Experimental investigation on the performance of PVC foam core sandwich panels subjected to contact underwater explosion

Journal Pre-proofs Experimental investigation on the performance of PVC foam core sandwich panels subjected to contact underwater explosion Tianyu Zhou, Yuansheng Cheng, Yanjie Zhao, Lunping Zhang, Haikun Wang, Ganchao Chen, Jun Liu, Pan Zhang PII: DOI: Reference:

S0263-8223(19)32710-2 https://doi.org/10.1016/j.compstruct.2019.111796 COST 111796

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

22 July 2019 25 November 2019 9 December 2019

Please cite this article as: Zhou, T., Cheng, Y., Zhao, Y., Zhang, L., Wang, H., Chen, G., Liu, J., Zhang, P., Experimental investigation on the performance of PVC foam core sandwich panels subjected to contact underwater explosion, Composite Structures (2019), doi: https://doi.org/10.1016/j.compstruct.2019.111796

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Full Title of Article: Experimental investigation on the performance of PVC foam core sandwich panels subjected to contact underwater explosion Authors: Tianyu Zhou 1,6, Yuansheng Cheng 1,2,3, Yanjie Zhao 4,5, Lunping Zhang 4, Haikun Wang 4,5, Ganchao Chen1, Jun Liu 1,2,3, Pan Zhang 1,2,3*

Corresponding affiliations: 1

School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

2

Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China

3

Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamic, Wuhan 430074, China

4

China Ship Scientific Research Center, Wuxi 214082, China

5

Maritime Defense Technologies Innovation Center, Wuxi 214082, China

6

Institute

of

Advanced

Manufacturing

Engineering,

Chongqing

University

of

Posts

and

Telecommunications, Chongqing 400065, China

Please send the proofs and address any correspondence on this paper to the corresponding authors:

Dr. P. Zhang

School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China P.R. China

Tel.: +86 27 87543258 Fax: +86 27 87542146

*

Corresponding author. Tel.: + 86 27 87543258; fax: +86 27 87542146. E-mail address: [email protected] (P. Zhang). 1

E-mail: [email protected]

2

Abstract: This paper presents a blast experiment to investigate the performance of sandwich panels with metallic face sheets and ungraded/graded polyvinyl chloride (PVC) foam cores subjected to contact underwater explosion. The deformation and failure modes of the sandwich panels were identified and classified. The protective effect of sandwich panel was also evaluated by setting a witness plate. Particular attention was concentrated on the effects of the charge weight, face-sheet configuration, core height, and core gradation. Experimental results reveal that the panel front face suffered severe petalling failure and generated structural fragments; the PVC foam experienced spider-web-like crack failure and perforation failure; while the back face failed into petalling mode or plastic deformation without fracture. The increase of charge weight worsened the panel failure level as expected, yet did not affect the failure mechanisms. Adopting a thick core would benefit sandwich panel in terms of both the energy absorption enhancement and the damage level reduction. The panel system with a thick back face and a thin front face performed better in protecting the witness plate than the one with reverse configuration. Moreover, through designing the graded core with high/middle/low configuration, the panel performance could be further improved. Keywords: Sandwich structure; Foam core; Graded material; Underwater explosion; Blast experiment

1. Introduction In the past few decades, an area that has been of interest to warship designers is to make the structure be light in weight, whilst withstand and mitigate the blast loadings. Hitherto, a number of new materials and structures have been proposed to address these concurrent objectives in naval and civic industries [1-4]. Especially for the sandwich structure, it consists of two thin, stiff, strong face sheets and a soft-core layer. This particular configuration endows them with the unique and unbeatable combination of properties, such as high strength-to-weight ratios, high stiffness-to-weight ratios, and superior energy absorbing capability [5, 6]. When subjected to blast loading, the separated face sheets were expected to provide an advanced bending stiffness, while soft core would absorb huge energy through crushing deformation [7]. It offers excellent potential for the mitigation of high-intensity dynamic loads, and thus protects the personnel or objects located behind them [8, 9]. It is well known that the underwater explosion is one of the main threat factors to induce serious damage to warships. Therefore, numerous attentions have been devoted to this topic regarding conventional ship structure 3

in the early days [10]. From the 1980s, the work to address a similar problem with foam core sandwich structures was followed by related researchers [11]. More recently, Fleck and Deshpande [12] theoretically demonstrated the superior performance of sandwich panel with metallic foam core over the monolithic counterpart of equal mass to resist underwater explosion. It is mainly due to the fact that the reduced mass of the sandwich front face leads to a reduction of the impulse transmitted to the structure during the fluid-structure interaction (FSI) process. By employing the shock tube apparatus, Latourte et al. [13] studied the dynamic behavior of the sandwich panel with polyvinyl chloride (PVC) foam core. Avachat and Zhou [14, 15] analyzed the damage of composites sandwich structures with PVC foam core loaded by water-based impulses. In their tests, high-speed photography was employed to reveal the failure mechanisms of sandwich panel, including core indentation, core shear, core-face debonding, face sheet buckling and delamination, structural collapse and rupture. As expected, the existence of core layer could affect the failure mechanisms of sandwich panel. Arora et al. [16] employed the high-speed DIC technology to monitor the deformation of the sandwich panel with styrene acrylonitrile (SAN) foam core subjected to underwater explosion. The results indicated that the medium behind the sandwich panel has a significant effect on the failure mechanism. Chen et al. [17] performed combined experimental and numerical investigation into the deformation and damage characteristics of aluminum foam sandwich panel under air blast loading. The optimal mass allocation strategies for the reduction of deformation response were systematically analyzed. Huang et al. [18] conducted an experimental investigation into the dynamic failure of PVC foam core sandwich panels subjected to water-based impulsive loading. It revealed that the back face deflection is sensitive to impulse intensity, while the front face deflection is sensitive to the density of core. To gain further improvement in blast resistance, a series of novel design concepts have recently been developed based on the conventional sandwich structures, such as filling the empty space of periodic cellular core with foam material [19-21], inserting the ductile interlayer between the face sheets and the foam core [22], and adopting functionally graded foam as the core layer [23-25]. Especially for the last one, both the density and the strength of core layer could be designed to vary in the thickness direction. This intentional design is expected to optimize the mechanical properties of the overall graded material. Due to the potential in the enhancement of shock wave mitigation, a growing number of studies focus on the performance of sandwich structures with graded cores under blast loading. For instance, Wang et al. [23] and Gardner et al. [24] employed a shock tube apparatus to examine the effect of core layer gradation and the number of graded foam core layers 4

on the blast resistance. Zhou et al. [25] examined the dynamic performance of sandwich panels with ungraded and graded PVC foam cores by conducting air blast tests. Jing and Zhao [26] investigated the dynamic response and energy absorption of sandwich panels with layered gradient foam core under air blast loading. Jin et al. [27] numerically studied the graded effects of metallic foam cores for the spherical sandwich shells subjected to close-in underwater explosion. Chen et al. [28] searched for the optimal design of graded aluminum foam sandwich panel under air blast loading by adopting adaptive response surface method (ARSM) and multi-objective genetic algorithm (MOGA). Due to the high efficiency and low cost, underwater weapons for attacking the warships, such as the torpedo, mine, and depth charge, are extensively used in modern naval warfare. These weapons are designed to be detonated near or contact to the hull structure, which is known as contact underwater explosion. Keil [29] early reported the work on contact underwater explosion damage of ships, and developed an empirical formula to predict the hole radius on monolithic steel plates. Followed by Rajendran and Narasimhan [30], they proposed a new theoretical framework considering the effects of material strength and explosive parameters for the damage prediction of monolithic plates. Zhang et al. [31] experimentally investigated the behavior of multi-layered metallic structures loaded by contact underwater explosion. An experimental and numerical study on the monolithic plate was carried out by Ming et al. [32]. The results revealed the deformation and damage mechanisms of the monolithic plate, including the bulging, petalling failure and fragment ejection. The literature on the monolithic plates subjected to contact underwater explosion is abundant. Nevertheless, studies on the ungraded and graded sandwich panels loaded by contact underwater explosion are quite limited. In this paper, the experimental results of the sandwich panel with ungraded and functionally graded PVC foam core subjected to contact underwater explosion are presented. The blast performance of sandwich panels is evaluated by the response of the witness plates behind them. Deformation/failure modes of sandwich panel and witness plate are identified and classified in detail. Particular focus is placed on identifying the influence of the charge weight and key structural parameters (viz. face-sheet configuration, core height and core density gradient) on the performance of sandwich panel.

2. Experiment details 2.1. Background and experimental setup In general, the sandwich panel is always being used as a sacrificial structure to protect the object behind it from the potential threats of intensive loadings. Considering the back face of sandwich panel serves as the last 5

protective barrier, its deformation is usually used to evaluate the blast resistance when it succeeds to keep its integrity. However, the contact blast loading would likely cause the sandwich panels failing catastrophically. Once the back face undergoes fracture failure, the blast-induced fragments and the residual shock wave would directly impinge upon the protected object. Under this situation, the damage of the protected object deserves special attention. To get a quantitative insight into the protective effect of sandwich panel, a suite of apparatus (see Fig. 1(a)) was designed and fabricated for conducting contact underwater explosion tests. Fig. 1(b) illustrates the sketch of the set-up configuration. The main body of the apparatus is like a drum with an inner “septum”. The inner diameter of the steel drum is 1000 mm. A sandwich panel and a monolithic plate were employed in each test. The sandwich panel was fixed on the “top head” as the barrier structure to mitigate blast loading; while the monolithic plate was fixed on the “septum” as the witness plate to assess the protective effect of sandwich panel. Both sandwich panel and witness plate were bolted to the fixture using a 20 mm thick flange and a series of through bolts. Actually, the “top head” and “septum” were made by 30 mm thick steel plates to keep enough strength and stiffness, and had a circular hole with 460 mm in diameter at the central region. The chambers below the “top head” and “septum” provided the air-backed condition and sufficient deformation space for the sandwich panel and witness plate, respectively. By using lifting equipment, the whole test assembly was submerged in 500 mm depth, which is the separation distance from the front face of sandwich panel to the water surface. All experiments were implemented in a shock tank (at China Ship Scientific Research Center) with dimensions of 10 m × 3 m × 4 m, as shown in Fig. 1. The depth of water in the shock tank is about 3 m. To generate contact underwater explosion load, a cylindrical TNT explosive fixed on the top surface of the sandwich panel, as shown in Fig. 1(b), was remotely detonated by an instantaneous electrical detonator. [Insert Fig. 1] The present study aims to assess the protective effect of PVC foam core sandwich panels subjected to contact underwater explosion by using the maximum deflection of witness plate. Thus, it is essential to ensure that the witness plate experiences considerable plastic deformation without fracture damage. In the preliminary experiments, the equivalent solid plates were used as the target structure [33]. The results indicated that a 40 g charge would induce a capping with enough high momentum to penetrate the witness plate. Under this condition, the plastic deformation of witness plate cannot be employed to evaluate the protective performance of target 6

plates. Then, the charge weight was lowered to 17g and 26g to decrease the initial velocity of the blast-induced fragment. Meanwhile, a layer of water with a depth of 50 mm was infused into the upper chamber to decay the velocity of the fragment. By doing so, the witness plate only experienced large inelastic deformation without fracture. It provides acceptable results to evaluate the protective performance of the blast-loaded plate. Thus, the explosive arrangements and the application strategy of infused water (see Fig. 1) were adopted in the present study. 2.2. Specimens Two groups of circular sandwich panels with a diameter of 580 mm, were examined in the present study: i) ungraded sandwich panel and (ii)) functionally graded sandwich panel. The ungraded sandwich panels were fabricated from two metallic face sheets bonded to a single PVC foam core layer, as shown in Fig. 2(a). A total of six ungraded sandwich panels were manufactured as listed in Table 1. Firstly, to investigate the effect of charge weight on the deformation/failure modes, two nominally identical sandwich panels (UG-1 and UG-2) were loaded by explosives with different charge weight (W) of 17 g and 26 g, respectively. Then, the attention was turned to analyze the influences of geometric parameters on the dynamic response of PVC foam core sandwich panels. The sandwich panel UG-3 was considered as the reference panel, and the charge weight was kept constant at 26g. By intentionally varying both front face thickness (tf) and back face thickness (tb), panels UG-2 and UG-4 were employed for the investigation of face-sheet configuration effect based on equal weight design. Additionally, panels UG-5 and UG-6 with identical face-sheet configuration were employed to investigate the effect of core height (HC). The functionally graded sandwich panel was constructed by replacing the single-layer foam core with three PVC foam core layers, as schematically shown in Fig. 2(b). The thickness of each foam core layer was fixed at 11 mm. Two types of functionally graded sandwich panels with the same face-sheet configuration but different core layer gradations were designed and tested. Panel FG-1 consisted of a core gradation of H60/H130/H250 (low/middle/high density), while the core gradation of panel FG-2 was just the reverse of the one of panel FG-1. 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 1. [Insert Fig. 2] [Insert Table 1] The face sheets and foam cores were bonded together using epoxy adhesive at room temperature. Additionally, 7

a 2.8 mm thick circular solid plate, with the identical in-plane diameter of sandwich panel, was employed as the witness plate for each test. 2.3. Material properties The base material of the face sheets of sandwich panel and the witness plates is 304 stainless steel. The mechanical properties of it, 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 and tensile strength σp = 740 MPa. The core materials of sandwich panel used in present study were Divinycell H series PVC foams, which were manufactured by DIAB Group specifically for sandwich composite applications. Three types of Divinycell H foam were adopted, namely H60, H130, and H250. Table 2 lists the important material properties of the three foams from the manufacturer’s data (http://www.diabgroup.com), while Fig. 3 shows the typical quasi-static uniaxial compressive stress-strain curves of these foams. [Insert Table 2] [Insert Fig. 3] 3. Experimental results The experimental results are classified and presented according to three aspects: (1) observations with respect to typical deformation/failure modes of sandwich panel, (2) typical response of witness plate, and (3) quantitative results. Details of these three types of results are presented in the following subsections. [Insert Table 3] 3.1. Deformation and failure modes of sandwich panel 3.1.1. Face sheet Nurick and Radford [34] firstly classified the typical failure modes of circular monolithic plates subjected to localized central blast loads. The onset of these failure modes should be associated to the dynamic response process. When loaded by a localized central blast, the plate firstly undergoes a large global inelastic deformation accompanied by a circular thinning in the central region. However, the plate keeps its integrity, and no fracture failure takes place on the plate. It results in the plate failed in Mode Itc. As the thinning continues to grow, the partial tearing (identified as Mode II*c) occurs at the thinning ring. It is followed by the complete tearing (Mode IIc) in the central area, which detaches the circular cap from the plate. Then, radial cracks originate from the initial hole and propagate outward, while the subsequent rotation of plate segments leads to a number of petals. It is referred to as the “petalling” mechanism. 8

Herein, the face sheets of sandwich panels mainly exhibited two typical failure modes: Mode Itc and Petalling. Actually, according to whether a cap fragment is ejected from the central region or not, the Petalling failure mode could be divided into two subcategories as follows: 

Mode PI - petalling without the ejection of a cap fragment, and



Mode PII - petalling with the ejection of a cap fragment from the central region.

Table 3 lists the failure modes observed on the front and back faces. It seems that the front faces of all specimens failed in Mode PII. Fig. 4 shows the typical failure mode of front face. It is clearly seen that the radial crack originated from the central region and propagated outward, and finally divided the front face into several segments. Due to the rotation of plate segments, a number of petals were formed, producing a large hole in the central region, as shown in Fig. 4(a). Moreover, the central region was smoothly cut off and ejected as a cap fragment which is named as “front cap” here (see Fig. 4(b)). [Insert Fig. 4] The back face was loaded by the impact of front cap and the shock wave transmitted from core layer. From the observation of test results, three different modes (viz. Mode Itc, Mode PI and Mode PII) could be identified on the back faces, see Fig. 5. A typical back face failing in Mode Itc is shown in Fig. 5(a). Thanks to the mitigation effect of core, the shock wave was substantially weakened and homogenized by the time it reached back face. It results in that the back face deformed globally in the effective loading area. Meanwhile, the impact of front cap gave rise to the occurrence of localized dome in the center of back face. There exists a markable change in the displacement gradient at the boundary (namely, the inflexion point) between the global dome and inner dome. The high displacement gradient resulted in the plastic instability in the form of localized thinning, as shown in the enlarged image in Fig. 5 (a). The outline of the front cap is nearly circular, so that the occurrence of the circular thinning ring suggests a normal impact by the front cap. As the velocity of front cap increased, larger localized deformation would be obtained by back face and induce the increase of tensile stress. Once the tensile stress exceeded the material fracture toughness, the back face would fail to keep its integrity and fracture in the localized dome, which is referred as Mode PI failure mode, as shown in Fig. 5(b). Then, a crack originated from the center point and branched into two cracks near the localized dome, followed by the propagation along the radial direction. The intensity of localized impulse acting on the back face could be significantly increased with the increase of the the velocity of front cap. It results in that the central region was cut off as a cap fragment (named as “back cap”) with the irregular shape (see Fig. 5(d)). The remaining part 9

failed in a petalling pattern, as shown in Fig. 5(c). It is noteworthy that the fixing holes of the back face failed in Mode Itc experienced significant inelastic deformation, as shown in Fig. 5 (a). This is due to that the global bending and stretching deformation induced the considerable in-plane tensile force to the back face. The size of the tensile force would increase in the whole deformation process. Once the tensile force reached a threshold value, the fixing holes would go into the yielding state. However, for the back face failed in Mode PI and Mode PII, the impact of front cap gave rise to the initial fracture in the central region, followed by the propagation of the radial cracks. Due to the tearing failure in a large region exhibited by the back face, the state of membrane stretching of plate would be affected. Under this scenario, the tension force transmitted to the fixing holes was limited. Therefore, the plastic deformation of fixing holes of back face failed in Mode PI and Mode PII is not such evident (see Fig. 5(b) and (c)) relative to the scenario when the plate failed in Mode Itc. [Insert Fig. 5] 3.1.2. Characteristics of fragment In this study, the front and back caps were collected after testing, as shown in Fig. 6. From an examination of the released cap fragments, it is apparent that most of the front caps maintained a circular shape with a smooth edge. The diameters of the front caps were similar to the charge diameter. In contrast, the back caps possessed more irregular shape and larger size relative to the front caps. The onset of this phenomenon can be attributed to the different failure mechanisms exhibited by the central region of front and back faces. Generally, when transversely loaded by a localized blast/impact loading, the plate will obtain a non-uniform velocity field, resulting in a localized shear band formed in the vicinity of load boundary. Meanwhile, tensile behavior takes place due to the bending deformation of plate. It leads to either a tearing failure or a shearing failure, depending on the loading rate and intensity [35]. Under low-intensity impulse loading, the central region tends to experience a large bending deformation before the onset of rupture failure. Consequently, the tension-dominated tearing failure would form in the central region of plate. The tearing crack would like to originate from the point where the maximum deflection occurred. Then, the central region tear in a ‘‘petalling’’ fashion, and none cap fragment is formed in this subcategory (Mode PI). When the plate was subjected to high-intensity impulse loading, the shear stress in the shear band would be more remarkable. Pure shear failure is likely to occur in the central region and cut off the central region with a smooth edge. However, for the case of moderate-intensity impulsive loading, there exists both bending deformation and shearing deformation as expected. Therefore, a synthesis failure with tensile- and shear- dominated damage would occur in the central region of plate. An 10

undesirable deviation in boundary condition and impact loading is likely to affect the tearing failure. Finally, it will produce an irregular cap releaded from the loaded plate. For the front face, the high-intensity blast loading directly acted on the central region, resulting in the larger shear stress in the vicinity of the central region. Thus, the front cap was more likely to be smoothly cut off (see Fig. 6) by the pure shear failure. In contrast, a relatively lower impact loading acted on the back face due to the attenuation effect of core on the front cap velocity. The tearing failure dominated by the mixed mode of tensile and shear fracture formed on it. Consequently, the irregular cap released from back face could be observed, as shown in Fig. 6. Note that there is also some difference in the shape of back caps. A comparison of the back caps of ungraded panels shows that the back cap of panel UG-3 is significantly larger and more irregular than those of panels UG-4 and UG-5. The reason for this is that the panel UG-3 consists of a thicker back face relative to panel UG-4, and a higher core layer relative to the UG-5. It enhanced the shear strength of back face and the mitigation effect of core for panel UG-3. Thus, tensile behavior was more remarkable in the central region of the back face of panel UG-3, resulting in a more irregular back cap. Additionally, thanks to the superior energy absorption [36], the graded foam cores offerred a superior perforation resistance to the ungraded ones [37, 38]. It enhanced the effect of core on the attenuation of the momentum of front cap. Thus, the front cap of graded panel was more effectively decelerated before it reached the back face. It highlighted the tensile behavior in the central region. Consequently, the irregularities of the back caps of graded panels are more significant than those of ungraded ones, see Fig. 6. [Insert Fig. 6] 3.1.3. Foam core The core is compressed by front face and supported by back face. Hence, the failure mode of core shows a strong relationship with the failure mode of faces. However, all of the front faces failed in the same failure mode (viz, Mode PII). So, the failure mode of core would mainly depend upon the failure mode of back face. Fig. 7(a)-(c) show the post-mortem photographs of the cores of the panels whose back faces failed in different modes, respectively. When the back face of sandwich panel failed in Mode Itc, the core exhibited crushing and inelastic bending deformation (see Fig. 7(a)). With the development of bending deformation, the spider-web-like cracks emerged on the core. Additionally, loaded by the impact of front cap, the core layer was perforated in the central region. When the back face failed in Mode PI, the core would fail into a more serious situation as shown in Fig. 7(b). 11

The spider-web-like cracks became denser due to the larger bending deformation. Meanwhile, a circular hole caused by the impact of front cap was observed in the central region. On the other hand, the supporting effect of back face to the core would be absent once the petal of back face formed. Consequently, the core was sheared-off in this region and released a core fragment. Careful examination of the fragment (see Fig. 7(d)) reveals that the state of core compression gradually decreased from the center to the outskirts. However, the core compression was relatively low, presumably as a result of that the strength of core was high enough to move the back face at the plateau regime of foam material. Moreover, the visible soot deposit emerged near the central region. It suggests that the core had been scorched by the hot front cap and the hot gas produced by detonation. When the back face failed in Mode PII, the back face would lose its function of supporting effect on core. It would be inferred that severe spider-web-like cracks were formed on the core due to the large bending deformation. Then, the crack propagated through core thickness, and divided the core layer into multiple fragments (see Fig. 7(c)). [Insert Fig. 7] 3.2. Deformation and failure of witness plate The witness plates seems to remain intact and have no macroscopic plastic deflection when the back face of sandwich panels failed in Mode Itc and Mode PI. It implies that the sandwich panel with back face failed in Mode Itc or Mode PI could effectively shield the protected object from the blast loading. In contrast, once back face failed in Mode PII, the shock wave leaking from back face combined with the high-velocity fragments would work upon the witness plate and cause it to undergo a large inelastic deformation (mode Itc), as shown in Fig. 8(a). On the one hand, the witness plate exhibited a global bending deformation in the effective loading region. It occurred with a plastic hinge branding at the periphery of the effective loading area. On the other hand, a local indentation (see Fig. 8(b)) was observed in the central area of witness plate. Note that a shape scratch emerged in the local indentation. It reveals that the local indentation was associated with the impact of caps ejected by the front and back faces of sandwich panel. The failure modes of witness plates are also summarized in Table 3. [Insert Fig. 8] [Insert Table 3] 3.3. Quantitative experimental results After testing, the average crack lengths of the face sheets failed in Mode PI or Mode PII, as well as the 12

maximum deflections of the face sheets failed in Mode I, were measured. These data are listed in Table 3 and are used to quantify the damage level suffered by face sheets. Table 3 also includes the maximum permanent deflections of witness plates, which are used to evaluate the protective effect of sandwich panel. It should be pointed out that the location, where the maximum permanent deflection occurred, was not always at the center point of plate. It is due to the asymmetry of external loading caused by the asymmetric fracture of sandwich panel. 4. Analysis and discussion 4.1. Effect of charge weight In order to gain insight into the effect of charge weight, two identical specimens (panels UG-1 and UG-2) were loaded by explosives with distinct charge weights of 17 g and 26 g, respectively. The post-mortem results of panels UG-1 and UG-2 are shown in Fig. 9. From the observation on panel UG-1, it could be deduced that the front face firstly acquired a non-uniform velocity field through the interaction with contact explosion. It is followed by the onset of front cap released from the central region and the bending/stretching deformation of the remaining part. Then, several cracks originated from the central region and divided front face into several petals. Finally, the residual kinetic energy of front face and the follow-up load caused the subsequent propagation of cracks and the rotation of petals. The measured average crack length of front face is 66.7 mm. Loaded by the momentum transmitted from front face, the foam core experienced compression and bending deformation. The bending deformation was so large that the spider-web-like cracks originated at foam core and propagated all over it. Meanwhile, the core was perforated by the front cap, resulting in a perforation hole in the central region. Note that the diameter of the hole is about 75 mm, which is significantly larger than the dimension of front cap. The possible reason for this phenomenon is that the front cap perforated core at a velocity much higher than the deformation velocity of core. A perforation hole was initially formed in the core. Then, with the development of bending deformation, the hole would be stretched to some extent. Moreover, the scorching of core caused by the hot front cap and the hot gas also expanded the penetration hole. The back face suffered a localized dome deformation in the central region and a large global bending deformation at the peripheral region. The measured maximum deflection of back face is 72.44 mm. The photographs showing the deformation/failure modes of panel UG-2 loaded by a heavier explosive are also included in Fig. 9. As expected, panel UG-2 suffered severer petalling failure of front face and worst cracking failure of foam core relative to panel UG-1. Fig. 10 shows the side views of each component of panel 13

UG-1 and panel UG-2. It demonstrated the larger back face deformation experienced by the panel UG-2. To be specific, the maximum back face deflection of panel UG-2 is 94.42 mm, which is larger by 30.34 % relative to that of panel UG-1. A larger deformation means a higher tension force acting on the fixing holes. Therefore, the yielding phenomenon at the fixing holes is much more evident for panel UG-2 relative to panel UG-1, as shown in Fig. 9. However, the failure mechanisms displayed by two panels have a negligible fundamental difference. Although the back face of UG-2 underwent a more evident bending/stretching deformation (see Fig. 10), it still maintained its integrity. Consequently, the front face and foam core still got the supporting from back face even though obvious bending deformation occurred on them. Under this situation, there is no visible plastic deformation on the witness plate can be found. [Insert Fig. 9] [Insert Fig. 10] 4.2. Effect of face-sheet configuration The effect of face-sheet configuration was analyzed by varying both front and back face thicknesses on an equal weight basis (panels UG-2, UG-3, and UG-4), see Fig. 11. It seems that the response of sandwich panel was sensitive to face-sheet configuration. With the increase of front face thickness as well as the decrease of back face thickness, the hole in front face evidently expanded. The failure mode of back face transitioned from Mode Itc in panel UG-2 to Mode PII in panels UG-3 and UG-4. Additionally, the average length of cracks that emerged on the front and back faces is nearly proportional to the thickness of front face (see Fig. 12). It indicated that allocating more mass to back face, rather than front face, would effectively enhance the performance of PVC foam core sandwich panel in terms of the damage level of faces. Face-sheet configuration is expected to have an impact on the deformation mechanisms of the sandwich panel from two primary factors: fluid-structure interaction (FSI) effect and varying mechanical properties of face sheets. For the former, weakening the stiffness of front face by decreasing its thickness would produce a stronger rarefaction wave during the FSI [10]. As a result, the impulse imparted to sandwich panel and front cap was effectively attenuated. For the latter, thickening the back face would increase its fracture toughness and bending stiffness. On the one hand, the higher fracture toughness of back face avoided the premature failure of back face. On the other hand, the increase in the bending stiffness of back face enhanced the supporting effect on front face and core. Thus, the rotation of front face petals was significantly restricted for panel UG-2 with a thick back face. Additionally, a strong supporting effect on core would benefit the energy absorption of core through its crushing deformation, 14

which is critical to the weakening of the momentum transmitted to back face. Furthermore, the stronger supporting effect of back face also effectively limited the deformation of core. Therefore, the fragment failure of core was mitigated by allocating more mass from front face to back face. Especially for panel UG-2, the fragment failure of core had even been absolutely prevented. Nevertheless, the impact of front cap still formed a through-thickness hole in the central region. As aforementioned, the back face of panel UG-2 failed in Mode Itc. It succeeded to shield the witness plate from blast loading, and avoided the inelastic deformation occurring on the witness plate. In contrast, the back faces of panels UG-3 and UG-4 failed in Mode PII. The explosion energy could act on witness plate through high-velocity caps released from front and back faces as well as the residual shock wave leaking from back face. Hence, the witness plates showed a localized deformation mode, see Fig. 11. Fig. 12 compares the maximum deflection of witness plate for the sandwich panels. It suggests that the maximum deflection of witness plate was decreased with the increase of front face thickness and the decrease of back face thickness. In other words, a feasible way to improve the protective level of sandwich panel can be achieved by allocating more mass to the back face. [Insert Fig. 11] [Insert Fig. 12] 4.3. Effect of core height Three specimens with identical face-sheet configurations but different core heights, (viz. 17 mm for panel UG-5, 34 mm for panel UG-3, and 51 mm for panel UG-6,) were examined to investigate the influence of core height. With the increase of core height, the petalling failure observed on the front face was significantly limited in extent, while the failure mode of back face transitioned from Mode PII in panels UG-5 and UG-3 to Mode PI in panel UG-6, as shown in Fig. 13. The average crack lengths (see Fig. 14) on both front and back faces decreased with the increase of core height. It implied that the damage of face sheets was alleviated by thickening the core layer. This phenomenon should be associated with the three primary roles played by foam core: i) transferring the momentum as the communication between front face and back face, ii) absorbing shock wave energy by crushing deformation, and iii) enhancing the bending stiffness of sandwich panel by separating the face sheets. The momentum transfer is mainly determined by the stress state of core layer. However, the cores of panels UG-3, UG-5 and UG-6 experienced a slight compression deformation, and the foam material still lied in the plateau region. Thus the stress transmitted to back face is mainly determined by the yield strength of core 15

layer. Note the cores for these panels were manufactured from the same foam material. It means that the core layers of these panels performed nearly equally in terms of momentum transfer. Therefore, the difference would lie in the latter two roles, viz. the energy absorption and the bending stiffness of panel. As well known, the increase of core height could extend the shock wave propagation distance in core and provide more impact energy storage. It would increase the amount of energy absorbed by the core and mitigate the momentum transmitted to back face. Meanwhile, a higher core thickness would cause an enhancement in the bending stiffness of sandwich panel as a result of a larger second moment of cross section. It is conducive to alleviate the petalling failure of back face. Besides, increasing the height of core contributed to the deceleration of front cap, which lowered the intensity of localized impact on back face. Thus, a tearing failure, rather than a shearing failure, dominated the failure mechanism of the back face central region for panel UG-6 with a thicker core layer. Meanwhile, the higher bending stiffness of the sandwich panel with thicker core indeed assisted the front face to shrink the petalling failure region. However, adopting a thicker core layer weakened the supporting effect on front face. Consequently, more localized petalling failure was observed on the front face of panel UG-6. Fig. 13 also demonstrates that fragmentation failure of core was significantly mitigated by the increase of core height. It occurs as the bending deformation of core was restricted by the strengthened bending stiffness. Under the combined loading of the front and back caps and the shock wave leaking from back face, plastic deformation emerged on the witness plates for panels UG-5 and UG-3 with back face failed in Mode PII, see Fig. 13. As aforementioned, thickening the core layer provided assistance to the energy absorption effect of core and the attenuation effect on front cap velocity. Thus, the shock energy carried by the residual shock wave and caps was effectively reduced. It is known that the deformation mechanisms are closely related to external energy. The lower the external energy, the smaller the deformation of witness plate. Herein, the maximum deflection on the witness plate tended to decrease with the increase of core height, as shown in Fig. 14. It indicates that increasing the core height indeed served as an effective approach to enhance the protective effect on the witness plate. Especially for panel UG-6, it dissipated the most blast energy, and thus none inelastic deformation was experienced by the witness plate. [Insert Fig. 13] [Insert Fig. 14] 4.4. Effect of core gradation 16

To directly evaluate the effect of core gradation on the blast resistance performance, two typical graded sandwich panels (panels FG-1 and FG-2) were tested, as shown in Fig. 15. The first glance indicated that sandwich panels with different core gradation exhibited similar deformation/failure mechanisms, including Mode PII failure on both front and back faces, and fragmentation failure on core. However, the petalling region on the front face and the hole in the core of panel FG-1 with the core gradation of H60/H130/H250 were smaller relative to those of panel FG-2 with the reverse core gradation. The rotation of the back face petals of panel FG-2 is also more evident than that observed on panel FG-1. Additionally, the average crack length (see Fig. 16) of the front and back faces of panel FG-2 was larger relative to those of panel FG-1 by 65.02% and 15.56%, respectively. [Insert Fig. 15] [Insert Fig. 16] In general, panel FG-2 experienced a severer failure relative to panel FG-1. A reasonable understanding of this phenomenon should recall the three-stage response mode of sandwich panel proposed by Fleck and Deshpande [12]. When subjected to blast loading, the front face is firstly accelerated by the blast wave while the rest of the structure is stationary (namely the fluid-structure interaction phase), see Fig. 17 (a). Then, the core layer was compressed by the front face sheet (namely the core compression phase), see Fig. 17 (b). During the core compression phase, the back face would be accelerated by the momentum transmitted from core. The core compression deformation would continuously develop until back face acquires an identical velocity with the front face. Then the whole sandwich panel will go into the structural dynamic response phase. In this stage, all components of the sandwich panel move at an identical velocity and dissipate the kinetic energy by a combination of bending and stretching deformation, see Figure 18 (c). It means that the residual height of the crushed core keeps constant during this stage. Note that the face sheets of both panel FG-1 and FG-2 failed catastrophically in Mode PII. This damage was mainly formed during the structural dynamic response phase due to the short period of time during the other phases. As mentioned in the above subsection, the core layer would contribute to the dynamic response of sandwich panel from three aspects: i) transferring the momentum, ii) absorbing shock wave energy, and iii) enhancing the bending stiffness of sandwich panel. However, the momentum transfer and energy absorption of core work effectively when the core is compressed. Thus, the residual bending stiffness dominates the effect of core on the dynamic response of panel during the structural dynamic response phase. Note that the residual bending 17

stiffness is determined by the moment of inertia over the compressed section of panel. Obviously, the higher the compression deformation of core, the lower the moment of inertia of sandwich panel. Therefore, the residual bending stiffness of sandwich panel is reduced by the core compression. Fig. 18 shows the core fragments released from the central region of panels with different core gradations. For both panels FG-1 and FG-2, the softest core layer (H60) had gone into severe damage due to its lower strength. However, the other core layers of panels FG-1 experienced lower compression deformation relative to the panel FG-2. This is due to that the strength of the core layers in panel FG-1 increased monotonously from the front face to back face. One can speculate that the entire graded core deformed progressively from the first core layer to the third core layer [25]. Thanks to the mitigation effect of the upstream core layer to shock wave, the downstream core layer experienced relative lower crushing deformation. To be specific, panel FG-1 displayed lower crushing deformation of the hardest core layer (H250) and the medium strength core layer (H130) than panel FG-2 by 91% and 6%, respectively. The lower core compression deformation of panel FG-1 enhanced its residual bending stiffness. Consequently, the more serious damage was experienced by panel FG-2, rather than panel FG-1. [Insert Fig. 17] [Insert Fig. 18] Due to the back faces of panels FG-1 and FG-2 failed in Mode PII, the caps with high velocity and the shock wave leaking from the back face would impinge upon the witness plates. It results in the witness plates exhibited a global bending deformation accompanied with a local indentation in the central region, as shown in Fig. 15. Thanks to the severe damage of core and face sheets, panel FG-2 dissipated a large amount of explosion energy. It made panel FG-2 serve as an optimum energy absorbing structure, and effectively reduced the energy transmitted to witness plate. Consequently, the witness plate for panel FG-2 experienced a lower maximum deflection relative to that for panel FG-1 by 16.37%, as shown in Fig. 16. Therefore, the panel with high/middle/low core gradation had an advantage in protective performance over the one with low/middle/high core gradation. 5. Conclusions Based on a self-designed experimental set-up, a series of experimental investigations were conducted to study the performance of sandwich panels with ungraded/graded PVC foam cores subjected to contact underwater explosion. It is proposed to evaluate the protective effect of the sandwich panel by analyzing the deformation level of the witness plate. The typical deformation/failure modes of sandwich panels were classified and 18

discussed in terms of faces, core layer, and witness plate. Main attention focused on the influences of charge mass, face-sheet configuration, core height and core gradation. From present study, the following conclusions can be drawn: 1.

Loaded by contact underwater explosion, the front face of tested sandwich panels mainly experienced Mode PII failure and released a circular fragment with the identical diameter of cylindrical explosive. The back face was likely to fail in three different modes: Mode Itc, Mode PI and Mode PII. The PVC foam core exhibited the compression, spider-web-like crack failure, fragmentation failure and perforation failure.

2.

For the sandwich panel with back face failed in Mode Itc or Mode PI, none visible plastic deformation occurred on the witness plate. Once the back face failed in Mode PII mode, the combined loading of the front and back caps and the shock wave leaking from back face would work upon witness plate. As a result, the witness plate suffered a global bending deformation accompanied with a local indentation in central region.

3.

In terms of the failure region of front face and maximum deflection of back face, the damage of sandwich panel would be aggravated by increasing charge weight. However, varying charge weight did not change the failure mechanisms of considered sandwich panels.

4.

Face-sheet configuration could affect the performance of sandwich panel through two primary mechanisms: FSI effect and varying mechanical properties of face sheets. Understanding these two mechanisms reveals that an effective design against contact underwater explosion would be achieved by decreasing the thickness of front face as well as increasing the thickness of back face.

5.

Adopting a thicker core would enhance the bending stiffness of sandwich panel, the mitigation effect on shock wave, and the attenuation effect on front cap velocity. Consequently, the petalling failure of front and back faces, the fragmentation failure of core and the plastic deformation of witness plate were effectively alleviated.

6.

Thanks to the low residual bending stiffness of overall sandwich panel and the excellent energy absorption characteristic of core, the panel with high/middle/low core gradation dissipated more explosion energy, relative to the one with low/middle/high core gradation. The panel with high/middle/low core gradation became the candidate for the barrier with excellent performance to protect the person or objects behind it. 19

Acknowledgments This work was accomplished under the support provided by National Natural Science Founding of P.R. China under grant numbers of 51679098, 51879112 and 51509096. The financial contributions are gratefully acknowledged. The authors wish to express sincere gratitude to Mr. Cong Liu and Mr. Changzai Zhang for their valuable assistance during the explosion testing.

20

References [1] Banhart J. Manufacture, characterisation and application of cellular metals and metal foams. Progress in Materials Science 2001;46(6):559-632. [2] Mouritz AP, Gellert E, Burchill P, et al. Review of advanced composite structures for naval ships and submarines. Composite Structures 2001;53(1):21-42. [3] Birman V, Kardomateas GA. Review of current trends in research and applications of sandwich structures. Composites Part B: Engineering 2018;142:221-40. [4] Kujala P, Klanac A. Steel sandwich panels in marine applications. Brodogradnja 2005;56(4):305-14. [5] Ashby MF, Evans A, Fleck NA, et al. Metal foams: a design guide. Boston: Butterworth-Heinemann; 2002. [6] Allen HG. Analysis and Design of Structural Sandwich Panels. Oxford: Pergamon Press; 1969. [7] Wadley HNG. Multifunctional periodic cellular metals. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2006;364(1838):31-68. [8] Zhu F, Zhao LM, Lu GX, et al. Deformation and failure of blast-loaded metallic sandwich panels—Experimental investigations. International Journal of Impact Engineering 2008;35(8):937-51. [9] Evans AG, Hutchinson JW, Ashby MF. Multifunctionality of cellular metal systems. Progress in Materials Science 1998;43(3):171-221. [10] Taylor GI. The pressure and impulse of submarine explosion waves on plates. Cambridge: Cambridge University Press; 1963. [11] Hall DJ. Examination of the effects of underwater blasts on sandwich composite structures. Composite Structures 1989;11(2):101-20. [12] Fleck NA, Deshpande VS. The Resistance of Clamped Sandwich Beams to Shock Loading. Journal of Applied Mechanics 2004;71(3):386-401. [13] Latourte F, Grégoire D, Zenkert D, et al. Failure mechanisms in composite panels subjected to underwater impulsive loads. Journal of the Mechanics and Physics of Solids 2011;59(8):1623-46. [14] Avachat S, Zhou M. High-speed digital imaging and computational modeling of dynamic failure in composite structures subjected to underwater impulsive loads. International Journal of Impact Engineering 2015;77:147-65. [15] Avachat S, Zhou M. Compressive response of sandwich plates to water-based impulsive loading. International Journal of Impact Engineering 2016;93:196-210. 21

[16] Arora H, Hooper PA, Dear JP. The Effects of Air and Underwater Blast on Composite Sandwich Panels and Tubular Laminate Structures. Experimental mechanics 2012;52(1):59-81. [17] Chen GC, Zhang P, Liu J, et al. Experimental and numerical analyses on the dynamic response of aluminum foam core sandwich panels subjected to localized air blast loading. Marine Structures 2019;65:343-61. [18] Huang W, Zhang W, Ye N, et al. Dynamic response and failure of PVC foam core metallic sandwich subjected to underwater impulsive loading. Composites Part B: Engineering 2016;97:226-38. [19] Zhang P, Cheng YS, Liu J, et al. Experimental study on the dynamic response of foam-filled corrugated core sandwich panels subjected to air blast loading. Composites Part B: Engineering 2016;105:67-81. [20] Cheng YS, Zhou TY, Wang H, et al. Numerical investigation on the dynamic response of foam-filled corrugated core sandwich panels subjected to air blast loading. Journal of Sandwich Structures & Materials 2019;21(3):838-64. [21] Cheng YS, Liu MX, Zhang P, et al. The effects of foam filling on the dynamic response of metallic corrugated core sandwich panel under air blast loading – Experimental investigations. International Journal of Mechanical Sciences 2018;145:378-88. [22] Bahei-El-Din YA, Dvorak GJ. Enhancement of blast resistance of sandwich plates. Composites Part B: Engineering 2008;39(1):120-7. [23] Wang E, Gardner N, Shukla A. The blast resistance of sandwich composites with stepwise graded cores. International Journal of Solids and Structures 2009;46(18–19):3492-502. [24] Gardner N, Wang E, Shukla A. Performance of functionally graded sandwich composite beams under shock wave loading. Composite Structures 2012;94(5):1755-70. [25] Zhou TY, Zhang P, Xiao W, et al. Experimental investigation on the performance of PVC foam core sandwich panels under air blast loading. Composite Structures 2019;226:111081. [26] Jing L, Zhao LM. Blast resistance and energy absorption of sandwich panels with layered gradient metallic foam cores. Journal of Sandwich Structures & Materials 2019;21(2):464-82. [27] Jin ZY, Yin CY, Chen Y, et al. Graded effects of metallic foam cores for spherical sandwich shells subjected to close-in underwater explosion. International Journal of Impact Engineering 2016;94:23-35. [28] Chen D, Jing L, Yang F. Optimal design of sandwich panels with layered-gradient aluminum foam cores under air-blast loading. Composites Part B: Engineering 2019;166:169-86. [29] Keil A. The response of ships to underwater explosions. Transactions of Society of Naval Architects and 22

Marine Engineers 1961;69:366-410. [30] Rajendran R, Narasimhan K. Damage prediction of clamped circular plates subjected to contact underwater explosion. International Journal of Impact Engineering 2001;25(4):373-86. [31] Zhang J, Shi XH, Guedes Soares C. Experimental study on the response of multi-layered protective structure subjected to underwater contact explosions. International Journal of Impact Engineering 2017;100:23-34. [32] Ming FR, Zhang AM, Xue YZ, et al. Damage characteristics of ship structures subjected to shockwaves of underwater contact explosions. Ocean Engineering 2016;117:359-82. [33] Chen GC, Cheng YS, Liu J, et al. Performance Evaluation of Air-Backed Metallic Circular Plates Subjected to Close-In Underwater Explosion. In: ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering, OMAE 2017. [34] Nurick GN, Radford AM. Deformation and tearing of clamped circular plates subjected to localised central blast loads. In: Reddy BD, editor. Recent developments in computational and applied mechanics: a volume in honour of John B Martin. Barcelona: International Centre for Numerical Methods in Engineering (CIMNE), 1997. p. 276-301. [35] Li QM, Jones N. Shear and adiabatic shear failures in an impulsively loaded fully clamped beam. International Journal of Impact Engineering 1999;22(6):589-607. [36] Cui L, Kiernan S, Gilchrist MD. Designing the energy absorption capacity of functionally graded foam materials. Materials Science and Engineering: A 2009;507(1–2):215-25. [37] Zeng HB, Pattofatto S, Zhao H, et al. Perforation of sandwich plates with graded hollow sphere cores under impact loading. International Journal of Impact Engineering 2010;37(11):1083-91. [38] Zhou J, Guan ZW, Cantwell WJ. The impact response of graded foam sandwich structures. Composite Structures 2013;97:370-7.

23

List of table and figure caption： Table 1

Information on the sandwich panel configuration and explosion.

Table 2

Summary of foam properties from the manufacturer (http://www.diabgroup.com).

Table 3

Experimental results of ungraded/graded foam core sandwich panels.

Fig. 1

(a) Picture of a typical experimental set-up just before submergence. (b) Sketch of the configuration of the experimental set-up used for contact underwater blast tests.

Fig. 2

Schematic of (a) the ungraded PVC foam core sandwich panel and (b) functionally graded PVC foam core sandwich panel.

Fig. 3

Uniaxial compressive stress versus strain curves of PVC foams.

Fig. 4

(a) Overall view revealing the deformation/failure modes of front face failed in Mode PII (UG-3) as well as (b) the enlarged image showing the state of front cap.

Fig. 5

Overall views revealing the deformation/failure modes of back face failed in (a) Mode Itc (UG-2), (b) Mode PI (UG-6) and (c) Mode PII (UG-3) as well as (d) the enlarged image showing the state of back cap.

Fig. 6

The post-test state of fragments released from front and back faces.

Fig. 7

Overall views showing the deformation/failure modes of core layer of the panels whose back face failed in (a) Mode Itc (UG-4), (b) Mode PI (UG-3) and (c) Mode PII (UG-1). (d) Magnification view showing the deformation of fragment released from core layer.

Fig. 8

(a) Overall view and (b) magnification view revealing the detail failure modes of witness plate for the sandwich panel whose back face failed in Mode PII (UG-3).

Fig. 9

Post-mortem photographs of the sandwich panels loaded by charges with different weights. (UG-1, W=17 g; UG-2, W=26 g.)

Fig. 10

Side view of the sandwich panels loaded by charges with different weights. (UG-1, W=17 g; UG-2, W=26 g.)

Fig. 11

Post-mortem photographs of the sandwich panels with different face-sheet configuration. (UG-2,

24

tf =0.90 mm, tb =1.80 mm; UG-3, tf =1.38 mm, tb =1.38 mm; UG-4, tf =1.80 mm, tb =0.90 mm.) Fig. 12

Influence of face-sheet configuration on the average length of crack on faces and the maximum deflection of witness plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 13

Post-mortem photographs of the sandwich panels with different core height. (UG-5, HC =17 mm; UG-3, HC =34 mm; UG-6, HC =54 mm. For panel UG-5, the core and faces were still joined together after test. The image of core could not be separately provided. However, the final state of core could be examined from the images of both front and back faces.)

Fig. 14

Influence of core height on the average length of crack on faces and the maximum deflection of witness plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 15

Post-mortem photographs of the sandwich panels with different core height. (FG-1, low/middle/high; FG-2, high /middle/low.)

Fig. 16

Influence of core gradation on the average length of crack on faces and the maximum deflection of witness plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 17

The schematic of the sandwich panel during the (a) fluid-structure interaction phase, (b) core compression phase and (c) structural dynamic response phase.

Fig. 18

Post-mortem photographs showing the states of core fragments released from the central region for (a) panel FG-1 and (b) panel FG-2.

25

Fig. 1 (a) Picture of a typical experimental set-up just before submergence. (b) Sketch of the configuration of the experimental set-up used for contact underwater blast tests.

26

Fig. 2 Schematic of (a) the ungraded PVC foam sandwich panel and (b) functionally graded PVC foam sandwich panel.

27

Fig. 3 Uniaxial compressive stress versus strain curves of PVC foams.

28

Fig. 4 (a) Overall view revealing the deformation/failure modes of front face failed in Mode PⅡ (UG-3) as well as (b) the enlarged image showing the state of front cap.

29

Fig. 5 Overall views revealing the deformation/failure modes of back face failed in (a) Mode Itc (UG-2), (b) Mode P Ⅰ (UG-6) and (c) Mode PⅡ (UG-3) as well as (d) the enlarged image showing the state of back cap.

30

Fig. 6 The post-test state of fragments released from faces.

31

Fig. 7 Overall views showing the deformation/failure modes of core layer of the panels whose back face failed in (a) Mode Itc (UG-4), (b) Mode PⅠ (UG-3) and (c) Mode PⅡ (UG-1). (d) Magnification view showing the deformation of fragment released from core layer.

32

Fig. 8 (a) Overall view and (b) magnification view revealing the detail failure modes of witness plate for the sandwich panel whose back face failed in Mode PⅡ (UG-3).

33

Fig. 9 Post-mortem photographs of the sandwich panels loaded by charges with different weights. (UG-1, W=17 g; UG-2, W=26 g.)

34

Figure 10 Side view of the sandwich panels loaded by charges with different weights. (UG-1, W=17 g; UG-2, W=26 g.)

35

Fig. 11 Post-mortem photographs of the sandwich panels with different face-sheet configuration. (UG-2, tf =0.90 mm, tb =1.80 mm; UG-3, tf =1.38 mm, tb =1.38 mm; UG-4, tf =1.80 mm, tb =0.90 mm.)

36

Fig. 12 Influence of face-sheet configuration on the average length of crack on faces and the maximum deflection of witness plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

37

Fig. 13 Post-mortem photographs of the sandwich panels with different core height. (UG-5, HC =17 mm; UG-3, HC =34 mm; UG-6, HC =54 mm. For panel UG-5, the core and faces were still joined together after test. The image of core could not be separately provided. However, the final state of core could be examined from the images of both front and back faces.)

38

Fig. 14 Influence of core height on the average length of crack on faces and the maximum deflection of witness plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

39

Fig. 15 Post-mortem photographs of the sandwich panels with different core height. (FG-1, low/middle/high; FG-2, high /middle/low.)

40

Fig. 16 Influence of core gradation on the average length of crack on faces and the maximum deflection of witness plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

41

Figure 17 The schematic of the sandwich panel during the (a) fluid-structure interaction phase, (b) core compression phase and (c) structural dynamic response phase.

42

Fig. 18 Post-mortem photographs showing the states of core fragments released from the central region for (a) panel FG-1 and (b) panel FG-2.

43

Table 1 Information of the sandwich panel configuration and explosion. Label

Charge

Front face

Back face

Core layer

Thickness

Total

Areal

weight

thickness

thickness

arrangement

of each

thickness

density

core layer

of core

(mm)

(mm)

(kg/m2)

(g)

(mm)

(mm)

UG-1

17

0.90

1.80

H250

34

34

29.56

UG-2

26

0.90

1.80

H250

34

34

29.56

UG-3

26

1.38

1.38

H250

34

34

30.03

UG-4

26

1.80

0.90

H250

34

34

29.56

UG-5

26

1.38

1.38

H250

17

17

25.78

UG-6

26

1.38

1.38

H250

51

51

34.28

FG-1

26

1.38

1.38

H60/H130/H250

11

33

26.37

FG-2

26

1.38

1.38

H250/H130/H60

11

33

26.37

44

Table 2 Summary of foam properties from the manufacturer (http://www.diabgroup.com). Nominal

Compressive

Compressive

Tensile

Tensile

Shear

Shear

Density

strength

modulus

strength

modulus

strength

modulus

(kg/m3)

(MPa)

(MPa)

(MPa)

(MPa)

(MPa)

(MPa)

H60

60

0.7～0.9

60～70

1.5～1.8

57～75

0.63～0.76

16～20

H130

130

2.4～3.0

145～170

3.5～4.8

135～175

1.9～2.2

40～50

H250

250

6.1～7.2

350～400

8.0～9.2

260～320

3.9～4.5

81～97

Foam type

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Table 3 Experimental results of ungraded/graded foam core sandwich panels. Label

Failure mode

Average crack length

Maximum deflection

(mm)

(mm)

Front face

Back face

Witness plate

Front face

Back face

Back face

Witness plate

UG-1

Mode PII

Mode Itc

-

66.7

-

72.44

0.00

UG-2

Mode PII

Mode Itc

-

119.3

-

94.42

0.00

UG-3

Mode PII

Mode PII

Mode Itc

137.8

223.8

-

10.24

UG-4

Mode PII

Mode PII

Mode Itc

144.5

225.6

-

15.94

UG-5

Mode PII

Mode PII

Mode Itc

229.8

230.0

-

19.72

UG-6

Mode PII

Mode PI

-

100.1

210.5

-

0.00

FG-1

Mode PII

Mode PII

Mode Itc

121.2

198.6

-

24.92

FG-2

Mode PII

Mode PII

Mode Itc

200.0

229.5

-

20.84

46

CRediT Author statement

Tianyu Zhou: Data Curation, Investigation, Writing - Original Draft, Writing – Review & Editing. Yuansheng Cheng: Funding acquisition, Project administration. Yanjie Zhao: Resources, Methodology. Lunping Zhang: Resources, Methodology. Haikun Wang: Resources, Methodology. Ganchao Chen: Methodology, Data Curation. Jun Liu: Conceptualization, Writing - Review & Editing. Pan Zhang: Supervision, Conceptualization, Methodology, Investigation, Writing – Review & Editing.

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