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Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading
Materials Science & Engineering A 696 (2017) 283–289
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Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading Jinwu Xiang, Jianxun Du
MARK
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School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Electron microscopy Aluminum alloys Failure Finite element method
Honeycomb structures are widely used in automotive and aerospace applications because of their outstanding characteristics of high strength and light weight. In this paper, a new honeycomb structure named as bionic honeycomb thin-walled structure (BHTS) which filled the column in different way inspired by the internal structure of the ladybeetle is proposed. The energy absorption characteristics of two kinds of BHTSs have been investigated comparing an original honeycomb structure with the same type of material under axial impact loading using nonlinear finite element software LS-DYNA. Dynamic loading has been carried out under the weight of 500 kg and the speed of 10 m/s. The results show that the energy absorption characteristic of BHTS which filled columns on its walls is better than that filled columns in its walls. Then the parameter studies in energy absorption of BHTS-2 have been carried out. It is found that energy absorption performance of BHTS-2 is best when the filled column number is 6 and diameter is 8 mm.
1. Introduction Nowadays, thin-walled structures with various cross-sectional geometries are widely used as energy absorbers in aeronautics and astronautics applications because of their low price, simple manufacture technology and higher energy absorption efficiency. Many relevant works have been carried out using combinations of theoretical researches [1], numerical simulations [2,3] and experimental studies [3–5]. Different cross-sectional shapes of the single thin-walled tube have significant differences on the energy absorption characteristics. Several cross-sectional figures such as hexagon, octagon, 12-sided and 16-sided star have been already studied experimentally [6]. The results revealed that the increase of the number of inward corners showed a notable change in energy absorption. More tubes with different shapes such as square tubes [7,8], circular tubes [9,10], rectangular tubes [11–13], pyramidal tubes [14], hexagonal tubes [15–17] and conical tubes [18–20] have been investigated widely. Two kinds of creative configurations including pentagon and cross section with different materials have also been studied [21]. Another novel cross-sectional shapes was proposed, which combines the square section and circular section [22]. A new method has been proposed to enhance energy absorption characteristic of structure by adding corners in the cross-section of the tube. Several kinds of multi-corner thin-walled columns used this way have been tested experimentally [23]. Some parametric studies of
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Corresponding author. E-mail address: [email protected] (J. Du).
http://dx.doi.org/10.1016/j.msea.2017.04.044 Received 1 March 2017; Received in revised form 8 April 2017; Accepted 11 April 2017 Available online 12 April 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
the longitudinally grooved square tubes under axial crushing have been carried out recently. It is found that the grooves could obviously increase the specific energy absorption of the structures [24–27]. Bitubular thin-walled column is another high-performance energy absorption structure. A wide variety of bi-tubular thin-walled column design has been reported in the literature. Several geometry parameters of bitubular tubes have been numerically investigated, including radial distance of concentric cylindrical tubes [28], the shape of the inner tubes and the location of diaphragms [29]. The simulation results showed that the efficiency of energy absorption could be improved by introducing interlayer to the tubes. Many foam-filled bi-tubular circular tubes have been investigated under axial loading and the parameter studies such as cross-sectional configurations and loading conditions have been carried out [9,30,31]. Rabczuk et al. [32] have proposed a homogenization method for sandwich structures consisting of two plates interlaced with beams and shells in a periodic, lattice structure. It could achieve a significant reduction in computation and modeling time for the analysis of sandwich structures by this computational method. They also have developed a simplified method for estimating the impulsive load in sandwich structures submerged in water due to a dynamic wave loading that accounts for fluid-structure interaction [33]. More previous studies have focused on the thin-walled structures and conventional honeycombs, while relatively less works have been done on the bionic honeycomb structures. However, because of the
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A. dichotoma elytra is shown in Fig. 2(e).
extremely low densities, the conventional honeycomb cell walls buckle easily under axial impact loading, which limits axial energy absorption capacity. It is found that the sandwich walls with core struts in honeycomb structures have superior mechanical properties to that with solid walls in conventional honeycomb structures [34]. In this paper, the energy absorption capability of this bionic honeycomb thin-walled structure (BHTS) were analyzed to reveal pathways to structures with superior characteristics [35]. The elytra of beetle possesses the characteristics of light weight and impact resistance because of thin-walled tube exists in the elytra's honeycomb structure [36–38]. A novel bionic integrated honeycomb plate has been designed based on internal structure of beetle elytra [39,40]. The shear and compressive mechanical properties of this bio-mimetic structure made of composite materials have been studied experimentally [41,42]. The bionic honeycombs' material components processing good performances have also been obtained by experimental tests [43]. However, the existing forms and geometric parameters of the thin-walled tubes which could make a significant effect on crashworthiness performance have been seldom researched. In this paper, two kinds of filling modes of thin-walled columns were studied, which named as Bionic Honeycomb thin-walled Structure (BHTS). The BHTS imitating the structural characteristic of elytra from different species of beetles were investigated under axial impact loading using finite element software LS-DYNA. The energy absorbing characteristics of different filling methods were compared and the BHTS with good performance was put forward. In addition, the effects of design variables of the filling tube such as filling density and filling tube diameter were studied on BHTS numerically.
2.2. Description of the beetle-based BHTS By imitating the inside structural characteristics of beetle elytra, two different forms of BHTSs were designed, as shown in Fig. 3(b) and (c). The bionic honeycomb structure (BHS) in Fig. 3(a) is entirely composed of honeycombs. The BHTS-1 in Fig. 3(b) is composed of honeycombs and circular tubes, while the circular tubes are all in the center of honeycombs. The BHTS-2 in Fig. 3(c) is also composed of honeycombs and circular tubes, however, the circular tubes are on the wall of honeycombs. In order to investigate the energy absorption performances of the different forms of the BHTSs, the equivalent crosssectional size of different components (i.e. honeycomb and tube) and the same length of the BHTSs are obtained. 2.3. Material properties of bionic structure The single-wall tubes were prepared using aluminum alloy AA6063 T6. The specific alloy has a density ρ=2.7×103 kg/m3, a Young's modulus E=68.2 GPa, the initial yield stress σy=162 MPa, the ultimate stress σu=192 MPa, and Poisson's ratio υ=0.3 (see Table 1) [44]. The tubes were modeled with the MAT_24 material law in LS-DYNA971. Because the aluminum alloy was considered insensitive to the strain rate, the strain rate was ignored. The fracture behavior of the aluminum alloy was neglected during these analyses [45]. 2.4. Structural crashworthiness criteria Four indicators are used to define the crashworthiness performance of the BBTS. The first indicator to estimate the energy absorption capabilities of the structure is the special energy absorption (SEA) defined as the ratio of the total energy EA absorbed by a structure to its mass M [46]:
2. Beetle-based BHTS 2.1. The internal structural characteristics of beetles' elytra Beetles are a group of insects which have the elytra to protect their bodies. Figs. 1 and 2 show two kinds of beetles (i.e. Coccinella septempunctata and Allomyrina dichotoma) which all have the elytra. The adult C. septempunctata ladybeetle was used as shown in Fig. 1(a). There are many honeycombs in the internal structure of its elytra, as shown in Fig. 1(b). In each honeycomb structure, there is a hollow column structure, as shown in Fig. 1(c) and (d). Due to the internal structure of C. septempunctata is quite complicated, the model of its structure is proposed, as shown in Fig. 1(e). The irregular honeycombs are green, while the hollow columns are yellow. The adult A. dichotoma beetle was used as shown in Fig. 2(a). Unlike the inside structure of C. septempunctata, in A. dichotoma elytra the hollow columns are on the wall of honeycombs, as shown in Fig. 2(b). Fig. 2(c) and (d) are the microstructure of hollow column. The schematic of internal structure of
SEA =
EA M
(1)
The area under the force-displacement curve represents the amount of absorbed energy EA [47]:
EA =
∫0
d
F(x)dx
(2)
Where d is the axial crushing displacement and F denotes the axial crushing force. For an energy absorption structure, a high value of crash load efficiency (CLE) is expected [48]:
CLE =
MCF ×100% MIF
(3)
Fig. 1. Internal structure of elytra: (a) The adult C. septempunctata ladybeetle, (b) the microscopy of internal structure of elytra, (c) the tubular structure in the elytron, (d) the internal hollow structure of the tube and (e) schematic of the internal structure of C. septempunctata elytra. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
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Fig. 2. Internal structure of elytra: (a) The adult A. dichotoma beetle, (b) internal structure of elytra filled with thin-walled tubes, (c) the tubular structure in the elytra, (d) the internal hollow structure of the tube and (e) schematic of C. septempunctata elytra [40].
Fig. 3. The cross-section of three different structures: (a) bionic honeycomb structure (BHS), without tubes, (b) bionic honeycomb-tubular structure (BHTS-1), tubes between walls, (c) bionic honeycomb-tubular structure (BHTS-2), tubes on the walls. Table 1 Mechanical properties of aluminum alloy material of bionic honeycomb structures. Density (kg/ m3)
Young's modulus (GPa)
Yield stress (MPa)
Ultimate stress (MPa)
Poisson's ratio
2700
68.2
162
192
0.3
Where MIF represents the peak force in the force versus displacement curve under the axial impact. The mean crush force (MCF) for a given deformation can be obtained as [49]:
EA MCF = d
Fig. 4. Schematic of the calculation finite element model with axial force.
The commercial software CATIA V5R20 is used to create the solid models representing the structures. Hypermesh 12.0 is used as preprocessor to impart the axial impact conditions, material properties, boundary conditions and meshing. The solver from the explicit nonlinear finite element software LS-DYNA is employed for the simulations; post-processing is treated using the softwares of Hyperview 12.0 and Hypergraph 12.0. Fig. 5 shows the curves related to the crushing force versus displacement for the triangular bi-tubular tube with five different mesh
(4)
3. Numerical simulation 3.1. Finite element modeling Due to the cross-sectional area of impactor is larger than that of membrane, membrane has a slight influence on mechanical properties of the whole structure [50]. To better investigate the impact resistance and energy absorption characteristics of the honeycombs with different configurations, the membrane on both sides of honeycomb structure is not considered in the numerical model. A scheme representing the structures' loading conditions is shown in Fig. 4. The bottom of the tube is clamped to the fixed bottom plate. The impactor and the fixed bottom plate are set as rigid bodies. A 500 kg rigid impactor with a initial velocity (v=10 m/s) is used to simulate the axial loading on the tubes. An automatic contact setup is used in the numerical simulation to consider the contact caused by the deformation of the tubular wall during crushing. The point-surface contact algorithm is adopted to consider the contact between the BHTS and the rigid wall. The dynamic and static friction coefficients during contact are set at 0.2. To avoid a zero energy deformation mode and volumetric locking a stiffness-based hourglass control and a reduced integration are used. The material failure of the aluminum alloy tube is neglected.
Fig. 5. Crushing force versus displacement curve of BHTS with different mesh sizes.
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Fig. 8. The crushing force versus displacement of different bionic honeycomb structures.
Fig. 6. Comparison of force versus displacement curves between experiment and simulation.
3.3. Comparison of energy absorption characteristics of three kinds of bionic structures densities. The error provided by the models which comprised by the element sizes of 1.5×1.5 mm and 2.0×2.0 mm is quite small, and the two mesh sizes show to provide sufficient accuracy to describe the crushing process. To reduce the computational cost, the mesh size of 2.0 mm×2.0 mm has been adopted for all the following studies.
The initial crushing forces of three bionic structures all reach a peak at the same displacement, then drop rapidly in varying levels. The maximum peak value of BHTS-2 is between BHS and BHTS-1, as shown in Fig. 8. Obviously, the mean force of the BHTS-1 and BHTS-2 are higher than that of BHS and the difference of BHTS-1 and BHTS-2 is not apparent. The energy absorption efficiencies of BHTS-2 and BHTS-1 are very closed, and obviously both higher than BHS, as shown in Fig. 9. The progressive collapse of three bionic structures are shown in Fig. 10. In order to better compare the energy absorption properties of bionic structures quantitatively, parametric data of numerical simulation are listed in Table 1. Table 1 shows that the SEA of BHTS-2 is 35.97% higher than that of BHS and 24.52% higher than that of BHTS-1 respectively; Compression force efficiency of BHTS-2 is 34.50% higher than that of BHS and 21.56% higher than that of BHTS-1, respectively. So comparing either the SEA or the CFE, the BHTS-2 is better than BHS and BHTS-1.
3.2. Validation of the FE model Lee et al. [51] have carried out experiments for thin-walled square columns under the axial impact loading. In their experiments they adopted aluminum AL6063 thin-walled extruded tubes with length of 200 mm. The weight of the cross head was 40 kg, and the impact velocity was 7.02 m/s. To validate our FE models, we have first reproduced the same types of empty single thin-walled square tubes with the same sizes and axial impact loading conditions, and compared our results with the experimental data of Lee et al. Figs. 6 and 7 show the comparisons between the experiments and the simulations. Fig. 7 shows that the collapse mode reproduced by the numerical simulation matches quite well the one from the experiment. Moreover, the curve of the crushing force versus displacement produced by simulation agrees well with the one from the experiments. These results validate our FE modeling approach for the subsequent use in evaluating the crushing performance of the BHTSs.
3.4. Parametric study of BHTS-2 Due to energy absorption properties of BHTS-2 is better than that of BHS and BHTS-1, the further study of BHTS-2 was carried out. The parameters of columns on the honeycomb wall have an important influence on the energy absorption characteristics of the BHTS-2. Therefore parameter analysis has a great significance on crashworthiness of BHTS-2. In this paper, a range of parametric studies with different column number n and column diameter d were investigated on
Fig. 7. Comparison of deformation patterns of thin-walled structure between experiment and simulation.
Fig. 9. The energy absorption versus displacement of different bionic honeycomb structures.
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Fig. 10. Progressive collapse of different BHTSs.
energy absorption performance. Then the parametric studies of the thickness and height of the BHTS-2 were carried out by numerical analysis. In this research, the thickness of honeycomb wall is the same as the thickness of columns.
Table 2 The results of numerical simulations on the energy absorption performance.
3.4.1. Influence of the number of columns Based on the numerical simulation data, the curves of energy absorption versus displacement are plotted in Fig. 11. It is obvious that the energy absorption characteristics increase gradually. It is clear that the energy absorption enhanced with the increase of the column numbers. When the column number is one, the absorbed energy is the lowest, while the columns are six, the absorbed energy is the highest. It is also demonstrated that the filling of columns enhances the energy absorption ability of BHTS-2 (Table 2). Table 3 summarizes the numerical data for BHTS-2 with different column numbers. The SEA values of structures increase gradually, while the SEA value of BHTS-2 filled with five columns is similar to that of BHTS-2 filled with six columns. The compression force efficiency of BHTS-2 is also enhanced with the increasing of column numbers.
Structures
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
BHS BHTS-1 BHTS-2
35.8532 56.7891 59.5184
62.9781 90.1557 77.7283
1.1137 1.7436 1.8185
0.0468 0.0671 0.0562
23.7970 25.9850 32.3576
56.9296 62.9900 76.5724
Table 3 Energy absorbing characteristics of axial crushing of BHTS-2 with different column numbers. n
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
1 2 3 4 5 6
39.4646 43.0154 45.3182 48.5125 51.8795 53.3719
63.4687 66.5581 68.3852 69.2712 72.1187 73.7120
1.2128 1.3196 1.3898 1.4883 1.5843 1.6222
0.0478 0.0494 0.0501 0.0513 0.0524 0.0535
25.3724 26.7125 27.7405 29.0117 30.2347 30.3215
62.1796 64.6283 66.2690 70.0327 71.9362 72.4060
show stepped increase with the diameter growth. When the diameter of column was 10 mm, and the energy absorption ability is close to that which diameter is 8 mm, This may be due to mutual influence of the columns which diameter is 10 mm, then caused the reduction of the energy absorption effect of the structure. Table 4 summarizes the numerical data for BHTS-2 with different column diameters. When the diameter of column is in the range of 2–8 mm, the SEA of BHTSs increase gradually. When the diameter of
3.4.2. Influence of the diameter of columns The diameter of the column has a significant influence on the energy absorbing properties of the BHTS under axial loading. In this study, the diameter of column ranges from 2 mm to 10 mm, and the interval is 2 mm. The internal absorption of the BHTSs increases monotonously with tube diameter. Fig. 12 shows that the energy absorption ability of large diameter has very difference from the small diameter. When the column diameter in the range of 2–8 mm, the SEA of the structures
Fig. 11. The energy absorption versus displacement of different numbers of columns.
Fig. 12. The energy absorption versus displacement of different diameters of columns.
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Table 4 Energy absorbing characteristics of axial crushing of BHTS-2 with different column diameters. d
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
2 4 6 8 10
41.6427 47.7482 52.6816 59.5184 60.9948
65.3939 70.1193 73.7079 77.7283 80.7089
1.2747 1.4631 1.6222 1.8185 1.8688
0.0482 0.0508 0.0535 0.0562 0.0588
26.4460 28.8011 30.3214 32.3576 31.7823
63.6798 68.0957 71.4735 76.5724 75.5738
Fig. 14. The energy absorption versus displacement of different heights.
characteristics of BHTS-2, crushing of BHTS-2 is simulated by changing the height h between 50 mm and 200 mm. Fig. 14 shows the energy absorption characteristics as the height h of BHTS-2 changes. By changing the height between 50 mm and 150 mm, the internal energy absorbed increase significantly. For the case of h equals to 200 mm, there is an obvious difference in the displacement versus internal energy curve when crushing is carried out to 50 mm, as shown in Fig. 14. The bucking of thin-walled tube of BHTS-2 results in a reduction of the energy absorption characteristic. Table 6 summarizes the numerical simulation data for BHTS-2 with different heights. When the height of BHTS-2 increased from 50 mm to 150 mm, the SEA values of BHTS-2 decrease gradually while the CFE values of that increase in the range of 30% and 50%. The values of SEA and CFE are all lowest when the height equals to 200 mm, which means that the energy absorption characteristics of this case is the worst between 50 mm and 200 mm.
Fig. 13. The energy absorption versus displacement of different thickness.
the column is 10 mm, the SEA value of the structure is lower than that of diameter is 8 mm. This phenomenon is consistent with the internal energy absorption effect. When the diameter is in the range of 2–8 mm, the compression force efficiency of BHTS is also enhanced with the increasing of column diameters. When the diameter is 10 mm, the compression force efficiency is reduced to 31.78 kJ/kg.
4. Conclusion and discussion 3.4.3. Influence of the thickness To investigate the effect of the thickness of the BHTS-2, a parametric study is conducted by changing the thickness between 0.5 mm and 3 mm. Fig. 13 shows the energy absorption versus different thickness of BHTS-2. It is obvious that the energy absorption characteristics increase gradually with the increase of the thickness. The results show that the BHTS-2 having the thickness equals to 3.0 mm has the maximum energy absorption characteristic. When the thickness of BHTS-2 is 0.5 mm, the energy absorption is the lowest. There is a close relationship between thickness and energy absorption. Table 5 summarizes the numerical data for BHTS-2 with different thickness. When the thickness of BHTS-2 increased from 0.5 mm to 3 mm, the SEA and CFE of BHTS-2 increase gradually. When the thickness of the BHTS is 3 mm, the SEA and CFE of the BHTS-2 is the best. For other cases of different thickness, the SEA values are more than 50 and the CFE values are more than 60%.
In this paper, two kinds of energy absorbed structures named as bionic honeycomb thin-walled structure (BHTS) with different column filled methods was proposed inspired by internal structure of beetle elytra. Then comparing the SEA and CFE between the column filled structure and column unfilled structure using nonlinear finite element code LS-DYNA. According to the numerical results, it can be found that the SEA of BHTS-2 is 35.97% higher than BHS and 24.52% higher than BHTS-1, respectively. Compression force efficiency of BHTS-2 is 34.50% higher than that of BHS and 21.56% higher than that of BHTS-1, respectively. It was discovered that energy absorption characteristics of the bionic structure which filled columns on its walls is better than the other two kinds of structures. The column diameter and the column number relationship to energy absorption ability are also investigated based on the BHTS-2. The highest energy absorption efficiency was found when the filled column number is 6 and diameter is 8 mm. A parametric study is conducted to investigate the effect of the thickness and height on energy absorption characteristics of BHTS-2. It is observed that by changing thickness t between 0.5 mm and 3.0 mm, the total absorbed energy and energy absorptive effectiveness increase gradually. By changing the height between 50 mm and 200 mm, the
3.4.4. Influence of the height In order to study the height h effect on energy absorption Table 5 Energy absorbing characteristics of axial crushing of BHTS-2 with different thickness. t/mm
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
0.5 1 1.5 2 2.5 3
22.0516 56.6273 94.4121 136.175 185.458 241.113
33.4953 77.7134 125.492 173.251 230.377 289.169
1.6890 3.5191 5.3624 7.5743 9.8739 12.6631
0.0311 0.0584 0.0834 0.1092 0.1346 0.1591
54.3086 60.2585 64.2974 69.3617 73.3574 79.5921
65.8349 72.8668 75.2335 78.5998 80.5019 83.3813
Table 6 Energy absorbing characteristics of axial crushing of BHTS-2 with different heights.
288
h/mm
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
50 100 150 200
71.0598 68.4270 65.7443 22.6013
229.7936 190.323 138.6764 78.0931
3.6094 6.6682 8.7722 4.8634
0.056 0.112 0.168 0.224
64.4535 59.5375 52.2154 21.7116
30.9233 35.9531 47.4084 28.9414
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energy absorptive effectiveness increase up to 47%, thereafter it decrease to 29% caused by buckling of the structure. The total energy absorption of BHTS-2 decrease gradually by changing the height from 50 mm to 200 mm. The results show that the bionic honeycomb thin-walled structures with filled columns inspired by the internal structure of beetle elytra have the best energy absorption characteristic under axial loading. This kind of honeycomb structure might be expected to be used as a replaceable structure in an automobile to improve crashworthiness. Future investigations should examine the manufacturability of this type of honeycomb structure and physical test to better correlate the results with the simulation works. Acknowledgment This work was supported by the National Natural Science Foundation of China (grant nos. 11402014 and 11572023). The authors gratefully acknowledge the financial support from China Scholarship Council. References [1] A. Niknejad, Y.T. Javan, Circular metal tubes during lateral compression between a V-shape indenter and a platen – theory and experiment, Proc. Inst. Mech. Eng. Part L: J. Mater.: Des. Appl. 229 (2015) 318–331. [2] D. Smith, C. Graciano, G. Martínez, P. Teixeira, Axial crushing of flattened expanded metal tubes, Thin Wall Struct. 85 (2014) 42–49. [3] J. Rouzegar, H. Assaee, A. Niknejad, S.A. Elahi, Geometrical discontinuities effects on lateral crushing and energy absorption of tubular structures, Mater. Des. 65 (2015) 343–359. [4] D. Smith, C. Graciano, G. Martínez, Quasi-static axial compression of concentric expanded metal tubes, Thin Wall Struct. 84 (2014) 170–176. [5] A. Niknejad, B. Rezaei, G.H. Liaghat, Empty circular metal tubes in the splitting process – theoretical and experimental studies, Thin Wall Struct. 72 (2013) 48–60. [6] Z. Fan, G. Lu, K. Liu, Quasi-static axial compression of thin-walled tubes with different cross-sectional shapes, Eng. Struct. 55 (2013) 80–89. [7] X. Zhang, Z. Wen, H. Zhang, Axial crushing and optimal design of square tubes with graded thickness, Thin Wall Struct. 84 (2014) 263–274. [8] A. Niknejad, M.M. Abedi, G.H. Liaghat, M.Z. Nejad, Absorbed energy by foam-filled quadrangle tubes during the crushing process by considering the interaction effects, Arch. Civ. Mech. Eng. 15 (2015) 376–391. [9] S. Azarakhsh, A. Rahi, A. Ghamarian, H. Motamedi, Axial crushing analysis of empty and foam-filled brass bitubular cylinder tubes, Thin Wall Struct. 95 (2015) 60–72. [10] L.N.S. Chiu, B.G. Falzon, D. Ruan, S. Xu, R.S. Thomson, B. Chen, W. Yan, Crush responses of composite cylinder under quasi-static and dynamic loading, Compos. Struct. 131 (2015) 90–98. [11] M. Shariatpanahi, A. Masoumi, A. Ataei, Optimum design of partially tapered rectangular thin-walled tubes in axial crushing, Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf. 222 (2008) 285–291. [12] A. Niknejad, S.M. Elahi, S.A. Elahi, S.A. Elahi, Theoretical and experimental study on the flattening deformation of the rectangular brazen and aluminum columns, Arch. Civ. Mech. Eng. 13 (2013) 449–464. [13] M. Mahdi Abedi, A. Niknejad, G. Hossein Liaghat, M. Zamani Nejad, Theoretical and experimental study on empty and foam-filled columns with square and rectangular cross section under axial compression, Int. J. Mech. Sci. 65 (2012) 134–146. [14] A. Alavi Nia, J. Haddad Hamedani, Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries, Thin Wall Struct. 48 (2010) 946–954. [15] X. Zhang, H. Zhang, Experimental and numerical investigation on crush resistance of polygonal columns and angle elements, Thin Wall Struct. 57 (2012) 25–36. [16] L. Aktay, B.H. Kröplin, A.K. Toksoy, M. Güden, Finite element and coupled finite element/smooth particle hydrodynamics modeling of the quasi-static crushing of empty and foam-filled single, bitubular and constraint hexagonal- and squarepacked aluminum tubes, Mater. Des. 29 (2008) 952–962. [17] M. Zarei Mahmoudabadi, M. Sadighi, A study on the static and dynamic loading of the foam filled metal hexagonal honeycomb – theoretical and experimental, Mater. Sci. Eng.: A 530 (2011) 333–343. [18] M.E.C.B. Mehmet, A. Guler, The effect of geometrical parameters on the energy absorption characteristics of thin-walled structures under axial impact loading, Int. J. Crashworthines 15 (2010) 377–390. [19] A. Ghamarian, H.R. Zarei, M.A. Farsi, N. Ariaeifar, Experimental and numerical crashworthiness investigation of the empty and foam-filled conical tube with
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading Jinwu Xiang, Jianxun Du
MARK
⁎
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Electron microscopy Aluminum alloys Failure Finite element method
Honeycomb structures are widely used in automotive and aerospace applications because of their outstanding characteristics of high strength and light weight. In this paper, a new honeycomb structure named as bionic honeycomb thin-walled structure (BHTS) which filled the column in different way inspired by the internal structure of the ladybeetle is proposed. The energy absorption characteristics of two kinds of BHTSs have been investigated comparing an original honeycomb structure with the same type of material under axial impact loading using nonlinear finite element software LS-DYNA. Dynamic loading has been carried out under the weight of 500 kg and the speed of 10 m/s. The results show that the energy absorption characteristic of BHTS which filled columns on its walls is better than that filled columns in its walls. Then the parameter studies in energy absorption of BHTS-2 have been carried out. It is found that energy absorption performance of BHTS-2 is best when the filled column number is 6 and diameter is 8 mm.
1. Introduction Nowadays, thin-walled structures with various cross-sectional geometries are widely used as energy absorbers in aeronautics and astronautics applications because of their low price, simple manufacture technology and higher energy absorption efficiency. Many relevant works have been carried out using combinations of theoretical researches [1], numerical simulations [2,3] and experimental studies [3–5]. Different cross-sectional shapes of the single thin-walled tube have significant differences on the energy absorption characteristics. Several cross-sectional figures such as hexagon, octagon, 12-sided and 16-sided star have been already studied experimentally [6]. The results revealed that the increase of the number of inward corners showed a notable change in energy absorption. More tubes with different shapes such as square tubes [7,8], circular tubes [9,10], rectangular tubes [11–13], pyramidal tubes [14], hexagonal tubes [15–17] and conical tubes [18–20] have been investigated widely. Two kinds of creative configurations including pentagon and cross section with different materials have also been studied [21]. Another novel cross-sectional shapes was proposed, which combines the square section and circular section [22]. A new method has been proposed to enhance energy absorption characteristic of structure by adding corners in the cross-section of the tube. Several kinds of multi-corner thin-walled columns used this way have been tested experimentally [23]. Some parametric studies of
⁎
Corresponding author. E-mail address: [email protected] (J. Du).
http://dx.doi.org/10.1016/j.msea.2017.04.044 Received 1 March 2017; Received in revised form 8 April 2017; Accepted 11 April 2017 Available online 12 April 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
the longitudinally grooved square tubes under axial crushing have been carried out recently. It is found that the grooves could obviously increase the specific energy absorption of the structures [24–27]. Bitubular thin-walled column is another high-performance energy absorption structure. A wide variety of bi-tubular thin-walled column design has been reported in the literature. Several geometry parameters of bitubular tubes have been numerically investigated, including radial distance of concentric cylindrical tubes [28], the shape of the inner tubes and the location of diaphragms [29]. The simulation results showed that the efficiency of energy absorption could be improved by introducing interlayer to the tubes. Many foam-filled bi-tubular circular tubes have been investigated under axial loading and the parameter studies such as cross-sectional configurations and loading conditions have been carried out [9,30,31]. Rabczuk et al. [32] have proposed a homogenization method for sandwich structures consisting of two plates interlaced with beams and shells in a periodic, lattice structure. It could achieve a significant reduction in computation and modeling time for the analysis of sandwich structures by this computational method. They also have developed a simplified method for estimating the impulsive load in sandwich structures submerged in water due to a dynamic wave loading that accounts for fluid-structure interaction [33]. More previous studies have focused on the thin-walled structures and conventional honeycombs, while relatively less works have been done on the bionic honeycomb structures. However, because of the
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A. dichotoma elytra is shown in Fig. 2(e).
extremely low densities, the conventional honeycomb cell walls buckle easily under axial impact loading, which limits axial energy absorption capacity. It is found that the sandwich walls with core struts in honeycomb structures have superior mechanical properties to that with solid walls in conventional honeycomb structures [34]. In this paper, the energy absorption capability of this bionic honeycomb thin-walled structure (BHTS) were analyzed to reveal pathways to structures with superior characteristics [35]. The elytra of beetle possesses the characteristics of light weight and impact resistance because of thin-walled tube exists in the elytra's honeycomb structure [36–38]. A novel bionic integrated honeycomb plate has been designed based on internal structure of beetle elytra [39,40]. The shear and compressive mechanical properties of this bio-mimetic structure made of composite materials have been studied experimentally [41,42]. The bionic honeycombs' material components processing good performances have also been obtained by experimental tests [43]. However, the existing forms and geometric parameters of the thin-walled tubes which could make a significant effect on crashworthiness performance have been seldom researched. In this paper, two kinds of filling modes of thin-walled columns were studied, which named as Bionic Honeycomb thin-walled Structure (BHTS). The BHTS imitating the structural characteristic of elytra from different species of beetles were investigated under axial impact loading using finite element software LS-DYNA. The energy absorbing characteristics of different filling methods were compared and the BHTS with good performance was put forward. In addition, the effects of design variables of the filling tube such as filling density and filling tube diameter were studied on BHTS numerically.
2.2. Description of the beetle-based BHTS By imitating the inside structural characteristics of beetle elytra, two different forms of BHTSs were designed, as shown in Fig. 3(b) and (c). The bionic honeycomb structure (BHS) in Fig. 3(a) is entirely composed of honeycombs. The BHTS-1 in Fig. 3(b) is composed of honeycombs and circular tubes, while the circular tubes are all in the center of honeycombs. The BHTS-2 in Fig. 3(c) is also composed of honeycombs and circular tubes, however, the circular tubes are on the wall of honeycombs. In order to investigate the energy absorption performances of the different forms of the BHTSs, the equivalent crosssectional size of different components (i.e. honeycomb and tube) and the same length of the BHTSs are obtained. 2.3. Material properties of bionic structure The single-wall tubes were prepared using aluminum alloy AA6063 T6. The specific alloy has a density ρ=2.7×103 kg/m3, a Young's modulus E=68.2 GPa, the initial yield stress σy=162 MPa, the ultimate stress σu=192 MPa, and Poisson's ratio υ=0.3 (see Table 1) [44]. The tubes were modeled with the MAT_24 material law in LS-DYNA971. Because the aluminum alloy was considered insensitive to the strain rate, the strain rate was ignored. The fracture behavior of the aluminum alloy was neglected during these analyses [45]. 2.4. Structural crashworthiness criteria Four indicators are used to define the crashworthiness performance of the BBTS. The first indicator to estimate the energy absorption capabilities of the structure is the special energy absorption (SEA) defined as the ratio of the total energy EA absorbed by a structure to its mass M [46]:
2. Beetle-based BHTS 2.1. The internal structural characteristics of beetles' elytra Beetles are a group of insects which have the elytra to protect their bodies. Figs. 1 and 2 show two kinds of beetles (i.e. Coccinella septempunctata and Allomyrina dichotoma) which all have the elytra. The adult C. septempunctata ladybeetle was used as shown in Fig. 1(a). There are many honeycombs in the internal structure of its elytra, as shown in Fig. 1(b). In each honeycomb structure, there is a hollow column structure, as shown in Fig. 1(c) and (d). Due to the internal structure of C. septempunctata is quite complicated, the model of its structure is proposed, as shown in Fig. 1(e). The irregular honeycombs are green, while the hollow columns are yellow. The adult A. dichotoma beetle was used as shown in Fig. 2(a). Unlike the inside structure of C. septempunctata, in A. dichotoma elytra the hollow columns are on the wall of honeycombs, as shown in Fig. 2(b). Fig. 2(c) and (d) are the microstructure of hollow column. The schematic of internal structure of
SEA =
EA M
(1)
The area under the force-displacement curve represents the amount of absorbed energy EA [47]:
EA =
∫0
d
F(x)dx
(2)
Where d is the axial crushing displacement and F denotes the axial crushing force. For an energy absorption structure, a high value of crash load efficiency (CLE) is expected [48]:
CLE =
MCF ×100% MIF
(3)
Fig. 1. Internal structure of elytra: (a) The adult C. septempunctata ladybeetle, (b) the microscopy of internal structure of elytra, (c) the tubular structure in the elytron, (d) the internal hollow structure of the tube and (e) schematic of the internal structure of C. septempunctata elytra. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
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Fig. 2. Internal structure of elytra: (a) The adult A. dichotoma beetle, (b) internal structure of elytra filled with thin-walled tubes, (c) the tubular structure in the elytra, (d) the internal hollow structure of the tube and (e) schematic of C. septempunctata elytra [40].
Fig. 3. The cross-section of three different structures: (a) bionic honeycomb structure (BHS), without tubes, (b) bionic honeycomb-tubular structure (BHTS-1), tubes between walls, (c) bionic honeycomb-tubular structure (BHTS-2), tubes on the walls. Table 1 Mechanical properties of aluminum alloy material of bionic honeycomb structures. Density (kg/ m3)
Young's modulus (GPa)
Yield stress (MPa)
Ultimate stress (MPa)
Poisson's ratio
2700
68.2
162
192
0.3
Where MIF represents the peak force in the force versus displacement curve under the axial impact. The mean crush force (MCF) for a given deformation can be obtained as [49]:
EA MCF = d
Fig. 4. Schematic of the calculation finite element model with axial force.
The commercial software CATIA V5R20 is used to create the solid models representing the structures. Hypermesh 12.0 is used as preprocessor to impart the axial impact conditions, material properties, boundary conditions and meshing. The solver from the explicit nonlinear finite element software LS-DYNA is employed for the simulations; post-processing is treated using the softwares of Hyperview 12.0 and Hypergraph 12.0. Fig. 5 shows the curves related to the crushing force versus displacement for the triangular bi-tubular tube with five different mesh
(4)
3. Numerical simulation 3.1. Finite element modeling Due to the cross-sectional area of impactor is larger than that of membrane, membrane has a slight influence on mechanical properties of the whole structure [50]. To better investigate the impact resistance and energy absorption characteristics of the honeycombs with different configurations, the membrane on both sides of honeycomb structure is not considered in the numerical model. A scheme representing the structures' loading conditions is shown in Fig. 4. The bottom of the tube is clamped to the fixed bottom plate. The impactor and the fixed bottom plate are set as rigid bodies. A 500 kg rigid impactor with a initial velocity (v=10 m/s) is used to simulate the axial loading on the tubes. An automatic contact setup is used in the numerical simulation to consider the contact caused by the deformation of the tubular wall during crushing. The point-surface contact algorithm is adopted to consider the contact between the BHTS and the rigid wall. The dynamic and static friction coefficients during contact are set at 0.2. To avoid a zero energy deformation mode and volumetric locking a stiffness-based hourglass control and a reduced integration are used. The material failure of the aluminum alloy tube is neglected.
Fig. 5. Crushing force versus displacement curve of BHTS with different mesh sizes.
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Fig. 8. The crushing force versus displacement of different bionic honeycomb structures.
Fig. 6. Comparison of force versus displacement curves between experiment and simulation.
3.3. Comparison of energy absorption characteristics of three kinds of bionic structures densities. The error provided by the models which comprised by the element sizes of 1.5×1.5 mm and 2.0×2.0 mm is quite small, and the two mesh sizes show to provide sufficient accuracy to describe the crushing process. To reduce the computational cost, the mesh size of 2.0 mm×2.0 mm has been adopted for all the following studies.
The initial crushing forces of three bionic structures all reach a peak at the same displacement, then drop rapidly in varying levels. The maximum peak value of BHTS-2 is between BHS and BHTS-1, as shown in Fig. 8. Obviously, the mean force of the BHTS-1 and BHTS-2 are higher than that of BHS and the difference of BHTS-1 and BHTS-2 is not apparent. The energy absorption efficiencies of BHTS-2 and BHTS-1 are very closed, and obviously both higher than BHS, as shown in Fig. 9. The progressive collapse of three bionic structures are shown in Fig. 10. In order to better compare the energy absorption properties of bionic structures quantitatively, parametric data of numerical simulation are listed in Table 1. Table 1 shows that the SEA of BHTS-2 is 35.97% higher than that of BHS and 24.52% higher than that of BHTS-1 respectively; Compression force efficiency of BHTS-2 is 34.50% higher than that of BHS and 21.56% higher than that of BHTS-1, respectively. So comparing either the SEA or the CFE, the BHTS-2 is better than BHS and BHTS-1.
3.2. Validation of the FE model Lee et al. [51] have carried out experiments for thin-walled square columns under the axial impact loading. In their experiments they adopted aluminum AL6063 thin-walled extruded tubes with length of 200 mm. The weight of the cross head was 40 kg, and the impact velocity was 7.02 m/s. To validate our FE models, we have first reproduced the same types of empty single thin-walled square tubes with the same sizes and axial impact loading conditions, and compared our results with the experimental data of Lee et al. Figs. 6 and 7 show the comparisons between the experiments and the simulations. Fig. 7 shows that the collapse mode reproduced by the numerical simulation matches quite well the one from the experiment. Moreover, the curve of the crushing force versus displacement produced by simulation agrees well with the one from the experiments. These results validate our FE modeling approach for the subsequent use in evaluating the crushing performance of the BHTSs.
3.4. Parametric study of BHTS-2 Due to energy absorption properties of BHTS-2 is better than that of BHS and BHTS-1, the further study of BHTS-2 was carried out. The parameters of columns on the honeycomb wall have an important influence on the energy absorption characteristics of the BHTS-2. Therefore parameter analysis has a great significance on crashworthiness of BHTS-2. In this paper, a range of parametric studies with different column number n and column diameter d were investigated on
Fig. 7. Comparison of deformation patterns of thin-walled structure between experiment and simulation.
Fig. 9. The energy absorption versus displacement of different bionic honeycomb structures.
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Fig. 10. Progressive collapse of different BHTSs.
energy absorption performance. Then the parametric studies of the thickness and height of the BHTS-2 were carried out by numerical analysis. In this research, the thickness of honeycomb wall is the same as the thickness of columns.
Table 2 The results of numerical simulations on the energy absorption performance.
3.4.1. Influence of the number of columns Based on the numerical simulation data, the curves of energy absorption versus displacement are plotted in Fig. 11. It is obvious that the energy absorption characteristics increase gradually. It is clear that the energy absorption enhanced with the increase of the column numbers. When the column number is one, the absorbed energy is the lowest, while the columns are six, the absorbed energy is the highest. It is also demonstrated that the filling of columns enhances the energy absorption ability of BHTS-2 (Table 2). Table 3 summarizes the numerical data for BHTS-2 with different column numbers. The SEA values of structures increase gradually, while the SEA value of BHTS-2 filled with five columns is similar to that of BHTS-2 filled with six columns. The compression force efficiency of BHTS-2 is also enhanced with the increasing of column numbers.
Structures
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
BHS BHTS-1 BHTS-2
35.8532 56.7891 59.5184
62.9781 90.1557 77.7283
1.1137 1.7436 1.8185
0.0468 0.0671 0.0562
23.7970 25.9850 32.3576
56.9296 62.9900 76.5724
Table 3 Energy absorbing characteristics of axial crushing of BHTS-2 with different column numbers. n
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
1 2 3 4 5 6
39.4646 43.0154 45.3182 48.5125 51.8795 53.3719
63.4687 66.5581 68.3852 69.2712 72.1187 73.7120
1.2128 1.3196 1.3898 1.4883 1.5843 1.6222
0.0478 0.0494 0.0501 0.0513 0.0524 0.0535
25.3724 26.7125 27.7405 29.0117 30.2347 30.3215
62.1796 64.6283 66.2690 70.0327 71.9362 72.4060
show stepped increase with the diameter growth. When the diameter of column was 10 mm, and the energy absorption ability is close to that which diameter is 8 mm, This may be due to mutual influence of the columns which diameter is 10 mm, then caused the reduction of the energy absorption effect of the structure. Table 4 summarizes the numerical data for BHTS-2 with different column diameters. When the diameter of column is in the range of 2–8 mm, the SEA of BHTSs increase gradually. When the diameter of
3.4.2. Influence of the diameter of columns The diameter of the column has a significant influence on the energy absorbing properties of the BHTS under axial loading. In this study, the diameter of column ranges from 2 mm to 10 mm, and the interval is 2 mm. The internal absorption of the BHTSs increases monotonously with tube diameter. Fig. 12 shows that the energy absorption ability of large diameter has very difference from the small diameter. When the column diameter in the range of 2–8 mm, the SEA of the structures
Fig. 11. The energy absorption versus displacement of different numbers of columns.
Fig. 12. The energy absorption versus displacement of different diameters of columns.
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Table 4 Energy absorbing characteristics of axial crushing of BHTS-2 with different column diameters. d
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
2 4 6 8 10
41.6427 47.7482 52.6816 59.5184 60.9948
65.3939 70.1193 73.7079 77.7283 80.7089
1.2747 1.4631 1.6222 1.8185 1.8688
0.0482 0.0508 0.0535 0.0562 0.0588
26.4460 28.8011 30.3214 32.3576 31.7823
63.6798 68.0957 71.4735 76.5724 75.5738
Fig. 14. The energy absorption versus displacement of different heights.
characteristics of BHTS-2, crushing of BHTS-2 is simulated by changing the height h between 50 mm and 200 mm. Fig. 14 shows the energy absorption characteristics as the height h of BHTS-2 changes. By changing the height between 50 mm and 150 mm, the internal energy absorbed increase significantly. For the case of h equals to 200 mm, there is an obvious difference in the displacement versus internal energy curve when crushing is carried out to 50 mm, as shown in Fig. 14. The bucking of thin-walled tube of BHTS-2 results in a reduction of the energy absorption characteristic. Table 6 summarizes the numerical simulation data for BHTS-2 with different heights. When the height of BHTS-2 increased from 50 mm to 150 mm, the SEA values of BHTS-2 decrease gradually while the CFE values of that increase in the range of 30% and 50%. The values of SEA and CFE are all lowest when the height equals to 200 mm, which means that the energy absorption characteristics of this case is the worst between 50 mm and 200 mm.
Fig. 13. The energy absorption versus displacement of different thickness.
the column is 10 mm, the SEA value of the structure is lower than that of diameter is 8 mm. This phenomenon is consistent with the internal energy absorption effect. When the diameter is in the range of 2–8 mm, the compression force efficiency of BHTS is also enhanced with the increasing of column diameters. When the diameter is 10 mm, the compression force efficiency is reduced to 31.78 kJ/kg.
4. Conclusion and discussion 3.4.3. Influence of the thickness To investigate the effect of the thickness of the BHTS-2, a parametric study is conducted by changing the thickness between 0.5 mm and 3 mm. Fig. 13 shows the energy absorption versus different thickness of BHTS-2. It is obvious that the energy absorption characteristics increase gradually with the increase of the thickness. The results show that the BHTS-2 having the thickness equals to 3.0 mm has the maximum energy absorption characteristic. When the thickness of BHTS-2 is 0.5 mm, the energy absorption is the lowest. There is a close relationship between thickness and energy absorption. Table 5 summarizes the numerical data for BHTS-2 with different thickness. When the thickness of BHTS-2 increased from 0.5 mm to 3 mm, the SEA and CFE of BHTS-2 increase gradually. When the thickness of the BHTS is 3 mm, the SEA and CFE of the BHTS-2 is the best. For other cases of different thickness, the SEA values are more than 50 and the CFE values are more than 60%.
In this paper, two kinds of energy absorbed structures named as bionic honeycomb thin-walled structure (BHTS) with different column filled methods was proposed inspired by internal structure of beetle elytra. Then comparing the SEA and CFE between the column filled structure and column unfilled structure using nonlinear finite element code LS-DYNA. According to the numerical results, it can be found that the SEA of BHTS-2 is 35.97% higher than BHS and 24.52% higher than BHTS-1, respectively. Compression force efficiency of BHTS-2 is 34.50% higher than that of BHS and 21.56% higher than that of BHTS-1, respectively. It was discovered that energy absorption characteristics of the bionic structure which filled columns on its walls is better than the other two kinds of structures. The column diameter and the column number relationship to energy absorption ability are also investigated based on the BHTS-2. The highest energy absorption efficiency was found when the filled column number is 6 and diameter is 8 mm. A parametric study is conducted to investigate the effect of the thickness and height on energy absorption characteristics of BHTS-2. It is observed that by changing thickness t between 0.5 mm and 3.0 mm, the total absorbed energy and energy absorptive effectiveness increase gradually. By changing the height between 50 mm and 200 mm, the
3.4.4. Influence of the height In order to study the height h effect on energy absorption Table 5 Energy absorbing characteristics of axial crushing of BHTS-2 with different thickness. t/mm
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
0.5 1 1.5 2 2.5 3
22.0516 56.6273 94.4121 136.175 185.458 241.113
33.4953 77.7134 125.492 173.251 230.377 289.169
1.6890 3.5191 5.3624 7.5743 9.8739 12.6631
0.0311 0.0584 0.0834 0.1092 0.1346 0.1591
54.3086 60.2585 64.2974 69.3617 73.3574 79.5921
65.8349 72.8668 75.2335 78.5998 80.5019 83.3813
Table 6 Energy absorbing characteristics of axial crushing of BHTS-2 with different heights.
288
h/mm
Pm/kN
Pmax/kN
Eint/kJ
m/kg
SEA (kJ/kg)
CFE/%
50 100 150 200
71.0598 68.4270 65.7443 22.6013
229.7936 190.323 138.6764 78.0931
3.6094 6.6682 8.7722 4.8634
0.056 0.112 0.168 0.224
64.4535 59.5375 52.2154 21.7116
30.9233 35.9531 47.4084 28.9414
Materials Science & Engineering A 696 (2017) 283–289
J. Xiang, J. Du
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