Dynamic response of sandwich panels with multi-layered aluminum foam/UHMWPE laminate cores under air blast loading Sipei Cai Data CurationVisualizationInvestigationWriting – Original DraftWriting – Review & Editing , Jun Liu ConceptualizationProject administration , Pan Zhang SupervisionConceptualizationMethodologyInvestigationWriting – Review & Editing , Chunpeng Li MethodologyData CurationVisualization , Yuansheng Cheng Funding acquisitionInvestigation PII: DOI: Reference:
S0734-743X(19)30372-0 https://doi.org/10.1016/j.ijimpeng.2019.103475 IE 103475
To appear in:
International Journal of Impact Engineering
Received date: Revised date: Accepted date:
15 April 2019 7 December 2019 8 December 2019
Please cite this article as: Sipei Cai Data CurationVisualizationInvestigationWriting – Original DraftWriting – Review Jun Liu ConceptualizationProject administration , Pan Zhang SupervisionConceptualizationMethodologyInvestigat Chunpeng Li MethodologyData CurationVisualization , Yuansheng Cheng Funding acquisitionInvestigation , Dynamic response of sandwich panels with multi-layered aluminum foam/UHMWPE laminate cores under air blast loading, International Journal of Impact Engineering (2019), doi: https://doi.org/10.1016/j.ijimpeng.2019.103475
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Highlights A new sandwich panel was proposed by introducing UHMWPE laminate into multi-layered foam core. Experiments and simulations were performed to investigate the blast responses of the sandwich panels. Effects of foam core gradation and application strategy of UHMWPE laminates were analyzed.
Full Title of Article: Dynamic response of sandwich panels with multi-layered aluminum foam/UHMWPE laminate cores under air blast loading
Authors: Sipei Cai 1, Jun Liu 1, Pan Zhang 1,2,3,4, Chunpeng Li 1, Yuansheng Cheng 1,3,4
Corresponding affiliations: 1
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
Collaborative Innovation Center for Advanced ship and Deep-Sea Exploration (CISSE), Shanghai 200240, China
Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamic (HUST), Wuhan 430074, 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
Tel.: +86 27 87543258 Fax: +86 27 87542146 E-mail: [email protected]
Corresponding author. Tel.: + 86 27 87543258; fax: +86 27 87542146. E-mail address: [email protected]
(P. Zhang) 2
Abstract: The air blast responses of sandwich panels with multi-layered aluminum foam/UHMWPE laminate cores were analyzed experimentally and numerically. The focus was placed on the effects of foam core gradation and the locations of UHMWPE laminates. Multiple failure modes were exhibited by the panels, including local indentation and global bending deformation of face sheets, crushing and fragmentation of foam core, debonding of adhesive, and delamination and fracture failure of UHMWPE laminate. Experimental results showed that the ascending density foam core was beneficial to decrease the face sheet deformations and to alleviate the shear-induced collapse of foam core. Incorporating the UHMWPE laminates would induce a lower front face deformation and a higher back face deformation. The phenomenon would be more evident with the UHMWPE laminates placed close to the front face. Numerical results demonstrated that deploying the UHMWPE laminate as a first layer core significantly lowered the center velocity of front face. The existence of UHMWPE laminate would change the response modes of the panels. Most of the blast energy was dissipated by the multi-layered cores. The UHMWPE laminates exhibited less efficient in absorbing energy than the aluminum foam. Generally, the findings revealed the undesirable performance of the panels with multi-layered aluminum foam/UHMWPE laminate core under air blast loading. Keywords: Sandwich structure; Multi-layered core; UHMWPE composite; Dynamic response; Blast loading
1 Introduction Sandwich structures constructed from two strong face sheets separated by a crushable core have played an important role in military and civil industries due to their lightweight, versatility and tailorable mechanical properties [1, 2]. To date, cores with diverse topologies, such as prismatic, lattice and stochastic porous foams, have been developed for sandwich structures. Extensive research is devoted to probing their responses under quasi-static [3, 4] or blast loading [5-7]. The concept that sandwich structures can bear larger bending loads and suffer higher level impulse than their equal-weight monolithic 3
counterparts has been established [8, 9] The face sheet thickness and the core configuration have a great effect on their deformation and damage [10, 11]. Aluminum foam, famous for its prominent capacity of stress wave attenuation, is preferred as the core of sandwich structures for blast protection. The low compressive strength and long plateau stress region of aluminum foam core endow it with great potential to dissipate blast energy . Compared to the sandwich structure with pyramidal core, the counterpart with aluminum foam core behaves better against the simulated shock loading . The failure mechanisms of the cylindrical and flat sandwich shells with aluminum foam core under blast loading were experimentally investigated by analyzing their failure/deformation responses [14, 15]. It further confirms the superior blast resistance of aluminum foam core sandwich structures. In recent years, the concept of functionally layered-gradient cores has been embraced and exploited preliminarily [15, 16]. An analytical model was developed to analyze the performance of double-layered core sandwich panels. Results reveal that adopting a multi-layered foam core could further ameliorate the blast resistance of sandwich panels . Protective structures are designed to be exposed to blast loading generated by uncased (bare) or cased charge during their lifetime. When the charge is cased, the synergistic effect of the blast wave and explosive-driven fragments is the main form of the explosive loading. It puts forward stringent requirements on the protective capability of sandwich structures. However, the aluminum foam core performs poorly in resisting the high-velocity penetration of fragments due to its low compressive and shearing strength . A feasible way to enhance the ballistic limit of whole sandwich structures can be achieved by increasing the face sheet thickness . Nevertheless, it will bring an evident increase in structural weight. Alternatively, the fiber-reinforced polymer (FRP) with high specific strength and stiffness may be an ideal constituent part for sandwich structures to meet the increasing comprehensive demand of both lightweight and ballistic resistance. So far, plenty of fiber reinforcements have been developed, including carbon, glass, aramid and polyethylene fibers. Material tests show that ultra-high molecular weight polyethylene (UHMWPE) fiber has a low density of 970 kg/m3 and a high tensile strength of 2.5 GPa . Due to the lightweight and high tenacity of the UHMWPE fiber, its laminate products exhibit a higher mass efficiency against projectile impact than the armor steels and other FRPs 4
with aramid, carbon or glass fiber by more than 200% and 30%, respectively . It demonstrates that UHMWPE laminates have superior ballistic resistance. However, a paucity of experiments has been conducted on UHMWPE laminates to investigate their failure and energy dissipation mechanisms under air blast loading. The blast responses of UHMWPE beams were analyzed through the metal foam projectile impact . But the experiments cannot consider the effect of the high-temperature explosion product. Actually, a fusion region on the front side of the UHMWPE laminate can be observed under the near-field blast loading . It is because the UHMWPE laminate has a low melting temperature of about 150 °C . The onset of the fusion phenomenon would reduce the residual bending stiffness and strength as well as the blast resistance of UHMWPE laminates. Therefore, UHMWPE laminates are unsuitable for being exposed to explosion. A new sandwich panel was proposed by introducing UHMWPE laminates into multi-layered aluminum foam cores. The intentional design aimed to improve the comprehensive protection of the sandwich panels against the impact of blast wave and explosive-driven fragments. Two sets of experiments were conducted on the sandwich panels under the blast loading generated by the uncased (bare) and cased explosive charge, separately. The objective of the present paper is to analyze the dynamic responses of the sandwich panels subjected to the bare charge loading. The effects of foam core gradation and the application strategies of the UHMWPE laminates on the blast performance of the panels were evaluated experimentally. Finite element simulations were also performed to reveal the velocity responses and energy absorption characteristics of the panels. In the next stage, the dynamic responses of the sandwich panels under the combined loadings with blast and fragments will be investigated.
2 Experimental procedure 2.1 Specimens The sandwich panels are composed of two face sheets and a multi-layered core, as sketched in Figure 1. The in-plane dimensions of the panel are 452 mm (L) × 440 mm (B). Two groups of multi-layered sandwich panels with different core configurations were designed. One is the multi-layered aluminum foam core sandwich panel, Figure 1(b). The other one is the multi-layered hybrid aluminum 5
foam/UHMWPE laminate core sandwich panel, Figure 1(c) and (d). It is noteworthy that the latter group can be further divided into two kinds of configurations according to the application strategy of the UHMWPE laminate: with one relatively thick UHMWPE laminate layer (Figure 1(c)) and with two papery UHMWPE laminate interlayers (Figure 1(d)). The thicknesses of both the front face sheet (tf) and back face sheet (tb) are 1.38 mm for all the specimens. The thicknesses of the multi-layered core are numbered in sequence from front side to back side. The through-holes on the panel were designed to assemble the sandwich panel during the fabrication process and to fix it during blast testing.
Figure 1 (a) Schematic of multi-layered core sandwich panel. Cross-sectional views of the sandwich panels with (b) multi-layered aluminum foam core, (c) multi-layered hybrid aluminum foam/thick UHMWPE laminate core and (d) multi-layered hybrid aluminum foam/papery UHMWPE laminates core. The base material of the face sheets is 304 stainless steel whose mechanical properties are summarized in Table 1 . The aluminum foams with closed-cell microstructure were supplied by Sichuan Yuantaida Non-ferrous Metals Co., Ltd, China. Three classes of aluminum foams with different densities (250 kg/m3, 450 kg/m3 and 650 kg/m3) were used in the experiments. The quasi-static uniaxial compressive stress-strain curves of the aluminum foams are depicted in Figure 2. The UHMWPE laminates were made of the Dyneema® HB26 with cross-ply layup. To form the required thickness laminate plates, a hot-pressing process was operated to bond [0/90/0/90] intermediate stacks together under the pressure of 16.5 MPa at the temperature of 125 °C for 30 minutes. The HB26 laminate has a density of 980 kg/m3, a 6
tensile elastic modulus of 51.1 GPa, a tensile strength of 1.15 GPa, a failure strain of 2.6%, an out-of-plane compression strength of ~700 MPa and an interlaminar shear strength of 7.85 MPa [26, 27]. The components of the panels, namely metallic face sheets, aluminum foam layers and UHMWPE laminate layers, were first prefabricated into the designed dimensions. In consideration of the low melting temperature of the UHMWPE laminate, the components were bonded together in a specific sequence by using epoxy resin adhesive at a temperature of 60 °C for 3 hours. Table 1 Material properties and Johnson–Cook parameters of 304 stainless steel . Johnson-Cook parameter
Bulk modulus, K
Shear modulus, G
Yield stress, A
Hardening constant, B
Hardening, exponent, n
Strain rate constant, c
Thermal softening exponent, m
Room temperature, Tr
Material melting temperature, Tm
Ref. strain rate, ̇
Figure 2 Uniaxial compressive stress-strain curves of closed-cell aluminum foams. 2.2 Blast testing 7
The air blast experiments were conducted in an explosive chamber which has dimensions of 5 m inner diameter by 7.5 m height. Figure 3 shows the detailed schematic program of the experimental set-up. The panel was peripherally clamped between a rigid supporting plate and a picture frame by M16 bolts. The clamping system provided the panel with an exposed area of 300 mm (Le) × 288 mm (Be). Four I-beams were employed to sustain the supporting plate, while the rubber pad under the I-beams was used to stabilize the whole clamping system. The blast wave was generated by the detonation of a 55 g cylindrical TNT explosive with a diameter of 35 mm and a height of 37.2 mm. The stand-off distance (SoD) was defined as the distance from the center of explosive to the top surface of the front face sheet.
Figure 3 A sketch of experimental set-up. 2.3 Design of experiments The panel designation, the arrangements and thicknesses of the multi-layered cores, and the stand-off distance are given in Table 2. The definitions of the abbreviations used in Table 2 are summarized as follows: AF - the multi-layered aluminum foam core sandwich panel, TP - the multi-layered hybrid aluminum foam/UHMWPE laminate core sandwich panel with one thick 8
UHMWPE laminate, PP - the multi-layered hybrid aluminum foam/UHMWPE laminate core sandwich panel with two papery UHMWPE laminates, PE - the UHMWPE laminate, LF - the aluminum foam core with the density of 250 kg/m3, MF - the aluminum foam core with the density of 450 kg/m3, HF - the aluminum foam core with the density of 650 kg/m3. Table 2 Detailed information of the tested multi-layered core sandwich panels. Designation Information of panels Arrangement of cores (Front Back)
(mm) (mm) (mm) (mm) (mm) (kg/m2)
Note: AF - the multi-layered aluminum foam core sandwich panel, TP - the multi-layered hybrid aluminum foam/UHMWPE laminate core sandwich panel with one thick UHMWPE laminate, PP - the multi-layered hybrid aluminum foam/UHMWPE laminate core sandwich panel with two papery UHMWPE laminates, PE - the UHMWPE laminate, LF - the aluminum foam core with the density of 250 kg/m3, MF - the aluminum foam core with the density of 450 kg/m3, HF - the aluminum foam core with the density of 650 kg/m3.
For the AF panels, the thickness of one aluminum foam layer is 10 mm. Under the constraint of equal weight design, both TP panels and PP panels were constructed based on AF panels. TP panels were formed by using an UHMWPE laminate layer as a replacement for one aluminum foam layer with a density of 450 kg/m3. According to the difference in material density, the thickness of the UHMWPE 9
laminate layer of TP panels is about 4 mm. PP panels were configured by introducing two UHMWPE laminates with a thickness of 1 mm into the interface between the components of AF panels. Correspondingly, the thickness of each aluminum foam layer of PP panels is 8 mm. Panels AF-1 and AF-2 were considered as baseline panels. They were configured with ungraded foam core layers but tested under different SoDs (100 mm for panel AF-1 and 50 mm for panel AF-2). Panels AF-3, AF-4, AF-5, and panels TP-4, TP-5 were selected to analyze the effect of the foam core gradation. Panels TP-1, TP-2, TP-3, and panels PP-1, PP-2 were designed to investigate the effect of the locations of UHMWPE laminates.
3 Experimental results and discussions All the tested panels were cross-sectioned by water-jet cutting to reveal the failure modes of the multi-layered core. Additionally, the details of the failure of the UHMWPE composite were examined through the Dino-Lite Microscope. The measured permanent maximum deflections of the face sheets are summarized in Table 2.
3.1 The sandwich panels with multi-layered aluminum foam core 3.1.1 Results of baseline panels
Figure 4(a) and (b) show the front faces of the tested baseline panels. Local indentation was the dominant deformation mode of the front faces due to the localized blast wave. For the SoD of 100 mm, a relatively mild indentation deformation was formed by local plastic bending in the front face of panel AF-1, as shown in Figure 4(a). When the SoD was decreased to 50 mm, the blast load intensified and became more localized. Accordingly, the indentation in the front face of panel AF-2 was more evident than that of panel AF-1, see Figure 4(b). It caused the occurrence of stretching deformation within the indentation area, Figure 4(d). The thinning phenomenon was obvious in the central area. The thinning level reached up to 30% original thickness. The multi-layered foam core of panel AF-1 exhibited a local crushing deformation under the SoD of 100 mm, as shown in Figure 4(c). The first two foam layers were fully densified at the central area, while the third foam layer underwent a partial compression deformation. According to the extent of core 10
compression, the multi-layered core of panel AF-1 could be divided into two zones from the center to the outskirts, namely the partially compacted region and the compacted-absent region. Slight debonding failure occurred at the interfaces between adjacent foam layers of panel AF-1. In the meantime, a cambered cavity between the front face sheet and the crushed foam layer was formed within the compression region. It was caused by the difference in the deformation velocity between the front face and foam layer. By contrast, the central region of the foam layers of panel AF-2 was fully crushed, as observed in Figure 4(d). The difference in the crushing rate of the foam material at the center would even be significant. It triggered the formation of slanted shear cracks in the multi-layered core of panel AF-2. The shear cracks nearly passed through the core thickness, which blocked the propagation of bending stress waves. Those foam material outside the shear cracks therefore experienced negligible bending deformation. Consequently, obvious debonding failure appeared at the interface between the foam core and back face due to the incompatible deformation. The deformation extent of back face sheets was alleviated significantly because of the mitigation effect of the multi-layered foam cores. The back face of panel AF-1 exhibited a global plastic bending deformation, see Figure 4(e). Close examination revealed that plastic hinges formed at the four clamped edges (red dash line). However, the plastic hinge lines were obscure near the corners because of the localized blast loading. The stationary plastic hinges were more apparent for panel AF-2 due to the higher out-of-plane deformation, as shown in Figure 4(f). Besides, the back face profile of panel AF-2 resembled a superimposed mode of a global bending and a central inner dome. It is similar to the deformation mode of monolithic plates under near-field blast loading . 3.1.2 Effect of foam core gradation
Relative to panel AF-2 with an ungraded layered core, panels AF-3, AF-4 and AF-5 were configured with graded foam cores in the arrangements of LF-MF-HF (ascending), HF-MF-LF (descending) and HF-LF-MF, respectively. The deformation/failure modes of the latter three sandwich panels are presented in Figure 5. A highly localized dishing deformation of the front face and a global inelastic deformation of the back face could be observed for the three panels with graded foam cores. Such responses were similar to those observed on panel AF-2. However, partial tearing appeared at the central area of the front face of 11
panel AF-5, as shown in Figure 5(c). The phenomenon can be also observed on solid plates subjected to localized blast loading [29, 30]. The onset of the partial tearing should be associated with the influence of the failure mechanism of the graded foam core on the front face deformation response.
Figure 4 Photographs showing the deformation/failure modes of the baseline panels. Front faces of (a) panel 12
AF-1 and (b) panel AF-2; multi-layered cores of (c) panel AF-1 and (d) panel AF-2; back faces of (e) panel AF-1 and (f) panel AF-2.
Figure 5 Cross-sectional views showing overall deformation/failure modes of (a) panel AF-3, (b) panel AF-4 and (c) panel AF-5. The effect of foam core gradation on the deformation/failure mode of foam core was obvious. For panel AF-3 with ascending foam core gradation, its multi-layered foam core displayed a combination mode of crushing deformation and plugging failure, Figure 5(a). The first layer core, which was LF foam with the lowest compressive resistance, would go into densification regime rapidly under the impact of the front face. It caused the front face to directly impinge on the second layer core (MF). The central segment of the second layer core was sheared off from the surrounding part. The onset of the phenomenon was ascribed to the fact that the deformation velocity of the front face outpaced the allowable dynamic crushing rate of MF foam core . The sheared-off segment was further crushed into the densification state because its plateau stress was insufficient to compress the third layer core (HF). Subsequently, the front face continued deforming under its own inertia and the action of blast wave. The third layer core failed in the same manner as the second one. Consequently, plugging failure was formed at the panel center. In general, the response of the multi-layered core of panel AF-3 was identified as a progressive process. When the HF foam was deployed at the first layer, the multi-layered foam core was more susceptive to 13
experience shear failure. Hence, noticeable shear plugging could be found in the foam cores of panels AF-4 and AF-5, see Figure 5(b) and (c), respectively. The difference of core configuration between these two panels lay in the arrangements of their second and third layer cores. For panel AF-4, deploying MF foam as the second layer core could partly increase the overall bending stiffness of its first two core layers. Therefore, shearing failure occurred in the first layer. Some shear-induced cracks appeared through the thickness of the second layer, Figure 5(b). The third layer foam core (LF) was compacted severely. Erosion failure was apparent at its central region due to the impact of the upper foam core fragments. Additionally, larger voids in LF foam would reduce the effective contact surface between the third layer and the back face. It was likely to weaken the bonding strength of the interface. Thus, debonding failure covered the entire deformable area of the back face. For panel AF-5, its second layer core was LF foam. Lower foam density of the second layer core meant weaker support to the first layer core. It would lower the overall bending rigidity of the first two layers of panel AF-5. Therefore, the foam core plugging area of panel AF-5 was shrunk relative to panel AF-4, as shown in Figure 5(c). The decrease of the plugging area would reduce the front face deformation region. As a result, the front face of panel AF-5 obtained a higher downward velocity on the premise of receiving equal momentum, leading to the excessive stretching deformation at the center of the front face. Besides, a transverse crack travelling parallel to the bonding interface emerged in the second layer due to the low fracture toughness of LF foam core . Similar phenomenon also existed in the first layer (LF) of panel AF-3. The transverse crack plunged into the interface between the second and third layer core and finally induced the debonding failure. Comparison among the panels with different foam core gradation in terms of permanent midpoint face sheet deflections is illustrated by plotting histograms, as shown in Figure 6. The three panels with graded foam cores would not always possess a superior blast performance over panel AF-2. Using panel AF-2 with ungraded foam core as a benchmark, the other three panels (in the order: AF-3, AF-4 and AF-4) with graded foam cores induce differences by -3.41%, -2.73% and 10.69% for front face deflection; -9.63%, 15.93% and 8.25% for back face deflection, respectively. The multi-layered core of panel AF-3 exhibited a progressive failure mechanism so that the panel underwent the lowest front face deflection due to the continuous support from the core. However, for panel AF-2, AF-4 and AF-5, the premature plugging 14
failure impeded the foam cores to resist the movement of the front faces in the initial stage. As a rule of thumb, the lower the back face deflection, the better the blast resistance of sandwich panels. Panel AF-3 with ascending density foam core exhibited the best blast resistance among the four panels. Panels AF-4 and AF-5 experienced larger back face deflections than panel AF-2 by 15.93% and 8.25%, respectively. It is due to that the back faces of these two panels were impacted by the sheared-off foam fragments. The findings were consistent with the results reported by Wang et al. . The ascending-arranged foam core would retard the formation of cracks and core catastrophic collapse. It is beneficial for keeping the front face intact and reducing the back face deflection.
Figure 6 Effects of foam core gradations on the permanent face sheet deflections of AF panels. 3.2 The sandwich panels with multi-layered hybrid aluminum foam/UHMWPE laminate core 3.2.1 Effect of the location of UHMWPE layer
Panels TP-1, TP-2 and TP-3 were constructed from panel AF-1 by replacing its first core layer, second core layer and third core layer with an UHMWPE laminate, respectively. The cross-sectional views of the three TP panels are displayed in Figure 7. A localized indent deformation of the front face and a global large plastic deformation of the back face could be still found on the three panels. However, the level of the indent deformation on the front face strongly depended upon the location of the UHMWPE layer. The UHMWPE laminate has high elastic modulus and tensile strength so that it possesses high flexural rigidity and membrane stretching strength. Thus, placing the UHMWPE laminate below front face could provide 15
strong support to the front face to restrain its deformation. In summary, the closer the UHMWPE layer was placed to the front face, the lower indent deformation the front face experienced.
Figure 7 Cross-sectional and microscopic photographs showing the deformation/failure modes of (a) panel TP-1, (b) panel TP-2 and (c) panel TP-3. The location of the UHMWPE layer would affect the deformation/failure modes of the multi-layered cores. When the UHMWPE layer was applied as the first core layer, more foam material would be involved in the crushing deformation, as shown in Figure 7(a). Moreover, the relatively uniform load transmitted from the UHMWPE layer to foam core layers induced an apparent bending deformation on them. The second core layer, which was a foam layer, would effectively mitigate the stress acting on the third core layer. Therefore, the measured compression of the third core layer was only 4.7 mm, which was lower than its crushing limit. As a comparison, the two foam core layers of panel TP-2 were separated by 16
the UHMWPE laminate, Figure 7(b). Its first foam core still experienced severe crushing deformation but limited bending deformation. The existence of the foam core provided deformation space for the front face. The localized deformation suffered by the front face would lead itself to slap against the UHMWPE layer locally. Consequently, the UHMWPE layer experienced small-scale bending deformation. The foam core layer beneath the UHMWPE layer crushed severely into the densification state at the center region. Interestingly, there existed a cavity pattern formed between the UHMWPE layer and the lower foam layer for panel TP-1 and panel TP-2. The presence of the cavity should be attributed to the considerable difference in the resistance to plastic flow between the two layers. The foam layer with lower resistance would maintain a much higher deformation than the UHMWPE layer. As a result, the interface between the two core layers went into the tension state. The debonding and delamination failure dominated by the tension stress occurred. Microscopy images indicated that the UHMWPE layer experienced fiber fracture failure at the center of the back side where evident membrane stretching deformation happened. Filaments were pulled out from the laminate at the fracture site. It is similar to the failure mechanism of UHMWPE laminates under tensile tests . For panel TP-3 with the UHMWPE layer placed close to the back face, the crushing deformation profile of the foam layers coordinated well with the deformed front face and UHMWPE layer, see Figure 7(c). The first foam layer was compressed into the densification state, while the second foam layer was close to being densified. Since the attenuating and scattering effect of the foam layers, the UHMWPE layer underwent a global bending deformation under the uniform loading. Delamination failure emerged at the back side of the UHMWPE layer, as shown in Figure 7(c). The onset of the failure should be a result of the rarefaction wave reflected from the back face. The effect of the location of the UHMWPE layer on the permanent midpoint deflections of face sheets was assessed, as shown in Figure 8. Note that the results of baseline panel AF-1 were also included in Figure 8 for a clear comparison of blast performance. Three TP panels displayed a lower front face deflection and a higher back face deflection relative to panel AF-1 regardless of the location of the UHMWPE layer. Taking panel AF-1 as a benchmark, panels TP-1, TP-2 and TP-3 exhibited a decrease in front face deflections by 37.08%, 11.53% and 9.69%; and induced an increase of back face deflections by 32.51%, 27.49% and 5.96%, respectively. Understanding the root cause of the phenomenon should recall 17
the deformation mechanisms of front face and back face. Under the localized blast loading, the front face suffered localized indent deformation. It meant that the supporting effect from the layered core was critical to front face deformation. The introduction of the UHMWPE layer exactly enhanced the supporting effect. As the UHMWPE layer was placed closer to front face, the supporting effect would be improved, resulting in a decrease of the front face deflection. The global inelastic deformation of back face was associated with the load acting on it and the global bending stiffness of the whole panel. Note that the UHMWPE material is good at absorbing impact energy via extensive bulging mechanisms . Herein, the limited localized or global bending deformation of the UHMWPE layer implied a limited contribution on the dissipation of blast energy. As a result, higher momentum would transmit from layered cores to back faces. On the other hand, the panels with an UHMWPE layer had a lower second moment of cross section relative to panel AF-1, because the thickness of the UHMWPE layer was only 0.4 time the thickness of the foam layer. Therefore, adopting an UHMWPE layer was unfavorable for reducing back face deformation. There existed differences in the back face deflections among the panels with an UHMWPE layer. In general, the lower the front face deflection, the higher the back face deflection. It suggested that the equilibrium state between the front face deformation and the back face deformation was reset by the location of the UHMWPE layer.
Figure 8 Effects of UHMWPE laminate locations on the permanent face sheet deflections of TP panels. 3.2.2 Effect of foam core gradation 18
The results indicate that it was more advantageous to limit the back face deformation by placing the UHMWPE layer near to back side of panels. The present section aims to exploit the potential in blast performance improvement by introducing the graded foam cores. The multi-layered core of panel TP-4 consisted of LF foam layer, HF foam layer and UHMWPE layer from front face to back face. Panel TP-5 was constructed by switching the locations of the two foam layers of panel TP-4.
Figure 9 Cross-sectional and microscopic photographs showing the deformation/failure modes of (a) panel TP-4 (LF-HF-PE) and (b) panel TP-5 (HF-LF-PE).
Figure 10 Graph comparing the measured cross-section profiles of the back faces of panel TP-4, panel TP-5 and panel AF-2.
Figure 9 shows the cross-sections of the two multi-layered hybrid core sandwich panels with graded foam core under the SoD of 50 mm. The localized blast loading caused the front faces to deform locally, yielding a local indentation deformation mode. The central part of the two foam layers was crushed into powders under the action of front face. The deformed front face subsequently slapped against the UHMWPE layer. Finally, momentum would be transmitted to the central part of back face. As a result, the inner dome profile of the back faces of the two panels displayed more obvious than that of panel AF-2, see Figure 10. Note that the shear crack failure appeared in a larger-scale at the first core layer of panel TP-5 relative to that of panel TP-4. It was because the HF foam layer with a higher bending resistance would be harmful to release the shear stress state. Once the shear crack passed through the foam layer, the fragment failure occurred at the center region of the foam layers. Consequently, a cavity was formed between the front face and the UHMWPE layer. Shear crack failure created a large cavity in panel TP-5. The sufficient bending deformation experienced by the first foam layer of panel TP-4 induced a transverse crack. In addition, the UHMWPE layers of panels TP-4 and TP-5 exhibited visible plastic deformation accompanied by delamination and fiber fracture. Increased blast loading exacerbated the deformation incompatibility between the foam core and the UHMWPE layer, which enlarged the delamination of the UHMWPE laminates in the two TP panels relative to panel TP-3. The UHMWPE layer was harder to access plastic deformation phase relative to the back face due to its superior tenacity. As a result, the back face possessed a higher deformation than the UHMWPE layer. It induced the formation of the cavity between the UHMWPE layer and the back face, as well as the appearance of the inter-ply delamination failure of the UHMWPE layer. Moreover, the fiber fracture could be observed at the back face of the UHMWPE layer because of the relatively high bending deformation. The face sheet midpoint deflections of panel TP-4, panel TP-5 and the baseline panel AF-2 are plotted in Figure 11. By comparison, panel TP-4 presented smaller front and back face deflections than panel 20
TP-5. It meant that adopting an ascending foam core gradation was beneficial to improve the blast performance of TP panels. The finding was consistent with the one from the sandwich panels with multi-layered aluminum foam core. However, panel TP-4 displayed a lower front face deflection and a higher back face deflection than the baseline panel AF-2 by 18.40% and 16.51%, respectively. In general, the UHMWPE laminate in TP panels performed more like a solid plate that mainly experienced plastic bending deformation. The failure mechanisms reported by Fallah et al. , such as edge buckling, in-plane shear and pulling-in of the side, were absent in the present experiments. This should be associated with the boundary condition of the UHMWPE laminate core. Periphery clamped boundary and rear support from the aluminum foam or back face would suppress the deformation of the UHMWPE laminate. It restricted the formation of the various failure mechanism and impeded large-scale fiber to be engaged in stretching deformation. Furthermore, the medium-thick UHMWPE laminate would reduce the total thickness of the aluminum foam layers, which limited the deformation space of the front face. Hence, the introduction of the 4 mm thick UHMWPE laminate core was not beneficial for the energy-absorption improvement and the shock wave attenuation of the multi-layered cores under the air blast loading.
Figure 11 Effects of foam core gradation or papery UHMWPE interlayers on the permanent face sheet deflections of the sandwich panels with multi-layered hybrid cores. 3.2.3 Effect of papery UHMWPE interlayers 21
Two panels with multi-layered hybrid cores consisting of three aluminum foam layers and two papery UHMWPE laminate interlayers were manufactured. The panel named PP-1 was constructed with the papery UHMWPE laminates placed between the adjacent foam layers, while the other one named PP-2 was characterized by locating the papery UHMWPE laminates between the face sheets and foam layers. The intentional design attempted to relieve the slapping phenomenon by thickening the aluminum foam and increase the energy-absorption of UHMWPE laminates by experiencing large stretching deformation.
Figure 12 Cross-sectional and microscopic photographs showing the deformation/failure modes of (a) panel PP-1 (MF-PE-MF-PE-MF) and (b) panel PP-2 (PE-MF-MF-MF-PE). Photographs of the cross-sections of the two PP panels tested under the SoD of 50 mm are presented in Figure 12. The deformation modes of the face sheets of PP panels were similar to that of baseline panel AF-2, such as the localized indent deformation of the front face and the global plastic deformation of the back face. However, the failure modes of the multi-layered cores were affected by the papery UHMWPE laminates. To be specific, the severe slanted shear crack observed in panel AF-2 became extinct in PP panels, which was a result of the interface impedance mismatch effect on the arrestment of shear crack. For panel PP-1, the central part of the aluminum foam was fully crushed, see Figure 12(a). Its two papery 22
UHMWPE laminates experienced such severe bending and stretching deformation that serious rupture of fiber and matrix happened. The difference in deformation between the foam layers and UHMWPE interlayers yielded tension stress at the interfaces, resulting in the delamination failure of UHMWPE interlayers. In contrast, panel PP-2 only exhibited severe fracture failure on the UHMWPE interlayer close to the front face, while the other one close to the back face mainly experienced evident global bending deformation without any rupture, as shown in Figure 12(b). It seemed that the UHMWPE interlayer experienced spring-back deformation, resulting in a cavity between the UHMWPE interlayer and the back face. In addition, the delamination failure also prevailed in the interfaces of the two papery UHMWPE laminates. The midpoint deflections of the face sheets of panels PP-1 and PP-2 are also included in Figure 11. Likewise, incorporating the papery UHMWPE interlayers would reduce the front face deflections. Relative to panel AF-2, panels PP-1 and PP-2 displayed smaller front face deflections by 7.52% and 10.10%, respectively. Nevertheless, thicker foam layers involved in compression deformation caused PP panels to exhibit larger front face deflections than TP panels. Note that the papery UHMWPE laminate in panel PP-2 could provide direct support to the front face. Therefore, panel PP-2 experienced marginally lower front face deflection than panel PP-1. By contrast, PP panels had a smaller back face deflection than TP panels, because they could avoid the slapping phenomenon. Moreover, the lower front face deflection and less fiber fracture in the second UHMWPE interlayer would cause the back face of panel PP-2 to dissipate more blast energy. As a result, panel PP-2 possessed a little higher back face deflection than panel PP-1, implying a better blast resistance of panel PP-1 among the sandwich panels with multi-layered hybrid cores. However, panel PP-1 still displayed a higher back face deflection relative to panel AF-2 by 6.20%.
4 Finite element simulation 4.1 Numerical modeling and validation To gain insight into the structural responses that were not measured in the experiments, 3D finite element (FE) simulations were conducted by using the ANSYS/Autodyn software. In the 3D FE model, the fixture system and the clamped region of the panels were not considered due to their negligible 23
deformation, see Figure 13(b). Clamped boundary was directly applied to the periphery of the deformable area of the panels. Note that the explosive loading acting on the panels exhibited a feature of localization under the two SoDs. Therefore, the ambient air media was modeled in cuboid with reduced in-plane dimensions which only covered an area of 140 mm × 140 mm at the panel center . Flow-out boundary condition was employed to the outer surfaces of the air block to simulate an infinite air field. Additionally, a quarter-model was established due to the symmetry of the structure and loading. The symmetric boundary was applied to the nodes at the planes of X = 0 and Y = 0, as shown in Figure 13(b).
Figure 13 Procedure of remapping from 2D model to 3D model. (a) Pressure contour of 2D model before remapping. (b) Pressure contour of 3D model after remapping. The face sheets were modeled by Belytschko-Tsay shell elements while the layered cores were meshed with Lagrange solid elements. The air and the explosive were modeled by multi-material Euler elements. The characteristic element sizes were generally set as 2 mm for both the structural elements and Euler elements, except that the UHMWPE laminate was discretized by 1 mm thick elements in thickness direction. Mesh sensitivity study indicated that the element sizes could well balance the simulation accuracy and efficiency. The structural interactions among different components of the sandwich panels were defined by frictionless contact with the penalty algorithm. Adjacent components were joined together via the ―Bonded Face Connections‖ option. The ―Euler-Lagrange/Shell interaction‖ was applied to fulfill the coupling between the fluid and structures. Importantly, the artificial coupling thickness of the shell 24
elements should be at least twice the element size of the surrounding Eulerian domain . To better capture the character of the blast wave, an axisymmetric fine-meshed 2D model with the element size of 0.3 mm was employed to simulate the initial detonation process of the TNT explosive until the blast wave approached the front faces, Figure 13(a). Remapping technique of the ANSYS/Autodyn allowed remapping the final pressure distribution of the 2D model into the 3D model as an initial loading condition , as shown in Figure 13. Johnson-Cook model was used to characterize the dynamic plastic behavior of the 304 stainless steel. The dynamic flow stress (σ𝑦 ), which is a function of strain, strain rate and temperature, can be expressed as: σ𝑦 = [𝐴 + 𝐵(
𝑒𝑞 𝑛 𝑝 ) ] *1
+ 𝑐𝑙𝑛 (
𝑒𝑞 ̇ 𝑝
where A, B, n, c, ε̇ and m are material constants.
)+ *1 − ( 𝑒𝑞 𝑝
𝑇 − 𝑇𝑟 𝑚 ) + 𝑇𝑚 − 𝑇𝑟
are equivalent plastic strain and
equivalent plastic strain rate, respectively. Tr is room temperature, while T and Tm are the absolute temperature and melting temperature of the material, respectively. The Johnson-Cook parameters of the 304 stainless steel were listed in Table 1 . Moreover, a failure criterion based on the equivalent plastic strain was employed to simulate the fracture of the face sheets. According to Ref. , the failure strain of the 304 stainless steel was set to 0.42. Crushable foam model was adopted to describe the compression behavior of the aluminum foam core. The compression data of the three aluminum foams can be obtained from the curves shown in Figure 2. The erosion criterion of instantaneous geometric strain (IGS) was applied to delete the distorted elements of foam core. The IGSs were set to 1.2, 1.35 and 1.5 for LF, MF and HF, respectively. Strain rate effect of the aluminum foam was not considered in the simulations . The constitutive response of HB26 laminate was simulated via a nonlinear orthotropic material model that involves orthotropic coupling of the material volumetric and deviatoric response, orthotropic hardening, stress-based composite failure criteria and orthotropic energy-based softening. The details about the nonlinear orthotropic material model and the corresponding parameters provided by Nguyen et al.  are given in the Appendix. 25
The material properties of the air and TNT charge were described by the ideal gas equation of state and the Jones–Wilkins–Lee (JWL) equation of state, respectively. The values of the related parameters was directly taken from the ANSYS/Autodyn material library . The initial internal energy of air was set as 206.8 kJ/kg to produce the atmospheric pressure. To validate the accuracy of the proposed numerical model, the predicted midpoint deflections of face sheets were compared with the experimentally measured values of the tested specimens, as shown in Figure 14. Good agreement between the predicted and experimental results was confirmed, because the points in Figure 14 are close to the perfect match line. Furthermore, two typical panels (named TP-1 and TP-4) respectively tested at the SoDs of 100 mm and 50 mm were selected to check the correlation between the simulations and experiments in terms of deformation/failure modes, as shown in Figure 15. Most details of the deformation/failure modes observed in the experiments were captured by the results of the proposed FE model. Therefore, it demonstrated that the prediction capability of the developed FE model was acceptable.
Figure 14 Comparisons between the experimental and numerical midpoint permanent deflections of the face sheets.
Figure 15 Comparisons between the experimental and numerical deformation/failure patterns of (a) panel TP-1 and (b) panel TP-4.
4.2 Velocity response Panels AF-1, TP-1, TP-2, TP-3 and panels AF-2, TP-4 were selected to analyze the effect of the core configurations on the velocity responses under the SoDs of 100 mm and 50 mm, respectively, as shown in Figure 16. It should be noted that the record time started from the detonation instant of the TNT charge.
Figure 16 Velocity history curves of the center of panel face sheets. (a) panel AF-1, (b) panel TP-1, (c) panel TP-2, (d) panel TP-3, (e) panel AF-2 and (f) panel TP-4. For the SoD of 100 mm, the front faces commenced to deform at t = 22 μs when the shock wave acted on the panels, see Figure 16(a)-(d). From the moment on, the center velocities of the front faces increased rapidly and reached their peak values simultaneously at t = 40 μs. The peak velocities of the front faces were 287.8 m/s, 235.4 m/s, 290.2 m/s and 293.5 m/s for panels AF-1, TP-1, TP-2 and TP-3, respectively. The UHMWPE laminate would provide strong resistance to the front face deformation if it was deployed at the first layer. Therefore, the peak velocity of the front face of panel TP-1 was smaller than that of panel 28
AF-1 by 18.21%. The foam cores of AF panels were thicker than those of TP panels. A thicker foam core would induce a longer duration for stress wave to arrive at the back faces of AF panels. As a result, the back face of panel AF-1 began to move at t = 68 μs. It was ~16 μs later than TP panels. The increasing slopes and the peak velocities of the back faces were lower than that of the front faces due to the mitigation of the foam cores. Examination of the velocity curves indicated that the deceleration times of the back faces were larger than the equalized time (teq). The dynamic behavior coincided with the feature of ―strong-core‖ mode, named Regime A defined by Tilbrook et al. . It implied that the core strength was strong enough to deform the back face with low stiffness easily under the low-intensity blast loading. Besides, the debonding failure weakened the restraint on the deformation of back faces. Therefore, the center velocities of the back faces decreased at a slower rate and even occurred the fluctuation phenomenon, especially for TP panels. Figure 16(e) and (f) present the center velocities of the face sheets of panels AF-2 and TP-4. With the SoD decreased to 50 mm, the front faces began to deform at t = 11 μs. The blast load resulting from the explosive detonated at 50 mm SoD caused the front faces to attain a peak velocity of ~700 m/s. Besides, panel TP-4 had a higher front face velocity than panel AF-2 by 6.46%, due to the lower compression strength of LF foam. Similarly, panel AF-2 had a delay in the starting time of the back face deformation relative to panel TP-4 by about 16 μs. The peak velocities of the back faces were much lower than that of the front faces. Careful examination on the relationship between the center velocities of the front face and back face indicated that the dynamic behavior of panel AF-2 was consistent with Regime A as well. The ―slapping‖ mechanism of panel TP-4 could be identified from the velocity curves displayed in Figure 16(f). The center velocity of the back face rose sharply to its peak value when the foam core layers were compressed into the densification state. It conformed with the feature of Regime B , which meant that the existence of UHMWPE laminate would change the response modes of the panels under the high-intensity blast loading. According to the conclusions drawn by Zhou et al. , the graded cores with ascending relative density are favorable for the blast performance of the sandwich panels whose dynamic response modes lie in Regime A and Regime B. Therefore, the velocity characteristics observed in Figure 16 could complementally confirm the better blast performance of panels AF-3 and TP-4 with ascending 29
density foam cores. However, the larger transmitted momentum induced by the ―slapping‖ regime would make panel TP-4 possess higher back face velocity than panel AF-2 by 64.17%. 4.3 Energy absorption characteristic To analyze the energy absorption characteristic of the sandwich panels, the plastic energy dissipated by their components is illustrated via a stack bar diagram, as shown in Figure 17. Note that the bar charts of the multi-layered cores are additionally filled with different patterns to distinguish the core materials. Moreover, the numbers located upon each stack bar are served as a scale to quantify the contribution of the panel components. Under the SoD of 100 mm, the multi-layered cores contributed the majority of energy absorption by the ratio of above 76.13%. The UHMWPE layer itself exhibited less efficient in energy absorption relative to the foam core layer, while its location influenced the total energy dissipation of the panels. Placing the UHMWPE laminate as the first or second core layer would lead to a reduction in the total energy dissipated by the panels. Using panel AF-1 as a benchmark, panel TP-1 and panel TP-2 induced a decrease of energy absorption by 15.65% and 3.40%, respectively. However, placing the UHMWPE laminate at the third core layer would enhance the energy absorption of foam core layers, which compensated the amount lost by the UHMWPE layer. As a result, the total energy dissipation of panel TP-3 was virtually identical to that of panel AF-1. As expected, the decrease of the SoD led to a huge increase in the total plastic energy dissipation of the panels. Under the SoD of 50 mm, more severe indent deformation experienced by the front faces would increase their own energy absorption. However, the complete crushing of the foam cores would exhaust the potential to dissipate more energy for the multi-layered cores. Thus, the proportion of the energy absorbed by the multi-layered cores dropped below 68.53%. As the foam core was densified, the energy absorption of each foam layer was nearly equal for the panels with ungraded foam cores, such as panel AF-2, panel PP-1 and panel PP-2. Besides, the energy absorbed by the foam core layers had a positive correlation with their compressive strength for the panels with the graded form cores. Although the amount and proportion of the energy dissipated by the UHMWPE laminates of TP panels were improved, they still presented limited energy absorption relative to the foam core layers. Moreover, the papery UHMWPE laminates 30
suffered by the extremely stretching deformation did not exhibit remarkable enhancement in the energy absorption. It indicated that the UHMWPE laminates had an inferior energy absorption capacity than the aluminum foam core under the air blast loading. It was probably why the best ones of TP panels and PP panels still underwent undesirable back face deformation.
Figure 17 Energy dissipation of the components of the considered panels.
5 Summary and outlook Air blast experiments and finite element simulations were conducted to investigate the dynamic responses of multi-layered aluminum foam core sandwich panels (AF) and multi-layered hybrid aluminum foam/UHMWPE laminates core sandwich panels (TP and PP). Attention was paid to the effects of foam 31
core gradation and the application strategy of UHMWPE laminates on the blast performance of the panels. Based on the present results, the following conclusions can be drawn: (1) Regardless of core configuration, local indentation and global bending were the dominant deformation modes of the front faces and back faces of the panels, respectively. The foam core underwent partial compression under low-intensity blast loading and suffered completely crushing accompanied by shearing failure under high-intensity blast loading. (2) The ascending density foam core could alleviate the shear-induced collapse appeared in the descending density foam core and thereby reduce the face sheet deflections of AF panels. Similar phenomenon also existed in TP panels with graded foam core placed upon the UHMWPE layer. (3) Placing the UHMWPE layer close to panel back face could increase the indentation deformation of front face and the global deformation of UHMWPE layer, and reduce the permanent deformation of back face. (4) Incorporation of papery UHMWPE laminates would arrest shear cracks in the foam core. PP panel with the papery laminates located between adjacent foam layers performed better than the one with the papery laminates deployed between the face sheets and foam cores regarding the back face deformation. (5) The best sandwich panels with multi-layered hybrid aluminum foam/UHMWPE laminate core performed poorer in terms of back face deflection than the baseline AF panels by ~6%. (6) Deploying the UHMWPE laminate as the first layer core could significantly reduce the velocity of the back face under low-intensity blast loading. AF panels exhibited ―strong-core‖ response, while TP panels tended to go into ―slapping‖ mode under high-intensity blast loading. (7) Most part of blast energy was dissipated by the multi-layered cores. However, the contribution of UHMWPE laminate on the energy absorption was limited relative to the aluminum foam cores. At the present stage, it can be concluded that the introduction of UHMWPE laminates into the core of sandwich structures failed to upgrade the performance under bare blast loading. Note that sandwich panels, as a type of protective structure, are likely to resist detonated cased charges which contain two main effects: the impulse effect and penetration effect. Related research has demonstrated the superior performance of 32
UHMWPE laminate under ballistic impact. Therefore, the protective performance of the sandwich panels with multi-layered hybrid aluminum foam/UHMWPE laminate cores under the combined loading is worthy of further investigation.
Acknowledgements The work is supported by the National Natural Science Foundation of China (Grant Nos. 51679098, 51879112, and 51509096) and the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (Grant No. KFJJ19-05M). The financial contributions are gratefully acknowledged.
Appendix Table A lists the nonlinear orthotropic material model parameters for HB26 laminate. It mainly includes three parts, namely the equation of state (EoS), strength model and failure model. The orthotropic EoS allows formulating the constitutive response of anisotropic material in the elastic regime. The pressure (p) can be defined by the combination form of the volumetric and deviatoric components: 𝑝 = 𝑝(
𝑣𝑜𝑙 , 𝑒)
1 − (𝐶11 + 𝐶21 + 𝐶31 ) 3
1 − (𝐶12 + 𝐶22 + 𝐶32 ) 3
where 𝐶𝑖𝑖 is the coefficient of the stiffness matrix. principal directions. 𝑝(
𝑣𝑜𝑙 , 𝑒)
𝑑 11 ,
1 − (𝐶13 + 𝐶23 + 𝐶33 ) 3
are the deviatoric strains in the
represents the pressure contribution from the volumetric strain which is
described by the Mie-Grüneisen EoS: 𝑝(
𝑣𝑜𝑙 , 𝑒)
= 𝑝𝑟 (𝑣) +
𝛤(𝑣) [𝑒 − 𝑒𝑟 (𝑣)] 𝑣
where v, e and 𝛤(𝑣) are referred to the volume, internal energy and Grüneisen coefficient, respectively. 𝑝𝑟 (𝑣) and 𝑒𝑟 (𝑣) separately denote the reference pressure and internal energy. Table A Nonlinear orthotropic material model parameters for HB26 laminate . Parameter
Equation of state: Orthotropic
Strength: Orthotropic yield 3
Plasticity constant 11
Young’s modulus 11
Plasticity constant 22
Plasticity constant 33
Young’s modulus 33
Plasticity constant 12
Poisson’s ratio 12
Plasticity constant 13
Poisson’s ratio 23
Plasticity constant 23
Poisson’s ratio 31
Plasticity constant 44
Plasticity constant 55
Plasticity constant 66
Young’s modulus 22
Shear modulus 12
Shear modulus 23 Shear modulus 31
Grüneisen coefficient Parameter C1
Eff. stress #3
Eff. stress #6
Eff. stress #7 Eff. stress #8
Failure: Orthotropic softening Tensile failure stress 11
Eff. stress #2
Eff. stress #5
Eff. stress #4
Eff. stress #1
Volumetric response: Shock
Eff. stress #9
ζeff#5 ζeff#6 ζeff#7 ζeff#8 ζeff#9
Tensile failure stress 22
Eff. stress #10
Tensile failure stress 33
Eff. plastic strain #1
Eff. plastic strain #2
Eff. plastic strain #3
Maximum shear stress 12 Maximum shear stress 23
Maximum shear stress 31
Fracture energy 11
Fracture energy 22
Fracture energy 33
Eff. plastic strain #4
Eff. plastic strain #5
Eff. plastic strain #6
Eff. plastic strain #7
Fracture energy 12
Eff. plastic strain #8
Fracture energy 23
Eff. plastic strain #9
Eff. plastic strain #10
Fracture energy 31
Note: the subscript 11 represents the out-of-plane direction of the material, while the subscript 22 and 33 denote the in-plane direction.
The plastic behavior of HB26 laminate is described by the quadratic yield surface given as follow: 2 2 2 𝑓(𝜎𝑖𝑗 ) = 𝑎11 𝜎11 + 𝑎22 𝜎22 + 𝑎33 𝜎33 + 2𝑎12 𝜎11 𝜎22 + 2𝑎23 𝜎22 𝜎33
(A.3) 2 2 2 +2𝑎13 𝜎11 𝜎33 + 2𝑎44 𝜎23 + 2𝑎55 𝜎31 + 2𝑎66 𝜎12 =𝑘
where 𝑎𝑖𝑗 and 𝜎𝑖𝑗 are the plasticity parameter and the stress in the principal material directions, respectively. k represents a state variable that defines the border of the yield surface. It can be determined by a master effective stress-effective plastic strain curve to simulate the material strain hardening. In the present work, the curve is defined by 10 piecewise points. More details on the determination of k can be consulted from Ref. .
Orthotropic softening failure model is used to model the damage of HB26 laminate. The failure model is based on a combined stress criterion: 2
2 2 𝜎𝑖𝑗 𝜎𝑖𝑖 𝜎𝑘𝑖 ( ) +( ) +( ) ≥ 1 for 𝑖, 𝑗, 𝑘 = 1,2,3 𝐹𝑖𝑖 (1 − 𝐷𝑖𝑖 ) 𝐹𝑖𝑗 (1 − 𝐷𝑖𝑗 ) 𝐹𝑘𝑖 (1 − 𝐷𝑘𝑖 )
where Fii is the failure strength of the material in the respective directions. Dii is the damage parameter following a linear relationship with stress and strain: 𝐷𝑖𝑖 = where L is the characteristic cell length.
𝐿𝜎𝑖𝑖,𝑓 𝑐𝑟 2𝐺𝑖𝑖,𝑓
is the crack strain. Gii, f is the fracture energy in the direction
of damage. Moreover, an erosion model based on the damage parameter is employed to remove the highly distorted elements . It is described by Equation A.6 which could be implemented through a user subroutine in Autodyn. 𝐷22 = 1, 𝐷33 = 1
where the subscript 22 and 33 denote the in-plane direction.
CRediT Author statement Sipei Cai: Data Curation, Visualization, Investigation, Writing – Original Draft, Writing – Review & Editing. Jun Liu: Conceptualization, Project administration. Pan Zhang: Supervision, Conceptualization, Methodology, Investigation, Writing – Review & Editing. Chunpeng Li: Methodology, Data Curation, Visualization. Yuansheng Cheng: Funding acquisition, Investigation. Conflict of interest statement The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Lists of figure and table captions：
(a) Schematic of multi-layered core sandwich panel. Cross-sectional views of the sandwich panels with (b) multi-layered aluminum foam core, (c) multi-layered hybrid aluminum foam/thick UHMWPE laminate core and (d) multi-layered hybrid aluminum foam/papery UHMWPE laminates core.
Uniaxial compressive stress-strain curves of closed-cell aluminum foams.
A sketch of experimental set-up.
Photographs showing the deformation/failure modes of the baseline panels. Front faces of (a) panel AF-1 and (b) panel AF-2; multi-layered cores of (c) panel AF-1 and (d) panel AF-2; back faces of (e) panel AF-1 and (f) panel AF-2.
Cross-sectional views showing overall deformation/failure modes of (a) panel AF-3, (b) panel AF-4 and (c) panel AF-5.
Effects of foam core gradations on the permanent face sheet deflections of AF panels.
Cross-sectional and microscopic photographs showing the deformation/failure modes of (a) panel TP-1, (b) panel TP-2 and (c) panel TP-3.
Effects of UHMWPE laminate locations on the permanent face sheet deflections of TP panels.
Cross-sectional and microscopic photographs showing the deformation/failure modes of (a) panel TP-4 (LF-HF-PE) and (b) panel TP-5 (HF-LF-PE).
Graph comparing the measured cross-section profiles of the back faces of panel TP-4, panel TP-5 and panel AF-2. 39
Effects of foam core gradation or papery UHMWPE interlayers on the permanent face sheet deflections of the sandwich panels with multi-layered hybrid cores.
Cross-sectional and microscopic photographs showing the deformation/failure modes of (a) panel PP-1 (MF-PE-MF-PE-MF) and (b) panel PP-2 (PE-MF-MF-MF-PE).
Procedure of remapping from 2D model to 3D model. (a) Pressure contour of 2D model before remapping. (b) Pressure contour of 3D model after remapping.
Comparisons between the experimental and numerical midpoint permanent deflections of the face sheets.
Comparisons between the experimental and numerical deformation/failure patterns of (a) panel TP-1 and (b) panel TP-4.
Velocity history curves of the center of panel face sheets. (a) panel AF-1, (b) panel TP-1, (c) panel TP-2, (d) panel TP-3, (e) panel AF-2 and (f) panel TP-4.
Energy dissipation of the components of the considered panels.
Material properties and Johnson–Cook parameters of 304 stainless steel .
Detailed information of the tested multi-layered core sandwich panels.
Nonlinear orthotropic material model parameters for HB26 laminate .