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Experimental and numerical study of aluminum foam-cored sandwich tubes subjected to internal air blast
Composites Part B 125 (2017) 134e143
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Experimental and numerical study of aluminum foam-cored sandwich tubes subjected to internal air blast Minzu Liang, Fangyun Lu, Guodong Zhang, Xiangyu Li* College of Science, National University of Defense Technology, 410073 Changsha, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2017 Received in revised form 3 May 2017 Accepted 26 May 2017 Available online 29 May 2017
The blast response of aluminum foam-cored sandwich tubes that were subjected to internal air blast was investigated experimentally and numerically. Blast experiments were performed to capture the fundamental deformation, the maximum deflection of the inner face-sheet (MDIF), and the maximum deflection of the outer face-sheet (MDOF). A special MDOF (SMDOF) can be achieved by normalizing the MDOF with respect to the corresponding face-sheet radius and tube mass. Results confirm that the SMDOF of sandwich tubes is moderately sensitive to the core relative density, internal diameter, core thickness, and explosive charge. The finite element (FE) model was constructed using the Voronoi algorithm. After verifying the FE model, numerical studies were conducted to investigate the deformation process of sandwich tubes, the densification of double-layer cores, and the effects of core arrangement and face-sheet thickness on blast resistance. The SMDOF is influenced by the inner and outer face-sheets, whereas the special energy absorption (SEA) is mainly affected by the inner face-sheet. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Sandwich structure Tube Air-blast Voronoi
1. Introduction Foams, a new class of ultra-light materials, can absorb a large amount of kinetic energy because of their ability to undergo large deformation at a nearly constant plateau stress [1e3]. Foam-cored sandwich structures have received increasing attention because of their excellent property of withstanding blast loading, and have been extensively used in marine and other military applications [4e8]. The remarkable performances of sandwich structures depend on the innovative geometrical design of the foam core [8e11]. Furthermore, traditional blast-resistant devices perform with low efficiency and heavy weight [12,13]. Lightweight and improved blast-resistant containment vessels have become popular with the increase in terrorism [14]. The sandwich tube has been considered a novel structural design that can enhance blast-resistant vessels to contain explosive materials, and protect persons or equipment from internal explosion [15e17]. The foam-cored sandwich tube has better energy absorption (EA) capability than the monolithic blast-resistant tube because the sandwich structures can undergo extreme plastic deformation at an almost constant plateau stress [18e20]. * Corresponding author. E-mail addresses: [email protected] (M. Liang), [email protected] (F. Lu), [email protected] (G. Zhang), [email protected] (X. Li). http://dx.doi.org/10.1016/j.compositesb.2017.05.073 1359-8368/© 2017 Elsevier Ltd. All rights reserved.
The dynamic response of sandwich tubes received increasing attention over the last decade. Shen et al. [21] studied the dynamic response of sandwich tubes that were subjected to internal blast loading using experimental, numerical, and analytical methods. They concluded that sandwich tubes exhibit superior blast resistance compared with monolithic tubes with the same mass. Liu et al. [14] investigated the dynamic response and blast resistance of graded foam-cored sandwich tubes using the LS-DYNA software. They affirmed that sandwich tubes with thin inner face-sheets are superior to those with thick inner face-sheets. Moreover, they confirmed that the tube with a negative core configuration has the best blast resistance. Karagiozova et al. [12] proposed an analytical model for partially confined sandwich tubes to investigate the foam-crushing process and the outer face-sheet deflection. More recently, Liang et al. [22] used the FE model constructed using the random Voronoi algorithm to simulate the deformation process of sandwich tubes under internal blast loading, and investigated the effects of explosive charge, the face-sheet and core thicknesses, and core gradient on blast resistance. They verified that plastic dissipation and outer face-sheet deflection are two conflicting objectives in the evaluation of blast resistance. Studies on the dynamic response of sandwich tubes subjected to internal air-blast is limited because of the complex stress status caused by the multiple pressure reflections in sandwich tubes [23]. Although several investigations have been conducted, the
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underlying mechanism of the internal blast response of sandwich tubes has not been thoroughly understood and thus further investigation is necessary. In the present study, experimental and numerical studies were performed on aluminum foam-cored sandwich tubes that were subjected to air-blast loading. Initially, blast experiments were conducted to capture the fundamental deformation, the maximum deflection of the inner face-sheet (MDIF), and the maximum deflection of the outer face-sheet (MDOF). Subsequently, the effects of parameters, such as core relative density, internal diameter, core thickness, and explosive charge, on the MDOF were discussed. Then, the Voronoi algorithm was employed to create the FE model, which was validated by the experimental results. Finally, the FE results were utilized to investigate the deformation process of sandwich tubes, the densification of double-layer cores, and the effect of core arrangement and facesheet thickness on blast resistance.
2. Experimental procedure The sandwich tubes used in this study were produced with steel face-sheets and closed aluminum foam cores (Fig. 1). The face-sheet was cut from a commercial AISI 1045 steel tube. The foam core was cut from 100-mm thick foam panels by an electro-discharge machine to minimize the damage to the cell edges. The core was annealed at 393 K for 1 h to relieve the residual stresses in the foams during manufacturing. Three foams (F1, F2, and F3) were used in the experiments with corresponding relative densities of 0.11, 0.16, and 0.27, respectively. A sketch of the experimental setup is shown in Fig. 2. The experimental results were served as a validation basis for the subsequent simulation model. The height of the tube was fixed at 100 mm. The thickness of face-sheets was 1.5 mm. Table 1 presents the dimensions of the specimens and explosive charges. An aluminized explosive, JHL, was used in the blast experiments. The cylindrical explosive charge was held at the center of the sandwich tube using iron wires and detonated at its apex with a detonator. The length to radius ratio of the charge was equal to that of the internal face-sheet. The sandwich tube was supported by plastic
135
foams to reduce the influence of the reflected waves from the ground. The purpose of this setup is to minimize the end effects influence on the specimen. Each test was repeated twice. 3. Experimental results and discussion Table 3 shows that the tube specimens can be divided into four cases. Case 1 has different core densities (Groups T1, T3, and T5; Groups T2, T4, and T6; or Groups T7, T8, and T9). Case 2 has the same core thickness and density but different inner dimensions (Groups T2 and T7; Groups T4 and T8; or Groups T6 and T9). Case 3 has the same internal diameter but different core thicknesses (Groups T3 and T11; or Groups T4 and T12). Case 4 has the same tube but different explosive masses (Groups T1 and T2; Groups T3 and T4; Groups T5 and T6; or Groups T10, T11, and T12). Table 2 presents the deformation patterns, the MDIF, and the MDOF. Possible slippages between face-sheets and cores may appear because of the free contact between parts. To compare the maximum deflection of the tubes at equal masses, the MDOF was normalized with respect to the corresponding face-sheet radius and tube mass. The normalized maximum outer face-sheet deflection, called special MDOF (SMDOF), was used to evaluate the blast resistance performance. Fig. 3 plots the SMDOF of the tube specimens with different cases. Fig. 3(a) depicts the SMDOF of the tubes with different core densities. The low-density-cored specimen exhibited a SMDOF of 0.39 kg1 when the internal diameter was 64 mm, whereas the high-density-cored specimen exhibited 0.363 kg1, indicating a slight decrease. A similar tendency was observed when the internal diameter was 96 mm. The core density had a slight influence on the SMDOF. Fig. 3(b) shows that the SMDOF of the tubes with a small internal diameter is higher than that of the specimens with a large internal diameter. As the internal diameter of the specimen increased from 64 mm to 96 mm, the SMDOF decreased by 89.3% at a relative density of 0.11. As the blast pressure decayed exponentially in air, the large internal diameter led to low incident blast pulse on the internal face-sheet. Fig. 3(c) indicates that as the thickness of the core increased from 10 mm to 20 mm, the specimen's MDOF decreased by 94.9% at an explosive charge of 9.6 g and by 69.4% at an explosive charge of 14.1 g. An increase in core thickness was beneficial for decreasing the SMDOF at equivalent tube masses, and the rate of decrease was low when the charge was high. Fig. 3(d) illustrates that the SMDOF increases with the explosive charge. The SMDOF of the tubes at a charge of 14.1 g was approximately 58.4%e92.3% higher than that of the tubes at a charge of 9.6 g. 4. Numerical simulation 4.1. FE model
Fig. 1. The sandwich tube consisting with steel face-sheets and closed aluminum foam core.
FE analysis was carried out to elucidate the deformation process of the maximum radial deflection cross-section of sandwich tubes. The foam core was constructed using the 2D Voronoi algorithm. The FE model was generated by the MATLAB software [24]. Fig. 4 shows that the foam-generating process using the Voronoi algorithm can be divided into four stages [25e27]. First, N nuclei are randomly generated in a given area A based on the principle that the minimum distance between any two nuclei is larger than a given distance dmin. Fig. 4(a) shows that the given area in this paper is a cylindrical region. Second, these nuclei are copied to the surrounding regions by translation, thereby keeping a periodic boundary condition [Fig. 4(b)]. Third, the Delaunay triangulation and the Voronoi diagram are generated when the translation points close to a nucleus are connected to one another. Fig. 4(c) shows the
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Fig. 2. A sketch of experimental setup. (a) Side view, (b) Top view.
Table 1 Dimensions of specimens and explosive charges. Test
T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12
Face-sheet (mm) do
to
di
ti
90 90 90 90 90 90 122 122 122 110 110 110
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
67 67 67 67 67 67 99 99 99 67 67 67
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
typical Delaunay triangulation and the Voronoi diagram in the cylindrical region. Fourth, the Voronoi structure is constructed after the area from the given area A is deleted [Fig. 4(d)]. The irregular degree k of cells is given by Ref. [28].
k ¼ 1 dmin =d0
(1)
where d0 is the average distance of the adjacent nuclei,
d0 ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi .pffiffiffi 2A 3N
(2)
Numerical simulations of the deformation behavior were performed using the fluid-solid interaction (FSI) method with the ABAQUS/Explicit software [29]. Fig. 5 depicts the typical FE models of sandwich tubes with ungraded and graded cores. The core was sandwiched between face-sheets. The cylindrical explosive charge was placed at the center of the face-sheet. The core and face-sheets were modeled using a type of shell element (S4R) [30]. According to the mesh sensitivity analysis, the mesh size was set to approximately 0.7 mm. Self-contact was applied to all the foam cells. General contact was considered between the core and the facesheets with a friction coefficient of 0.02 [31,32]. To simulate the in-plane strain state of specimens, all the nodes in the model were constrained in the out-of-plane direction [25,33].
4.2. Material model The aluminum cell wall was assumed a perfectly elastic plastic model. Table 4 depicts the material properties. The Johnson Cook
Foam core
Core thickness (mm)
Explosive charge (g)
F1 F1 F2 F2 F3 F3 F1 F2 F3 F2 F2 F2
10 10 10 10 10 10 10 10 10 20 20 20
9.6 14.1 9.6 14.1 9.6 14.1 14.1 14.1 14.1 3.8 9.6 14.1
(JC) model was applied to capture the strain rate effects of the steel face-sheet [34]. The JC model is given as follows:
m i h 1 T*
s ¼ ½A þ Bεn 1 þ c ln ε_ *
(3)
where ε is the plastic strain of the material, ε_ * is the dimensionless strain rate ε_ =ε0 , and ε0 is the reference strain rate. T* ¼ (T Troom)/ (Tmelt Troom), and Troom and Tmelt are the room and melting temperatures, respectively. A is the quasi-static yield stress, B and n are the strain hardening coefficients, c is the strain rate hardening coefficient, and m is the thermal softening coefficient [35]. Table 5 shows the JC parameters. The Jones Wilkins Lee (JWL) model was used for the explosive products, and the pressure of the detonation products is given as follows [22]:
u u uE eR1 V þ Be 1 eR2 V þ e0 p ¼ Ae 1 R1 V R2 V V
(4)
where p is the pressure of detonation products; V is the relative volume; Ee0 is the detonation energy density; and Ae, Be, R1, R2, and u are the material constants. Table 6 presents the JWL parameters. Air was modeled by an ideal gas equation of state, and the pressure is given by Ref. [36].
p ¼ ðg 1Þre
(5)
where g is a constant, r is the air density, and e is the special internal energy. Table 7 presents the parameters of the ideal gas model.
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Table 2 Experimental results of the sandwich tubes.
Table 3 Four cases of the experiments. Case
Case 1
Case 2
Case 3
Case 4
Parametric analysis
Core density
Inner dimension
Core thickness
Charge mass
Experiment group
T1, T3 and T5 T2, T4 and T6 T7, T8 and T9
T2 and T7 T4 and T8 T6 and T9
T3 and T11 T4 and T12
T1 and T2 T3 and T4 T5 and T6 T10, T11 and T12
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Fig. 3. The SMDOF with different cases. (a) Case 1: core density, (b) Case 2: internal diameter, (c) Case 3: core thickness, (d) Case 4: explosive charge.
4.3. Validation of the FE model The experimental results were compared with the simulation predictions for the maximum radial deflection of the sandwich tubes in Table 8. The errors between the experimental and numerical results are acceptable. A good agreement was achieved between the numerical and experimental results. 5. Simulation results and discussions 5.1. Deformation process Fig. 6 shows that the tube deformation process can be generally described in three phases. In the first phase, explosive detonation leads to a high-pressure pulse that acts on the inner face-sheet. This occurrence induces an increase in velocity at the inner face-sheet in a very short period (Fig. 7). The inner face-sheet crushes the core and the velocity decreases gradually in the second phase. The core material near the inner face-sheet is fully compacted, whereas the remaining part remains undeformed. A fast propagating thin layer, called “shock front,” separates the crushed and undeformed parts. During the third phase, the outer face-sheet starts to deform after the core compacts fully. The inner face-sheet separates with the core when the velocities of the inner and outer face-sheets are equal. 5.2. Double-layer core densification In the second phase, the core densification process is
complicated for the sandwich tube with graded cores. Fig. 8 depicts that the double-layer core is sandwiched between face-sheets; layers 1 and 2 are locate inside and outside, respectively. For the double-layer core, the gradient is positive when the relative density of layer 1 is lower than that of layer 2. That the relative densities of layer 1 and layer 2 are r1 and r2, respectively, and that the corresponding plateau stresses are s1 and s2 are assumed. For a positive core, layer 1 is soft (s1 < s2). The inner layer deforms immediately after blast wave is reached. However, the reaction stress at the interface between the foam layers is the quasistatic plateau stress of layer 1 (s1). The reaction stress at the interface is still below the quasi-static plateau stress of layer 2. Therefore, layer 2 remains undeformed during the entire crushing process of layer 1. The densification wave occurs from the inside and then gradually propagates to the outside. Fig. 8(a) presents that one shock wave propagating from the inside to the outside during the completely crushing process occurs when the core gradient is positive. The deformation phenomenon coincides with the ungraded core [37]. When the core gradient is negative, layer 1 is hard (s1 > s2). The densification wave appears in layer 1 at the blast end initially. The reaction stress at the interface between the two layers is equal to the quasi-static plateau stress of layer 1 (s1), which exceeds the quasi-static plateau stress of layer 2 (s2). Young's modulus of the rigid-perfectly plastic-locking (R-PP-L) model material approaches infinite; therefore, the critical velocity is approximate to zero. Subsequently, a new compaction wave starts in layer 2. Fig. 8(b) exhibits that a compaction wave begins at the blast end of layer 1 initially, and then a new compaction wave starts at the proximal
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Fig. 4. Four stages of the foam-generating process using the Voronoi algorithm. (a) Nuclei in a given area, (b) Delaunay triangulation and Voronoi diagram. (c) Voronoi structure.
Fig. 5. FE models with ungraded and graded cores. (a) Ungraded core, (b) Double-layer core, and (c) Triple-layer core.
Table 4 The elastic perfectly plastic model parameters. Material
Density/(kg/m3)
Young modulus/(GPa)
Poisson ratio
Yield stress/(MPa)
Aluminum
2730
70
0.3
190
140
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Table 5 The JC model parameters. Material
A/(MPa)
B
n
c
m
Steel
507
0.0032
0.28
0.064
1.06
Table 6 The JWL model parameters. Material Detonation speed/(m/s) Ae JHL-3
7050
Be
u
R1
R2
Ee0/(J/m3) V0
6.11 0.107 0.35 4.4 1.2 0.089
1.0
Table 7 The linear polynomial model parameters. Material
r/(kg/m3)
g
e/(kJ/kg)
Air
1.293
1.4
2.068 105 Fig. 7. Displacement and velocity of inner and outer face-sheets.
Table 8 Comparison of the experimental and numerical results. Face-sheet (mm) do
to
di
ti
110 110 110
1.5 1.5 1.5
67 67 67
1.5 1.5 1.5
Charge Experimental (g) result (mm)
3.8 9.6 14.1
SEA ¼ EA=m
Simulation prediction (mm)
Difference (%)
MDIF
MDOF
MDIF
MDOF
MDIF
MDOF
1.7 24.5 40.2
0 1.2 11.5
1.6 23.8 38.4
0 1.1 10.8
5.9 2.9 4.4
0 8.3 6.1
end of layer 2 when the stress wave reaches the interface between the two layers. 5.3. Blast-resistant analysis For a tube structure, two criteria are considered to evaluate the blast-resistant capacity [38,39]. On the one hand, the MDOF of a blast-resistant structure should be reduced. For an equivalent mass, the SMDOF can be achieved by normalizing the MDOF with respect to the corresponding face-sheet radius and tube mass:
SMDOF ¼ MDOF=ðm$r0 Þ
(6)
where m is the mass of the tube and ro is the radius of the outer face-sheet. On the other hand, the sandwich tube is expected to absorb as much plastic energy as possible to reduce the level of the kinetic energy transferred to the protected objects [40]. For a lightweight application, a specific EA can be defined as follows:
(7)
The SMDOF and SEA are considered as two parameters that evaluate the protective capability [14,41]. The sandwich tube with low SMDOF and high SEA is a good choice for the protection requirements. Fig. 9 depicts six sandwich tubes with different core arrangements. Fig. 10 shows the temporal variation of normalized plastic dissipation and face-sheet deflection. Fig. 10(a) shows that the SEA of arrangement 1 (F1-F2-F3) is obviously larger than those of the other distributions and the SEA of arrangement 6 (F3-F2-F1) possesses the smallest value. The SEA increases by 15.8% from arrangement 6 to 1. Fig. 10(b) shows the deflection histories of the tube with different core distributions. Arrangement 1 displays the largest SMDOF, and arrangement 5 (F3-F1-F2) exhibits the smallest SMDOF, which is only 58.9% of the SMDOF achieved by arrangement 1. The SEA increases 13.5% from arrangement 5 to 1. Table 9 shows the uniform foam-filled specimens with different face-sheet thicknesses. The specimens can be divided into three cases. Case 1 has the same inner face-sheet but different outer facesheets (Groups S3, S4, and S5). Case 2 has the same outer face-sheet but different inner face-sheets (Groups S2, S4, and S6). In Case 3, the thickness of the inner face-sheet is equal to that of the outer face-sheet. Case 3 has different face-sheet thicknesses (Groups S1, S4, and S7). Fig. 11 shows the temporal variation of normalized plastic dissipation and face-sheet deflection. For Case 1, the SEAs of the tubes with different outer face-sheets are almost identical. However, the SMDOFs of S5 (outer face-sheet thickness: 2 mm) are
Fig. 6. Three phases for the structure response process of foam filled sandwich tube.
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Fig. 8. Deformation processes of foam cores with positive and negative gradients.
Fig. 9. Sandwich tubes with different core arrangements. (a) Arrangement 1: F1-F2-F3, (b) arrangement 2: F1-F3-F2, (c) arrangement 3: F2-F1-F3, (d) arrangement 4: F2-F3-F1, (e) arrangement 5: F3-F1-F2, and (f) arrangement 6: F3-F2-F1.
94.4% and 57.9% smaller than those of S3 (outer face-sheet thickness: 1 mm) and S4 (outer face-sheet thickness: 1.5 mm), respectively. For Case 2, the SEA of the tube increases as the thickness of
the inner face-sheet decreases. The SEA decreases 61.9% as the thickness of the inner face-sheet increases from 1 mm (S2) to 2 mm (S6). No outer face deflection for S6 occurs, as the core does not
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Fig. 10. Influence of core arrangement on the histories of plastic dissipation and outer-face deflection. (a) Plastic dissipation histories, (b) Face-sheet deflection histories.
Table 9 The specimens with different face-sheet thicknesses. Specimen
Inner face thickness (mm)
Outer face thickness (mm)
S1 S2 S3 S4 S5 S6 S7
1.0 1.0 1.5 1.5 1.5 2.0 2.0
1.0 1.5 1.0 1.5 2.0 1.5 2.0
deform completely. The SMDOF is small when the thickness of the inner face-sheet is large (S4 and S6). As the thickness of the inner face-sheet increases from 1 mm to 1.5 mm, the SMDOF decreases by 91.2%. For Case 3, the SEA and SMDOF simultaneously decrease with face-sheet thickness. The SMDOF is influenced by the inner and outer face-sheets. However, the SEA is mainly affected by the inner face-sheet because the core plays a major role in the SEA of the sandwich tubes and the inner face-sheet compacts the core before the outer face-sheet deformation.
6. Conclusions
investigate the blast response of aluminum foam-cored sandwich tubes that were subjected to internal air-blast loading. Blast experiments were performed to capture the fundamental deformation, the MDIF, and the MDOF. The results confirm that the MDOF of sandwich tubes is moderately sensitive to the core relative density, internal diameter, core thickness, and explosive charge. The core density has a slight influence on the SMDOF. The SMDOF increases when the internal diameter decreases, core thickness decreases, or explosive charge increases. The FE model was constructed using the Voronoi algorithm. The FE model was validated by the FE results. The FE results agree well with the experimental results. Numerical simulations were conducted to investigate the deformation process of sandwich tubes, the densification of double-layer cores, and the effect of core arrangement and face-sheet thickness on blast-resistance. The tube deformation process can be generally described in three phases: inner face-sheet acceleration, core compaction, and outer facesheet deformation. For a positive core, one shock wave that propagates from the inside to the outside during the complete crushing process occurs. For a negative core, two compaction waves simultaneously propagate outside. The SMDOF is influenced by the inner and outer face-sheets. However, the SEA is mainly affected by the inner face-sheet because the core plays a major role in the SEA of sandwich tubes and the inner face-sheet compacts the core before the outer face-sheet deformation.
Experimental and numerical analyses were performed to
Fig. 11. Effect of face-sheet thickness on plastic dissipation and face-sheet deflection histories. (a) Plastic dissipation histories, (b) Face-sheet deflection histories.
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Acknowledgements The authors gratefully acknowledge financial supported by the National Natural Science Foundation of China (NSFC) under grant No. 11132012. References [1] Gibson L, Ashby M. Cellular solids. Cambridge, UK: Cambridge University Press; 1997. [2] Zhou H, Wang X, Zhao Z. High velocity impact mitigation with gradient cellular solids. Compos Part B Eng 2016;85:93e101. [3] Barnes AT, Ravi-Chandar K, Kyriakides S, Gaitanaros S. Dynamic crushing of aluminum foams: Part I e Experiments. Int J Solids Struct 2014;51(9): 1631e45. [4] Zhang X, An L, Ding H. Dynamic crushing behavior and energy absorption of honeycombs with density gradient. J Sandw Struct Mater 2014;16(2):125e47. [5] Li S, Li X, Wang Z, Wu G, Lu G, Zhao L. Finite element analysis of sandwich panels with stepwise graded aluminum honeycomb cores under blast loading. Compos Part A Appl S 2016;80:1e12. [6] Li S, Lu G, Wang Z, Zhao L, Wu G. Finite element simulation of metallic cylindrical sandwich shells with graded aluminum tubular cores subjected to internal blast loading. Int J Mech Sci 2015;96e97:1e12. [7] Zhang P, Cheng YS, Liu J, Li Y, Zhang CZ, Hou HL, et al. Experimental study on the dynamic response of foam-filled corrugated core sandwich panels subjected to air blast loading. Compos Part B Eng 2016;105:67e81. [8] Jackson M, Shukla A. Performance of sandwich composites subjected to sequential impact and air blast loading. Compos Part B Eng 2011;42(2): 155e66. [9] Yazici M, Wright J, Bertin D, Shukla A. Experimental and numerical study of foam filled corrugated core steel sandwich structures subjected to blast loading. Compos Struct 2014;110:98e109. [10] Zhang JJ, Wang ZH, Zhao LM. Dynamic response of functionally graded cellular materials based on the Voronoi model. Compos Part B Eng 2016;85:176e87. [11] Sun Z, Shi SS, Guo X, Hu XZ, Chen HR. On compressive properties of composite sandwich structures with grid reinforced honeycomb core. Compos Part B Eng 2016;94:245e52. [12] Karagiozova D, Langdon GS, Nurick GN, Niven T. The influence of a low density foam sandwich core on the response of a partially confined steel cylinder to internal air-blast. Int J Impact Eng 2016;92:32e49. [13] Jing L, Wang Z, Shim VPW, Zhao L. An experimental study of the dynamic response of cylindrical sandwich shells with metallic foam cores subjected to blast loading. Int J Impact Eng 2014;71:60e72. [14] Liu X, Tian X, Lu TJ, Zhou D, Liang B. Blast resistance of sandwich-walled hollow cylinders with graded metallic foam cores. Compos Struct 2012;94(8):2485e93. [15] Hoo Fatt MS, Surabhi H. Blast resistance and energy absorption of foam-core cylindrical sandwich shells under external blast. Compos Struct 2012;94(11): 3174e85. [16] Fatt MSH, Gao Y, Sirivolu D. Foam-core, curved composite sandwich panels under blast. J Sandw Struct Mater 2013;15(3):261e91. [17] Li S, Wang Z, Wu G, Zhao L, Li X. Dynamic response of sandwich spherical shell with graded metallic foam cores subjected to blast loading. Compos Part A Appl S 2014;56:262e71. [18] Jin XC, Wang ZH, Ning JG, Xiao GS, Liu EQ, Shu XF. Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading. Compos Part B Eng 2016;106:206e17.
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[19] Ashby MF, Evans T, Fleck NA, Hutchinson J, Wadley H, Gibson L. Metal foams: a design guide. Elsevier; 2000. [20] Wang E, Gardner N, Shukla A. The blast resistance of sandwich composites with stepwise graded cores. Int J Solids Struct 2009;46(18e19):3492e502. [21] Shen J, Lu G, Zhao L, Zhang Q. Short sandwich tubes subjected to internal explosive loading. Eng Struct 2013;55:56e65. [22] Liang MZ, Zhang GD, Lu FY, Li XY. Blast resistance and design of sandwich cylinder with graded foam cores based on the Voronoi algorithm. Thin-Walled Struct 2017;112:98e106. [23] Jing L, Wang ZH, Zhao LM. The dynamic response of sandwich panels with cellular metal cores to localized impulsive loading. Compos Part B Eng 2016;94:52e63. [24] Zhu HX, Thorpe SM, Windle AH. The effect of cell irregularity on the high strain compression of 2D Voronoi honeycombs. Int J Solids Struct 2006;43(5): 1061e78. [25] Zheng Z, Yu J, Li J. Dynamic crushing of 2D cellular structures: a finite element study. Int J Impact Eng 2005;32(1e4):650e64. [26] Kader MA, Islam MA, Hazell PJ, Escobedo JP, Saadatfar M, Brown AD, et al. Modelling and characterization of cell collapse in aluminium foams during dynamic loading. Int J Impact Eng 2016;96:78e88. [27] Alsayednoor J, Harrison P. Evaluating the performance of microstructure generation algorithms for 2-d foam-like representative volume elements. Mech Mater 2016;98:44e58. [28] Zhu HX, Hobdell JR, Windle AH. Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs. J Mech Phys Solids 2001;49(4): 857e70. [29] Hibbitt KS, Inc. ABAQUS/Explicit User's manual, version 6.9-3. Providence, RI, USA: Dassault Systemes Simulia Corp; 2010. [30] Zhang J, Wang Z, Zhao L. Dynamic response of functionally graded cellular materials based on the Voronoi model. Compos Part B Eng 2016;85:176e87. [31] Zheng Z, Wang C, Yu J, Reid SR, Harrigan JJ. Dynamic stressestrain states for metal foams using a 3D cellular model. J Mech Phys Solids 2014;72:93e114. [32] Li Z, Zhang J, Fan J, Wang Z, Zhao L. On crushing response of the threedimensional closed-cell foam based on Voronoi model. Mech Mater 2014;68:85e94. [33] Liao S, Zheng Z, Yu J. Dynamic crushing of 2D cellular structures: local strain field and shock wave velocity. Int J Impact Eng 2013;57:7e16. [34] Liang MZ, Li XY, Lu FY. Effects of U-notches on the dynamic fracture and fragmentation of explosively driven cylinders. Theor Appl Fract Mech 2015;77:50e8. [35] Satapathy S, Landen D. Expanding ring experiments to measure hightemperature adiabatic properties. Int J Impact Eng 2006;33(1):735e44. [36] Li X, Wang Z, Zhu F, Wu G, Zhao L. Response of aluminium corrugated sandwich panels under air blast loadings: experiment and numerical simulation. Int J Impact Eng 2014;65:79e88. [37] Darvizeh R, Davey K. A transport approach for analysis of shock waves in cellular materials. Int J Impact Eng 2015;82:59e73. [38] Jing L, Wang Z, Zhao L. An approximate theoretical analysis for clamped cylindrical sandwich shells with metallic foam cores subjected to impulsive loading. Compos Part B Eng 2014;60:150e7. [39] Liu H, Cao ZK, Yao GC, Luo HJ, Zu GY. Performance of aluminum foamesteel panel sandwich composites subjected to blast loading. Mater Des 2013;47: 483e8. [40] Langdon GS, Karagiozova D, von Klemperer CJ, Nurick GN, Ozinsky A, Pickering EG. The air-blast response of sandwich panels with composite face sheets and polymer foam cores: experiments and predictions. Int J Impact Eng 2013;54:64e82. [41] Jing L, Wang Z, Ning J, Zhao L. The dynamic response of sandwich beams with open-cell metal foam cores. Compos Part B: Eng 2011;42(1):1e10.
Contents lists available at ScienceDirect
Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Experimental and numerical study of aluminum foam-cored sandwich tubes subjected to internal air blast Minzu Liang, Fangyun Lu, Guodong Zhang, Xiangyu Li* College of Science, National University of Defense Technology, 410073 Changsha, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2017 Received in revised form 3 May 2017 Accepted 26 May 2017 Available online 29 May 2017
The blast response of aluminum foam-cored sandwich tubes that were subjected to internal air blast was investigated experimentally and numerically. Blast experiments were performed to capture the fundamental deformation, the maximum deflection of the inner face-sheet (MDIF), and the maximum deflection of the outer face-sheet (MDOF). A special MDOF (SMDOF) can be achieved by normalizing the MDOF with respect to the corresponding face-sheet radius and tube mass. Results confirm that the SMDOF of sandwich tubes is moderately sensitive to the core relative density, internal diameter, core thickness, and explosive charge. The finite element (FE) model was constructed using the Voronoi algorithm. After verifying the FE model, numerical studies were conducted to investigate the deformation process of sandwich tubes, the densification of double-layer cores, and the effects of core arrangement and face-sheet thickness on blast resistance. The SMDOF is influenced by the inner and outer face-sheets, whereas the special energy absorption (SEA) is mainly affected by the inner face-sheet. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Sandwich structure Tube Air-blast Voronoi
1. Introduction Foams, a new class of ultra-light materials, can absorb a large amount of kinetic energy because of their ability to undergo large deformation at a nearly constant plateau stress [1e3]. Foam-cored sandwich structures have received increasing attention because of their excellent property of withstanding blast loading, and have been extensively used in marine and other military applications [4e8]. The remarkable performances of sandwich structures depend on the innovative geometrical design of the foam core [8e11]. Furthermore, traditional blast-resistant devices perform with low efficiency and heavy weight [12,13]. Lightweight and improved blast-resistant containment vessels have become popular with the increase in terrorism [14]. The sandwich tube has been considered a novel structural design that can enhance blast-resistant vessels to contain explosive materials, and protect persons or equipment from internal explosion [15e17]. The foam-cored sandwich tube has better energy absorption (EA) capability than the monolithic blast-resistant tube because the sandwich structures can undergo extreme plastic deformation at an almost constant plateau stress [18e20]. * Corresponding author. E-mail addresses: [email protected] (M. Liang), [email protected] (F. Lu), [email protected] (G. Zhang), [email protected] (X. Li). http://dx.doi.org/10.1016/j.compositesb.2017.05.073 1359-8368/© 2017 Elsevier Ltd. All rights reserved.
The dynamic response of sandwich tubes received increasing attention over the last decade. Shen et al. [21] studied the dynamic response of sandwich tubes that were subjected to internal blast loading using experimental, numerical, and analytical methods. They concluded that sandwich tubes exhibit superior blast resistance compared with monolithic tubes with the same mass. Liu et al. [14] investigated the dynamic response and blast resistance of graded foam-cored sandwich tubes using the LS-DYNA software. They affirmed that sandwich tubes with thin inner face-sheets are superior to those with thick inner face-sheets. Moreover, they confirmed that the tube with a negative core configuration has the best blast resistance. Karagiozova et al. [12] proposed an analytical model for partially confined sandwich tubes to investigate the foam-crushing process and the outer face-sheet deflection. More recently, Liang et al. [22] used the FE model constructed using the random Voronoi algorithm to simulate the deformation process of sandwich tubes under internal blast loading, and investigated the effects of explosive charge, the face-sheet and core thicknesses, and core gradient on blast resistance. They verified that plastic dissipation and outer face-sheet deflection are two conflicting objectives in the evaluation of blast resistance. Studies on the dynamic response of sandwich tubes subjected to internal air-blast is limited because of the complex stress status caused by the multiple pressure reflections in sandwich tubes [23]. Although several investigations have been conducted, the
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underlying mechanism of the internal blast response of sandwich tubes has not been thoroughly understood and thus further investigation is necessary. In the present study, experimental and numerical studies were performed on aluminum foam-cored sandwich tubes that were subjected to air-blast loading. Initially, blast experiments were conducted to capture the fundamental deformation, the maximum deflection of the inner face-sheet (MDIF), and the maximum deflection of the outer face-sheet (MDOF). Subsequently, the effects of parameters, such as core relative density, internal diameter, core thickness, and explosive charge, on the MDOF were discussed. Then, the Voronoi algorithm was employed to create the FE model, which was validated by the experimental results. Finally, the FE results were utilized to investigate the deformation process of sandwich tubes, the densification of double-layer cores, and the effect of core arrangement and facesheet thickness on blast resistance.
2. Experimental procedure The sandwich tubes used in this study were produced with steel face-sheets and closed aluminum foam cores (Fig. 1). The face-sheet was cut from a commercial AISI 1045 steel tube. The foam core was cut from 100-mm thick foam panels by an electro-discharge machine to minimize the damage to the cell edges. The core was annealed at 393 K for 1 h to relieve the residual stresses in the foams during manufacturing. Three foams (F1, F2, and F3) were used in the experiments with corresponding relative densities of 0.11, 0.16, and 0.27, respectively. A sketch of the experimental setup is shown in Fig. 2. The experimental results were served as a validation basis for the subsequent simulation model. The height of the tube was fixed at 100 mm. The thickness of face-sheets was 1.5 mm. Table 1 presents the dimensions of the specimens and explosive charges. An aluminized explosive, JHL, was used in the blast experiments. The cylindrical explosive charge was held at the center of the sandwich tube using iron wires and detonated at its apex with a detonator. The length to radius ratio of the charge was equal to that of the internal face-sheet. The sandwich tube was supported by plastic
135
foams to reduce the influence of the reflected waves from the ground. The purpose of this setup is to minimize the end effects influence on the specimen. Each test was repeated twice. 3. Experimental results and discussion Table 3 shows that the tube specimens can be divided into four cases. Case 1 has different core densities (Groups T1, T3, and T5; Groups T2, T4, and T6; or Groups T7, T8, and T9). Case 2 has the same core thickness and density but different inner dimensions (Groups T2 and T7; Groups T4 and T8; or Groups T6 and T9). Case 3 has the same internal diameter but different core thicknesses (Groups T3 and T11; or Groups T4 and T12). Case 4 has the same tube but different explosive masses (Groups T1 and T2; Groups T3 and T4; Groups T5 and T6; or Groups T10, T11, and T12). Table 2 presents the deformation patterns, the MDIF, and the MDOF. Possible slippages between face-sheets and cores may appear because of the free contact between parts. To compare the maximum deflection of the tubes at equal masses, the MDOF was normalized with respect to the corresponding face-sheet radius and tube mass. The normalized maximum outer face-sheet deflection, called special MDOF (SMDOF), was used to evaluate the blast resistance performance. Fig. 3 plots the SMDOF of the tube specimens with different cases. Fig. 3(a) depicts the SMDOF of the tubes with different core densities. The low-density-cored specimen exhibited a SMDOF of 0.39 kg1 when the internal diameter was 64 mm, whereas the high-density-cored specimen exhibited 0.363 kg1, indicating a slight decrease. A similar tendency was observed when the internal diameter was 96 mm. The core density had a slight influence on the SMDOF. Fig. 3(b) shows that the SMDOF of the tubes with a small internal diameter is higher than that of the specimens with a large internal diameter. As the internal diameter of the specimen increased from 64 mm to 96 mm, the SMDOF decreased by 89.3% at a relative density of 0.11. As the blast pressure decayed exponentially in air, the large internal diameter led to low incident blast pulse on the internal face-sheet. Fig. 3(c) indicates that as the thickness of the core increased from 10 mm to 20 mm, the specimen's MDOF decreased by 94.9% at an explosive charge of 9.6 g and by 69.4% at an explosive charge of 14.1 g. An increase in core thickness was beneficial for decreasing the SMDOF at equivalent tube masses, and the rate of decrease was low when the charge was high. Fig. 3(d) illustrates that the SMDOF increases with the explosive charge. The SMDOF of the tubes at a charge of 14.1 g was approximately 58.4%e92.3% higher than that of the tubes at a charge of 9.6 g. 4. Numerical simulation 4.1. FE model
Fig. 1. The sandwich tube consisting with steel face-sheets and closed aluminum foam core.
FE analysis was carried out to elucidate the deformation process of the maximum radial deflection cross-section of sandwich tubes. The foam core was constructed using the 2D Voronoi algorithm. The FE model was generated by the MATLAB software [24]. Fig. 4 shows that the foam-generating process using the Voronoi algorithm can be divided into four stages [25e27]. First, N nuclei are randomly generated in a given area A based on the principle that the minimum distance between any two nuclei is larger than a given distance dmin. Fig. 4(a) shows that the given area in this paper is a cylindrical region. Second, these nuclei are copied to the surrounding regions by translation, thereby keeping a periodic boundary condition [Fig. 4(b)]. Third, the Delaunay triangulation and the Voronoi diagram are generated when the translation points close to a nucleus are connected to one another. Fig. 4(c) shows the
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Fig. 2. A sketch of experimental setup. (a) Side view, (b) Top view.
Table 1 Dimensions of specimens and explosive charges. Test
T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12
Face-sheet (mm) do
to
di
ti
90 90 90 90 90 90 122 122 122 110 110 110
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
67 67 67 67 67 67 99 99 99 67 67 67
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
typical Delaunay triangulation and the Voronoi diagram in the cylindrical region. Fourth, the Voronoi structure is constructed after the area from the given area A is deleted [Fig. 4(d)]. The irregular degree k of cells is given by Ref. [28].
k ¼ 1 dmin =d0
(1)
where d0 is the average distance of the adjacent nuclei,
d0 ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi .pffiffiffi 2A 3N
(2)
Numerical simulations of the deformation behavior were performed using the fluid-solid interaction (FSI) method with the ABAQUS/Explicit software [29]. Fig. 5 depicts the typical FE models of sandwich tubes with ungraded and graded cores. The core was sandwiched between face-sheets. The cylindrical explosive charge was placed at the center of the face-sheet. The core and face-sheets were modeled using a type of shell element (S4R) [30]. According to the mesh sensitivity analysis, the mesh size was set to approximately 0.7 mm. Self-contact was applied to all the foam cells. General contact was considered between the core and the facesheets with a friction coefficient of 0.02 [31,32]. To simulate the in-plane strain state of specimens, all the nodes in the model were constrained in the out-of-plane direction [25,33].
4.2. Material model The aluminum cell wall was assumed a perfectly elastic plastic model. Table 4 depicts the material properties. The Johnson Cook
Foam core
Core thickness (mm)
Explosive charge (g)
F1 F1 F2 F2 F3 F3 F1 F2 F3 F2 F2 F2
10 10 10 10 10 10 10 10 10 20 20 20
9.6 14.1 9.6 14.1 9.6 14.1 14.1 14.1 14.1 3.8 9.6 14.1
(JC) model was applied to capture the strain rate effects of the steel face-sheet [34]. The JC model is given as follows:
m i h 1 T*
s ¼ ½A þ Bεn 1 þ c ln ε_ *
(3)
where ε is the plastic strain of the material, ε_ * is the dimensionless strain rate ε_ =ε0 , and ε0 is the reference strain rate. T* ¼ (T Troom)/ (Tmelt Troom), and Troom and Tmelt are the room and melting temperatures, respectively. A is the quasi-static yield stress, B and n are the strain hardening coefficients, c is the strain rate hardening coefficient, and m is the thermal softening coefficient [35]. Table 5 shows the JC parameters. The Jones Wilkins Lee (JWL) model was used for the explosive products, and the pressure of the detonation products is given as follows [22]:
u u uE eR1 V þ Be 1 eR2 V þ e0 p ¼ Ae 1 R1 V R2 V V
(4)
where p is the pressure of detonation products; V is the relative volume; Ee0 is the detonation energy density; and Ae, Be, R1, R2, and u are the material constants. Table 6 presents the JWL parameters. Air was modeled by an ideal gas equation of state, and the pressure is given by Ref. [36].
p ¼ ðg 1Þre
(5)
where g is a constant, r is the air density, and e is the special internal energy. Table 7 presents the parameters of the ideal gas model.
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Table 2 Experimental results of the sandwich tubes.
Table 3 Four cases of the experiments. Case
Case 1
Case 2
Case 3
Case 4
Parametric analysis
Core density
Inner dimension
Core thickness
Charge mass
Experiment group
T1, T3 and T5 T2, T4 and T6 T7, T8 and T9
T2 and T7 T4 and T8 T6 and T9
T3 and T11 T4 and T12
T1 and T2 T3 and T4 T5 and T6 T10, T11 and T12
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Fig. 3. The SMDOF with different cases. (a) Case 1: core density, (b) Case 2: internal diameter, (c) Case 3: core thickness, (d) Case 4: explosive charge.
4.3. Validation of the FE model The experimental results were compared with the simulation predictions for the maximum radial deflection of the sandwich tubes in Table 8. The errors between the experimental and numerical results are acceptable. A good agreement was achieved between the numerical and experimental results. 5. Simulation results and discussions 5.1. Deformation process Fig. 6 shows that the tube deformation process can be generally described in three phases. In the first phase, explosive detonation leads to a high-pressure pulse that acts on the inner face-sheet. This occurrence induces an increase in velocity at the inner face-sheet in a very short period (Fig. 7). The inner face-sheet crushes the core and the velocity decreases gradually in the second phase. The core material near the inner face-sheet is fully compacted, whereas the remaining part remains undeformed. A fast propagating thin layer, called “shock front,” separates the crushed and undeformed parts. During the third phase, the outer face-sheet starts to deform after the core compacts fully. The inner face-sheet separates with the core when the velocities of the inner and outer face-sheets are equal. 5.2. Double-layer core densification In the second phase, the core densification process is
complicated for the sandwich tube with graded cores. Fig. 8 depicts that the double-layer core is sandwiched between face-sheets; layers 1 and 2 are locate inside and outside, respectively. For the double-layer core, the gradient is positive when the relative density of layer 1 is lower than that of layer 2. That the relative densities of layer 1 and layer 2 are r1 and r2, respectively, and that the corresponding plateau stresses are s1 and s2 are assumed. For a positive core, layer 1 is soft (s1 < s2). The inner layer deforms immediately after blast wave is reached. However, the reaction stress at the interface between the foam layers is the quasistatic plateau stress of layer 1 (s1). The reaction stress at the interface is still below the quasi-static plateau stress of layer 2. Therefore, layer 2 remains undeformed during the entire crushing process of layer 1. The densification wave occurs from the inside and then gradually propagates to the outside. Fig. 8(a) presents that one shock wave propagating from the inside to the outside during the completely crushing process occurs when the core gradient is positive. The deformation phenomenon coincides with the ungraded core [37]. When the core gradient is negative, layer 1 is hard (s1 > s2). The densification wave appears in layer 1 at the blast end initially. The reaction stress at the interface between the two layers is equal to the quasi-static plateau stress of layer 1 (s1), which exceeds the quasi-static plateau stress of layer 2 (s2). Young's modulus of the rigid-perfectly plastic-locking (R-PP-L) model material approaches infinite; therefore, the critical velocity is approximate to zero. Subsequently, a new compaction wave starts in layer 2. Fig. 8(b) exhibits that a compaction wave begins at the blast end of layer 1 initially, and then a new compaction wave starts at the proximal
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139
Fig. 4. Four stages of the foam-generating process using the Voronoi algorithm. (a) Nuclei in a given area, (b) Delaunay triangulation and Voronoi diagram. (c) Voronoi structure.
Fig. 5. FE models with ungraded and graded cores. (a) Ungraded core, (b) Double-layer core, and (c) Triple-layer core.
Table 4 The elastic perfectly plastic model parameters. Material
Density/(kg/m3)
Young modulus/(GPa)
Poisson ratio
Yield stress/(MPa)
Aluminum
2730
70
0.3
190
140
M. Liang et al. / Composites Part B 125 (2017) 134e143
Table 5 The JC model parameters. Material
A/(MPa)
B
n
c
m
Steel
507
0.0032
0.28
0.064
1.06
Table 6 The JWL model parameters. Material Detonation speed/(m/s) Ae JHL-3
7050
Be
u
R1
R2
Ee0/(J/m3) V0
6.11 0.107 0.35 4.4 1.2 0.089
1.0
Table 7 The linear polynomial model parameters. Material
r/(kg/m3)
g
e/(kJ/kg)
Air
1.293
1.4
2.068 105 Fig. 7. Displacement and velocity of inner and outer face-sheets.
Table 8 Comparison of the experimental and numerical results. Face-sheet (mm) do
to
di
ti
110 110 110
1.5 1.5 1.5
67 67 67
1.5 1.5 1.5
Charge Experimental (g) result (mm)
3.8 9.6 14.1
SEA ¼ EA=m
Simulation prediction (mm)
Difference (%)
MDIF
MDOF
MDIF
MDOF
MDIF
MDOF
1.7 24.5 40.2
0 1.2 11.5
1.6 23.8 38.4
0 1.1 10.8
5.9 2.9 4.4
0 8.3 6.1
end of layer 2 when the stress wave reaches the interface between the two layers. 5.3. Blast-resistant analysis For a tube structure, two criteria are considered to evaluate the blast-resistant capacity [38,39]. On the one hand, the MDOF of a blast-resistant structure should be reduced. For an equivalent mass, the SMDOF can be achieved by normalizing the MDOF with respect to the corresponding face-sheet radius and tube mass:
SMDOF ¼ MDOF=ðm$r0 Þ
(6)
where m is the mass of the tube and ro is the radius of the outer face-sheet. On the other hand, the sandwich tube is expected to absorb as much plastic energy as possible to reduce the level of the kinetic energy transferred to the protected objects [40]. For a lightweight application, a specific EA can be defined as follows:
(7)
The SMDOF and SEA are considered as two parameters that evaluate the protective capability [14,41]. The sandwich tube with low SMDOF and high SEA is a good choice for the protection requirements. Fig. 9 depicts six sandwich tubes with different core arrangements. Fig. 10 shows the temporal variation of normalized plastic dissipation and face-sheet deflection. Fig. 10(a) shows that the SEA of arrangement 1 (F1-F2-F3) is obviously larger than those of the other distributions and the SEA of arrangement 6 (F3-F2-F1) possesses the smallest value. The SEA increases by 15.8% from arrangement 6 to 1. Fig. 10(b) shows the deflection histories of the tube with different core distributions. Arrangement 1 displays the largest SMDOF, and arrangement 5 (F3-F1-F2) exhibits the smallest SMDOF, which is only 58.9% of the SMDOF achieved by arrangement 1. The SEA increases 13.5% from arrangement 5 to 1. Table 9 shows the uniform foam-filled specimens with different face-sheet thicknesses. The specimens can be divided into three cases. Case 1 has the same inner face-sheet but different outer facesheets (Groups S3, S4, and S5). Case 2 has the same outer face-sheet but different inner face-sheets (Groups S2, S4, and S6). In Case 3, the thickness of the inner face-sheet is equal to that of the outer face-sheet. Case 3 has different face-sheet thicknesses (Groups S1, S4, and S7). Fig. 11 shows the temporal variation of normalized plastic dissipation and face-sheet deflection. For Case 1, the SEAs of the tubes with different outer face-sheets are almost identical. However, the SMDOFs of S5 (outer face-sheet thickness: 2 mm) are
Fig. 6. Three phases for the structure response process of foam filled sandwich tube.
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Fig. 8. Deformation processes of foam cores with positive and negative gradients.
Fig. 9. Sandwich tubes with different core arrangements. (a) Arrangement 1: F1-F2-F3, (b) arrangement 2: F1-F3-F2, (c) arrangement 3: F2-F1-F3, (d) arrangement 4: F2-F3-F1, (e) arrangement 5: F3-F1-F2, and (f) arrangement 6: F3-F2-F1.
94.4% and 57.9% smaller than those of S3 (outer face-sheet thickness: 1 mm) and S4 (outer face-sheet thickness: 1.5 mm), respectively. For Case 2, the SEA of the tube increases as the thickness of
the inner face-sheet decreases. The SEA decreases 61.9% as the thickness of the inner face-sheet increases from 1 mm (S2) to 2 mm (S6). No outer face deflection for S6 occurs, as the core does not
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Fig. 10. Influence of core arrangement on the histories of plastic dissipation and outer-face deflection. (a) Plastic dissipation histories, (b) Face-sheet deflection histories.
Table 9 The specimens with different face-sheet thicknesses. Specimen
Inner face thickness (mm)
Outer face thickness (mm)
S1 S2 S3 S4 S5 S6 S7
1.0 1.0 1.5 1.5 1.5 2.0 2.0
1.0 1.5 1.0 1.5 2.0 1.5 2.0
deform completely. The SMDOF is small when the thickness of the inner face-sheet is large (S4 and S6). As the thickness of the inner face-sheet increases from 1 mm to 1.5 mm, the SMDOF decreases by 91.2%. For Case 3, the SEA and SMDOF simultaneously decrease with face-sheet thickness. The SMDOF is influenced by the inner and outer face-sheets. However, the SEA is mainly affected by the inner face-sheet because the core plays a major role in the SEA of the sandwich tubes and the inner face-sheet compacts the core before the outer face-sheet deformation.
6. Conclusions
investigate the blast response of aluminum foam-cored sandwich tubes that were subjected to internal air-blast loading. Blast experiments were performed to capture the fundamental deformation, the MDIF, and the MDOF. The results confirm that the MDOF of sandwich tubes is moderately sensitive to the core relative density, internal diameter, core thickness, and explosive charge. The core density has a slight influence on the SMDOF. The SMDOF increases when the internal diameter decreases, core thickness decreases, or explosive charge increases. The FE model was constructed using the Voronoi algorithm. The FE model was validated by the FE results. The FE results agree well with the experimental results. Numerical simulations were conducted to investigate the deformation process of sandwich tubes, the densification of double-layer cores, and the effect of core arrangement and face-sheet thickness on blast-resistance. The tube deformation process can be generally described in three phases: inner face-sheet acceleration, core compaction, and outer facesheet deformation. For a positive core, one shock wave that propagates from the inside to the outside during the complete crushing process occurs. For a negative core, two compaction waves simultaneously propagate outside. The SMDOF is influenced by the inner and outer face-sheets. However, the SEA is mainly affected by the inner face-sheet because the core plays a major role in the SEA of sandwich tubes and the inner face-sheet compacts the core before the outer face-sheet deformation.
Experimental and numerical analyses were performed to
Fig. 11. Effect of face-sheet thickness on plastic dissipation and face-sheet deflection histories. (a) Plastic dissipation histories, (b) Face-sheet deflection histories.
M. Liang et al. / Composites Part B 125 (2017) 134e143
Acknowledgements The authors gratefully acknowledge financial supported by the National Natural Science Foundation of China (NSFC) under grant No. 11132012. References [1] Gibson L, Ashby M. Cellular solids. Cambridge, UK: Cambridge University Press; 1997. [2] Zhou H, Wang X, Zhao Z. High velocity impact mitigation with gradient cellular solids. Compos Part B Eng 2016;85:93e101. [3] Barnes AT, Ravi-Chandar K, Kyriakides S, Gaitanaros S. Dynamic crushing of aluminum foams: Part I e Experiments. Int J Solids Struct 2014;51(9): 1631e45. [4] Zhang X, An L, Ding H. Dynamic crushing behavior and energy absorption of honeycombs with density gradient. J Sandw Struct Mater 2014;16(2):125e47. [5] Li S, Li X, Wang Z, Wu G, Lu G, Zhao L. Finite element analysis of sandwich panels with stepwise graded aluminum honeycomb cores under blast loading. Compos Part A Appl S 2016;80:1e12. [6] Li S, Lu G, Wang Z, Zhao L, Wu G. Finite element simulation of metallic cylindrical sandwich shells with graded aluminum tubular cores subjected to internal blast loading. Int J Mech Sci 2015;96e97:1e12. [7] Zhang P, Cheng YS, Liu J, Li Y, Zhang CZ, Hou HL, et al. Experimental study on the dynamic response of foam-filled corrugated core sandwich panels subjected to air blast loading. Compos Part B Eng 2016;105:67e81. [8] Jackson M, Shukla A. Performance of sandwich composites subjected to sequential impact and air blast loading. Compos Part B Eng 2011;42(2): 155e66. [9] Yazici M, Wright J, Bertin D, Shukla A. Experimental and numerical study of foam filled corrugated core steel sandwich structures subjected to blast loading. Compos Struct 2014;110:98e109. [10] Zhang JJ, Wang ZH, Zhao LM. Dynamic response of functionally graded cellular materials based on the Voronoi model. Compos Part B Eng 2016;85:176e87. [11] Sun Z, Shi SS, Guo X, Hu XZ, Chen HR. On compressive properties of composite sandwich structures with grid reinforced honeycomb core. Compos Part B Eng 2016;94:245e52. [12] Karagiozova D, Langdon GS, Nurick GN, Niven T. The influence of a low density foam sandwich core on the response of a partially confined steel cylinder to internal air-blast. Int J Impact Eng 2016;92:32e49. [13] Jing L, Wang Z, Shim VPW, Zhao L. An experimental study of the dynamic response of cylindrical sandwich shells with metallic foam cores subjected to blast loading. Int J Impact Eng 2014;71:60e72. [14] Liu X, Tian X, Lu TJ, Zhou D, Liang B. Blast resistance of sandwich-walled hollow cylinders with graded metallic foam cores. Compos Struct 2012;94(8):2485e93. [15] Hoo Fatt MS, Surabhi H. Blast resistance and energy absorption of foam-core cylindrical sandwich shells under external blast. Compos Struct 2012;94(11): 3174e85. [16] Fatt MSH, Gao Y, Sirivolu D. Foam-core, curved composite sandwich panels under blast. J Sandw Struct Mater 2013;15(3):261e91. [17] Li S, Wang Z, Wu G, Zhao L, Li X. Dynamic response of sandwich spherical shell with graded metallic foam cores subjected to blast loading. Compos Part A Appl S 2014;56:262e71. [18] Jin XC, Wang ZH, Ning JG, Xiao GS, Liu EQ, Shu XF. Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading. Compos Part B Eng 2016;106:206e17.
143
[19] Ashby MF, Evans T, Fleck NA, Hutchinson J, Wadley H, Gibson L. Metal foams: a design guide. Elsevier; 2000. [20] Wang E, Gardner N, Shukla A. The blast resistance of sandwich composites with stepwise graded cores. Int J Solids Struct 2009;46(18e19):3492e502. [21] Shen J, Lu G, Zhao L, Zhang Q. Short sandwich tubes subjected to internal explosive loading. Eng Struct 2013;55:56e65. [22] Liang MZ, Zhang GD, Lu FY, Li XY. Blast resistance and design of sandwich cylinder with graded foam cores based on the Voronoi algorithm. Thin-Walled Struct 2017;112:98e106. [23] Jing L, Wang ZH, Zhao LM. The dynamic response of sandwich panels with cellular metal cores to localized impulsive loading. Compos Part B Eng 2016;94:52e63. [24] Zhu HX, Thorpe SM, Windle AH. The effect of cell irregularity on the high strain compression of 2D Voronoi honeycombs. Int J Solids Struct 2006;43(5): 1061e78. [25] Zheng Z, Yu J, Li J. Dynamic crushing of 2D cellular structures: a finite element study. Int J Impact Eng 2005;32(1e4):650e64. [26] Kader MA, Islam MA, Hazell PJ, Escobedo JP, Saadatfar M, Brown AD, et al. Modelling and characterization of cell collapse in aluminium foams during dynamic loading. Int J Impact Eng 2016;96:78e88. [27] Alsayednoor J, Harrison P. Evaluating the performance of microstructure generation algorithms for 2-d foam-like representative volume elements. Mech Mater 2016;98:44e58. [28] Zhu HX, Hobdell JR, Windle AH. Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs. J Mech Phys Solids 2001;49(4): 857e70. [29] Hibbitt KS, Inc. ABAQUS/Explicit User's manual, version 6.9-3. Providence, RI, USA: Dassault Systemes Simulia Corp; 2010. [30] Zhang J, Wang Z, Zhao L. Dynamic response of functionally graded cellular materials based on the Voronoi model. Compos Part B Eng 2016;85:176e87. [31] Zheng Z, Wang C, Yu J, Reid SR, Harrigan JJ. Dynamic stressestrain states for metal foams using a 3D cellular model. J Mech Phys Solids 2014;72:93e114. [32] Li Z, Zhang J, Fan J, Wang Z, Zhao L. On crushing response of the threedimensional closed-cell foam based on Voronoi model. Mech Mater 2014;68:85e94. [33] Liao S, Zheng Z, Yu J. Dynamic crushing of 2D cellular structures: local strain field and shock wave velocity. Int J Impact Eng 2013;57:7e16. [34] Liang MZ, Li XY, Lu FY. Effects of U-notches on the dynamic fracture and fragmentation of explosively driven cylinders. Theor Appl Fract Mech 2015;77:50e8. [35] Satapathy S, Landen D. Expanding ring experiments to measure hightemperature adiabatic properties. Int J Impact Eng 2006;33(1):735e44. [36] Li X, Wang Z, Zhu F, Wu G, Zhao L. Response of aluminium corrugated sandwich panels under air blast loadings: experiment and numerical simulation. Int J Impact Eng 2014;65:79e88. [37] Darvizeh R, Davey K. A transport approach for analysis of shock waves in cellular materials. Int J Impact Eng 2015;82:59e73. [38] Jing L, Wang Z, Zhao L. An approximate theoretical analysis for clamped cylindrical sandwich shells with metallic foam cores subjected to impulsive loading. Compos Part B Eng 2014;60:150e7. [39] Liu H, Cao ZK, Yao GC, Luo HJ, Zu GY. Performance of aluminum foamesteel panel sandwich composites subjected to blast loading. Mater Des 2013;47: 483e8. [40] Langdon GS, Karagiozova D, von Klemperer CJ, Nurick GN, Ozinsky A, Pickering EG. The air-blast response of sandwich panels with composite face sheets and polymer foam cores: experiments and predictions. Int J Impact Eng 2013;54:64e82. [41] Jing L, Wang Z, Ning J, Zhao L. The dynamic response of sandwich beams with open-cell metal foam cores. Compos Part B: Eng 2011;42(1):1e10.