was interesting to see that not all the SEA s of the hierarchical cores were higher than those of the regular core. When
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absorbed energy mainly by plastic deformation in the front and back facesheets; whilst for a high density core, the core could absorb substantial energy apart from the front and back facesheets. Therefore, the back facesheet contributed on relatively less energy absorption when adopting a high density core, as shown in Fig. 18 (b) (where impulse I = 0.07 ). As a result, the sandwich panel with a high density core had a lower back facesheet deflection than that with a low density core. Based upon the above analysis, it can be concluded that a thinner wall thickness (i.e. low core density) contributes to a better blast re0.06); whereas sistance (lower deflection) for a low level impulse (I 0.07). an opposition conclusion can be drawn for a high impulse (I 3.2.2. Dynamic responses of the core layer Fig. 19 exhibits the energy absorption of the core layer with different cell-wall thicknesses under different impulses. It can be seen that increase in impulse led to increase in energy absorption of the core. Under the same impulse, the thicker the cell-wall thickness, the more the energy absorption of the core. In order to investigate the capacity of the energy absorption of the cores, Fig. 20 graphed the SEA of the cores with different cell-wall thicknesses under different impulses. The SEAs of these four hierarchical cores increased with the impulse loading; and interestingly, the thinner the cell-wall thickness, the higher the SEA of the core for its lighter mass. According to Figs. 18 and 20, the energy absorption of the core with a greater wall thickness was higher, but its SEA was lower simply because of the heavier mass. 3.3. Influence of the core layer height The effect of core layer height was analyzed in this section; and three hierarchical sandwich panels with different core heights (H) were compared under different impulse loadings, where the specific structural hierarchical parameter was kept to be the same at = 0.2 . The corresponding geometric dimensions were summarized in Table 4 for clarity. 3.3.1. Dynamic responses in the back facesheets The maximum deflections at the center point of the back facesheets of the hierarchical sandwich panels were compared in Fig. 21 for different core heights under different impulses. The results showed that the maximum deflection of the back facesheet of Mul0.2-H10-t0.1 was the greatest, whilst the Mul0.2-H30-t0.1 was the smallest under the same impulse, which was somewhat similar to the study reported in Ref. [1]. To better understand the results, Fig. 22 plotted the plastic energy dissipation histories of the sandwich panels with different core heights under a large and a small impulse, respectively. In the early stage of the response, the core was compressed by the front facesheet, resulting in core crushing and significant energy dissipation. Most of the energy was dissipated by the large deformation of the front facesheet and core compression. Since the core was easier to deform, and provided
Fig. 17. Comparison of SEA of the different honeycomb cores under different actual impulse loadings (a) and dimensionless impulses (b).
relative density reached the densification stage; but the core with a high relative density could still bear further deformation to absorb blast energy. That is to say, the sandwich panel with a low density core
Table 3 Labels and parameters of the hierarchical core specimens with different honeycomb cell-wall thicknesses. Label Mul0.2-H30-t0.06 Mul0.2-H30-t0.08 Mul0.2-H30-t0.10 Mul0.2-H30-t0.12
0.2 0.2 0.2 0.2
Thickness of the cell-wall (mm)
Height of the core (mm)
Mass of the core (g)
0.06 0.08 0.10 0.12
30 30 30 30
40.99 48.97 57.24 65.50
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Fig. 18. Comparison of the maximum back facesheet deflection (a) energy absorption (b) of sandwich panel components with different cell-wall thicknesses under different impulse loads.
considerable buffering effect, the back facesheet of the sandwich with a higher core deformed less. Note that the cores of 10 mm and 30 mm absorbed the same level of energy, in which the front facesheet of Mul0.2-H30-t0.1 produced a greater deflection and absorbed more energy than that of Mul0.2-H10-t0.1.
This is because that the energies absorbed by the front and back facesheets of Mul0.2-H30-t0.1 were higher than those by Mul0.2-H20-t0.1. By taking into account the mass of the core, Fig. 25 compares the SEAs of the cores with different heights under different impulse loadings. Although the energy absorptions of all these cores were at almost the same level (Fig. 24), their SEAs were different because the masses of the cores differed. Under the same impulse loading, the SEA of Mul0.2H10-t0.1 core was the highest, whereas Mul0.2-H30-t0.1 the lowest, as shown in Fig. 25.
3.3.2. Dynamic responses in the core layer Fig. 23 shows the energy absorption of the hierarchical cores with different heights under different impulses. When the impulse loading was lower than 0.06, the energy absorbed by the hierarchical core was at almost the same level. When the impulse loading was higher than 0.06, the core of Mul0.2-H10-t0.1 absorbed the least energy, while the core of Mul0.2-H20-t0.1 absorbed the most. This can be interpreted as that when the impulse loading was larger than 0.06, the core of Mul0.2H10-t0.1 was densified, whereas the cores of Mul0.2-H20-t0.1 and Mul0.2-H30-t0.1 were not completely squeezed yet, as shown in Fig. 24. Interestingly, the core of Mul0.2-H30-t0.1 absorbed less energy than Mul0.2-H20-t0.1 when the impulse loading was higher than 0.06.
4. Conclusion The finite element analysis of the sandwich panels with hierarchical honeycomb cores was performed under impulse loading in this study. By comparing the dynamic responses of the back facesheets and the honeycomb cores, the effects of the structural hierarchical parameter , cell-wall thickness and core height on the structural resistance to blast were studied systematically.
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Fig. 19. Energy absorption of the cores with different cell-wall thicknesses under different actual impulse loadings (a) and dimensionless impulses (b).
Fig. 20. SEA of the cores with different cell-wall thicknesses under different actual impulse loadings (a) and dimensionless impulses (b).
It was found that the structural hierarchical parameter had a relatively less influence on the maximum deflection at the center points of the back facesheet, but great effects on the SEA of the cores; specifically the smaller the , the higher the SEA of the core. The maximum deflection on the back facesheet of the regular honeycomb core was smaller than those of the hierarchical honeycomb cores when the impulse was lower than 0.05, but greater when the impulse loading was higher than 0.06. The effects of cell-wall thickness of the honeycomb core were investigated by comparing the responses of the specimens with different cell-wall thicknesses (i.e. 0.6, 0.8, 1.0 and 1.2 mm). It was found that the thinner the cell-wall thickness, the higher the structural resistance to blast load if the impulse was relatively low, but the result was opposite when the impulse loading was high. The influence of the
hierarchical core height was also investigated. It was shown that while the SEA of the core of Mul0.2-H30-t0.1 was the lowest, its blast resistance was the highest. It should be pointed out that the conclusions mentioned above were drawn without considering the material failure of sandwich components. The failure behavior of sandwich structure under blast loading can be a topic of the future studies. Apart from the blast resistance, the cost performance of sandwich panels also should be considered in the future [41]. To maximize the blast resistance and minimize the production cost, design the topological hierarchy of the core structures using deterministic/uncertainty optimization algorithms can be another important tool [42–46]. It can generate a more effective explosion-proof structure through proper hierarchical architecture of core materials.
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Table 4 Labels and parameters of the hierarchical core specimens with different heights. Number Mul0.2-H10-t0.1 Mul0.2-H20-t0.1 Mul0.2-H30-t0.1
0.2 0.2 0.2
Thickness of the core (mm)
Height of the core (mm)
Mass of the core (g)
0.1 0.1 0.1
10 20 30
19.08 38.16 57.24
Fig. 22. The energy absorption history of the sandwich components with different core heights (10 mm and 30 mm) under a small and a large impulses (a) I = 0.04 (b).I = 0.065.
Fig. 21. Maximum back facesheet deflections of sandwich panels with different hierarchical core heights under different actual impulse loadings (a) and dimensionless impulses (b).
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Fig. 25. SEA of the hierarchical cores with different heights under different actual impulse loadings (a) and dimensionless impulses (b).
Fig. 23. Energy absorption of the hierarchical cores with different heights under different actual impulse loadings (a) and dimensionless impulses (b).
Acknowledgments The project was supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (51621004), Australian Research Council (ARC) Discovery Early Career Researcher Award (DECRA Recipient - Dr Guangyong Sun), ARC Discovery (DP190103752), National Natural Science Foundation of China (51575172, 11602161), Natural Science Foundation of Shanxi Province (201601D021025), and the Science Fund of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (31615008). References [1] X. Li, P. Zhang, Z. Wang, G. Wu, L. Zhao, Dynamic behavior of aluminum honeycomb sandwich panels under air blast: experiment and numerical analysis, Compos. Struct. 108 (2014) 1001–1008. [2] Pham Hon Cong, Nguyen Duy Khanh, Nguyen Dinh Khoa, Nguyen dinh Duc, New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT, Compos. Struct. 185 (2018) 455–465. [3] Gabriele Imbalzano, Steven Linforth, Tuan Duc Ngo, Peter Vee Sin Lee, Phuong Tran, Blast resistance of auxetic and honeycomb sandwich panels:
Fig. 24. Deformation pattern of cores of Mul0.2-H10-t0.1, Mul0.2-H20-t0.1 and Mul0.2-H30-t0.1 under the same impulse load of 0.06.
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[24] F. Zhu, L. Zhao, G. Lu, E. Gad, A numerical simulation of the blast impact of square metallic sandwich panels, Int. J. Impact Eng. 5 (36) (2009) 687–699. [25] F. Zhu, Z. Wang, G. Lu, L. Zhao, Analytical investigation and optimal design of sandwich panels subjected to shock loading, Mater. Des. 1 (30) (2009) 91–100. [26] M. Yamashita, M. Gotoh, Impact behavior of honeycomb structures with various cell specifications-numerical simulation and experiment, Int. J. Impact Eng. 1–4 (32) (2005) 618–630. [27] K.P. Dharmasena, H.N.G. Wadley, Z. Xue, J.W. Hutchinson, Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading, Int. J. Impact Eng. 9 (35) (2008) 1063–1074. [28] L. Deng, A.W. Wang, L.W. Mao, Dynamic Response analysis of square honeycomb sandwich plates subjected to blast loading, Appl. Mech. Mater. 477–478 (2014) 160–164. [29] G.N. Nurick, G.S. Langdon, Y. Chi, N. Jacob, Behaviour of sandwich panels subjected to intense air blast – Part 1: Experiments, Compos. Struct. 4 (91) (2009) 433–441. [30] D. Karagiozova, G.N. Nurick, G.S. Langdon, Behaviour of sandwich panels subject to intense air blasts – Part 2: numerical simulation, Compos. Struct. 4 (91) (2009) 442–450. [31] J. Xiong, Y. Du, D. Mousanezhad, et al., Sandwich structures with prismatic and foam cores: a Review, Adv. Eng. Mater. 21 (2018) 1–19. [32] B. Han, Z. Zhang, Q. Zhang, et al., Recent advances in hybrid lattice-cored sandwiches for enhanced multifunctional performance, Extreme Mech. Lett. 10 (2017) 58–69. [33] J. Fang, G. Sun, N. Qiu, et al., On hierarchical honeycombs under out-of-plane crushing, Int. J. Solids Struct. 135 (2018) 1–13. [34] A. Ajdari, B.H. Jahromi, J. Papadopoulos, H. Nayeb-Hashemi, A. Vaziri, Hierarchical honeycombs with tailorable properties, Int. J. Solids Struct. 11–12 (49) (2012) 1413–1419. [35] Y. Zhang, M. Lu, C.H. Wang, G. Sun, G. Li, Out-of-plane crashworthiness of bioinspired self-similar regular hierarchical honeycombs, Compos. Struct. 144 (2016) 1–13. [36] G. Sun, H. Jiang, J. Fang, G. Li, Q. Li, Crashworthiness of vertex based hierarchical honeycombs in out-of-plane impact, Mater. Des. 110 (2016) 705–719. [37] X.M. Xiang, G. Lu, G.W. Ma, X.Y. Li, D.W. Shu, Blast response of sandwich beams with thin-walled tubes as core, Eng. Struct. 127 (2016) 40–48. [38] X. Jin, Z. Wang, J. Ning, G. Xiao, E. Liu, X. Shu, Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading, Compos. B Eng. 106 (2016) 206–217. [39] Z. Xue, J.W. Hutchinson, A comparative study of impulse-resistant metal sandwich plates, Int. J. Impact Eng. 10 (30) (2004) 1283–1305. [40] Nurick, Shave, The deformation and tearing of thin square plates subjected to impulsive loads-An experimental study, Int. J. Impact Eng. 18 (1996) 99–116. [41] G. Sun, M. Deng, G. Zheng, Q. Li, Design for cost performance of crashworthy structures made of high strength steel, Thin-Walled Struct. 138 (2019) 458–472. [42] G. Sun, H. Yu, Z. Wang, Z. Xiao, Q. Li, Energy absorption mechanics and design optimization of CFRP/aluminium hybrid structures for transverse loading, Int. J. Mech. Sci. 150 (2019) 767–783. [43] G. Sun, T. Liu, J. Fang, G.P. Steven, Q. Li, Configurational optimization of multi-cell topologies for multiple oblique loads, Struct. Multidiscip. Optim. 57 (2) (2018) 469–488. [44] G. Sun, H. Zhang, J. Fang, G. Li, Q. Li, A new multi-objective discrete robust optimization algorithm for engineering design, Appl. Math. Model. 53 (2018) 602–621. [45] T. Liu, G. Sun, J. Fang, J. Zhang, Q. Li, Topographical design of stiffener layout for plates against blast loading using a modified ant colony optimization algorithm, Struct. Multidiscip. Optim. 58 (2) (2019) 335–350. [46] G. Sun, J. Tian, T. Liu, X. Yan, X. Huang, Crashworthiness optimization of automotive parts with tailor rolled blank, Eng. Struct. 169 (2018) 201–215.
comparisons and parametric designs, Compos. Struct. 183 (2018) 242–261. [4] Qi Chang, Alex Remennikov, Lian-Zheng Pei, Shu Yang, Zhi-Hang Yu, Tuan D. Ngo, Impact and close-in blast response of auxetic honeycomb-cored sandwich panels: experimental and numerical simulations, Compos. Struct. 180 (2017) 161–178. [5] Sameh Ahmed, Khaled Galal, Effectiveness of FRP sandwich panels for blast resistance, Compos. Struct. 163 (2017) 454–464. [6] Tangying Liu, Guangyong Sun, Jianguang Fang, Jingtao Zhang, Qing Li, Topographical design of stiffener layout for plates against blast loading using a modified ant colony optimization algorithm, Struct. Multidiscip. Optim. 59 (2) (2019) 335–350. [7] A. Vaziri, J.W. Hutchinson, Metal sandwich plates subject to intense air shocks, Int. J. Solids Struct. 6 (44) (2007) 2021–2035. [8] Julio F. Davalos, P. Qiao, Modeling and characterization of fiber-reinforced plastic honeycomb sandwich panels for highway bridge applications, Compos. Struct. 52 (2001) 441–452. [9] G. Sun, E. Wang, H. Wang, Z. Xiao, Q. Li, Low-velocity impact behaviour of sandwich panels with homogeneous and stepwise graded foam cores, Mater. Des. 60 (2018) 1117–1136. [10] G. Sun, D. Chen, H. Wang, P. Hazell, Q. Li, High-velocity impact behaviour of aluminium honeycomb sandwich panels with different structural configurations, Int. J. Impact Eng. 122 (2018) 119–136. [11] J. Zhang, R. Zhou, M. Wang, Q. Qin, Y. Ye, T. Wang, Dynamic response of doublelayer rectangular sandwich plates with metal foam cores subjected to blast loading, Int. J. Impact Eng. 122 (2018) 265–275. [12] G. Sun, X. Huo, D. Chen, Q. Li, Experimental and numerical study on honeycomb sandwich panels under bending and in-panel compression, Mater. Des. 133 (2017) 154–168. [13] G. Sun, D. Chen, X. Huo, G. Zheng, Q. Li, Experimental and numerical studies on indentation and perforation characteristics of honeycomb sandwich panels, Compos. Struct. 184 (2018) 110–124. [14] Q. Qin, X. Zheng, J. Zhang, C. Yuan, T. Wang, Dynamic response of square sandwich plates with a metal foam core subjected to low-velocity impact, Int. J. Impact Eng. 111 (2018) 222–235. [15] Z. Sun, D. Li, W. Zhang, S. Shi, X. Guo, Topological optimization of biomimetic sandwich structures with hybrid core and CFRP face sheets, Compos. Sci. Technol. 142 (2017) 79–90. [16] M. Rashad, T.Y. Yang, Numerical study of steel sandwich plates with RPF and VR cores materials under free air blast loads, Steel Compos. Struct. 27 (6) (2018) 717–725. [17] S. Li, G. Lu, Z. Wang, L. Zhao, G. Wu, Finite element simulation of metallic cylindrical sandwich shells with graded aluminum tubular cores subjected to internal blast loading, Int. J. Mech. Sci. 96–97 (2015) 1–12. [18] S. Li, Z. Wang, G. Wu, L. Zhao, X. Li, Dynamic response of sandwich spherical shell with graded metallic foam cores subjected to blast loading, Compos. Appl. Sci. Manuf. 56 (2014) 262–271. [19] Y.A. Khalifa, W.W. El-Dakhakhni, M. Campidelli, M.J. Tait, Performance assessment of metallic sandwich panels under quasi-static loading, Eng. Struct. 158 (2018) 79–94. [20] Manmohan Dass Goel, V.A. Matsagar, Anil K. Gupta, Blast resistance of stiffened sandwich panels with aluminum cenosphere syntactic foam, Int. J. Impact Eng. 77 (2015) 134–146. [21] W. Huang, W. Zhang, N. Ye, Y. Gao, P. Ren, Dynamic response and failure of PVC foam core metallic sandwich subjected to underwater impulsive loading, Compos. B Eng. 97 (2016) 226–238. [22] J. Wang, C. Shi, N. Yang, et al., Strength, stiffness, and panel peeling strength of carbon fiber-reinforced composite sandwich structures with aluminum honeycomb cores for vehicle body, Compos. Struct. 184 (2018) 1189–1196. [23] Y. Chi, G.S. Langdon, G.N. Nurick, The influence of core height and face plate thickness on the response of honeycomb sandwich panels subjected to blast loading, Mater. Des. 4 (31) (2010) 1887–1899.
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Full length article
Dynamic response of sandwich panel with hierarchical honeycomb cores subject to blast loading
T
Guangyong Suna,b,∗, Jingtao Zhanga, Shiqiang Lia,c, Jianguang Fangb, Erdong Wanga, Qing Lib a
State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, China School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia c Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China b
ARTICLE INFO
ABSTRACT
Keywords: Sandwich panel Hierarchical structure Blast resistance Energy absorption Impulse loadings Explosion-proof structure
This paper introduces a novel hierarchical core structure to sandwich panel for bearing the blast loading, in which each vertex of a regular hexagonal cell was replaced with a smaller hexagonal unit. The finite element (FE) models of such hierarchical honeycomb sandwich panels were established and validated with the experiments under different impulse loads. The hierarchical honeycomb cores were compared with the regular honeycomb counterpart in terms of the peak deflection on the back facesheet, compression and specific energy absorption (SEA) of the core. The results showed that the maximum deflection at the back facesheet of the hierarchical honeycomb sandwich panels were smaller than the regular honeycomb counterpart for a higher level of blast load (specifically, the dimensionless impulse higher than 0.06). It was found that the structural hierarchical parameter (i.e. the ratio of the newly-introduced smaller hexagonal edge length (L1) to the regular hexagon edge length (L0)), had limited influence on the maximum deflection of back facesheet of the sandwich panel, but had a significant effect on the SEA of the cores.
1. Introduction Blast is a major threat to structural safety and public security, which has drawn extensive attention all over the world recently. To address this issue, numerous studies have been conducted to improve the blast resistance of vehicles and buildings. In this regard, explosion-proof structures have proven to be effective in reducing blast impact, thereby protecting vehicles and buildings from devastating damage. As a class of explosion-proof structures which are able to dissipate sizable explosive energy through large plastic deformation under impact/blast loading [1–6], sandwich panels have been extensively used in a broad range of areas, such as aerospace, automotive, marine, defense and railway industry [7–10]. They have exhibited compelling advantages, such as high strength-to-weight ratio, high stiffness-to-weight ratio, high thermal isolation capacity, and excellent energy absorption and structural protection characteristics [11–15].
∗
To date, polymeric foams, honeycombs, metallic foams and functionally graded materials have been used as the core fillers of sandwich structures for explosion-proof applications, attributable to their lightweight, energy absorption efficiency, and high specific stiffness [16–21]. In these candidate materials, the aluminum honeycomb has exhibited superior performance in the compressive modulus and shear strength [22]. From the mechanical point of view, it is very similar to the I-beam with enhanced overall structural stiffness, stability, compressive capacity and bending characteristics. There have been substantial studies on the blast resistance of regular honeycomb sandwich plates based upon experiment, simulation and analysis [23–30]. For example, Chi et al. [23] studied a circular sandwich panel with an aluminum honeycomb core subjected to blast loadings by analyzing the influence of core height and facesheet thickness experimentally. Zhu et al. [24] performed the FE simulations to investigate the effects of blast loading and responses of honeycomb
Corresponding author. State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, China. E-mail address: [email protected] (G. Sun).
https://doi.org/10.1016/j.tws.2019.04.029 Received 17 October 2018; Received in revised form 1 April 2019; Accepted 15 April 2019 Available online 05 July 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
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sandwich panels in terms of deformation/failure modes and the deflection in the back facesheet. Yamashita and Gotoh [26] investigated the effects of the cell shape and foil thickness on the crush behavior; and showed that the crush strength was higher for a smaller branch angle and a greater thickness. Dharmasena et al. [27] compared the energy absorption of sandwich panels with the solid plates that have the same areal density under three levels of impulse loads; and they found that the cellular wall buckling and core densification increased with the impulse loading. From these abovementioned studies, the mechanical characteristics of the regular honeycomb sandwich panels have been explored extensively for their broad applications in engineering practice [31,32], but the investigation into a hierarchical honeycomb core is rare. The hierarchical honeycomb structures have been studied for its appealing lightweight potential and superior mechanical characteristics [33–36]. For example, Fang et al. [33] systematically studied the hierarchical honeycomb for outof-plane crash using the experimental, analytical and numerical
approaches; further showing the crashworthiness features and benefits of multi-level structural hierarchy. Ajdari et al. [34] investigated the hierarchical honeycomb structures using the analytical, numerical and experimental methods; and they found that the first- and second-order hierarchical honeycombs can be 2.0 and 3.5 times stiffer than a regular honeycomb with the same mass. Zhang et al. [35] modeled hierarchical honeycombs (the 1st and 2nd order hierarchies) under an impact loading. The results exhibited that the hierarchical honeycomb could improve the crushing strength and crushing force of the honeycomb sandwiches effectively. To enhance the crashing characteristics of the hierarchical honeycombs, Sun et al. [36] investigated the first- and second-order hierarchical configurations under an “out-of-plane” loading. The results demonstrated that the specific energy absorptions (SEA) of the first- and second-order hierarchical honeycombs could be enhanced by 81.3% and 185.7%, respectively. These preliminary studies demonstrated that the hierarchical honeycombs have substantially better crashworthiness behaviors.
Fig. 1. (a) Top view of honeycombs (b) Single unit-cell of regular honeycomb and hierarchical honeycomb (c) 3D view of regular honeycomb and hierarchical honeycomb.
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Fig. 2. Symmetric model of the sandwich panel for blast loading.
While the hierarchical honeycomb structures have exhibited superior mechanical characteristics, to the authors’ best knowledge, their resistance to blast loading has not been explored to date. The present study aimed to fill this knowledge gap by scrutinizing the resistance of sandwich panels with a novel hierarchical honeycomb core to the impulse loadings. The 3D finite element (FE) model of the honeycomb sandwich panel was first created and validated against the experimental results. The effects of the loading intensity and hierarchical core configuration on the back-panel deflection and energy absorption were quantified. It showed that the blast resistance of the hierarchical honeycomb sandwich panel is superior to the regular honeycomb core. This new core structure is expected to substantially enhance the sandwich capacity of explosion proof for various applications.
0
Note that = 0 downgrades to a regular honeycomb. The sandwich panel to be investigated here consists of steel front facesheet, steel back facesheet and aluminum honeycomb core, as shown in Fig. 2(a). In this study, all the parameters of the honeycomb sandwich panels are summarized in Table 1. And all the honeycomb sandwich panels were of a square shape and had the same overall area of W × W and the same effective area of W1 × W1, which was exposed to the impulsive load as illustrated in Fig. 2(b). 2.2. Finite element model The numerical simulations were conducted by using explicit nonlinear FE code LS-DYNA 971. The FE model comprised two facesheets and a core layer with either a regular honeycomb or a hierarchical honeycomb structure. Due to the symmetry of the sandwich panel and blast loading, only 1/2 of the sandwich panels were modeled to reduce the computational cost. Thus a symmetric boundary condition about the y-z plane was imposed, as shown in Fig. 2 (a). Further, the boundaries of all the sandwich components were fully clamped through the nodal constraints without deformation, and the area of boundary conditions are shown in Fig. 2 (b). In FE modeling, the Belytschko-Tasy shell elements were used for both the honeycomb cell foils and facesheets. A convergence test was conducted, and the deflection history of the central point on the front facesheet was selected to be a criterion as suggested in Refs. [1,37]. Five different mesh sizes, specifically 0.6, 0.8, 1.0, 1.2 and 1.4 mm, were employed, respectively. Fig. 3 shows the histories of the deflection at the central point of the front facesheet, which indicated that 1 mm mesh size was sufficient to balance the simulation accuracy and computational efficiency.
2. Structural configurations and finite element model 2.1. Geometric description According to Ajdari et al.'s work [34], we proposed to replace each three-edge vertex of a regular hexagonal lattice with a smaller hexagon to obtain the hierarchical honeycombs, as illustrated in Fig. 1. A specific structural organization parameter ( ) that defines the hierarchical honeycomb in relation to the regular configuration was introduced in terms of the ratio of newly proposed hierarchical hexagonal side length (L1) to the original side length (L0 = 10mm ) of the regular hexagon, i.e., = L1/ L 0 , as illustrated in Fig. 1. To avoid overlapping with the original edges, some geometric constraints must be imposed as,
0
L1
(1)
L 0 /2
(2)
0.5
which leads to Table 1 The parameters of the sandwich panels. Parameters
Thicknesses of front facesheet (tf) 1.6 mm
Thicknesses of back facesheet (tb) 1.6 mm
Core height (H) 30 mm
501
wall thickness (t) 0.1 mm
Overall area (W × W) 300 × 300 mm
2
Effective area (W1× W1) 250 × 250 mm2
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Automatic surface-to-surface contact was defined in between the honeycomb core and the facesheets. The automatic single surface contact was adopted for modeling the self-contact of honeycomb foil surfaces. The static and dynamic friction coefficients were set to be 0.3 and 0.2, respectively [1]. In the FE simulations, the facesheets and honeycomb were modeled in LS-DYNA material Type 3. The material properties of the steel facesheets and aluminum core were taken from the literature [20,24], respectively. Herein, we assume that those materials are sufficiently plastic to resist the failure under blast loading. The facesheets were made of the mild steel, whose strain rate effect was accounted using the Cowper and Symonds model [18]. Thus, the yield stress was calculated mathematically as: 0 0
=1+
1/
C
(3)
where 0 is the dynamic flow stress; 0 is the initial yield stress, is the equivalent strain rate. The material properties of the mild steel facesheet material include the density st = 7800kg/m3, Poisson's ratio
Fig. 3. Mesh size sensitivity for the deflection at the central front facesheet.
Fig. 4. Comparison of the FE simulation with the experimental results [29].
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G. Sun, et al. st = 0.3, Young's modulus Est = 210GPa , and yield stress st = 300MPa [20]. The rate parameters of mild steel, i.e. C = 40.4 s−1 and α = 5 [37], were adopted to simulate the strain-rate effect of the facesheet materials in the blast simulations. The honeycombs were made of aluminum alloy and the strain rate is neglected for its insensitivity in general [24,38] in this study. The density of the honeycomb core material (aluminum alloy A5052) is 3 Poisson's ratio Young's modulus Al = 0.33 , Al = 2680kg/m , EAl = 70GPa , and yield stress Al = 265MPa [24]. In this study, a uniformly distributed blast loading, as reported in literature [30], was applied to be a pressure pulse on the front facesheet of the sandwich panel. The pressure is described in terms of time as follows:
p (t ) = p0 e
with the experiments of regular honeycomb core under the blast loads as reported in literature e.g. Refs. [29,30]. A regular honeycomb can be considered as a zeroth order hierarchy with = L1/ L 0 = 0 . The dimension of the experimental honeycomb specimens was 244 × 244 × 1.6 mm, whose facesheets were also made of mild steel square plates and core was made of aluminum alloy. Since the facesheets were not adhered to the honeycomb surfaces in the experiments, the energy absorption due to debonding was neglected. All the specimens had a circular explosive area of diameter 106 mm. The impulse was obtained using the measured swing of the pendulum. A uniformly distributed blast loading was applied as a pressure pulse on the frontal facesheet of the sandwich panel. The pressure was depicted in Eq. (4). The pressure pulses were defined in terms of the
(4)
t/t 0
where p0 is the initial pressure, and obviously, the pressure decays exponentially with a decay period of t 0 = 50µs . The impulse was defined as follows
I0 = W12
0
p (t ) dt
(5)
where W1 is the characteristic length of effective area of the sandwich panel, and the unit of the impulse is N⋅s. 2.3. Validation of the FE model As no in-house experimental tests have been conducted for the sandwich panel with a hierarchical aluminum honeycomb core under the blast loading, the FE model was validated through a comparison Table 2 The mass of hierarchical honeycomb core for different hierarchical parameters. Label
Hierarchical parameter
Mass of the core (g)
0 1–0.1 1–0.2 1–0.3 1–0.4 1–0.5
0 0.1 0.2 0.3 0.4 0.5
40.99 48.97 57.24 65.50 72.86 80.49
Fig. 6. Comparison of the maximum back facesheet deflections of the regular ( = 0 ) and hierarchical ( > 0 ) honeycomb sandwiches under different actual impulse loadings (a) and dimensionless impulses (b).
Fig. 5. Plot of the maximum and residual deflection at different time points.
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momentum conservation, as
I0 = R2
0
p (t ) dt
(6)
where R is the radius of the explosive area, and R = 53mm here. The impulses used in the validation varied from 4.4 N⋅s to 30.3 N s. A comparison between the experimental results [29] and the numerical simulations is shown in Fig. 4 (a), which graphed the maximum deflections ( max ) in the back facesheet of sandwich panels under different impulse loadings (I0 ). It is clear that the predicted FE results matched with the experimental results fairly well. Further, the deformation modes of sandwich core were compared in Fig. 4(b) for the experimental and numerical results, which agreed with one another very well. Thus, it was confident that the material model, contact algorithms, element type and size, boundary conditions, etc. adopted in the finite element model were sufficiently suitable for predicting the blasting responses of sandwich panels with hierarchical honeycomb cores. The validated numerical model could be extended to explore the blast resistance of sandwich panels under the relative large impulse range (100–300 N s) because they adopted the same modeling method.
Fig. 7. Comparison of the energy absorption in the back facesheet of the regular ( = 0 ) and hierarchical honeycomb with = 0.2 sandwich panels under a low impulse ( I = 0.04 ).
3. Results and discussion 3.1. Effects of structural hierarchical parameter In order to investigate the effects of hierarchical parameter on the blast resistance of the sandwich panel, was varied from 0.1 to 0.5 with an increment of 0.1 for the hierarchical honeycomb core. The corresponding mass of hierarchical honeycomb core was given in Table 2. The dynamic responses of the sandwich panel were quantified in terms of the maximum deflection, residual deflection, energy absorption in the back facesheet, as well as the deformation mode and energy absorption of the core here. The difference between the maximum deflection and residual deflection is illustrated in Fig. 5. Generally, the terrorist bombing in real life are often occurred under in a relatively large impulse. To explore the blast resistance of the regular and hierarchical honeycomb core sandwich structures under a relatively large impulse, the impulses in the following parametric analysis will be varied from 100 N s to 300 N s. 3.1.1. Dynamic responses of the back facesheet As a protective structure, sandwich panel is expected to assure and/ or maximize the safety of the targets behind the back facesheet. Thus, the maximum deflection of the center point of the back facesheet was
Fig. 9. Comparison of the energy absorption in the back facesheet of the regular ( = 0 ) and hierarchical honeycomb with = 0.2 sandwich panels under a high impulse (I = 0.07 ).
Fig. 8. Maximum core compression at the center point of back facesheet under different actual impulse loadings (a) and dimensionless impulses (b). 504
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Fig. 10. Comparison of the energy absorption by the back facesheet under different actual impulse loadings (a) and dimensionless impulses (b). Fig. 11. Comparison of the residual deflections of the back facesheet under different actual impulse loadings (a) and dimensionless impulses (b).
selected as a key indicator for assessing the structural resistance to the blast loading. The impulses and the deflections in the FE simulations were presented in a dimensionless form herein, similarly to Ref. [39], as,
I =
=
maximum deflection of the center point in the back facesheet, and W 1 is the characteristic length of the sandwich structure in the effective explosion area. To characterize the deformation of sandwich panels, Nurick and Shave [40] first identified three failure modes observed in the blastloaded plates, namely, Mode I: large ductile deformation; Mode II: tensile-tearing and deformation; and Mode III: transverse shear failure. In this present study, the back facesheet showed a typical Mode I response with substantial ductile deformation. The maximum deflections at the center point of the back facesheet of the regular and hierarchical
I0 m max
W1
y/
(7) (8)
where m is the mass per unit area of the sandwich, y is the yield stress of the core aluminum, is the density of core aluminum, max is the
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Fig. 12. Deflections (a) and deformation (b) process of hierarchical honeycomb cores under different impulse loadings.
honeycomb panel were graphed in Fig. 6 for the different impulse loadings considered here. When the dimensionless impulse I was less than 0.05, the maximum deflection of the back facesheet of the regular honeycomb panel was much smaller than that of the hierarchical honeycomb sandwich panels. This is because the core of the regular honeycomb has less number of cell-walls and is more deformable in comparison with the hierarchical counterparts; as a result, the regular honeycomb panel yielded a greater front facesheet deflection and more severe deformation in the core, making these two components absorb more energy. Consequently, this led to a smaller deflection and less energy absorption in the back facesheet of the regular honeycomb panel, as shown in Fig. 7. When the impulse is large (e.g. I = 0.07 ), the compression ratio of core (defined as the ratio of core compression to core original height) of
the regular honeycomb sandwich panel is greater than the compression ratios of hierarchical honeycomb cores, as shown in Fig. 8. In such loading levels, the regular honeycomb panel absorbed the blast energy mainly by plastic deformation in the front and back facesheets. In contrast, the cores of the hierarchical honeycomb were able to absorb considerable energy in addition to the front and back facesheets. This contributed on relatively less energy absorption in the back facesheet as shown in Fig. 9. Thus, the back facesheet deflections of the hierarchical honeycomb sandwich panels were smaller than that of the regular honeycomb panel. Figs. 10 and 11 show the energy absorption and residual deflections, also known as plastic deflections of the back facesheets, under several different impulses, respectively. The residual deflection is an important indicator for measuring the protection of the target objects behind the
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Fig. 13. Deformation process of hierarchical core at different time points.
Fig. 14. The typical deformation mode of the hierarchical honeycomb core.
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increased with the impulse. The regular core sandwich panel had a less residual deflection in comparison with all these hierarchical counterparts when the dimensionless impulse was less than 0.05; however it intersected the hierarchical curves when the impulse was in between 0.05 and 0.06 as shown. Further, the regular honeycomb panel had a greater residual deflection than all the hierarchical counterparts when the impulse was higher than 0.06. Note that the residual deflections of the back facesheet in all these hierarchical panels tended to be nearly the same, whereas the difference of deflections between the regular and hierarchical panels became wider with increase in the impulse loading. The underlying mechanism is fairly similar to that for elucidating the maximum deflection at the center point of the back facesheet. To illustrate the influence on the deflection mode of the back facesheet, the deflections and deformation patterns in the back facesheet of the hierarchical honeycomb core ( = 0.2 ) are shown for different impulses in Fig. 12. It can be seen from Fig. 12 (a) that the maximum residual deflection on the back facesheet of the hierarchical honeycomb mainly occurred around its central area. From Fig. 12 (b), it is also clear that the deformation of the front and back facesheets mainly exhibited a global mode under different impulses. As can be seen from this figure, when the load was small, the deformation of the sandwich plate mainly occurred in the front panel and core, and no separation took place between the core and back facesheet. When the load increased, the core became densified and the back facesheet experienced larger deformation. At the same time, the back facesheet began to separate from the core. When the core layer was densified, the back facesheet started playing a main role in further energy absorption. Therefore, when the level of blast load was high, increasing energy absorption capacity of the core would be beneficial to reduce the deformation of the back facesheet. 3.1.2. Dynamic responses of the core layer The difference of these abovementioned sandwich panels was due to the different configurations of the honeycomb core, which considerably influenced the structural resistance to blast loading. This subsection will analyze the dynamic responses of the core layer in terms of the deformation mode, core compression and energy absorption. From this study, all the deformation processes of the cores were fairly similar; and Fig. 13 illustrates a typical process of core compression response, which depicts the core of hierarchical honeycomb with = 0.2 loaded by impulse of I = 0.059 . It can be seen that the core deformed at t = 159µs for a uniform blast; and the center region of the core deformed faster than the edge area. At about t = 479µs the core had been densified and the compression in the center region was most severe. A typical deformation mode of the core as reported in Ref. [1] is shown in Fig. 14. It can be seen that there were three characteristic regions that can be observed in the simulations. (1) Fully-folded region, which appeared in the center of the panel and transmitted high blast loading from the front facesheet to the back facesheet. In this region, the maximum deflection on the back facesheet appeared at the center; (2) Partially-folded region, where the curvatures of the top and bottom surfaces of the core were different, led to certain shear, in which the core would deform with both compression and shearing; (3) Clamped region, whose degree of freedoms were completely constrained to simulate the clamped frame; and thus there was actually no deformation in this region (as seen on the sides in Fig. 14). As shown in Fig. 8, it was noted that the core compression ratio of the regular honeycomb was always severe under the same impulse
Fig. 15. Comparison of energy absorption of the regular ( =0) and hierarchical ( >0) honeycomb cores under different actual impulse loadings (a) and dimensionless impulses (b).
sandwich panel [16]. A smaller residual deflection on the back facesheet is commonly regarded to be beneficial for structural safety under blast loading. As shown in Fig. 10, with increase in impulse loading, the energy absorbed by the back facesheet increased gradually. It is observed that when the impulse was less than 0.045, the energy absorbed by the back facesheet of the regular honeycomb sandwich panel was lower than those of all the hierarchical counterparts. However, when the impulse was greater than 0.055, the back facesheet in the regular honeycomb core absorbed more energy than those of the hierarchical counterparts. Interestingly, it is observed that all the back facesheet with the hierarchical cores absorbed nearly the same energy. As shown in Fig. 11, the residual deflections of the back facesheet
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Fig. 16. Comparison of structure deformation of the regular ( = 0 ) and hierarchical ( = 0.2 ) honeycomb cores.
loading. This was because the regular honeycomb core had a smaller number of cell-walls and corners, and thus it was more deformable than the hierarchical counterparts. Moreover, the core compression ratio of the regular honeycomb to hierarchical honeycomb ( = 0.1) were much higher than the others when the impulse loading is relatively small (e.g. I = 0.04 ). When the impulse reached I = 0.065, the difference of core compression ratios between the regular and hierarchical honeycombs was around 2.7–6.1%. In addition, the core compressions ratio of the hierarchical honeycomb with = 0.2, 0.3, 0.4 and 0.5 were fairly similar when the impulse varied from I = 0.035 to I = 0.065, indicating that the structural hierarchical parameter had a relatively small influence on the core compression ratio of the honeycomb sandwich panel when the blast load I < 0.065. Fig. 15 compares the energy absorption of the different core components in the honeycomb sandwich panels. It is clear that the hierarchical honeycomb core was able to absorb more energy through plastic deformation than the regular counterpart under the same impulse loading. This is because the hierarchical honeycomb core has more corners in the cross-section and a smaller folding wavelength [33], leading to more folds for absorbing energy as shown in Fig. 16. Therefore, the hierarchical honeycomb cores are able to absorb more impact energy [36] and generate much better resistance against blast loading. In order to take into account the mass of the core, the specific energy absorption (SEA) was adopted here to describe the energy absorption efficiency of the core, as,
SEA =
EA M
= 0.1, the hierarchical core yielded the highest SEA . When > 0.1, the SEA decreased with increasing . The regular honeycomb achieved a lower SEA than the hierarchical cores for = 0.1, 0.2 and 0.3, but a higher SEA for = 0.4 and 0.5 when the impulse was smaller than 0.045. When the impulse was higher than 0.06, the SEA of the regular honeycomb was higher than those of the hierarchical honeycombs except for the case of = 0.1. The SEA of the hierarchical core with = 0.1 was the highest of all the configurations simulated, which confirmed that the design region might need to be in a range of 0.06 0.2 [36]. The literature [36] stated that the honeycombs with the first- and second-order hierarchy can improve SEA in comparison with the regular honeycomb that had the same density, leading to better crashworthiness. More specifically, SEA of the hierarchical 0.2 [36]. core reached its maximum in the region of 0.06 3.2. Influence of wall thickness To explore the effects of the wall thickness, four honeycomb sandwich panels with different cell-wall thicknesses were compared for the same hierarchical parameter ( = 0.2) in this section, as seen in Table 3. 3.2.1. Dynamic responses of the back facesheets The maximum deflections at the center point of back facesheet with different wall thicknesses of hierarchical core are shown in Fig. 18 (a) for different impulses. When the impulse was less than 0.06, the thinner the wall thickness, the lower the maximum deflection. This is because that the core with a low relative density was easy to deform; and thus the core compression was greater than those with a high relative density. From Fig. 18 (b), it can be seen that at impulse I = 0.04 , the energy absorbed by the core and back facesheet of Mul0.2-H30-t0.12 (t = 0.12) is higher than that of Mul0.2-H30-t0.06 (t = 0.06) (referring the labeling system in Table 3), implying that the back facesheet of Mul0.2-H30-t0.06 generated a smaller deflection. When the impulse was greater than 0.07, the core with a low
(9)
where EA is the energy absorbed by the core and M is the mass of the core. Fig. 17 compares the SEA s of the different core configurations under different impulses. It was interesting to see that not all the SEA s of the hierarchical cores were higher than those of the regular core. When
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absorbed energy mainly by plastic deformation in the front and back facesheets; whilst for a high density core, the core could absorb substantial energy apart from the front and back facesheets. Therefore, the back facesheet contributed on relatively less energy absorption when adopting a high density core, as shown in Fig. 18 (b) (where impulse I = 0.07 ). As a result, the sandwich panel with a high density core had a lower back facesheet deflection than that with a low density core. Based upon the above analysis, it can be concluded that a thinner wall thickness (i.e. low core density) contributes to a better blast re0.06); whereas sistance (lower deflection) for a low level impulse (I 0.07). an opposition conclusion can be drawn for a high impulse (I 3.2.2. Dynamic responses of the core layer Fig. 19 exhibits the energy absorption of the core layer with different cell-wall thicknesses under different impulses. It can be seen that increase in impulse led to increase in energy absorption of the core. Under the same impulse, the thicker the cell-wall thickness, the more the energy absorption of the core. In order to investigate the capacity of the energy absorption of the cores, Fig. 20 graphed the SEA of the cores with different cell-wall thicknesses under different impulses. The SEAs of these four hierarchical cores increased with the impulse loading; and interestingly, the thinner the cell-wall thickness, the higher the SEA of the core for its lighter mass. According to Figs. 18 and 20, the energy absorption of the core with a greater wall thickness was higher, but its SEA was lower simply because of the heavier mass. 3.3. Influence of the core layer height The effect of core layer height was analyzed in this section; and three hierarchical sandwich panels with different core heights (H) were compared under different impulse loadings, where the specific structural hierarchical parameter was kept to be the same at = 0.2 . The corresponding geometric dimensions were summarized in Table 4 for clarity. 3.3.1. Dynamic responses in the back facesheets The maximum deflections at the center point of the back facesheets of the hierarchical sandwich panels were compared in Fig. 21 for different core heights under different impulses. The results showed that the maximum deflection of the back facesheet of Mul0.2-H10-t0.1 was the greatest, whilst the Mul0.2-H30-t0.1 was the smallest under the same impulse, which was somewhat similar to the study reported in Ref. [1]. To better understand the results, Fig. 22 plotted the plastic energy dissipation histories of the sandwich panels with different core heights under a large and a small impulse, respectively. In the early stage of the response, the core was compressed by the front facesheet, resulting in core crushing and significant energy dissipation. Most of the energy was dissipated by the large deformation of the front facesheet and core compression. Since the core was easier to deform, and provided
Fig. 17. Comparison of SEA of the different honeycomb cores under different actual impulse loadings (a) and dimensionless impulses (b).
relative density reached the densification stage; but the core with a high relative density could still bear further deformation to absorb blast energy. That is to say, the sandwich panel with a low density core
Table 3 Labels and parameters of the hierarchical core specimens with different honeycomb cell-wall thicknesses. Label Mul0.2-H30-t0.06 Mul0.2-H30-t0.08 Mul0.2-H30-t0.10 Mul0.2-H30-t0.12
0.2 0.2 0.2 0.2
Thickness of the cell-wall (mm)
Height of the core (mm)
Mass of the core (g)
0.06 0.08 0.10 0.12
30 30 30 30
40.99 48.97 57.24 65.50
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Fig. 18. Comparison of the maximum back facesheet deflection (a) energy absorption (b) of sandwich panel components with different cell-wall thicknesses under different impulse loads.
considerable buffering effect, the back facesheet of the sandwich with a higher core deformed less. Note that the cores of 10 mm and 30 mm absorbed the same level of energy, in which the front facesheet of Mul0.2-H30-t0.1 produced a greater deflection and absorbed more energy than that of Mul0.2-H10-t0.1.
This is because that the energies absorbed by the front and back facesheets of Mul0.2-H30-t0.1 were higher than those by Mul0.2-H20-t0.1. By taking into account the mass of the core, Fig. 25 compares the SEAs of the cores with different heights under different impulse loadings. Although the energy absorptions of all these cores were at almost the same level (Fig. 24), their SEAs were different because the masses of the cores differed. Under the same impulse loading, the SEA of Mul0.2H10-t0.1 core was the highest, whereas Mul0.2-H30-t0.1 the lowest, as shown in Fig. 25.
3.3.2. Dynamic responses in the core layer Fig. 23 shows the energy absorption of the hierarchical cores with different heights under different impulses. When the impulse loading was lower than 0.06, the energy absorbed by the hierarchical core was at almost the same level. When the impulse loading was higher than 0.06, the core of Mul0.2-H10-t0.1 absorbed the least energy, while the core of Mul0.2-H20-t0.1 absorbed the most. This can be interpreted as that when the impulse loading was larger than 0.06, the core of Mul0.2H10-t0.1 was densified, whereas the cores of Mul0.2-H20-t0.1 and Mul0.2-H30-t0.1 were not completely squeezed yet, as shown in Fig. 24. Interestingly, the core of Mul0.2-H30-t0.1 absorbed less energy than Mul0.2-H20-t0.1 when the impulse loading was higher than 0.06.
4. Conclusion The finite element analysis of the sandwich panels with hierarchical honeycomb cores was performed under impulse loading in this study. By comparing the dynamic responses of the back facesheets and the honeycomb cores, the effects of the structural hierarchical parameter , cell-wall thickness and core height on the structural resistance to blast were studied systematically.
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Fig. 19. Energy absorption of the cores with different cell-wall thicknesses under different actual impulse loadings (a) and dimensionless impulses (b).
Fig. 20. SEA of the cores with different cell-wall thicknesses under different actual impulse loadings (a) and dimensionless impulses (b).
It was found that the structural hierarchical parameter had a relatively less influence on the maximum deflection at the center points of the back facesheet, but great effects on the SEA of the cores; specifically the smaller the , the higher the SEA of the core. The maximum deflection on the back facesheet of the regular honeycomb core was smaller than those of the hierarchical honeycomb cores when the impulse was lower than 0.05, but greater when the impulse loading was higher than 0.06. The effects of cell-wall thickness of the honeycomb core were investigated by comparing the responses of the specimens with different cell-wall thicknesses (i.e. 0.6, 0.8, 1.0 and 1.2 mm). It was found that the thinner the cell-wall thickness, the higher the structural resistance to blast load if the impulse was relatively low, but the result was opposite when the impulse loading was high. The influence of the
hierarchical core height was also investigated. It was shown that while the SEA of the core of Mul0.2-H30-t0.1 was the lowest, its blast resistance was the highest. It should be pointed out that the conclusions mentioned above were drawn without considering the material failure of sandwich components. The failure behavior of sandwich structure under blast loading can be a topic of the future studies. Apart from the blast resistance, the cost performance of sandwich panels also should be considered in the future [41]. To maximize the blast resistance and minimize the production cost, design the topological hierarchy of the core structures using deterministic/uncertainty optimization algorithms can be another important tool [42–46]. It can generate a more effective explosion-proof structure through proper hierarchical architecture of core materials.
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Table 4 Labels and parameters of the hierarchical core specimens with different heights. Number Mul0.2-H10-t0.1 Mul0.2-H20-t0.1 Mul0.2-H30-t0.1
0.2 0.2 0.2
Thickness of the core (mm)
Height of the core (mm)
Mass of the core (g)
0.1 0.1 0.1
10 20 30
19.08 38.16 57.24
Fig. 22. The energy absorption history of the sandwich components with different core heights (10 mm and 30 mm) under a small and a large impulses (a) I = 0.04 (b).I = 0.065.
Fig. 21. Maximum back facesheet deflections of sandwich panels with different hierarchical core heights under different actual impulse loadings (a) and dimensionless impulses (b).
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Fig. 25. SEA of the hierarchical cores with different heights under different actual impulse loadings (a) and dimensionless impulses (b).
Fig. 23. Energy absorption of the hierarchical cores with different heights under different actual impulse loadings (a) and dimensionless impulses (b).
Acknowledgments The project was supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (51621004), Australian Research Council (ARC) Discovery Early Career Researcher Award (DECRA Recipient - Dr Guangyong Sun), ARC Discovery (DP190103752), National Natural Science Foundation of China (51575172, 11602161), Natural Science Foundation of Shanxi Province (201601D021025), and the Science Fund of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (31615008). References [1] X. Li, P. Zhang, Z. Wang, G. Wu, L. Zhao, Dynamic behavior of aluminum honeycomb sandwich panels under air blast: experiment and numerical analysis, Compos. Struct. 108 (2014) 1001–1008. [2] Pham Hon Cong, Nguyen Duy Khanh, Nguyen Dinh Khoa, Nguyen dinh Duc, New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT, Compos. Struct. 185 (2018) 455–465. [3] Gabriele Imbalzano, Steven Linforth, Tuan Duc Ngo, Peter Vee Sin Lee, Phuong Tran, Blast resistance of auxetic and honeycomb sandwich panels:
Fig. 24. Deformation pattern of cores of Mul0.2-H10-t0.1, Mul0.2-H20-t0.1 and Mul0.2-H30-t0.1 under the same impulse load of 0.06.
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[24] F. Zhu, L. Zhao, G. Lu, E. Gad, A numerical simulation of the blast impact of square metallic sandwich panels, Int. J. Impact Eng. 5 (36) (2009) 687–699. [25] F. Zhu, Z. Wang, G. Lu, L. Zhao, Analytical investigation and optimal design of sandwich panels subjected to shock loading, Mater. Des. 1 (30) (2009) 91–100. [26] M. Yamashita, M. Gotoh, Impact behavior of honeycomb structures with various cell specifications-numerical simulation and experiment, Int. J. Impact Eng. 1–4 (32) (2005) 618–630. [27] K.P. Dharmasena, H.N.G. Wadley, Z. Xue, J.W. Hutchinson, Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading, Int. J. Impact Eng. 9 (35) (2008) 1063–1074. [28] L. Deng, A.W. Wang, L.W. Mao, Dynamic Response analysis of square honeycomb sandwich plates subjected to blast loading, Appl. Mech. Mater. 477–478 (2014) 160–164. [29] G.N. Nurick, G.S. Langdon, Y. Chi, N. Jacob, Behaviour of sandwich panels subjected to intense air blast – Part 1: Experiments, Compos. Struct. 4 (91) (2009) 433–441. [30] D. Karagiozova, G.N. Nurick, G.S. Langdon, Behaviour of sandwich panels subject to intense air blasts – Part 2: numerical simulation, Compos. Struct. 4 (91) (2009) 442–450. [31] J. Xiong, Y. Du, D. Mousanezhad, et al., Sandwich structures with prismatic and foam cores: a Review, Adv. Eng. Mater. 21 (2018) 1–19. [32] B. Han, Z. Zhang, Q. Zhang, et al., Recent advances in hybrid lattice-cored sandwiches for enhanced multifunctional performance, Extreme Mech. Lett. 10 (2017) 58–69. [33] J. Fang, G. Sun, N. Qiu, et al., On hierarchical honeycombs under out-of-plane crushing, Int. J. Solids Struct. 135 (2018) 1–13. [34] A. Ajdari, B.H. Jahromi, J. Papadopoulos, H. Nayeb-Hashemi, A. Vaziri, Hierarchical honeycombs with tailorable properties, Int. J. Solids Struct. 11–12 (49) (2012) 1413–1419. [35] Y. Zhang, M. Lu, C.H. Wang, G. Sun, G. Li, Out-of-plane crashworthiness of bioinspired self-similar regular hierarchical honeycombs, Compos. Struct. 144 (2016) 1–13. [36] G. Sun, H. Jiang, J. Fang, G. Li, Q. Li, Crashworthiness of vertex based hierarchical honeycombs in out-of-plane impact, Mater. Des. 110 (2016) 705–719. [37] X.M. Xiang, G. Lu, G.W. Ma, X.Y. Li, D.W. Shu, Blast response of sandwich beams with thin-walled tubes as core, Eng. Struct. 127 (2016) 40–48. [38] X. Jin, Z. Wang, J. Ning, G. Xiao, E. Liu, X. Shu, Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading, Compos. B Eng. 106 (2016) 206–217. [39] Z. Xue, J.W. Hutchinson, A comparative study of impulse-resistant metal sandwich plates, Int. J. Impact Eng. 10 (30) (2004) 1283–1305. [40] Nurick, Shave, The deformation and tearing of thin square plates subjected to impulsive loads-An experimental study, Int. J. Impact Eng. 18 (1996) 99–116. [41] G. Sun, M. Deng, G. Zheng, Q. Li, Design for cost performance of crashworthy structures made of high strength steel, Thin-Walled Struct. 138 (2019) 458–472. [42] G. Sun, H. Yu, Z. Wang, Z. Xiao, Q. Li, Energy absorption mechanics and design optimization of CFRP/aluminium hybrid structures for transverse loading, Int. J. Mech. Sci. 150 (2019) 767–783. [43] G. Sun, T. Liu, J. Fang, G.P. Steven, Q. Li, Configurational optimization of multi-cell topologies for multiple oblique loads, Struct. Multidiscip. Optim. 57 (2) (2018) 469–488. [44] G. Sun, H. Zhang, J. Fang, G. Li, Q. Li, A new multi-objective discrete robust optimization algorithm for engineering design, Appl. Math. Model. 53 (2018) 602–621. [45] T. Liu, G. Sun, J. Fang, J. Zhang, Q. Li, Topographical design of stiffener layout for plates against blast loading using a modified ant colony optimization algorithm, Struct. Multidiscip. Optim. 58 (2) (2019) 335–350. [46] G. Sun, J. Tian, T. Liu, X. Yan, X. Huang, Crashworthiness optimization of automotive parts with tailor rolled blank, Eng. Struct. 169 (2018) 201–215.
comparisons and parametric designs, Compos. Struct. 183 (2018) 242–261. [4] Qi Chang, Alex Remennikov, Lian-Zheng Pei, Shu Yang, Zhi-Hang Yu, Tuan D. Ngo, Impact and close-in blast response of auxetic honeycomb-cored sandwich panels: experimental and numerical simulations, Compos. Struct. 180 (2017) 161–178. [5] Sameh Ahmed, Khaled Galal, Effectiveness of FRP sandwich panels for blast resistance, Compos. Struct. 163 (2017) 454–464. [6] Tangying Liu, Guangyong Sun, Jianguang Fang, Jingtao Zhang, Qing Li, Topographical design of stiffener layout for plates against blast loading using a modified ant colony optimization algorithm, Struct. Multidiscip. Optim. 59 (2) (2019) 335–350. [7] A. Vaziri, J.W. Hutchinson, Metal sandwich plates subject to intense air shocks, Int. J. Solids Struct. 6 (44) (2007) 2021–2035. [8] Julio F. Davalos, P. Qiao, Modeling and characterization of fiber-reinforced plastic honeycomb sandwich panels for highway bridge applications, Compos. Struct. 52 (2001) 441–452. [9] G. Sun, E. Wang, H. Wang, Z. Xiao, Q. Li, Low-velocity impact behaviour of sandwich panels with homogeneous and stepwise graded foam cores, Mater. Des. 60 (2018) 1117–1136. [10] G. Sun, D. Chen, H. Wang, P. Hazell, Q. Li, High-velocity impact behaviour of aluminium honeycomb sandwich panels with different structural configurations, Int. J. Impact Eng. 122 (2018) 119–136. [11] J. Zhang, R. Zhou, M. Wang, Q. Qin, Y. Ye, T. Wang, Dynamic response of doublelayer rectangular sandwich plates with metal foam cores subjected to blast loading, Int. J. Impact Eng. 122 (2018) 265–275. [12] G. Sun, X. Huo, D. Chen, Q. Li, Experimental and numerical study on honeycomb sandwich panels under bending and in-panel compression, Mater. Des. 133 (2017) 154–168. [13] G. Sun, D. Chen, X. Huo, G. Zheng, Q. Li, Experimental and numerical studies on indentation and perforation characteristics of honeycomb sandwich panels, Compos. Struct. 184 (2018) 110–124. [14] Q. Qin, X. Zheng, J. Zhang, C. Yuan, T. Wang, Dynamic response of square sandwich plates with a metal foam core subjected to low-velocity impact, Int. J. Impact Eng. 111 (2018) 222–235. [15] Z. Sun, D. Li, W. Zhang, S. Shi, X. Guo, Topological optimization of biomimetic sandwich structures with hybrid core and CFRP face sheets, Compos. Sci. Technol. 142 (2017) 79–90. [16] M. Rashad, T.Y. Yang, Numerical study of steel sandwich plates with RPF and VR cores materials under free air blast loads, Steel Compos. Struct. 27 (6) (2018) 717–725. [17] S. Li, G. Lu, Z. Wang, L. Zhao, G. Wu, Finite element simulation of metallic cylindrical sandwich shells with graded aluminum tubular cores subjected to internal blast loading, Int. J. Mech. Sci. 96–97 (2015) 1–12. [18] S. Li, Z. Wang, G. Wu, L. Zhao, X. Li, Dynamic response of sandwich spherical shell with graded metallic foam cores subjected to blast loading, Compos. Appl. Sci. Manuf. 56 (2014) 262–271. [19] Y.A. Khalifa, W.W. El-Dakhakhni, M. Campidelli, M.J. Tait, Performance assessment of metallic sandwich panels under quasi-static loading, Eng. Struct. 158 (2018) 79–94. [20] Manmohan Dass Goel, V.A. Matsagar, Anil K. Gupta, Blast resistance of stiffened sandwich panels with aluminum cenosphere syntactic foam, Int. J. Impact Eng. 77 (2015) 134–146. [21] W. Huang, W. Zhang, N. Ye, Y. Gao, P. Ren, Dynamic response and failure of PVC foam core metallic sandwich subjected to underwater impulsive loading, Compos. B Eng. 97 (2016) 226–238. [22] J. Wang, C. Shi, N. Yang, et al., Strength, stiffness, and panel peeling strength of carbon fiber-reinforced composite sandwich structures with aluminum honeycomb cores for vehicle body, Compos. Struct. 184 (2018) 1189–1196. [23] Y. Chi, G.S. Langdon, G.N. Nurick, The influence of core height and face plate thickness on the response of honeycomb sandwich panels subjected to blast loading, Mater. Des. 4 (31) (2010) 1887–1899.
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