Experimental investigation on the performance of PVC foam core sandwich panels under air blast loading

Composite Structures 226 (2019) 111081

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Experimental investigation on the performance of PVC foam core sandwich panels under air blast loading

T

Tianyu Zhoua, Pan Zhanga,b,c, , Wei Xiaod, Jun Liua,b,c, Yuansheng Chenga,b,c ⁎

a

School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China c Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamic, Wuhan 430074, China d China Ship Development and Design Center, China b

ARTICLE INFO

ABSTRACT

Keywords: Sandwich structure Graded foam core Blast loading Failure mode

The performance of sandwich panels with metallic face-sheets and polyvinyl chloride (PVC) foam ungraded/ graded cores under air blast loading was investigated experimentally. In present paper, the performance of interest included the permanent deformation, failure modes and the associated mechanisms underlying the overall response. The majority of the paper was concentrated on the effects of geometric parameters and core gradation on the blast performance of panels. Experimental results showed that regardless of the panel configuration considered here, the panels exhibited a localized dishing deformation of front face and a global dome deformation of back face. The way to achieve a more effective design against air blast is to increase the thickness of the face sheet towards the blast rather than the other sheet. The panel system with a low-density (large thickness) core appeared to be favorable for the mitigation of back face deformation and core cracking failure. Effect of core gradation indicated that placing the low density material at the third core layer and the high density material at the second core layer, thus reducing the momentum transmitted to back face and increasing the crushing deformation of graded core, helped enhance the blast resistance of panel. Furthermore, the comparisons of blast performance between ungraded sandwich panel and graded panels were made. It turned out that overall graded panels did not always outperform the ungraded panel. An optimal core gradation would bring benefits for blast resistance in terms of the face sheet deformation and core cracking failure, but also was required to face the risk of delamination failure.

1. Introduction Sandwich structures, constructed from two thin, stiff, strong face sheets separated by compressible porous (cellular) cores, have very important applications in the aerospace, naval, building and automobile industries [1,2]. Due to their construction, they are highly efficient at bearing bending loads and famous for their superior stiffness and strength over the monolithic counterparts. Moreover, the low strengths and large compressive strains make porous (cellular) core materials attractive for energy absorbing applications [3,4]. The sandwich structures with porous (cellular) cores therefore offer potential for the mitigation of high-intensity dynamic loads created by impacts and shock waves in air or water environments [5], and thus protect personnel or objects located behind them [6]. Numerous attentions have been devoted to study the dynamic response of sandwich structures subjected to blast loading. A variety of micro-

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architectured materials have been developed as cores in sandwich structures, such as honeycombs [7-9], corrugated [10-12], lattice truss [13], balsa wood [14], stochastic cellular foams [15,16], etc. The sandwich panels with theses core topologies have been developed as the ideal substitutions of monolithic counterparts for blast protection purposes. Especially for the stochastic cellular foam material, the microstructure of cellular material endows it with the merit ability to exhibit a long plateau stress region during compressive response. This is attractive for energy absorption in crushing and impulsive loading applications. A great many experimental and numerical works have been done to study the dynamic behavior of the cellular foam core sandwich structures. It is found that the sandwich panels with metallic foam cores have a higher blast resistance than monolithic counterparts of equal mass [15]. By using ballistic pendulum system, Zhu et al. [17] examined the blast resistance of sandwich panel and found the aluminum foam core constitutes a major contribution towards the energy dissipation. The advantage of aluminum foam core sandwich panels in blast

Corresponding author at: School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. E-mail address: [email protected] (P. Zhang).

https://doi.org/10.1016/j.compstruct.2019.111081 Received 8 February 2018; Received in revised form 23 August 2018; Accepted 28 May 2019 Available online 30 May 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. (a) Sketch of the configuration of the explosion tank used for blast tests. (b) Picture of a typical set-up at the test site just before detonation. (c) Picture of the cylindrical TNT explosive used in experiments.

wave attenuation has also been further verified by Liu et al. [16]. However, the blast performance of sandwich panel depends on the geometric parameters and loading conditions. Qi et al. [18] numerically studied the performance of sandwich panel with aluminum foam core subjected to blast loading. They demonstrated that a low-stiffness front face results in a large level of foam core compression and energy absorption, while a high-stiffness back face is suitable for reducing the deflection of panel. Huang et al. [19] experimentally examined the dynamic failure of PVC foam core sandwich panels subjected to water-based impulsive loading. The result showed that the density of cores had a significant effect on the deflection of back face. On the other hand, the existence of the core layer could affect the failure mechanisms of the sandwich panel. Latourte et al. [20] employed the shock tube apparatus to explore the failure modes of monolithic and sandwich plates with PVC foam core. The dynamic response of cylindrical sandwich shells with aluminum foam core was tested by Jing et al. [21], and typical failure mechanisms were observed, including core crushing, shear failure and delamination. Avachat and Zhou [22,23] analyzed the damage of composites sandwich structures with PVC foam core subjected to underwater impulsive loads, and found that the primary failure modes were shear cracking of the front panel and core collapse. To gain further improvement in the blast resistance, a series of novel design concepts have recently been developed based on the conventional sandwich structures. For instance, a desirable design was achieved by filling all or a part of the empty space of periodic cellular core with metallic or polymeric foams. Relevant work by Yazici et al. [24,25] and Zhang et al. [26,27] indicated that foam filling provided benefits in blast resistance enhancement due to the sufficient crushing deformation of foam fillers and the enhanced buckling resistance of core webs. As another attempt for blast resistance improvement, ductile interlayers were inserted between the outer face-sheet and the foam core to absorb a significant part of the incident energy and to protect the foam core from excessive deformation [28]. Adopting the concept of functionally graded materials to design the cellular cores is an alternative way to enhance blast resistance of sandwich structures. It is known that the cellular material with a specific density has a unique plateau stress. The advantage of the core material in the blast mitigation could not be activated unless the compression stress in the core

reaches the limited value. Therefore, the functionally graded cores are expected to widen the range of limited stress levels and to improve the energy absorption capability [29]. Due to the potential high efficiency and low cost, a growing number of studies focused on the performance of sandwich structures with functionally graded foam cores under impulsive loading. To name a few, Wang et al. [30] and Gardner et al. [31] employed a shock tube apparatus to examine the effect of core layer gradation and the number of monotonically graded foam core layers on the blast resistance. Jin et al. [29] numerically studied the graded effects of metallic foam cores for the spherical sandwich shells subjected to close-in underwater explosion. Liu et al. [32] and Li et al. [33] applied the functionally graded materials into the cores of sandwich cylinders and spherical shells, and found that the arrangement of the core layers has significant effects on the dynamic plastic responses of panels under air blast loading. The objective of present paper is to investigate the dynamic performance of foam core sandwich panels by conducting air blast tests. Permanent deflection, deformation/failure modes and associated mechanisms were identified and quantified for sandwich panels with ungraded and functionally graded PVC foam cores. The outline of this paper is as follows. First, the information about the experimental set-up is given. Next, geometry of the foam core sandwich panels considered, and material properties of panel constituents are described. Then, the following section is devoted to reporting the influence of geometric parameters on the performance of ungraded panel and the effect of core gradation on the performance of graded panel. Finally, a summary of main findings and their implications are discussed in the last section. 2. Experiment details 2.1. Experimental setup All of the ungraded and graded PVC foam core sandwich panels were subjected to air blast loading. The tests were performed in an explosion tank with a diameter of 5 m and a height of 7.5 m, as shown in Fig. 1(a). The set-up mainly consists of the double shell body, ventilation system, drainage system, vibration isolation system, sound 2

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Fig. 2. (a) Schematic of the PVC foam sandwich panel. (b) Cross-sectional view of the ungraded sandwich panel. (c) Cross-sectional view of the functionally graded sandwich panel.

Fig. 3. Microscope images showing the cell microstructure of four PVC foams. Table 1 Summary of foam properties (http://www.diabgroup.com).

isolation system and illuminating system. A heavy steel frame used for clamping the test sandwich panels was placed at the tank bottom center to avoid the effect of wall reflection. The panels were bolted to the heavy steel frame using 32 high tensile bolts with a 300 mm × 288 mm exposure area to the blast wave, Fig. 1(b). To generate the blast load, a 55 g cylindrical TNT explosive with a radius of 17.5 mm and a height of 37.2 mm was placed over the panel center and the detonation was remotely initiated via an instantaneous electrical detonator, Fig. 1(c). The location of charge was fixed by using several plastic lines to achieve the 100 mm stand-off distance (from the center of explosive to the top surface of panel).

Property (unit)

H60

H130

H200

H250

Nominal Density (kg/m3) Compressive strength (MPa) Compressive modulus (MPa) Tensile strength (MPa) Tensile modulus (MPa) Shear strength (MPa) Shear modulus (MPa)

60 0.7–0.9 60–70 1.5–1.8 57–75 0.63–0.76 16–20

130 2.4–3.0 145–170 3.5–4.8 135–175 1.9–2.2 40–50

200 4.5–5.4 265–310 6.3–7.1 210–250 3.2–3.5 65–73

250 6.1–7.2 350–400 8.0–9.2 260–320 3.9–4.5 81–97

2.2. Specimens Rectangle sandwich panels with ungraded and graded cores were fabricated by two thin 304 stainless steel face-sheets and PVC foam cores, as shown in Fig. 2. The in-plane dimensions of panels are 452 mm by 440 mm. Herein, the ungraded core sandwich panel is a conventional sandwich structure with single-layer foam core (Fig. 2(b)), while the graded core sandwich panel contains a three-layer foam core (Fig. 2(c)). The face-sheets and foam cores were bonded together using epoxy adhesive. The mechanical properties of face-sheet base material, which were measured by standard quasi-static tests, are as follows: elastic modulus E = 200 GPa, density ρ = 7900 kg/m3, yield strength σs = 310 MPa, tensile strength σp = 740 MPa, and failure strain εf = 0.42. The core materials used in present study were Divinycell H series PVC foams, which were manufactured by DIAB Group specifically for sandwich composite applications. Four types of Divinycell H foam were adopted, namely H60, H130, H200 and H250. Fig. 3 shows the microscope images of the PVC foam samples. The cell structures of the four foams are very similar and the only difference appears in the cell wall thickness and cell sizes, which accounts for the different densities and mechanical properties of the foams. Table 1 lists the important material properties of the four foams from the manufacturer’s data (http://www.diabgroup.com). Typical quasi-static uniaxial compressive stress-strain curves of these four foams are shown in Fig. 4. It can be seen that the stress-strain curves consist of an initial elastic regime followed by a stress plateau regime over a wide range of strains prior to the densification regime.

Fig. 4. Uniaxial compressive stress versus strain curves of PVC foams.

2.3. Design of the experiments 2.3.1. Ungraded single-layer sandwich panels In this stage, the sandwich panel USP-1, composed of two identical face sheets with thickness of 1.38 mm and a single-layer H250 foam core with thickness of 14 mm, is considered as the reference panel and the other panels are employed to explore the effects of geometrical parameters. Panels USP-2, USP-3, and panels USP-4, USP-5 are selected for investigation of the front face sheet thickness effect and the back face sheet thickness effect; while panels USP-6, USP-7, and panels USP-8, USP-9 are used to study the effects of the core thickness and core density, respectively. The specifications of the ungraded singlelayer sandwich panels are listed in Table 2. 3

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Table 2 Structural information of sandwich panels with ungraded and graded cores. Label

Front face thickness (mm)

Back face thickness (mm)

Core layer arrangement

Thickness of each core layer (mm)

Total thickness of the core (mm)

Areal density (kg/ m3)

USP-1 USP-2 USP-3 USP-4 USP-5 USP-6 USP-7 USP-8 USP-9 FGP-1 FGP-2 FGP-3

1.38 0.90 1.80 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38

1.38 1.38 1.38 0.90 1.80 1.38 1.38 1.38 1.38 1.38 1.38 1.38

H250 H250 H250 H250 H250 H250 H250 H200 H130 H60/H130/H200 H200/H130/H60 H130/H200/H60

14 14 14 14 14 9 20 17.5 27 9 9 9

14 14 14 14 14 9 20 17.5 27 27 27 27

25.17 21.40 28.46 21.40 28.46 23.92 26.67 25.17 25.18 25.18 25.18 25.18

2.3.2. Functionally graded sandwich panels In this stage, to probe into the potential of performance improvement of foam core sandwich panel, the functionally graded foam core becomes a substitute for the single-layer foam core. Three types of sandwich panels with same face sheet configuration but different core layer gradation were designed, as schematically shown in Fig. 5. Panel FGP-1 consisted of a core gradation of H60/H130/H200 (low/middle/ high density), while the core gradation of panel FGP-2 was just the reverse of the one of panel FGP-1. In addition, panel FGP-3 consisted of a core gradation of H130/H200/H60 (middle/high/low density). The thickness of each foam core layer was fixed at 9 mm. Note that the first core layer was the one first subjected to air blast loading. The details about geometric information of functionally graded sandwich panels are also included in Table 2.

Table 3 Permanent deflection and core layer compression of specimens. Label

3. Experimental results and discussions After testing, all panels were cross-sectioned by water-jet cutting to reveal the failure modes and mechanisms of face sheets and foam cores. In addition, the Dino-Lite Microscope was employed to examine the failure mechanisms of foams in a microscopic view. The mid-point permanent deflections of face-sheets and the compression value of each core layer were measured and listed in Table 3.

Permanent face sheet deflection (mm)

Permanent core compression (mm/%)

Front

Back

First layer

Second layer

Third layer

USP-1 USP-2 USP-3 USP-4 USP-5 USP-6 USP-7 USP-8 USP-9

21.74 26.06 17.74 23.52 21.20 20.70 24.00 24.74 29.60

21.56 26.89 18.38 24.62 20.64 24.18 19.08 20.76 13.12

– – – – – – – – –

– – – – – – – – –

FGP-1 FGP-2 FGP-3

30.28 26.98 28.66

13.34 12.96 12.40

2.74 (20%) 3.07 (22%) 2.32 (17%) 2.64 (19%) 4.36 (31%) 2.18 (24%) 5.32 (27%) 4.56 (26%) 17.78 (66%) 8.22 (91%) 5.18 (58%) 6.56 (73%)

5.96 (66%) 5.36 (60%) 4.88 (54%)

4.12 (46%) 5.48 (61%) 6.06 (67%)

3.1. Ungraded single-layer sandwich panels 3.1.1. Reference panel USP-1 Fig. 6(a) shows the half-sectional view of the as-tested reference panel USP-1. The front face of this panel mainly suffered a deformation mode characterized by an inner dome superimposed on the global deformation. This deformation mode is similar to that of a solid plate subjected to localized blast loading [34]. The back face sheet underwent a global dome deformation. The measured maximum deflections of front face and back face are 21.74 mm and 21.56 mm, separately. Due to the localized dishing deformation of front face, the indentation and compression deformation of foam core mainly occurred at the panel center. The foam core compressed about 2.74 mm, or only 20% of its original thickness (14 mm). Three microscopy images (see Fig. 6(b)–(d)) show the microstructural profiles of core foam cell along the direction towards outskirts. It is evident from Fig. 6(b) that at the center region, the thin cell walls collapsed due to elastic/plastic buckling. This bulk failure of foam core decreased from center to outskirts. The core compression was relatively low, presumably as a result of that the high impulse imparted to the front face causes it to move away from the explosion at a velocity higher than the allowable dynamic crush rate of the foam core. Due to the localization of the blast loading, less compression load acted on the core near to gripping boundary where is far away from the stand-off point. Thus, the foams remained intact after testing, as shown in Fig. 6(d). The cross-section of panel USP-1 highlighted the presence of face-sheet-core interface debonding at panel faces, and the debonding region propagated to the boundary, as shown in Fig. 6(a). This indicated relatively weak adhesion. Here, it is evident that there existed noticeable clearance at the face-sheet-core interfaces. This phenomenon is in part due to the discrepancy on the bending/

Fig. 5. Sketch of the functionally graded sandwich panels with different core configuration. 4

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Fig. 6. Post-mortem photographs of the ungraded single-layer sandwich panel USP-1. (a) Cross sectional view revealing the detailed failure modes of panel USP-1. (b)–(d) Microscopic pictures showing the deformation state of PVC foam core from center to outskirts.

stretching resistance of face-sheets and foam core. The foam core would be less capable of accommodating the panel face deformation once the debonding failure appeared. Note that two macroscopic cracks emerged at the foam core. One crack was located at quarter span and had propagated completely through the core, and the other one was short-lived and situated near the other side support, see Fig. 6(a). The onset of complete core cracking would relieve the transverse shear state at the support. Therefore, the core cracking was not observed at the same side support.

panel USP-3 with a thicker front face displayed lower front and back deflections by 18.40% and 14.75%, respectively. Change in front face thickness is expected to have an impact on the deformation mechanisms of sandwich structure from the aspects of fluid-structure interaction effect and bending/stretching resistance. From the previous study [35], the influence of front face thickness on the fluid-structure interaction effect is negligible under this circumstance. So, the difference in deflections is a direct reflection of the variation of bending/stretching resistance of front face. Furthermore, the shock loading transferred from front face to foam core is also associated with deformation resistance of front face. The lower the deformation resistance of front face, the higher the shock loading level on foam core. Therefore, panel USP-2 with thin front face experienced heavy core compression, bending and cracking failure, as shown in Fig. 7(a). The measured core layer compression is 3.07 mm, which is higher by 12% relative to panel USP-1. Note the heavy amount of collapse seen in the foam core cells at panel center, see Fig. 7(c). Due to the tensile stress induced by large bending deformation at panel center, two center cracks originated from the tensile surface and propagated through the core thickness finally. Then, a visible foam fragment was almost formed at core center, as shown in Fig. 7(b). Another two cracks propagated through core thickness at quarter spans, and other two short-lived cracks were located at the supports, see Fig. 7(a).

3.1.2. Effect of front face-sheet thickness Relative to the reference panel USP-1, panel USP-2 is of a thinner front face while panel USP-3 is of a thicker front face. The post-mortem results of panel USP-2 and panel USP-3 are shown in Figs. 7 and 8, respectively. At the first glance, a localized dishing deformation of front face and a global inelastic deformation of back face could be observed for these two panels. Such responses are similar to those observed for panel USP-1. Close examination of Figs. 6(a), 7(a) and 8(a) shows that the inner dome deformation of front face would be limited in size and extent with the increase of front face thickness. The measured deflections for these two panels are listed in Table 3. Using the reference panel USP-1 as a benchmark, panel USP-2 with thinner front face exhibited larger front and back deflections by 19.87% and 24.84%, and

Fig. 7. Post-mortem photographs of the ungraded single-layer sandwich panel USP-2. (a) Cross sectional view revealing the detailed failure modes of panel USP-2. (b) Enlarged view showing the failure of foam core at panel center. (c) and (d) Microscopic pictures displaying the deformation state of PVC foam core at panel center and support respectively. 5

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Fig. 8. Post-mortem photographs of the ungraded single-layer sandwich panel USP-3. (a) Cross sectional view revealing the detailed failure modes of panel USP-3. (b) Enlarged view showing the cracking region. (c) and (d) Microscopic pictures displaying the deformation state of PVC foam core at panel center and support respectively.

For panel USP-3 with thick front face, it is clearly seen that the damage of core has been effectively mitigated with the help from the higher resistance of front face, as shown in Fig. 8(a). The core layer compression was decreased to 2.32 mm. A great many visible voids could be found in the core (seen in Fig. 8(c)), implying the foam core lied in the plateau region. In addition, increasing the front face thickness could relieve the tension and shear states in foam core. Therefore, a shortlived tension-dominated crack, rather than penetrative crack observed for panels USP-1 and USP-2, formed at the quarter span of panel USP-3. No shear crack could even be found near the boundary.

experienced lower front and back deflections by 2.48% and 4.27%, respectively. One important role of back face is to provide support to foam core. Obviously, a thicker back face would possess a higher deformation resistance, which means a stronger supporting effect to foam core. A strong supporting effect should be beneficial to foam core to enhance its energy absorption through crushing deformation and inhibit the germination and propagation of cracks. Therefore, the core compression of panel USP-4 with a thin back face thickness was reduced to 2.64 mm, while the one of panel USP-5 with a thick back face thickness was increased to 4.36 mm. Moreover, the foam core of panel USP-4 tended to fail in shear crack, and two heavy core cracks formed symmetrically at quarter spans, as shown in Fig. 9(a). The shear cracking was so severe that the central part of foam core broke away from the whole core, and finally contacted with the deformed back face sheet, as shown in Fig. 9(b). In addition, the shear cracking would relieve the bending/ stretching state of foam core. Consequently, it can be observed in Fig. 9(a) that the foam core exhibited a limited bending deformation and no tensile crack appeared at panel center. As a comparison, the foam cell walls of panel USP-5 exhibited more severe buckling failure in microscopic view due to the high compression deformation, see

3.1.3. Effect of back face-sheet thickness One panel (USP-4) with thin back face sheet and another (USP-5) with thick one were tested. Figs. 9 and 10 present the post-mortem photographs of these two panels, separately. Similar to the effect of front face thickness, the back face thickness has negligible influence on the deformation modes of face sheets, as shown in Fig. 9(a) and Fig. 10(a). As expected, the permanent deflections of both front face and back face were reduced as the increase of back face thickness. Relative to the reference panel USP-1, panel USP-4 suffered larger front and back deflections by 8.19% and 14.19%, and panel USP-5

Fig. 9. Post-mortem photographs of the ungraded single-layer sandwich panel USP-4. (a) Cross sectional view revealing the detailed failure modes of panel USP-4. (b) Enlarged view of the heavy cracking region. (c) and (d) Microscopic pictures displaying the deformation state of PVC foam core at panel center and support respectively. 6

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Fig. 10. Post-mortem photographs of the ungraded single-layer sandwich panel USP-5. (a) Cross sectional view revealing the detailed failure modes of panel USP-5. (b) Enlarged view showing the cracking region. (c) and (d) Microscopic pictures displaying the deformation state of PVC foam core at panel center and support respectively.

a higher front face deflection by 12.15%, and panel USP-7 with a thicker core displayed a higher front face deflection by 10.40% and a lower front face deflection by 11.50%. Obviously, the result means that the core thickness has a different effect on the deformation of front face and back face. The onset of this phenomenon is associated with the deformation mechanisms of face sheets. The global deformation of back face is strongly dependent upon the overall stiffness of panel, while the localized deformation of front face is closely related to its local stiffness. The panel with a thicker core has a higher second moment of cross section, resulting in a higher overall stiffness. However, a thicker core would have a weaker supporting effect to front face and provide more space available for the deformation of front face. Therefore, the increase of core thickness would reduce the back face deflection, but would also cause an undesirable front face deflection. Along with the change in panel bending resistance, the deformation mechanisms of foam core would vary with the core thickness. The foam core of panel USP-6 underwent a more evident global bending deformation, as shown in Fig. 11(a). Moreover, the considerable bending deformation induced not only the tension-dominated crack at core center (Fig. 11(b)), but also the shear-dominated cracks at quarter span and support (Fig. 11(a)). The tension-dominated crack caused the serious damage and the onset of material erosion, as shown in Fig. 11(b). In contrast, the local bending deformation, instead of global bending deformation, became the primary deformation mode of the foam core of panel USP-7 with a thicker core, as shown in Fig. 12(a). This would result in the crack failure being suppressed. Therefore, only a short-live crack, originating from the back surface (in tension) and being arrested near the middle surface of core, appeared at the central region of foam core, as shown in Fig. 12(b). Although the deformation region is limited, the crushing deformation level is more considerable for the foam core of panel USP-7. In the macroscopic view, the measured core compression at panel center is 5.32 mm, which is about 27% of its original thickness and larger by 35% relative to that of USP-1. Correspondingly, the distinct collapse of foam cells could be observed at the core center, as shown in Fig. 12(c).

Fig. 10(c). The more energy absorbed by foam core crushing deformation, the less momentum obtained by foam core to move downward. Although there still existed a through-thickness crack at the quarter span, the residual momentum of foam core was not enough to make it impact upon the back face, as shown in Fig. 10(b). The crack observed on panel USP-1 near the support was absent in panel USP-5. This phenomenon further implies that the cracking failure of the core could be reduced by increasing the back face thickness. 3.1.4. Effect of face sheet configuration To study the effect of face sheet configuration, the panel structural parameters should be intentionally designed with same core configuration, but opposite thickness on front face and back face. In present study, the face-sheet configurations of panel USP-4 and panel USP-5 were just the reverse of those of panel USP-2 and panel USP-3, respectively. Comparison of the permanent deflections reveals that the panel having a higher front face thickness and a lower back face thickness possesses the superior blast resistance. To be specific, panel USP-4 displayed smaller front and back face deflections than panel USP-2 by 9.75% and 8.44%, while panel USP-3 displayed smaller front and back face deflections than panel USP-5 by 16.32% and 10.95%, separately. An implication of this result is that increasing front face thickness, rather than increasing back face thickness, is an efficient way to achieve optimum sandwich panel against blast loading. A similar conclusion has been drawn for the corrugated core sandwich panel under air blast loading by Zhang et al. [12]. Careful examination of post-mortem images (Figs. 7–10) indicates that panels with thicker front face and thinner back face exhibited lower damage level on their foam core. The main reason for those findings should be that the panel with thicker front face would obtain less kinetic energy during the fluid-structure interaction. The whole process of fluid-structure interaction satisfies the conservation of momentum theorem. So, a heavy front face tends to obtain lower kinematic velocity. 3.1.5. Effect of core thickness Figs. 11 and 12 show the post-mortem photographs of panel USP-6 with a thinner core and panel USP-7 with a thicker core, separately. There is still no noticeable difference in the deformation modes of face sheets of these two panels, compared with the deformation modes exhibited by panel USP-1. However, the measured permanent deflections reveal findings which merit attention with respect to the deformation mechanisms of face sheets. Compared with panel USP-1, panel USP-6 with a thinner core exhibited a lower front face deflection by 4.78% and

3.1.6. Effect of core density With both face sheet configuration and areal density being the same as those of reference panel USP-1, another two panels (USP-8 and USP-9) with lower densities foam core were designed. Note that the lower density foam core necessitates larger core thickness to maintain a constant whole weight. Unsurprisingly, the front faces of two panels mainly exhibited localized indenting deformation, while the back faces showed themselves as a global dome. Careful contrast of the deformation modes (Figs. 6(a), 13(a) and 7

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Fig. 11. Post-mortem photographs of the ungraded single-layer sandwich panel USP-6. (a) Cross sectional view revealing the detailed failure modes of panel USP-6. (b) Enlarged view reporting the core details in the center region. (c) and (d) Microscopic pictures displaying the deformation state of PVC foam core at panel center and support respectively.

14(a)) shows up the difference in the influence of core density on front face and back face. Decreasing the core density would aggravate the indenting deformation of front face, and ameliorate the global deformation of back face. Using the results of panel USP-1 as the basis for comparison, panel USP-8 with a little lower core density experienced a higher front face deflection by 13.8% and a lower back face deflection by 3.7%, while panel USP-9 with a much lower core density displayed a higher front face deflection by 36.2% and a lower back face deflection by 39.1%. The changes in mechanical properties of foam core should be the root cause of this phenomenon. Lower foam density means lower core strength, which indicates a weak support to front face and a low stress transmitted to back face. Generally speaking, the core compression is determined by the difference in the deflections of front face and back face. The rule of core density on the face sheet deflection implies that the core with a low density tends to experience high-level crushing deformation. The measured core compressions of panel USP-8 and panel USP-9 are 4.56 mm and 17.78 mm, which are 26% and 66% of their original thicknesses, respectively. It can be inferred that the foam material of panel USP-8 still lied in the plateau region, so that visible voids could be found in the foam cells, as shown in Fig. 13(c). Yet, high-level crushing deformation obtained in foam core of panel USP-9 (see Fig. 14(b)) suggests that the deformation behavior of foam material

went into the densification region. Microscopic view (see Fig. 14(e)) of the core center confirmed the densification phenomenon without visible voids. The effect of core density on the crack failure of foam core is more complicated, because the crack failure depends upon two factors: the stress state and the fracture toughness of foam core. Although adopting a foam core with low density could relieve the stress state, it has to face the susceptive fracture toughness. Therefore, the crack failure of panel USP-8 seems to be mitigated relative to panel USP-1. Only a short-lived crack could be found near the gripping boundary, as shown in Fig. 13(b). However, the crack failure of panel USP-9 is more severe. A macroscopic crack, nearly propagating through core thickness, emerged at the partially crushed region of foam core, as shown in Fig. 14(a). Furthermore, another two short-lived cracks could be found from the local enlargement views shown in Fig. 14(c) and (d). This poor performance should be attributed to the low fracture toughness. Instead, the optimal foam core processing proper strength is likely to perform well in restraining the crack failure. 3.2. Functionally graded sandwich panels The previous section revealed that the low-density foam core showed itself as a good energy absorber in the sandwich panel system with a single-layer core. However, the present section attempts to use

Fig. 12. Post-mortem photographs of the ungraded single-layer sandwich panel USP-7. (a) Cross sectional view revealing the detailed failure modes of panel USP-7. (b) Enlarged view showing the cracking region. (c) and (d) Microscopic pictures displaying the deformation state of PVC foam core at panel center and support respectively. 8

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Fig. 13. Post-mortem photographs of the ungraded single-layer sandwich panel USP-8. (a) Cross sectional view revealing the detailed failure modes of panel USP-8. (b) Enlarged view showing the cracking region. (c) and (d) Microscopic pictures showing the deformation state of PVC foam core at panel center and support respectively.

Fig. 14. Post-mortem photographs of the ungraded single-layer sandwich panel USP-9. (a) Cross sectional view revealing the detailed failure modes of panel USP-9. (b) Magnified picture reporting the crushing deformation of core and the debonding failure between front face and foam core. (c) and (d) Magnified pictures showing two short-lived cracks in foam core at quarter span and support respectively. (e) and (f) Microscopic pictures showing the cell structures of PVC foam core at panel center and support separately.

three-layered functionally graded foam core as a replacement for the low-density single-layer foam core, aiming at exploring the potential of performance improvement of sandwich panel.

debonding. As expected, the front face underwent a localized dishing deformation under the localized blast loading, while the back face suffered a global bending deformation. The measured maximum deflections of front face and back face are 30.28 mm and 13.34 mm, respectively. Note that the strength of the core layers increased monotonously from the first layer to the third layer. The upper core layer needs to experience a high strain level to produce a stress level required to initiate the compression of next core layer. Consequently, one can speculate that the core layers would be compressed layer by layer. In general, the whole core underwent bending and crushing deformation to accommodate the gross out-of-plane deflections of

3.2.1. Effects of core gradation For the panel FGP-1, as shown in Fig. 15, the core gradation was from the foam of lowest density (H60) to the foam of highest density (H200). In this case, several major deformation mechanisms were observed (see Fig. 15(a)): localized dishing of front face, global bending of back face, evident bending and crushing of core and face-sheet-core interface 9

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Fig. 15. Post-mortem photographs of the functionally graded sandwich panel FGP-1. (a) Cross sectional view revealing the detailed failure modes of panel FGP-1. (b) Enlarged view reporting the cracking failure in tension at core center. (c) Enlarged view showing the deformation of whole core at panel center. (d) Enlarged view reporting the cracking failure in shear at the clamped edge region. (e), (f) and (g) Microscopic pictures showing the cell structures of each core layer at panel center respectively.

face sheets, as shown in Fig. 15(a). The deformation levels of core layers reduced from the first layer to the third layer, Fig. 15(c). Three core layers exhibited strain levels of approximately 91%, 66% and 46%, respectively. It is obviously shown that the first and second core layers went into a state of densification regime. The graphs (see Fig. 15(e) and (f)) of microscopic features of these two core layers confirmed the densification phenomenon without visible voids in foam layer. However, it is evident from Fig. 15(g) that there still existed visible voids in the third core layer, revealing that the foam material lied in the plateau region rather than the densification region. Therefore, the capability of this foam layer (with the highest density) to dissipate blast energy has not been utilized sufficiently. It appears that the extensive bending of whole core resulted in the onset of core cracking failure at panel center. The enlarged view shown in Fig. 15(b) indicates that the cracks propagated through the third core layer, and were arrested at the interface between the second core layer and third core layer. In addition, an unexpected shear crack was found at the second core layer near the clamped edge, as shown in Fig. 15(d). One possible reason is that the high shear flow near the neutral plane induced the shear band formation. In the panel FGP-2, as shown in Fig. 16, core gradation was from the foam of highest density (H200) to the foam of lowest density (H60). In this case, the deformation modes exhibited by face sheets were similar to those observed in panel FGP-1. Herein, the measured maximum deflections of front face and back face are 26.98 mm and 12.96 mm, respectively. Failure modes displayed by the whole core included crushing, bending, cracking and delamination, as shown in Fig. 16(a). Note that the first core layer still underwent heavy crushing deformation companied by evident bending deformation. Otherwise, the other two core layers mainly experienced crushing deformation. Moreover,

each core layer exhibited the almost same residual thickness, as shown in Fig. 16(c). The strain level of each core layer due to crushing is around 60%. It is obvious that these findings are different from those from panel FGP-1. Fig. 16(e), (f) and (g) show the microscopic features of three core layers from the first layer to the third layer, respectively. Severe collapse failure of core cell walls could be observed, and there existed little voids in core. At the panel center region, two tensile cracks shown in the third core layer of panel FGP-1 were absent at panel FGP2 instead two shear dominated cracks appeared at the first core layer, as shown in Fig. 16(b). Additionally, a long crack traveled through the third core layer and spread a certain distance at the interface between the second core layer and third core layer, as shown in Fig. 16(d). The crack on the interface led to the core delamination, where the second core layer separated from the third core layer, see Fig. 16(a). For the panel FGP-3, as shown in Fig. 17, the core gradation began with the foam of middle density (H130), next the foam of highest density (H200), and then the lowest density foam (H60). In this case, the face sheets exhibited similar deformation modes as those of former two functionally graded sandwich panels, as shown in Fig. 17(a). The measured maximum deflections of front face and back face are 28.66 mm and 12.40 mm, respectively. The whole graded core experienced evident crushing and bending deformation and complied well with the deformation of face sheet, Fig. 17(a). Therefore, most part of the interface between the core and face sheets remained intact after testing. The enlarged view shown in Fig. 17(c) displays the permanent compressive state of each core layer. The measured amount of core layer compression from the first layer to the third one is 6.56 mm, 4.88 mm and 6.06 mm, corresponding to the strain levels of 73%, 54% 10

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Fig. 16. Post-mortem photographs of the functionally graded sandwich panel FGP-2. (a) Cross sectional view revealing the detailed failure modes of panel FGP-2. (b) Enlarged picture reporting the shear dominated crack of first core layer. (c) Enlarged view showing the deformation of whole core at panel center. (d) Enlarged view highlighting the cracking failure of third core layer. (e), (f) and (g) Microscopic pictures showing the cell structures of each core layer at panel center respectively.

comparison, both the panel FGP-2 and panel FGP-3 suffered not only core cracking failure but also delamination failure at core layer interface. Moreover, the effect of core gradation highlighted different levels of crushing deformation of each core layer, as listed in Table 3. A reasonable understanding of intrinsic mechanisms underlying these phenomena should recall the two primary roles played by the graded foam core: i) the mitigating of shock wave and ii) the transferring of momentum from the upstream component to the downstream one. The former role depends not only upon the scattering and splitting of stress wave due to the impedance mismatch on the interface but also upon the mechanical energy dissipation. The benefit from the impedance mismatch would rely upon the number of core layers and the materials used in core layers. Herein, each panel with different core gradation has the same number of core layers and the same core materials. Thus, each panel would experience equal benefit from the impedance mismatch of core layers. The difference in shock wave mitigating should be ascribed to the mechanical energy absorption. It is known that the energy dissipation mechanism is mainly determined by the deformation mechanisms. The front face was directly supported by the first core layer. A lower density material applied in the first core layer would produce a lower bending and crushing resistance of this core layer, resulting in a higher transverse deformation during the energy absorption process. Therefore, the front face underwent a higher deflection with the decrease of material density of first core layer. The downstream part of the third core layer is the back face. So, a higher density material (with higher plateau stress) used in third core layer would induce a higher momentum transferred to back face. As a result, it would cause an undesirable back face deflection. Therefore, panel FGP-1 experienced the largest front face deflection and back face deflection. The level of crushing deformation of each core layer was

and 67%, respectively. Both the first and third core layers crushed into densification, except for the second core layer (with the highest strength). The microscopy images shown in Fig. 17(e) and (g) display the appearance of densified foam. No visible voids could be seen, implying an efficient use of the energy dissipation of foam material. However, there existed some small voids in the second core layer, as shown in Fig. 17(f). Note that the delamination failure appeared at the interface between the second core layer and third core layer, Fig. 17(a). This was presumably due to the high out-of-plane tensile (beyond the fracture threshold value of adhesive layer) produced by the inconsistent deformation of two core layers. Two incline cracks appeared at the graded core. One crack originated in the first core layer, and grew along the thickness direction until it arrived at the interface. After propagating along the interface with a certain distance, the crack plunged into the second core layer and finally was arrested, as shown in Fig. 17(b). The other one was found in the third layer, and it was arrested by the interface, as shown in Fig. 17(d). As observed in experimental results shown Figs. 15(a), 16(a) and 17(a), the core gradation had no effect on the deformation modes of both front face and back face. Nevertheless, the permanent maximum deflections of face sheets varied with the change of core gradation, as shown in Fig. 18. From the point of view to minimize the front face sheet deflection, the panel FGP-2 with the core gradation of H200/ H130/H60 is the best one, followed by panel FGP-3 (H130/H200/H60) and then panel FGP-1 (H60/H130/H200). However, the sequence of functionally graded sandwich panels would be reordered according to the criterion of the minimization of back face sheet deflection, viz. panel FGP-3, panel FGP-2 and panel FGP-1. The three panels with different core gradation exhibited different failure modes of foam core. For the panel FGP-1, only three visible cracks were formed. As a 11

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Fig. 17. Post-mortem photographs of the functionally graded sandwich panel FGP-3. (a) Cross sectional view revealing the detailed failure modes of panel FGP-3. (b) Enlarged picture showing the propagation of core cracking in the first and second core layers. (c) Enlarged view showing the deformation of whole core at panel center. (d) Enlarged view reporting the cracking failure of third core layer. (e), (f) and (g) Microscopic pictures showing the cell structures of each core layer at panel center respectively.

lower back face deflection was therefore experienced by panel FGP-3. One should point out that the onset of delamination failure of core layer interface was related to the inconsistent deformation of the bonded core layers. When the material density of the upper core layer is lower than that of the lower one, the dynamic crush rate of upper core layer obviously outpaces the one of lower core layer. Under this circumstance, the adhesive layer would go into the state of compression. Conversely, if a relative high-density material is adopted by the upper core layer, the lower core layer is likely to move away from the explosion at a velocity outpacing the dynamic crush rate of upper core layer. Then, the large differential displacements result in an evident tensile stress in adhesive layer. Note that the adhesive layer is more likely to break away in tension due to its relative low fracture toughness under tensile condition. This is the reason why the delamination failure was only observed at panel FGP-2 and panel FGP-3. Therefore, it can be concluded that the optimization of core gradation was an effective strategy for blast resistance improvement but likely brought delamination failure onto the graded core.

Fig. 18. Maximum deflections of front and back face sheet of sandwich panels with different core arrangements.

3.2.2. Comparison with ungraded single-layer sandwich panel As aforementioned, under the condition of same areal density, the sandwich panels with ungraded single-layer core and functionally graded core were designed to make a comparison on the blast resistance. Apparently, there was no difference between the ungraded sandwich panel (viz. panel USP-9) and three graded sandwich panels (viz. panels FGP-1, FGP-2 and FGP-3) in the deformation modes of face sheets, as shown in Figs. 14(a), 15(a), 16(a) and 17(a). However, comparison of the permanent face sheet deflections indicates that the benefit of functionally graded panel was dependent upon the core

determined by the momentum intensity transferred from upstream part and the supporting effect of downstream part. A higher density material of either upstream part or downstream part would improve the crushing level of current core layer. So, the highest density material (H200) was applied at the second core layer of panel FGP-3. In contrast with panel FGP-2, this intentional design indeed increased the crushing deformation of the first core layer and third core layer. This means that the core of panel FGP-3 provided more assistance to mitigate the shock wave. A 12

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gradation. Both the graded panel FGP-2 and panel FGP-3 exhibited a lower face sheet deflection relative to the ungraded panel USP-9, but instead panel FGP-1 suffered a higher face sheet deflection, as shown in Fig. 18. Using the face sheet deflection of the ungraded panel USP-9 as a benchmark, the graded panel FGP-3 with middle/high/low core gradation gives a decrease of maximum deflections by 3.18% for front face and 5.49% for back face, respectively. Note that the existence of adhesive interfaces in the graded core could make an impact on the core failure mechanisms relative to the ungraded core. On the one hand, the adhesive interfaces would cause cracks propagating through the foam core to be arrested at these boundaries. As a result, the through-thickness cracking could be prevented by the graded core. On the other hand, since the adhesive interfaces were vulnerable to fail under external load, the delamination failure prevailed at the interfaces of graded cores. In general, an optimal design of core gradation would bring benefits for blast resistance in terms of the face sheet deformation and core cracking failure, but also was required to face the risk of delamination failure.

being crushed. In contrast, the whole core with decreasing relative density would be crushed simultaneously. The stress transmitted to back face therefore depends upon the strength of the softest layer. In addition, the energy absorption capability of the strongest core layer would be exploited much more sufficiently. So, the graded core with increasing relative density would dissipate less energy but transmit higher stress to back face relative to the one with decreasing relative density. The underlying mechanism of Regime D is similar to that of Regime C. The graded core with decreasing relative density still has the best energy absorption efficiency. Therefore, the graded core with decreasing relative density should be more suitable in Regime C and Regime D. The limited compression of graded core and evident deformation of back face sheet shown in the specimens of Ref. [30] meant that the response of those specimens went into Regime A. The response of the graded panels of Ref. [36] should belong to Regime B due to the negligible back face deformation and evident core crushing deformation. On the contrary, the grades panels of Refs. [32,37] exhibited considerable back face deformation and core crushing. This behavior coincided the feature of Regime C. Note that each core layer of graded panels of Ref. [38] went into the densification state and the back face suffered large plastic deformation. This is the feature of Regime D. Actually, the response of the graded panels of Ref. [33] and the graded specimens in present study should fall in between Regime C and Regime D, as a result of that only partial core layers were completely densified. Under this circumstance, the highest density material applied at the middle core layer is likely to improve the energy absorption of whole core. Therefore, the graded core with the middle/high/low gradation performs as well as or even better than that with high/middle/low gradation. In general, these inconsistent findings could be recognized reasonably. Suggestions of the optimal core gradation for blast resistance improvement should incorporate with the matching relationship between core stiffness and face-sheet stiffness and the level of impulsive load.

3.2.3. Comparison with other functionally grade sandwich structures Some useful studies regarding the effect of core gradation for the sandwich beam/plate/shell have been carried out in recent times. Surprisingly, inconsistent recommendations on the optimal design of core gradation were given by different research groups. For instance, an experimental study by Wang et al. [30] demonstrated that the sandwich panel with densities of the graded core increasing from the impinged side to the distal side possessed superior blast resistance. The similar conclusion has been drawn by Jing et al. [36] when they investigated the blast resistance of sandwich panels with layered gradient metallic foam core. However, numerical work by Liu et al. found that the graded core with decreasing relative density offers an excellent blast resistance for sandwich-walled hollow cylinders [32] and square sandwich plates [37]. Experimental work on the square sandwich plates with honeycomb core confirmed this phenomenon [38]. Furthermore, the graded core with decreasing relative density can also effectively improve the blast resistance of sandwich spherical shell, but the middle/high/low density core gradation has the best performance [33]. The finding of present paper is consistent with the result of Ref. [33]. Obviously, the intrinsic mechanisms underlying the inconsistent findings from literatures are critical for the application of graded core in sandwich structures. The performance of graded core should be related to the response type of sandwich structures. Four response types have been defined by Liang et al. [39] and Tilbrook et al. [40], as follows: Regime A is the condition that the core strength is strong enough to deform the back face sheet with low stiffness easily; Regime B is the one that the core is too soft to produce plastic deformation on back face sheet with high stiffness during the core compression process; Regime C is the instance where the core strength and back face stiffness were at an intermediate level and the impulsive load is relatively small; Regime D is similar to Regime C, but the impulsive load is relatively high to fully densify the whole core. For the Regime A, only partial foam core densification occurs and thus the stress transmitted to distal face is mainly determined by the yield strength of the softest layer of graded core. Moreover, the softer the first impacted core layer, the lower the work obtained by the panel. So, the graded core with increasing relative density behaves excellent in Regime A for resisting blast loading. In the Regime B, the effects of energy absorption of whole panel play a dominant role to the deformation of back face. Herein, the graded core with increasing relative density could improve the energy absorbed by front face and graded core to reduce the back face deformation. Different from Regime B, the back face would suffer plastic deformation during the compression phase in Regime C, and the graded cores with different gradation exhibit different deformation modes. For the graded core with increasing relative density, the entire graded core deforms progressively from the softest layer to the strongest layer. Thus, the stress transmitted to back face is determined by the core layer

4. Conclusions A series of experimental investigations were conducted to study the performance of sandwich panels with ungraded/graded foam cores subjected to air blast loading. Main attention of this study focused on the influences of front and back face thickness, core thickness and density, and the core gradation on the blast performance in terms of the permanent deformation, failure modes and associated mechanisms. In addition, the blast performance of sandwich panel with ungraded foam core was compared with that of panels with graded foam core. Based on the investigations, the following conclusions are drawn: 1. The sandwich panels with ungraded/graded foam cores mainly suffered a localized dishing deformation of front face and a global dome deformation of back face. Meantime, failure modes displayed by foam cores included crushing, bending, cracking and delamination. 2. Blast resistance in terms of permanent deformation could be enhanced by increasing the thickness of both two faces. However, by increasing the thickness of the face sheet towards the blast rather than the other sheet, one would be able to achieve a more effective design against air blast. A thinner front face would produce a higher level of crushing deformation of foam core. In contrast, a thinner back face would aggravate the cracking failure of foam core. 3. Adopting a thinner core resulted in a higher back face deflection and a lower front face deflection, as a result of the different deformation mechanisms associated with two faces. As for the foam core, a more evident bending and crushing deformation could be observed with the decrease of core thickness. 4. For the panels with same areal density, but different core density, the panel system with a low-density (large thickness) core appeared 13

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to be an excellent blast energy absorber for the mitigation of back face deformation. 5. Core gradation has an effect on the two primary mechanisms, namely the mitigating of shock wave and the transferring of momentum, underlying the overall performance of sandwich panels with graded core. Combining these mechanisms result in that the overall performance of the sandwich panel with middle/high/low core gradation is the best one, followed by the panel with high/ middle/low core gradation and the one with low/middle/high core gradation. 6. The comparison between the ungraded panel and graded panel under same areal density indicates that the graded panel with an optimal core gradation would bring benefits for blast resistance in terms of the face sheet deformation and core cracking failure, but also was required to face the risk of delamination failure. 7. The optimal core gradation depends upon the response types of graded sandwich panels. The graded core with increasing relative density behaves excellent in Regime A and Regime B for resisting blast loading, while the graded core with decreasing relative density is suitable in Regime C and Regime D.

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Acknowledgments The authors kindly acknowledge the financial support provided by National Natural Science Founding of P.R. China under grant numbers of 51509096 and 51679098. The authors also thank the support provided by the Fundamental Research Funds for the Central Universities under grant number of 2017KFYXJJ006. References [1] Banhart J. Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci 2001;46(6):559–632. [2] Karlsson KF, Tomas Åström B. Manufacturing and applications of structural sandwich components. Compos Pt A-Appl Sci Manuf 1997;28(2):97–111. [3] Lu G, Yu TY. Energy absorption of structures and materials. Cambridge: Woodhead Publishing Ltd; 2003. [4] Gibson LJ, Ashby MF. Cellular solids: structure and properties. 2nd ed. Cambridge: Cambridge University Press; 1999. [5] Wadley HNG. Multifunctional periodic cellular metals. Philos Trans R Soc A-Math Phys Eng Sci 1838;2006(364):31–68. [6] Zhu F, Lu G. A review of blast and impact of metallic and sandwich structures. EJSE Special Issue: Loading on Structures 2007:92–101. [7] Dharmasena KP, Wadley HNG, Xue Z, et al. Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading. Int J Impact Eng 2008;35(9):1063–74. [8] Zhu F, Zhao L, Lu G, et al. Deformation and failure of blast-loaded metallic sandwich panels—experimental investigations. Int J Impact Eng 2008;35(8):937–51. [9] Nurick GN, Langdon GS, Chi Y, et al. Behaviour of sandwich panels subjected to intense air blast – Part 1: Experiments. Compos Struct 2009;91(4):433–41. [10] Zhang P, Liu J, Cheng YS, et al. Dynamic response of metallic trapezoidal corrugated-core sandwich panels subjected to air blast loading – an experimental study. Mater Des 2015;65:221–30. [11] Li X, Wang Z, Zhu F, et al. Response of aluminium corrugated sandwich panels under air blast loadings: experiment and numerical simulation. Int J Impact Eng 2014;65:79–88. [12] Zhang P, Cheng YS, Liu J, et al. Experimental and numerical investigations on laserwelded corrugated-core sandwich panels subjected to air blast loading. Mar Struct 2015;40:225–46. [13] Cui X, Zhao L, Wang Z, et al. Dynamic response of metallic lattice sandwich structures to impulsive loading. Int J Impact Eng 2012;43:1–5.

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