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Experimental and numerical studies on multi-layered corrugated sandwich panels under crushing loading
Accepted Manuscript Experimental and Numerical Studies on Multi-Layered Corrugated Sandwich Panels under crushing loading Shujuan Hou, Chengfu Shu, Shuyun Zhao, Xu Han, Qing Li PII: DOI: Reference:
S0263-8223(15)00118-X http://dx.doi.org/10.1016/j.compstruct.2015.02.039 COST 6224
To appear in:
Composite Structures
Please cite this article as: Hou, S., Shu, C., Zhao, S., Han, X., Li, Q., Experimental and Numerical Studies on MultiLayered Corrugated Sandwich Panels under crushing loading, Composite Structures (2015), doi: http://dx.doi.org/ 10.1016/j.compstruct.2015.02.039
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Experimental and Numerical Studies on Multi-Layered Corrugated Sandwich Panels under crushing loading Shujuan Houa, b*, Chengfu Shua, b, Shuyun Zhaoa, b, Xu Hana, b†, Qing Lic a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan410082, China
b
College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China c
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Abstract The multi-layered corrugated sandwich panels are investigated by experimental studies and numerical simulations under the quasi-static crushing loading. The structures are made up of trapezoidal aluminum cores and aluminum alloy sheets. Three different configurations of corrugated sandwich panels were contrastively studied, which are regularly-arranged, the stagger-arranged and the cross-arranged (0°/90°) corrugated sandwich panels. The layers of corrugated sandwich panels vary from two to six. The corrugated cores were fabricated by a self-made mould and then bonded to interlayer layer and face sheets so as to produce different specimens. The force-displacement curves of these panels were yielded from the experimental tests; and the energy absorption mechanism were studied for each panels. It was found that the sandwich configuration and number of layers core played an important role in the failure mechanism and energy absorption. The finite element models were created to correlate the experimental results. It was found that the simulation and experimental force-displacement curves agreed well with each other. The results provided us with the data and guideline for further studies on crashworthiness optimization of the multi-layered corrugated sandwich panels. Keywords: multi-layered; corrugated sandwich panel; energy absorption; crashworthiness; *
[email protected].
†
Corresponding author: Xu Han, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan
410082, China. Tel: +86-731-88821809. E-mail: [email protected]. 1
experimental test, finite element modeling. 1. Introduction Nowadays lightweight and higher performances are both the increasing requirements, and are also the critical issues confronted in engineering field. Take transportation industry as an example, there have been a broad range of studies reported on thin-walled structures (Hou et al., 2008 and 2011), in which the plastic deformation is commonly used to absorb substantial kinetic energy when crash occurs. As a class of effective structural components, the corrugated panels have been widely used in engineering practice for its lightweight and high strength-to-weight ratio. For this reason, such structures gain increasing attention aiming to make it more crashworthy. In the current studies, most are focused on metal single-layered corrugated sandwich panels. In this aspect of research, some experiments and numerical simulations have been conducted to understand the properties of the single-layered corrugated structures under quasi-static or dynamic/impact loading. For example, Liang et al. (2001) optimized metallic corrugated core sandwich panels subjected to blast loads. The corrugated sandwich panels have high stiffness in some applications. Cote et al.(2006) investigated the out-of-plane compressive, transverse and longitudinal shear responses of the corrugated cores at three relative densities in a range of 0.03£r£0.1 by experiments and FE simulation. They found that the compressive strength of the diamond cores was sensitive to the aspect ratio of the specimen. Tilbrook et al. (2007) explored the dynamic off-plane compression of sandwich panels with stainless steel corrugated and Y-frame cores, which demonstrated that the rear face stress and dynamic deformation modes could be predicted by FE simulation with a reasonable accuracy. Seong et al. (2010) researched the bending response of the bi-directionally corrugated core with two additional design parameters of the pass angle and corrugation length, which can reduce anisotropic behaviors of corrugated sandwich panels with open channel cores under the bending load and thus enable quasi-isotropic behavior in bending. Qin et al. (2011) studied the corrugated sandwich panels struck by a heavy mass, which was found to have a higher impact resistance compared to monolithic solid plate of the same mass. Zhang et al. (2012) studied the compressive behavior of U-type corrugated cores 2
sandwich panels, which showed that the deformation mode of the core plates under lateral crushing force has great effects on the crushing performance. Biagi et al. (2012) studied in-plane column response and buckling deformation of metallic corrugated core sandwich panels under a longitudinal load. But they didn’t give response and deformation patterns under a lateral load. Recently, Hou et al. (2013) explored the trapezoidal and triangular corrugated sandwich panels under the quasi-static loading by using both the experiment and FE analysis. The optimum parameters of the two corrugated sandwich panels were obtained by using optimization design technique. Giorgio et al. (2013) investigated a single-layered aluminum sandwich panel with sinusoidal corrugated core, and used an equivalent material formulation for the complex shaped core. After that, Zhang et al. (2013) investigated the compressive strengths and dynamic response of single-layered metal corrugate sandwich panels with unfilled and foam-filled sinusoidal plate cores. In the aspect of research for composite corrugated sandwich panels, Mamalis et al. (2002) investigated the crash behavior and energy absorption characteristics of hybrid square sandwich composite tubular components with corrugated cores under the axial compressive loading. Chang et al. (2005) studied the bending behavior of corrugated-core sandwich plates with various boundary conditions by numerical analyses. Aktay et al.(2005) investigated the damage behavior of composite sandwich panels under high-velocity impact in which the simulation was well correlated to the experiment in terms of contact force history. Talbi et al.(2009) developed analytical homogenization model for the finite element modeling of composite corrugated cardboard. Fan et al.(2010) indicated that the composite material had a long stable deformation plateau and densification after initial buckling failure by quasi-static compression tests. Dayyani et al. (2012) made numerical and experimental investigations on mechanical behavior of composite corrugated core. Rejab et al. (2013) compared the differences of the compressive responses and failure modes of corrugated-core sandwich panels made of aluminum alloy, a glass fiber reinforced plastic and a carbon fiber reinforced plastic respectively, in which the effects of number of unit cells and cell wall thickness were studied. However, there are a few studies on metal multi-layered corrugated sandwich panels. Dharmasena et al. (2009) studied only the dynamic response of a multi-layered cross-arranged 3
(0°/90°) triangular corrugated sandwich. Wang et al. (2011) studies the energy absorption properties of multi-layered corrugated paperboard in various ambient humidity and didn’t consider the metal multi-layered corrugated panels. Kılıçaslan et al. (2013) explored the impact responses of seven layers of trapezoidal aluminum panels with 00 /900 corrugated layer orientation and 00/00 orientation under two local loadings. Above all, there are few researches on the multi-layered metal corrugated sandwich panels with layers varying. There are also few researches on energy-absorption characteristics of metal multi-layered corrugated sandwich panels under planar compression loading. Therefore, metal multi-layered trapezoidal corrugated sandwich panels were studied by using the experimental and numerical methods. The aim of the present paper is to obtain the force-displacement curves of the trapezoidal corrugated sandwich panels with different numbers of corrugated core layers and orientations under the quasi-static compression. The failure mechanisms and energy absorption of the multi-layered corrugated sandwich panels were also explored through a series of experimental test. The three-dimensional finite element (FE) models of the specimens were developed by using ANSYS/LS-DYNA, and were also validated by the experimental results, which will benefit the future crashworthiness optimization of metal multi-layered corrugated sandwich panels. 2. Experiments 2.1 Experimental Specimens The core cell and interlayer sheet material of the corrugated sandwich panels are Aluminum 5052-O plates with a thickness of 0.2 mm. Aluminum 2024-T4 sheet with a thickness of 1 mm is used to be the material for the face plates. Following the manufacturing specification (Hou et al., 2013), the trapezoidal cores were fabrication by using an in-house mould (Fig.1).An epoxy adhesive was used to bond the face plates, the cores and interlayer sheets for no less than 24 hours under constant pressure at the room temperature. The configuration of the core is depicted in Fig.2(a). For the core component, L1=7mm, L2 =5.5mm and w=55°. The size of specimen are 70mm in length and width. Three different configurations of trapezoidal corrugated sandwich panels are studied here: namely the regularly-arranged core with 00/00 layer orientation, stagger-arranged core with 00/00 layer 4
orientation and perpendicularly-arranged core with 00/900 layer orientation, as shown in Fig.2(b)-(d), respectively. In this study, the responses of the corrugated sandwich panels were first analyzed for the failure mechanisms and energy absorption experimentally. The effects of the configurations of the cores and layer variation of the cores are then investigated. Finally, the initial imperfection is analyzed by comparing the experiment with the finite element simulation. Fig.1 Self-madeMould. Fig.2 Specimens: (a) the shape of the core cell, (b) the regularly-arranged corrugated sandwich panels, (c) the stagger-arranged corrugated sandwich panels, and (d) the cross-arranged (0 0/900) corrugated sandwich panels.
2.2 Experimental set-up Compressing the panels quasi-statically normal to its plane is a common way to test the energy absorbing ability of the structure (Fan et al., 2011). The compression tests were conducted on the INSTRON-3382 test machine with a maximum force of 100 kN in line with the ASTM standard C365/C365M-05 (Hou et al., 2013). Fig.3 shows apparatus of the test machine and specimen being placed in-between the platens, where specimen was pressed by applying a uniform compression at a nominal displacement rate of 2mm/min, shown in Fig.4. The data of the force and displacement in the loading process will be passed from the sensor mounted in the test machine to the computer, in which the force-displacement data was recorded until the specimen was completely crushed. Fig.3. The test machine and specimens. Fig.4. Experimental set-up of the compressive test.
3. Finite Element Modeling The corrugated sandwich panels were modeled using the explicit finite element (FE) code ANSYS/LS-DYNA, which allows simulating nonlinear large deformation effectively. Fig.5 exemplifies some FE models for different configurations of two layers corrugated sandwich panels. Elastic-plastic material properties (Hou et al., 2012) are used to model the corrugated sandwich panel materials. The detailed material parameters are summarized in 5
Table1. For the quasi-static loading process, effect of strain rate was not considered here. Fig.53D FE model of two-layer corrugated sandwich panels: (a) the regularly-arranged, (b) the stagger-arranged, and (c) cross-arranged(00/900) configurations. Table 1 The properties of materials.
The face plates, the cores and interlayer sheets were meshed using quadrilateral Belytschko-Tsay shell elements (Hallquist, 1998) with five integration points across the thickness. To generate the compression, the upper and lower smooth indenters were modeled using the model of *RIGIDWALL (Hou et al., 2007 and 2009; Yin et al., 2011) in the ANSYS/LS-DYNA
code,
including
the
upper
smooth
indenter
modeled
by
*RIGIDWALL_GEOMETRIC_FLAT_MOTION_ID with a constant speed of 1 m/s and the lower one by *RIGIDWALL_GEOMETRIC_FLAT_ID. Since the total CPU time for an explicit solution was too long by use of the same speed (2 mm/min) as in the experiments, a constant faster speed of 1m/s was adopted in the simulation (Wang and Fan, 2003). Adhesion between the cores, face plates and interlayer sheets was assumed to be perfectly bonded and a TIED_NODES_TO_SURFACE_OFFSET contact algorithm was used. Meanwhile, an automatic single surface contact (Hou et al., 2007 and 2009; Yin et al., 2011) was considered in order to take into account self-contacting interfaces during compression. The static and dynamic friction coefficients were set to be 0.3 and 0.2, respectively, as suggested by Kılıçaslan et al. (2013). 4. Results and Discussions 4.1 Compressive responses of the multi-layered corrugated sandwich panels The force-displacement curves of the regularly-arranged configuration with different layers of core are depicted inFig.6. In general, all the curves consist of three stages: namely the elastic stage, the plateau stage and the densification stage. No abrupt loading peak and drop were observed in these curves. The photographic images in Fig.7 clearly illustrated the process of such curves (from a three layer specimen). It is seen that all layers withstood the force and no cores and interlayer sheets were found crushed individually. Firstly, the bending 6
of the interlayer sheets, especially the edge area where there were no kinematic constraints, resulted in no peak force (Jin et al., 2013)which is smaller than that due to the bending of cores. With the bending of the interlayer sheets, the buckling and the progressive densification of the cores, the force keeps climbing. Meanwhile, from Fig.6, it was noted that the force had a small fall in some regions. That was also due to buckling of core cells and the translation of the interlayer sheets. When all cores and interlayer sheets were densified, the force increased rapidly. Fig.6. The force-displacement experimental curves of the regularly-arranged corrugated sandwich panels with various layers core. Fig.7.Images of the deformation of the regularly-arranged corrugated sandwich panels with three layers core.
Fig.8. shows the force-displacement curves of the stagger-arranged and cross-arranged (00/900) corrugated sandwich panels. These curves also exhibit three stages of responses. However, the trend of the curves somewhat differs from that of the regularly-arranged panels, which rises up elastically firstly and then drops due to the core buckling. When all cores and interlayer sheets were crushed, the densification of the corrugated sandwich panels raised the curves steeply. As shown in Fig.9, taking the panels with three layer cores for example, there are more than one peak points because a peak was formed when the core buckled in some layer, then the curves climbed up again to form another peak when the force was transmitted to the other layer. Fig.10 exhibits the deformation of these three layer corrugated sandwich panels. For the stagger configuration as in Fig.10a, it was seen that the bottom two layers buckled first and then the top layer began to buckle together with the densification of two bottom layer. For the perpendicular configuration as in Fig.10b, it was showed that the top layer which had different orientation buckled first and then the two parallel layers followed. This explained the reason why the curves in Fig. 9 had more one peak. Fig.8.The force-displacement experimental curves of the corrugated sandwich panels with various layers core: (a) the stagger-arranged, and (b) the cross-arranged (00/900). Fig.9. The force-displacement experimental curves of the corrugated sandwich panels with three 7
layers core: (a) the staggered-arranged, and (b) the cross-arranged (00/900). Fig.10.Images of the deformation for the three-layeredcorrugated sandwich panels: (a) the staggered-arranged, and (b) the cross-arranged (00/900).
4.2 The effect of core configurations From the above experiments, it was found that the configurations of cores played an important role in the crushing mechanism of the corrugated sandwich panels. In the curves of the regular configuration, there was no peak force, whereas the force-displacement curves of the stagger and perpendicular configurations had evident fluctuation. The deformation modes of these panels differ due to the different layout of core panels. Fig.11 compares the difference of these three corrugated sandwich panels with the same number of layers core. At the elastic stage, the stagger configuration had the highest force. The peak forces in the elastic stage are listed in Table 2. All the plateau forces of these three different configurations fluctuate around 1 kN. The densification of the regular configuration began earlier than those of the stagger and perpendicular configurations, as summarized in Table 3. From Fig. 11 and Table 3, it can be concluded that the 00/900perpendicular core configurations is the best one among the three considered panels, due to its longest plateau stage and highest energy-absorption. Fig.11. The force-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Table 2The peak crushing forces of three corrugated sandwich panels in the elastic stage. Table 3The displacements (D)and energy-absorptions (EA) of three corrugated sandwich panels before their own densifications.
The energy absorption of the corrugated sandwich panels was calculated by integrating force-displacement curves(Kılıçaslan et al.,2013). The absorbed energy (E) was formulated as: d
E (d ) = ò F ( x)dx 0
(1)
where d is crash distance (Yin et al., 2013). As shown in Fig.12, it was clearly shown that the value of the energy absorption of the regularly-arranged corrugated sandwich panels was less
8
than that of the other two configurations before densification. At the same time, the energy absorptions of the stagger and perpendicular configurations were basically equal. Table 4 summarized the energy absorption of these three structures under the same deformation displacements. Concerning the energy absorption under the same deformation displacement and the peak force in Table 2, it can also be concluded from Fig. 12 and Table 4 that the cross-arranged (0°/90°)core configuration seems to be the best one. Nevertheless, the stagger-arranged core configuration is better than the regularly-arranged one.
Fig.12. The energy-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Table 4The energy absorptions of three corrugated sandwich panels before densification of the regularly-arranged sandwich panels
4.3 The effect of the number of layers core FromFig.6, Fig.8(a) and Table 2, the peak force for the regular and stagger configuration decrease when the layer numbers increase, which indicate the effect of interlayer sheets. With the increased number of layers, more interlayer sheets became involved, which can reduce the peak force of the multi-layered sandwich structures. The significant difference was the prolongation of the plateau stage with the increase of the layer numbers, which lead to more energy absorption before densifications, as shown in Fig.13 and Table 3. This illustrate that the energy absorption is largely due to the span of the plateau stage. Fig.13.The energy-displacement experimental curves of three corrugated sandwich panels with various layers: (a) the regularly-staggered, (b) the regularly-arranged partial enlargement, (c) the stagger-arranged, (d) the stagger-arranged partial enlargement, (e) the cross-arranged (0 0/900) , and (f) the cross-arranged (00/900) partial enlargement.
4.4 Comparison between numerical and experimental results Fig.14 depicted the comparison of experimental and numerical force-displacement curves of the regularly-arranged corrugated sandwich panels, which showed good agreement. The small difference was due to some initial imperfection in the specimen preparation and
9
de-bonding occurred during the compression. The de-bonding phenomenon was not serious because no abrupt deformation occurred, as indicated in Fig.15. Fig.16 illustrated the deformation comparisons between experiment and simulation for the regularly-arranged corrugated sandwich panels with six layers considered. It can be seen that the deformation processes and patterns are very consistent between experimental and numerical results. This further confirmed that the FE modeling of corrugated sandwich panels is effective for a further research and crashworthiness optimization. Fig.14.Comparisons of the force-displacement curves of the regularly-arranged corrugated sandwich panels between the experiment and the simulation: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.15.Deformation of the regularly-arranged multi-layered corrugated sandwich panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.16.Comparison of the deformation between experiment and simulation for the regularly-arranged multi-layered corrugated sandwich panels with six layers core.
Fig.17and 18 showed the experimental and simulation results of the stagger-arranged and cross-arranged (0°/90°) panels, respectively. It is found that peak forces are higher in the simulation than in the experiment, which was considered to be mainly due to the initial imperfections, such as offset cores and de-bonding. To investigate the influence of initial imperfection, we attempted to model the imperfection in FE modeling. When we modeled the structural imperfections detailed in the same way as the specimen, the force-displacement curves matched much better as shown in Fig.19, where the comparison curves between experiments and simulations with original imperfections for three-layered stagger-arrange and cross-arranged panels. From Fig 17-19, it can be seen that imperfections weakened the structure and made it buckle more easily. Meanwhile, de-bonding had great influences on the force-displacement curves, reduced the peak forces and delayed the densification. Meanwhile, it was found that experimental de-bonding in the cross-arranged (0°/90°) panels were the severest among three corrugated sandwich panels. In Fig. 20, the severest de-bonding was illustrated, which were 3-layered, 5-layered and 6-layered cross-arranged
10
panels. The configuration of cores was considered to be the fundamental reason for de-bonding. Indeed, de-bonding process is rather complex as illustrated in Fig.20. The time span of contact simulation is very difficult defined. So the time span in simulation can’t perfectly match that in the experiment. This adds the difficulty to model the real de-bonding time.
Fig.17Comparisons of the force-displacement curves between experiment and simulation for the stagger-arranged panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.18. Comparisons of the force-displacement curves between experiment and simulation for the cross-arranged (0°/90°) panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.19.Comparisons of the force-displacement curves between experiment and simulation with original imperfection for three-layered panels: (a) stagger-arranged, (b) cross-arranged (0 0/900). Fig.20.The de-bonding phenomenon of the cross-arranged(00/900) corrugated sandwich panels: (a) 3 layers, (b) 5 layers, (c) 6 layers.
5. Conclusions In this study, three different configurations of the multi-layered corrugated sandwich panels were studied under the quasi-static compression test experimentally and numerically. The trapezoidal cores, prepared by using the self-made mould, were bonded to the interlayer sheets and face plates to produce a series of multi-layered corrugated sandwich panels. After analyzing the experimental results, it was found that there are three clear stages in the force-displacement curves of compression: elastic stage, plateau stage and densification stage. The experiment showed that the force of the regular configuration slowly increased in the elastic stage, whereas those of the stagger and cross configurations had a clear peak. With the increase of the layers, the plateau forces and the peak forces decreased for the three configurations. Increase in layer number also led to the prolongation of plateau stage, which made better energy absorption prior to the densification of the panels. The energy absorption of the regular and stagger panels decreased with the increase in the layer numbers in the beginning, whilst cross panels had no such property due to the arrangement of the core layers. 11
It is concluded that the cross-arranged (00/900) panels is better than the regular-arrange and stagger-arranged panels not only in the energy absorption but also in the aspect of peak crushing force. Then, the stagger-arranged panel is better than the regular-arranged one. Moreover, the FE simulation was also conducted for three different multi-layered corrugated sandwich panels. The FE results for the regular configuration agreed well with the experimental counterpart. The differences between experiments and simulations for the stagger and perpendicular panels were analyzed in detail. It is found that the initial imperfection and the de-bonding played an important role in the differences between experiments and simulations. Imperfections of specimens weakened the structure and made it buckle more easily. Meanwhile, de-bonding had great influences on the force-displacement curves, reduced the peak forces and delayed the densification. The time span in simulation can’t perfectly match that in the experiment, which adds the difficulty to model the real de-bonding time.
Acknowledgments The financial supports from National Natural Science Foundation of China (11232004, 11372106), New Century Excellent Talents Program in University (NCET-12-0168) and Hunan Provincial Natural Science Foundation of China (12JJ7001) are gratefully acknowledged. Moreover, Joint Center for Intelligent New Energy Vehicle is also gratefully acknowledged.
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quasi-static load by using LS-DYNA. Mechanical Engineering 25, 20-23. Wang, Z.W., 2011. Energy absorption properties of multi-layered corrugated paperboard in various ambient humidities. Materials & Design 32, 3476-3485. Yin, H.F., Wen, G.L., Hou, S.J., Chen, K., 2011. Crushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubes. Materials & Design 32, 4449-4460. Yin, H.F., Wen, G.L., Hou, S.J., Qing, Q.X., 2013. Multiobjective crashworthiness optimization of functionally lateral graded foam-filled tubes. Materials & Design 44, 414-428. Zhang, Y.C., Zhang, S.L., Wang, Z.L., Liu, K., 2012. Quasi-static compressive behavior ofU-type corrugated cores corrugated sandwich panels. Journal of Ship Mechanics 12, 1417-1426. Zhang, J.X., Qin, Q.H., Wang, T.J., 2013. Compressive strengths and dynamic response of corrugated metal sandwich plates with unfilled and foam-filled sinusoidal plate cores. Acta Mechanics 224, 759-775.
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Figure Captions: Fig.1. Self-made Mould. Fig.2. Specimens: (a) the shape of the core cell, (b) the regularly-arranged corrugated sandwich panels, (c) the stagger-arranged corrugated sandwich panels, and (d) the cross-arranged (00/900) corrugated sandwich panels. Fig.3. The test machine. Fig.4. Experimental set-up of the compressive test. Fig.5. 3D FE model of two-layer corrugated sandwich panels: (a) the regularly-arranged, (b) the stagger-arranged, and (c) cross-arranged configurations. Fig.6. The force-displacement experimental curves of the regularly-arranged corrugated sandwich panels with various layers core. Fig.7.Images of the deformation of the regularly-arranged corrugated sandwich panels with three layers core. Fig.8. The force-displacement experimental curves of the corrugated sandwich panels with various layer core: (a) the stagger-arranged, and (b) the cross-arranged (00/900). Fig.9. The force-displacement experimental curves of the corrugated sandwich panels with three layer core: (a) the staggered-arranged, and (b) the cross-arranged (00/900). Fig.10.Images of the deformation for the three-layered corrugated sandwich panels: (a) the staggered-arranged, and (b) the cross-arranged (00/900). Fig.11. The force-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.12. The energy-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.13.The energy-displacement experimental curves of three corrugated sandwich panels with various layers: (a) the regularly-staggered, (b) the regularly-arranged partial enlargement, (c) the stagger-arranged, (d) the stagger-arranged partial enlargement, (e) the cross-arranged (00/900) , and (f) the cross-arranged (00/900) partial enlargement. Fig.14.Comparisons of the force-displacement curves of the regularly-arranged corrugated 16
sandwich panels between the experiment and the simulation: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.15.Deformation of the regularly-arranged multi-layered corrugated sandwich panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.16.Comparison of the deformation between experiment and simulation for the regularly-arranged multi-layered corrugated sandwich panels with six layers core. Fig.17.Comparisons of the force-displacement curves between experiment and simulation for the stagger-arranged panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.18.Comparisons of the force-displacement curves between experiment and simulation for the cross-arranged (0°/90°) panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.19.Comparisons of the force-displacement curves between experiment and simulation with original imperfection for three-layered panels: (a) stagger-arranged, (b) cross-arranged (00/900). Fig.20.The de-bonding phenomenon of the cross-arranged(00/900) corrugated sandwich panels: (a) 3 layers, (b) 5 layers, (c) 6 layers.
17
Table Captions: Table 1 The parameters of materials. Table 2 The peak crushing forces of three corrugated sandwich panels in the elastic stage. Table 3 The displacements (D)and energy-absorptions (EA) of three corrugated sandwich panels before their own densifications. Table 4 The energy absorptions of three corrugated sandwich panels before densification of the regularly-arranged sandwich panels.
18
Fig.1. Self-made Mould.
19
(a)
(b)
(c)
(d)
Fig.2. Specimens: (a) the shape of the core cell, (b) the regularly-arranged corrugated sandwich panels, (c) the stagger-arranged corrugated sandwich panels, and (d) the cross-arranged (00/900) corrugated sandwich panels.
20
Fig.3. The test machine.
21
Fig.4. Experimental set-up of the compressive test.
22
(a)
(b)
(c)
Fig.5. 3D FE model of two-layer corrugated sandwich panels: (a) the regularly-arranged, (b) the stagger-arranged, and (c) cross-arranged (00/900) configurations.
23
Fig.6. The force-displacement experimental curves of the regularly-arranged corrugated sandwich panels with various layers core.
24
t=0
t=2min
t=3min
t=4min
t=7min
t=8min
Fig.7. Images of the deformation of the regularly-arranged corrugated sandwich panels with three layer core.
25
(a) the stagger-arranged
(b) the cross-arranged (00/900) Fig.8. The force-displacement experimental curves of the corrugated sandwich panels with various layer core. (a) the stagger-arranged, and (b) the cross-arranged (0 0/900).
26
(a) the staggered-arranged
(b) ) the cross-arranged (00/900) Fig.9. The force-displacement experimental curves of the corrugated sandwich panels with three layer core: (a) the staggered-arranged, and (b) the cross-arranged (00/900).
27
t=0min
t=2min
t=3min
t=4min
t=5min
t=6min
t=7min
t=8min (a)
t=0min
t=1min
t=2min
t=4min
t=5min
t=6min
t=7min
t=8min
(b) Fig.10. Images of the deformation for the three-layered corrugated sandwich panels: (a) the staggered-arranged, and (b) the cross-arranged (00/900).
28
(a)
(b)
(c)
(d)
(e) Fig.11. The force-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
29
(a)
(b)
(c)
(d)
(e) Fig.12. The energy-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
30
(a)
(b)
(c)
(d)
(e) (f) Fig.13. The energy-displacement experimental curves of three corrugated sandwich panels with various layers: (a) the regularly-staggered, (b) the regularly-arranged partial enlargement, (c) the stagger-arranged, (d) the stagger-arranged partial enlargement, (e) the cross-arranged (00/900) , and (f) the cross-arranged (00/900) partial enlargement.
31
(a)
(b)
(c)
(d)
(e) Fig.14. Comparisons of the force-displacement curves of the regularly-arranged corrugated sandwich panels between the experiment and the simulation. (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
32
(a)
(b)
(c)
(d)
(e) Fig.15. Deformation of the regularly-arranged multi-layered corrugated sandwich panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
33
t=0min
t=3min
t=4min
t=6min
t=7min Fig.16. Comparison of the deformation between experiment and simulation for the regularly-arranged multi-layered corrugated sandwich panels with six layers core.
34
(a) 2 layers
(b) 3 layers
(c) 4 layers
(d) 5 layers
(e) 6 layers Fig.17. Comparisons of the force-displacement curves between experiment and simulation for the stagger-arranged panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers.
35
(a) 2 layers
(b) 3 layers
(c) 4 layers
(d) 5 layers
(e) 6 layers Fig.18. Comparisons of the force-displacement curves between experiment and simulation for the cross-arranged (0°/90°) panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers.
36
(b) cross-arranged (00/900)
(a) Stagger-arranged
Fig.19. Comparisons of the force-displacement curves between experiment and simulation with original imperfection for three-layered panels: (a) stagger-arranged, (b) cross-arranged (00/900).
37
(a) 3 layers
(b) 5 layers
(c) 6 layers Fig.20. The de-bonding phenomenon of the cross-arranged (00/900) corrugated sandwich panels: (a) 3 layers, (b) 5 layers, (c) 6 layers.
38
Tables:
Table 1 The parameters of materials
Face sheet (Al-2024 aluminum alloy)
Core and interlayer sheets (5052-O aluminum alloy)
2700.00 72.40 28.00
2685.00 69.60 2.50
(MPa)
75.80
65.50
n
0.33
0.33
Property
r (kg/m3) E(GPa) ET(GPa)
sy
39
Table 2 The peak crushing forces of three corrugated sandwich panels in the elastic stage Regularly-arranged 2 layers core 3 layers core 4 layers core 5 layers core 6 layers core
Staggered-arranged
1.024kN 0.859kN 0.851kN 0.848kN 0.818kN
1.291kN 1.183kN 1.148kN 1.228kN 1.013kN
40
00/900 1.079kN 1.121kN 0.862kN 0.841kN 0.917kN
Table 3 The displacements (D) and energy-absorptions (EA) of three corrugated sandwich panels before their own densifications
Regularly-arranged 2 layers core 3 layers core 4 layers core 5 layers core 6 layers core
00/900
Staggered-arranged
D
EA
D
EA
D
EA
6mm 8mm 11mm 18mm 24mm
5.32J 6.13J 7.78J 10.91J 21.07J
7.5mm 12mm 16mm 20mm 24mm
7.69J 10.64J 14.95J 18.39J 22.46J
8mm 14mm 16mm 24mm 29mm
7.65J 15.03J 15.22J 24.36J 29.35J
41
Table 4 The energy absorptions of three corrugated sandwich panels before densification of the regularly-arranged sandwich panels Regularly-arranged Staggered-arranged 00/900
D 2 layers core 3 layers core 4 layers core 5 layers core 6 layers core
6mm 8mm 11mm 18mm 24mm
EA
D
5.32J 6.13J 7.78J 10.91J 21.07J
6mm 8mm 11mm 18mm 24mm
42
EA 6.27J 6.56J 9.51J 13.92J 22.49J
D 6mm 8mm 11mm 18mm 24mm
EA 5.57J 7.77J 9.38J 14.14J 21.66J
S0263-8223(15)00118-X http://dx.doi.org/10.1016/j.compstruct.2015.02.039 COST 6224
To appear in:
Composite Structures
Please cite this article as: Hou, S., Shu, C., Zhao, S., Han, X., Li, Q., Experimental and Numerical Studies on MultiLayered Corrugated Sandwich Panels under crushing loading, Composite Structures (2015), doi: http://dx.doi.org/ 10.1016/j.compstruct.2015.02.039
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Experimental and Numerical Studies on Multi-Layered Corrugated Sandwich Panels under crushing loading Shujuan Houa, b*, Chengfu Shua, b, Shuyun Zhaoa, b, Xu Hana, b†, Qing Lic a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan410082, China
b
College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China c
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Abstract The multi-layered corrugated sandwich panels are investigated by experimental studies and numerical simulations under the quasi-static crushing loading. The structures are made up of trapezoidal aluminum cores and aluminum alloy sheets. Three different configurations of corrugated sandwich panels were contrastively studied, which are regularly-arranged, the stagger-arranged and the cross-arranged (0°/90°) corrugated sandwich panels. The layers of corrugated sandwich panels vary from two to six. The corrugated cores were fabricated by a self-made mould and then bonded to interlayer layer and face sheets so as to produce different specimens. The force-displacement curves of these panels were yielded from the experimental tests; and the energy absorption mechanism were studied for each panels. It was found that the sandwich configuration and number of layers core played an important role in the failure mechanism and energy absorption. The finite element models were created to correlate the experimental results. It was found that the simulation and experimental force-displacement curves agreed well with each other. The results provided us with the data and guideline for further studies on crashworthiness optimization of the multi-layered corrugated sandwich panels. Keywords: multi-layered; corrugated sandwich panel; energy absorption; crashworthiness; *
[email protected].
†
Corresponding author: Xu Han, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan
410082, China. Tel: +86-731-88821809. E-mail: [email protected]. 1
experimental test, finite element modeling. 1. Introduction Nowadays lightweight and higher performances are both the increasing requirements, and are also the critical issues confronted in engineering field. Take transportation industry as an example, there have been a broad range of studies reported on thin-walled structures (Hou et al., 2008 and 2011), in which the plastic deformation is commonly used to absorb substantial kinetic energy when crash occurs. As a class of effective structural components, the corrugated panels have been widely used in engineering practice for its lightweight and high strength-to-weight ratio. For this reason, such structures gain increasing attention aiming to make it more crashworthy. In the current studies, most are focused on metal single-layered corrugated sandwich panels. In this aspect of research, some experiments and numerical simulations have been conducted to understand the properties of the single-layered corrugated structures under quasi-static or dynamic/impact loading. For example, Liang et al. (2001) optimized metallic corrugated core sandwich panels subjected to blast loads. The corrugated sandwich panels have high stiffness in some applications. Cote et al.(2006) investigated the out-of-plane compressive, transverse and longitudinal shear responses of the corrugated cores at three relative densities in a range of 0.03£r£0.1 by experiments and FE simulation. They found that the compressive strength of the diamond cores was sensitive to the aspect ratio of the specimen. Tilbrook et al. (2007) explored the dynamic off-plane compression of sandwich panels with stainless steel corrugated and Y-frame cores, which demonstrated that the rear face stress and dynamic deformation modes could be predicted by FE simulation with a reasonable accuracy. Seong et al. (2010) researched the bending response of the bi-directionally corrugated core with two additional design parameters of the pass angle and corrugation length, which can reduce anisotropic behaviors of corrugated sandwich panels with open channel cores under the bending load and thus enable quasi-isotropic behavior in bending. Qin et al. (2011) studied the corrugated sandwich panels struck by a heavy mass, which was found to have a higher impact resistance compared to monolithic solid plate of the same mass. Zhang et al. (2012) studied the compressive behavior of U-type corrugated cores 2
sandwich panels, which showed that the deformation mode of the core plates under lateral crushing force has great effects on the crushing performance. Biagi et al. (2012) studied in-plane column response and buckling deformation of metallic corrugated core sandwich panels under a longitudinal load. But they didn’t give response and deformation patterns under a lateral load. Recently, Hou et al. (2013) explored the trapezoidal and triangular corrugated sandwich panels under the quasi-static loading by using both the experiment and FE analysis. The optimum parameters of the two corrugated sandwich panels were obtained by using optimization design technique. Giorgio et al. (2013) investigated a single-layered aluminum sandwich panel with sinusoidal corrugated core, and used an equivalent material formulation for the complex shaped core. After that, Zhang et al. (2013) investigated the compressive strengths and dynamic response of single-layered metal corrugate sandwich panels with unfilled and foam-filled sinusoidal plate cores. In the aspect of research for composite corrugated sandwich panels, Mamalis et al. (2002) investigated the crash behavior and energy absorption characteristics of hybrid square sandwich composite tubular components with corrugated cores under the axial compressive loading. Chang et al. (2005) studied the bending behavior of corrugated-core sandwich plates with various boundary conditions by numerical analyses. Aktay et al.(2005) investigated the damage behavior of composite sandwich panels under high-velocity impact in which the simulation was well correlated to the experiment in terms of contact force history. Talbi et al.(2009) developed analytical homogenization model for the finite element modeling of composite corrugated cardboard. Fan et al.(2010) indicated that the composite material had a long stable deformation plateau and densification after initial buckling failure by quasi-static compression tests. Dayyani et al. (2012) made numerical and experimental investigations on mechanical behavior of composite corrugated core. Rejab et al. (2013) compared the differences of the compressive responses and failure modes of corrugated-core sandwich panels made of aluminum alloy, a glass fiber reinforced plastic and a carbon fiber reinforced plastic respectively, in which the effects of number of unit cells and cell wall thickness were studied. However, there are a few studies on metal multi-layered corrugated sandwich panels. Dharmasena et al. (2009) studied only the dynamic response of a multi-layered cross-arranged 3
(0°/90°) triangular corrugated sandwich. Wang et al. (2011) studies the energy absorption properties of multi-layered corrugated paperboard in various ambient humidity and didn’t consider the metal multi-layered corrugated panels. Kılıçaslan et al. (2013) explored the impact responses of seven layers of trapezoidal aluminum panels with 00 /900 corrugated layer orientation and 00/00 orientation under two local loadings. Above all, there are few researches on the multi-layered metal corrugated sandwich panels with layers varying. There are also few researches on energy-absorption characteristics of metal multi-layered corrugated sandwich panels under planar compression loading. Therefore, metal multi-layered trapezoidal corrugated sandwich panels were studied by using the experimental and numerical methods. The aim of the present paper is to obtain the force-displacement curves of the trapezoidal corrugated sandwich panels with different numbers of corrugated core layers and orientations under the quasi-static compression. The failure mechanisms and energy absorption of the multi-layered corrugated sandwich panels were also explored through a series of experimental test. The three-dimensional finite element (FE) models of the specimens were developed by using ANSYS/LS-DYNA, and were also validated by the experimental results, which will benefit the future crashworthiness optimization of metal multi-layered corrugated sandwich panels. 2. Experiments 2.1 Experimental Specimens The core cell and interlayer sheet material of the corrugated sandwich panels are Aluminum 5052-O plates with a thickness of 0.2 mm. Aluminum 2024-T4 sheet with a thickness of 1 mm is used to be the material for the face plates. Following the manufacturing specification (Hou et al., 2013), the trapezoidal cores were fabrication by using an in-house mould (Fig.1).An epoxy adhesive was used to bond the face plates, the cores and interlayer sheets for no less than 24 hours under constant pressure at the room temperature. The configuration of the core is depicted in Fig.2(a). For the core component, L1=7mm, L2 =5.5mm and w=55°. The size of specimen are 70mm in length and width. Three different configurations of trapezoidal corrugated sandwich panels are studied here: namely the regularly-arranged core with 00/00 layer orientation, stagger-arranged core with 00/00 layer 4
orientation and perpendicularly-arranged core with 00/900 layer orientation, as shown in Fig.2(b)-(d), respectively. In this study, the responses of the corrugated sandwich panels were first analyzed for the failure mechanisms and energy absorption experimentally. The effects of the configurations of the cores and layer variation of the cores are then investigated. Finally, the initial imperfection is analyzed by comparing the experiment with the finite element simulation. Fig.1 Self-madeMould. Fig.2 Specimens: (a) the shape of the core cell, (b) the regularly-arranged corrugated sandwich panels, (c) the stagger-arranged corrugated sandwich panels, and (d) the cross-arranged (0 0/900) corrugated sandwich panels.
2.2 Experimental set-up Compressing the panels quasi-statically normal to its plane is a common way to test the energy absorbing ability of the structure (Fan et al., 2011). The compression tests were conducted on the INSTRON-3382 test machine with a maximum force of 100 kN in line with the ASTM standard C365/C365M-05 (Hou et al., 2013). Fig.3 shows apparatus of the test machine and specimen being placed in-between the platens, where specimen was pressed by applying a uniform compression at a nominal displacement rate of 2mm/min, shown in Fig.4. The data of the force and displacement in the loading process will be passed from the sensor mounted in the test machine to the computer, in which the force-displacement data was recorded until the specimen was completely crushed. Fig.3. The test machine and specimens. Fig.4. Experimental set-up of the compressive test.
3. Finite Element Modeling The corrugated sandwich panels were modeled using the explicit finite element (FE) code ANSYS/LS-DYNA, which allows simulating nonlinear large deformation effectively. Fig.5 exemplifies some FE models for different configurations of two layers corrugated sandwich panels. Elastic-plastic material properties (Hou et al., 2012) are used to model the corrugated sandwich panel materials. The detailed material parameters are summarized in 5
Table1. For the quasi-static loading process, effect of strain rate was not considered here. Fig.53D FE model of two-layer corrugated sandwich panels: (a) the regularly-arranged, (b) the stagger-arranged, and (c) cross-arranged(00/900) configurations. Table 1 The properties of materials.
The face plates, the cores and interlayer sheets were meshed using quadrilateral Belytschko-Tsay shell elements (Hallquist, 1998) with five integration points across the thickness. To generate the compression, the upper and lower smooth indenters were modeled using the model of *RIGIDWALL (Hou et al., 2007 and 2009; Yin et al., 2011) in the ANSYS/LS-DYNA
code,
including
the
upper
smooth
indenter
modeled
by
*RIGIDWALL_GEOMETRIC_FLAT_MOTION_ID with a constant speed of 1 m/s and the lower one by *RIGIDWALL_GEOMETRIC_FLAT_ID. Since the total CPU time for an explicit solution was too long by use of the same speed (2 mm/min) as in the experiments, a constant faster speed of 1m/s was adopted in the simulation (Wang and Fan, 2003). Adhesion between the cores, face plates and interlayer sheets was assumed to be perfectly bonded and a TIED_NODES_TO_SURFACE_OFFSET contact algorithm was used. Meanwhile, an automatic single surface contact (Hou et al., 2007 and 2009; Yin et al., 2011) was considered in order to take into account self-contacting interfaces during compression. The static and dynamic friction coefficients were set to be 0.3 and 0.2, respectively, as suggested by Kılıçaslan et al. (2013). 4. Results and Discussions 4.1 Compressive responses of the multi-layered corrugated sandwich panels The force-displacement curves of the regularly-arranged configuration with different layers of core are depicted inFig.6. In general, all the curves consist of three stages: namely the elastic stage, the plateau stage and the densification stage. No abrupt loading peak and drop were observed in these curves. The photographic images in Fig.7 clearly illustrated the process of such curves (from a three layer specimen). It is seen that all layers withstood the force and no cores and interlayer sheets were found crushed individually. Firstly, the bending 6
of the interlayer sheets, especially the edge area where there were no kinematic constraints, resulted in no peak force (Jin et al., 2013)which is smaller than that due to the bending of cores. With the bending of the interlayer sheets, the buckling and the progressive densification of the cores, the force keeps climbing. Meanwhile, from Fig.6, it was noted that the force had a small fall in some regions. That was also due to buckling of core cells and the translation of the interlayer sheets. When all cores and interlayer sheets were densified, the force increased rapidly. Fig.6. The force-displacement experimental curves of the regularly-arranged corrugated sandwich panels with various layers core. Fig.7.Images of the deformation of the regularly-arranged corrugated sandwich panels with three layers core.
Fig.8. shows the force-displacement curves of the stagger-arranged and cross-arranged (00/900) corrugated sandwich panels. These curves also exhibit three stages of responses. However, the trend of the curves somewhat differs from that of the regularly-arranged panels, which rises up elastically firstly and then drops due to the core buckling. When all cores and interlayer sheets were crushed, the densification of the corrugated sandwich panels raised the curves steeply. As shown in Fig.9, taking the panels with three layer cores for example, there are more than one peak points because a peak was formed when the core buckled in some layer, then the curves climbed up again to form another peak when the force was transmitted to the other layer. Fig.10 exhibits the deformation of these three layer corrugated sandwich panels. For the stagger configuration as in Fig.10a, it was seen that the bottom two layers buckled first and then the top layer began to buckle together with the densification of two bottom layer. For the perpendicular configuration as in Fig.10b, it was showed that the top layer which had different orientation buckled first and then the two parallel layers followed. This explained the reason why the curves in Fig. 9 had more one peak. Fig.8.The force-displacement experimental curves of the corrugated sandwich panels with various layers core: (a) the stagger-arranged, and (b) the cross-arranged (00/900). Fig.9. The force-displacement experimental curves of the corrugated sandwich panels with three 7
layers core: (a) the staggered-arranged, and (b) the cross-arranged (00/900). Fig.10.Images of the deformation for the three-layeredcorrugated sandwich panels: (a) the staggered-arranged, and (b) the cross-arranged (00/900).
4.2 The effect of core configurations From the above experiments, it was found that the configurations of cores played an important role in the crushing mechanism of the corrugated sandwich panels. In the curves of the regular configuration, there was no peak force, whereas the force-displacement curves of the stagger and perpendicular configurations had evident fluctuation. The deformation modes of these panels differ due to the different layout of core panels. Fig.11 compares the difference of these three corrugated sandwich panels with the same number of layers core. At the elastic stage, the stagger configuration had the highest force. The peak forces in the elastic stage are listed in Table 2. All the plateau forces of these three different configurations fluctuate around 1 kN. The densification of the regular configuration began earlier than those of the stagger and perpendicular configurations, as summarized in Table 3. From Fig. 11 and Table 3, it can be concluded that the 00/900perpendicular core configurations is the best one among the three considered panels, due to its longest plateau stage and highest energy-absorption. Fig.11. The force-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Table 2The peak crushing forces of three corrugated sandwich panels in the elastic stage. Table 3The displacements (D)and energy-absorptions (EA) of three corrugated sandwich panels before their own densifications.
The energy absorption of the corrugated sandwich panels was calculated by integrating force-displacement curves(Kılıçaslan et al.,2013). The absorbed energy (E) was formulated as: d
E (d ) = ò F ( x)dx 0
(1)
where d is crash distance (Yin et al., 2013). As shown in Fig.12, it was clearly shown that the value of the energy absorption of the regularly-arranged corrugated sandwich panels was less
8
than that of the other two configurations before densification. At the same time, the energy absorptions of the stagger and perpendicular configurations were basically equal. Table 4 summarized the energy absorption of these three structures under the same deformation displacements. Concerning the energy absorption under the same deformation displacement and the peak force in Table 2, it can also be concluded from Fig. 12 and Table 4 that the cross-arranged (0°/90°)core configuration seems to be the best one. Nevertheless, the stagger-arranged core configuration is better than the regularly-arranged one.
Fig.12. The energy-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Table 4The energy absorptions of three corrugated sandwich panels before densification of the regularly-arranged sandwich panels
4.3 The effect of the number of layers core FromFig.6, Fig.8(a) and Table 2, the peak force for the regular and stagger configuration decrease when the layer numbers increase, which indicate the effect of interlayer sheets. With the increased number of layers, more interlayer sheets became involved, which can reduce the peak force of the multi-layered sandwich structures. The significant difference was the prolongation of the plateau stage with the increase of the layer numbers, which lead to more energy absorption before densifications, as shown in Fig.13 and Table 3. This illustrate that the energy absorption is largely due to the span of the plateau stage. Fig.13.The energy-displacement experimental curves of three corrugated sandwich panels with various layers: (a) the regularly-staggered, (b) the regularly-arranged partial enlargement, (c) the stagger-arranged, (d) the stagger-arranged partial enlargement, (e) the cross-arranged (0 0/900) , and (f) the cross-arranged (00/900) partial enlargement.
4.4 Comparison between numerical and experimental results Fig.14 depicted the comparison of experimental and numerical force-displacement curves of the regularly-arranged corrugated sandwich panels, which showed good agreement. The small difference was due to some initial imperfection in the specimen preparation and
9
de-bonding occurred during the compression. The de-bonding phenomenon was not serious because no abrupt deformation occurred, as indicated in Fig.15. Fig.16 illustrated the deformation comparisons between experiment and simulation for the regularly-arranged corrugated sandwich panels with six layers considered. It can be seen that the deformation processes and patterns are very consistent between experimental and numerical results. This further confirmed that the FE modeling of corrugated sandwich panels is effective for a further research and crashworthiness optimization. Fig.14.Comparisons of the force-displacement curves of the regularly-arranged corrugated sandwich panels between the experiment and the simulation: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.15.Deformation of the regularly-arranged multi-layered corrugated sandwich panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.16.Comparison of the deformation between experiment and simulation for the regularly-arranged multi-layered corrugated sandwich panels with six layers core.
Fig.17and 18 showed the experimental and simulation results of the stagger-arranged and cross-arranged (0°/90°) panels, respectively. It is found that peak forces are higher in the simulation than in the experiment, which was considered to be mainly due to the initial imperfections, such as offset cores and de-bonding. To investigate the influence of initial imperfection, we attempted to model the imperfection in FE modeling. When we modeled the structural imperfections detailed in the same way as the specimen, the force-displacement curves matched much better as shown in Fig.19, where the comparison curves between experiments and simulations with original imperfections for three-layered stagger-arrange and cross-arranged panels. From Fig 17-19, it can be seen that imperfections weakened the structure and made it buckle more easily. Meanwhile, de-bonding had great influences on the force-displacement curves, reduced the peak forces and delayed the densification. Meanwhile, it was found that experimental de-bonding in the cross-arranged (0°/90°) panels were the severest among three corrugated sandwich panels. In Fig. 20, the severest de-bonding was illustrated, which were 3-layered, 5-layered and 6-layered cross-arranged
10
panels. The configuration of cores was considered to be the fundamental reason for de-bonding. Indeed, de-bonding process is rather complex as illustrated in Fig.20. The time span of contact simulation is very difficult defined. So the time span in simulation can’t perfectly match that in the experiment. This adds the difficulty to model the real de-bonding time.
Fig.17Comparisons of the force-displacement curves between experiment and simulation for the stagger-arranged panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.18. Comparisons of the force-displacement curves between experiment and simulation for the cross-arranged (0°/90°) panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.19.Comparisons of the force-displacement curves between experiment and simulation with original imperfection for three-layered panels: (a) stagger-arranged, (b) cross-arranged (0 0/900). Fig.20.The de-bonding phenomenon of the cross-arranged(00/900) corrugated sandwich panels: (a) 3 layers, (b) 5 layers, (c) 6 layers.
5. Conclusions In this study, three different configurations of the multi-layered corrugated sandwich panels were studied under the quasi-static compression test experimentally and numerically. The trapezoidal cores, prepared by using the self-made mould, were bonded to the interlayer sheets and face plates to produce a series of multi-layered corrugated sandwich panels. After analyzing the experimental results, it was found that there are three clear stages in the force-displacement curves of compression: elastic stage, plateau stage and densification stage. The experiment showed that the force of the regular configuration slowly increased in the elastic stage, whereas those of the stagger and cross configurations had a clear peak. With the increase of the layers, the plateau forces and the peak forces decreased for the three configurations. Increase in layer number also led to the prolongation of plateau stage, which made better energy absorption prior to the densification of the panels. The energy absorption of the regular and stagger panels decreased with the increase in the layer numbers in the beginning, whilst cross panels had no such property due to the arrangement of the core layers. 11
It is concluded that the cross-arranged (00/900) panels is better than the regular-arrange and stagger-arranged panels not only in the energy absorption but also in the aspect of peak crushing force. Then, the stagger-arranged panel is better than the regular-arranged one. Moreover, the FE simulation was also conducted for three different multi-layered corrugated sandwich panels. The FE results for the regular configuration agreed well with the experimental counterpart. The differences between experiments and simulations for the stagger and perpendicular panels were analyzed in detail. It is found that the initial imperfection and the de-bonding played an important role in the differences between experiments and simulations. Imperfections of specimens weakened the structure and made it buckle more easily. Meanwhile, de-bonding had great influences on the force-displacement curves, reduced the peak forces and delayed the densification. The time span in simulation can’t perfectly match that in the experiment, which adds the difficulty to model the real de-bonding time.
Acknowledgments The financial supports from National Natural Science Foundation of China (11232004, 11372106), New Century Excellent Talents Program in University (NCET-12-0168) and Hunan Provincial Natural Science Foundation of China (12JJ7001) are gratefully acknowledged. Moreover, Joint Center for Intelligent New Energy Vehicle is also gratefully acknowledged.
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Figure Captions: Fig.1. Self-made Mould. Fig.2. Specimens: (a) the shape of the core cell, (b) the regularly-arranged corrugated sandwich panels, (c) the stagger-arranged corrugated sandwich panels, and (d) the cross-arranged (00/900) corrugated sandwich panels. Fig.3. The test machine. Fig.4. Experimental set-up of the compressive test. Fig.5. 3D FE model of two-layer corrugated sandwich panels: (a) the regularly-arranged, (b) the stagger-arranged, and (c) cross-arranged configurations. Fig.6. The force-displacement experimental curves of the regularly-arranged corrugated sandwich panels with various layers core. Fig.7.Images of the deformation of the regularly-arranged corrugated sandwich panels with three layers core. Fig.8. The force-displacement experimental curves of the corrugated sandwich panels with various layer core: (a) the stagger-arranged, and (b) the cross-arranged (00/900). Fig.9. The force-displacement experimental curves of the corrugated sandwich panels with three layer core: (a) the staggered-arranged, and (b) the cross-arranged (00/900). Fig.10.Images of the deformation for the three-layered corrugated sandwich panels: (a) the staggered-arranged, and (b) the cross-arranged (00/900). Fig.11. The force-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.12. The energy-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.13.The energy-displacement experimental curves of three corrugated sandwich panels with various layers: (a) the regularly-staggered, (b) the regularly-arranged partial enlargement, (c) the stagger-arranged, (d) the stagger-arranged partial enlargement, (e) the cross-arranged (00/900) , and (f) the cross-arranged (00/900) partial enlargement. Fig.14.Comparisons of the force-displacement curves of the regularly-arranged corrugated 16
sandwich panels between the experiment and the simulation: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.15.Deformation of the regularly-arranged multi-layered corrugated sandwich panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers. Fig.16.Comparison of the deformation between experiment and simulation for the regularly-arranged multi-layered corrugated sandwich panels with six layers core. Fig.17.Comparisons of the force-displacement curves between experiment and simulation for the stagger-arranged panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.18.Comparisons of the force-displacement curves between experiment and simulation for the cross-arranged (0°/90°) panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers. Fig.19.Comparisons of the force-displacement curves between experiment and simulation with original imperfection for three-layered panels: (a) stagger-arranged, (b) cross-arranged (00/900). Fig.20.The de-bonding phenomenon of the cross-arranged(00/900) corrugated sandwich panels: (a) 3 layers, (b) 5 layers, (c) 6 layers.
17
Table Captions: Table 1 The parameters of materials. Table 2 The peak crushing forces of three corrugated sandwich panels in the elastic stage. Table 3 The displacements (D)and energy-absorptions (EA) of three corrugated sandwich panels before their own densifications. Table 4 The energy absorptions of three corrugated sandwich panels before densification of the regularly-arranged sandwich panels.
18
Fig.1. Self-made Mould.
19
(a)
(b)
(c)
(d)
Fig.2. Specimens: (a) the shape of the core cell, (b) the regularly-arranged corrugated sandwich panels, (c) the stagger-arranged corrugated sandwich panels, and (d) the cross-arranged (00/900) corrugated sandwich panels.
20
Fig.3. The test machine.
21
Fig.4. Experimental set-up of the compressive test.
22
(a)
(b)
(c)
Fig.5. 3D FE model of two-layer corrugated sandwich panels: (a) the regularly-arranged, (b) the stagger-arranged, and (c) cross-arranged (00/900) configurations.
23
Fig.6. The force-displacement experimental curves of the regularly-arranged corrugated sandwich panels with various layers core.
24
t=0
t=2min
t=3min
t=4min
t=7min
t=8min
Fig.7. Images of the deformation of the regularly-arranged corrugated sandwich panels with three layer core.
25
(a) the stagger-arranged
(b) the cross-arranged (00/900) Fig.8. The force-displacement experimental curves of the corrugated sandwich panels with various layer core. (a) the stagger-arranged, and (b) the cross-arranged (0 0/900).
26
(a) the staggered-arranged
(b) ) the cross-arranged (00/900) Fig.9. The force-displacement experimental curves of the corrugated sandwich panels with three layer core: (a) the staggered-arranged, and (b) the cross-arranged (00/900).
27
t=0min
t=2min
t=3min
t=4min
t=5min
t=6min
t=7min
t=8min (a)
t=0min
t=1min
t=2min
t=4min
t=5min
t=6min
t=7min
t=8min
(b) Fig.10. Images of the deformation for the three-layered corrugated sandwich panels: (a) the staggered-arranged, and (b) the cross-arranged (00/900).
28
(a)
(b)
(c)
(d)
(e) Fig.11. The force-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
29
(a)
(b)
(c)
(d)
(e) Fig.12. The energy-displacement experimental curves of three multi-layered corrugated sandwich panels with the same number of layers core: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
30
(a)
(b)
(c)
(d)
(e) (f) Fig.13. The energy-displacement experimental curves of three corrugated sandwich panels with various layers: (a) the regularly-staggered, (b) the regularly-arranged partial enlargement, (c) the stagger-arranged, (d) the stagger-arranged partial enlargement, (e) the cross-arranged (00/900) , and (f) the cross-arranged (00/900) partial enlargement.
31
(a)
(b)
(c)
(d)
(e) Fig.14. Comparisons of the force-displacement curves of the regularly-arranged corrugated sandwich panels between the experiment and the simulation. (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
32
(a)
(b)
(c)
(d)
(e) Fig.15. Deformation of the regularly-arranged multi-layered corrugated sandwich panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, and (e) 6 layers.
33
t=0min
t=3min
t=4min
t=6min
t=7min Fig.16. Comparison of the deformation between experiment and simulation for the regularly-arranged multi-layered corrugated sandwich panels with six layers core.
34
(a) 2 layers
(b) 3 layers
(c) 4 layers
(d) 5 layers
(e) 6 layers Fig.17. Comparisons of the force-displacement curves between experiment and simulation for the stagger-arranged panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers.
35
(a) 2 layers
(b) 3 layers
(c) 4 layers
(d) 5 layers
(e) 6 layers Fig.18. Comparisons of the force-displacement curves between experiment and simulation for the cross-arranged (0°/90°) panels: (a) 2 layers, (b) 3 layers, (c) 4 layers, (d) 5 layers, (e) 6 layers.
36
(b) cross-arranged (00/900)
(a) Stagger-arranged
Fig.19. Comparisons of the force-displacement curves between experiment and simulation with original imperfection for three-layered panels: (a) stagger-arranged, (b) cross-arranged (00/900).
37
(a) 3 layers
(b) 5 layers
(c) 6 layers Fig.20. The de-bonding phenomenon of the cross-arranged (00/900) corrugated sandwich panels: (a) 3 layers, (b) 5 layers, (c) 6 layers.
38
Tables:
Table 1 The parameters of materials
Face sheet (Al-2024 aluminum alloy)
Core and interlayer sheets (5052-O aluminum alloy)
2700.00 72.40 28.00
2685.00 69.60 2.50
(MPa)
75.80
65.50
n
0.33
0.33
Property
r (kg/m3) E(GPa) ET(GPa)
sy
39
Table 2 The peak crushing forces of three corrugated sandwich panels in the elastic stage Regularly-arranged 2 layers core 3 layers core 4 layers core 5 layers core 6 layers core
Staggered-arranged
1.024kN 0.859kN 0.851kN 0.848kN 0.818kN
1.291kN 1.183kN 1.148kN 1.228kN 1.013kN
40
00/900 1.079kN 1.121kN 0.862kN 0.841kN 0.917kN
Table 3 The displacements (D) and energy-absorptions (EA) of three corrugated sandwich panels before their own densifications
Regularly-arranged 2 layers core 3 layers core 4 layers core 5 layers core 6 layers core
00/900
Staggered-arranged
D
EA
D
EA
D
EA
6mm 8mm 11mm 18mm 24mm
5.32J 6.13J 7.78J 10.91J 21.07J
7.5mm 12mm 16mm 20mm 24mm
7.69J 10.64J 14.95J 18.39J 22.46J
8mm 14mm 16mm 24mm 29mm
7.65J 15.03J 15.22J 24.36J 29.35J
41
Table 4 The energy absorptions of three corrugated sandwich panels before densification of the regularly-arranged sandwich panels Regularly-arranged Staggered-arranged 00/900
D 2 layers core 3 layers core 4 layers core 5 layers core 6 layers core
6mm 8mm 11mm 18mm 24mm
EA
D
5.32J 6.13J 7.78J 10.91J 21.07J
6mm 8mm 11mm 18mm 24mm
42
EA 6.27J 6.56J 9.51J 13.92J 22.49J
D 6mm 8mm 11mm 18mm 24mm
EA 5.57J 7.77J 9.38J 14.14J 21.66J