Numerical investigation of the energy absorption ...

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Numerical investigation of the energy absorption characteristics of a fan-shaped deployable energy absorber ab

ab

D.Y. Hu , K.P. Meng

c

& Z.Y. Yang

a

Department of Aircraft Airworthiness Engineering, School of Transportation Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China b

Airworthiness Technologies Research Center, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China c

Department of Aircraft Structure Strength, The Solid Mechanics Research Centre, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China Published online: 13 Jan 2014.

To cite this article: D.Y. Hu, K.P. Meng & Z.Y. Yang (2014) Numerical investigation of the energy absorption characteristics of a fan-shaped deployable energy absorber, International Journal of Crashworthiness, 19:2, 126-138, DOI: 10.1080/13588265.2013.876147 To link to this article: http://dx.doi.org/10.1080/13588265.2013.876147

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International Journal of Crashworthiness, 2014 Vol. 19, No. 2, 126–138, http://dx.doi.org/10.1080/13588265.2013.876147

Numerical investigation of the energy absorption characteristics of a fan-shaped deployable energy absorber D.Y. Hua,b, K.P. Menga,b and Z.Y. Yangc* a Department of Aircraft Airworthiness Engineering, School of Transportation Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China; bAirworthiness Technologies Research Center, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China; cDepartment of Aircraft Structure Strength, The Solid Mechanics Research Centre, Beijing University of Aeronautics and Astronautics, Beijing, P.R. China

Downloaded by [Beihang University] at 18:39 24 March 2014

(Received 6 September 2013; accepted 13 December 2013) With the limitation of available space inside the aircraft and automotive structure, it is difficult to effectively improve the performance of energy absorber. To overcome this drawback, a fan-shaped deployable energy absorber (FDEA) is developed in this paper and numerical simulation is carried out to study the crushing characteristics of FDEA under quasi-static loading condition. The calculated results show that the crush pattern of FDEA can be divided into three categories: progressive symmetrical collapse, global bending collapse and mixed modes, which have different contribution to the energy absorption. Systematic parametric studies are also implemented with consideration of deployment angle, hinge radius and wall thickness of middle cells. Results indicate that the energy absorption decreases as the deployment angle increases, but increases with hinge radius and wall thickness. In addition, in consideration of practical application, a finite element model of multi-block is built and compared with single-block model. The specific energy absorption of multi-block is calculated to be higher than that of single-block, though the energy absorption is slightly lower. The outcome of this study can provide a design reference for the use of FDEA as energy absorbers in applications. Keywords: fan-shaped; deployable; crashworthiness; energy absorption; finite element; collapse

Notation L Length of the cell DL Stroking distance, i.e. crushed length of the cell Fpeak Peak load after crushing initiated E Absorbed energy, obtained by integrating crushing load with respect to stroking distance Fm Mean crush load, obtained by dividing the absorbed energy by the stroking distance, E/DL SAE Specific energy absorption (SAE), SAE ¼ E/M, where M is the total mass a Oblique load angle, axial direction of each cell relative to crushing direction t Cell wall thickness c Wall width R Hinge radius b Deployment angle 1. Introduction Over half a century, structure crashworthiness has gradually become one of the most important requirements in the automotive and aviation industries. Better protection against injuries in the case of potentially survivable accidents has attracted increasing attention. Consequently,

*Corresponding author. Email: [email protected] Ó 2014 Taylor & Francis

based on the crashworthy design principles [20,34], in order to improve occupant safety for the car and aircraft mishaps, special consideration is taken into account in the design of some critical structural components with lightweight energy absorber (EA), such as bumpers [22], aircraft frame [7], landing gear [3,10], energy absorbing seat [15,19] or subfloor [30], and so on. When the crash occurred, the EA can dissipate the impact of kinetic energy by progressively deforming and attenuating crash loads transmitted on occupants to an allowable level for human body. A considerable amount of literatures have been published about various types of EA [6,8,9,11,14,18,23,24,28,31,33] and suggested that the energy absorption capability can actually be assessed by crushing load and stroking distance. To improve energy absorption capability, two optimisation methods can be adopted: one is to increase crushing load (as shown in Figure 1(a)), and the other is to increase its stroking distance (as shown in Figure 1(b)). It is clear that the best choice is the combination of the longest stroking distance and the largest permitted crushing force. However, an EA is usually used inside the cars and aircrafts and the available space for EA is generally very limited. At present, most of the studies on the EA are focused

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Figure 1. Schematic diagram for two methods of improving absorbed energy: (a) the method of increasing load to improve absorbed energy and (b) the method of increasing stroking distance to improve absorbed energy.

on developing a variety of ways to increase crushing load at a confined stroking distance [2,6,8,9,11,14,18,23,24,28, 31–33]. Guler et al. [11] studied the effects of cross-sectional parameters of conventional thin-walled straight and conical shell on the crush behaviours. It was found that absorbed energy can be promoted by adjusting wall thickness and semi-apical angle of the conical shell to an optimum value. Salehghaffari et al. [28] used two new structural design solutions of rigid ring and groove to improve the collapse modes and crashworthiness characteristic of circular tube under axial loading. Zhang and Yu [33] investigated the effect of internal pressure on energy absorption of inflatable thinwalled circular tube. It was shown the crushing force of the tube can be improved by increasing internal pressure and the interaction between pressure and tube wall. Similar results were also obtained by using water [23] and metal foam [2,13,32] as fillers. In addition, compared to traditional metal structures, composite materials show higher energy absorption capabilities for their merits of high specific strength and outstanding designability. Hu et al. [14] carried out extensive experimental tests to investigate the energy absorption characteristics of brittle fibre/epoxy hybrid composite tubes and found composite materials can be enhanced by reasonable adjusting of the fibre hybridisation. In addition, fibre types, laminate configuration, geometry imperfection and so on [9,18,24,31], are also studied in detail. However, it should be pointed out that the crushing load cannot be increased without limit. On one hand, the crushing load should be just below the human tolerance and structure failure strength to avoid occupant injury and structure damage. On the other hand, EA cannot be triggered during water landing due to the high crushing load, which may cause more severe consequences than hard landing [4,25]. For above reasons, it is a big challenge to improve the effectiveness of the EA by only increasing the crushing load. In contrast, NASA sponsored a fundamental research to develop a novel externally deployable EA (DEA) to attenuate loads in the event of a helicopter crash in order

to overcome the limitation of stroking distance [5,16,21]. DEA is an expandable composite honeycomb like an airbag system. It has a flexible hinge which can allow the honeycomb to be packaged and stowed until needed for deployment during an emergency. Therefore, DEA can provide relatively large available stroke distance. The fullscale crash test and numerical simulation were both carried out and the results demonstrated that DEA has excellent energy absorption capabilities [5,16,21]. DEA is promised to be an effective EA to improve structure crashworthiness. In present paper, a fan-shaped DEA (FDEA) is proposed based on the concept of NASA’s DEA. Systematic numerical studies are conducted with consideration of the effects of thickness, hinge radius and deployment angle on the energy absorption characteristics. In addition, the model is expanded to multi-block FDEA, and comparison is also conducted with one-block FDEA model.

2. Geometry and finite element model 2.1. Geometry model of FDEA The schematic diagram of a typical design for the FDEA is shown in Figure 2, in which it can be observed that FDEA can be deployed from packaged status to fully deploying. The section of the cell becomes to be square when fully deploying, and hexagonal shape for partly deploying. The FDEA, fabricated of aluminium alloy 5A06-T5, is a deployable honeycomb structure like metal air bag. Figure 3 shows a representative cell with a hinge between adjacent walls. The hinge is designed with locking ability by using ratchet wheel mechanisms, as illustrated in Figure 4. FDEA is not allowed to be stowed again at the locking position. The FDEA can be secured to the fuselage outer skin with two rails mounted kneel beams. In addition, air pressure effects on the deployment system can be practically challenged. Several actuation methods have been proposed to deploy the FDEA,

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Figure 2. Schematic diagram and deploying process of the design of a fan-shaped deployable energy absorber.

including mechanical, pneumatic and mechanical/pneumatic combinations [17]. A simplest method is to apply tension by gathering the wire on an electromotor driven spool.

Figure 3. Geometry parameters of a single cell with hinges.

Figure 4. Schematic diagram of the design of hinge mechanism.

2.2. Finite element model of FDEA Numerical studies are performed using the finite element (FE) code ABAQUS, which is a general-purpose nonlinear FE analysis code. This software provides a large selection of element types, material models and automated contact procedures, which is suitable for the simulation of quasi-static crushing. Emphasis has been placed on the effect of geometric parameters on the crushing characteristic and energy absorption capability of FDEA. An FE model is developed using a pre-processing software HYPERMESH, as shown in Figure 5, in which three components are modelled: a typical FDEA structure, rigid fuselage and rigid impact surface. Details of the numerical model are summarised as following: The model of the FDEA is simulated by using a fournode shell element of designation S4R [1], which is interpreted as a quadrilateral element with four nodes, suitable for large strain analyses. Five integration points are used



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Figure 5. The FE model of FDEA under quasi-static crushing. Note: a is the oblique load angle; b is the deployment angle; crushing movement is vertical direction.

through the shell thickness to model bending. The hinge, an important component, is simplified by using a beam element of B31 with a circular profile. After convergence validation conducted, an element size of 5 mm is found to produce suitable results to effectively capture the collapse modes of the FDEA cells. A total of 22,560 elements are used for the FE model of FDEA.

The material is aluminium alloy (5A06-T5) with the following mechanical properties: Young’s modulus, E ¼ 7:0 e þ 4 MPa; material density, 2:7 e 3 g=mm3 and Poisson’s ratio, u ¼ 0:3. To accurately define the post-yield material response in the FE model, the true stress versus strain curve of the aluminium alloy is obtained by a standard tensile test, as shown in Figure 6. The data points of stress versus plastic strain are picked from the stress–strain curve, as illustrated in Table 1. The aluminium alloy is assumed to be isotropic strain hardening, and the effect of strain rate is neglected in the quasistatic analyses. Table 1. Stress–strain hardening data (based on the true stress– strain curves). Yield stress (MPa)

Figure 6. The true stress–strain curves of 5A06-T5 aluminium.

223.9 247.4 275.7 301.6 324.0 345.2 359.3 378.1

Plastic strain 0 0.007 0.016 0.028 0.040 0.055 0.067 0.1


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The explicit general contact in ABAQUS [1] is used to simulate the self-contact of the shell elements to capture the proper folding and compaction of the FDEA. The fuselage and impact surface is modelled as a discrete rigid surface since its properties have no significant effects on the analysis results. The base of FDEA is fully fixed to the fuselage using a tied constraint. A surface-to-surface contact between each rigid surface and the FDEA cell walls is defined using the finite sliding ‘penalty’ based contact algorithm with contact pairs and ‘hard’ contact. The coefficients of friction are assumed to be 0.1 for all the contact definition. The impact surface is constrained in all degrees of freedom. The rigid fuselage surface is constrained to translate vertically over a prescribed velocity of 1 mm/ms to simulate the quasi-static vertical crushing. The crushing load can be obtained by calculation of the reaction force of the fuselage.

In addition, the influences of initial imperfections on collapse modes and initial peak load are considered. As real distribution of imperfections is difficult to be obtained, the imperfections are introduced as a linear superposition of buckling eigenmodes using an eigenvalue buckling analysis in ABAQUS/Standard before the nonlinear crushing analysis performed in ABAQUS/Explicit [1]. 3. Results and discussion 3.1.

Simulation results

The explicit integral method is used to study the quasistatic crushing characteristic of FDEA. Figure 7 shows the typical deformed process of FDEA, in which it can be observed that the cell walls deformed by progressive buckling. Initial buckling takes place at the middle cells of the FDEA (as shown in Figures 7(b) and 7(c)), i.e. the

Figure 7. Typical crushing process of the FDEA under quasi-static crushing.



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Figure 8. Detailed sketch of crushing mode.

initial contact locates between middle cells and rigid impact surface. The peak load is then reached. The adjacent cells are crushed successively as they have a distance away from the impact surface, as shown in Figures 7(d)– 7(f). Three typical crush zones can be found in Figure 8: zone 1 where progressive symmetrical collapse dominates, zone 2 where there is the transition from progressive to global bending collapse and zone 3 where global bending collapse dominates the crushing response. For the middle cells, the collapse mode exhibits a

Figure 9. The curve of crushing load versus stroking distance.

representatively symmetrical collapse mode [26], as shown in Figure 8. In contrast, the adjacent cells show a tendency to slide sideways slightly and their collapse modes are quite complex, which can be attributed to the fact that the middle cells are subjected to the axial compressive loading, while the adjacent cells are subjected to the oblique loading. A similar mode can also be observed on the bending collapse of rectangular tubes leading to the decrease of the crushing load and energy absorption capability [12]. Furthermore, with the increase of the oblique load angle, a global bending (Euler) collapse can also be

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Table 2. Geometry parameter and numerical simulation results. Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14

L (mm)

c (mm)

t (mm)

b

R (mm)

Fpeak (KN)

Fm (N)

E (J)

SAE ð104 J=kgÞ

300 300 300 300 300 300 300 300 300 300 300 300 300 300

80 80 80 80 80 80 80 80 80 80 80 80 80 80

1 1 1 1 1 1 1 1 1 0.5 1.5 2 2.5 1

30 45 60 75 90 90 90 90 90 90 90 90 90 90

1 1 1 1 1 1.5 2 2.5 3 1 1 1 1 1

187.1 170.5 141.8 130.0 129.1 138.1 152.7 180.6 232.2 69.4 155.8 215.5 304.2 328.3

168.7 162.2 148.5 130.5 113.2 125.6 138.2 160.8 183.7 44.5 157.0 216.6 293.5 320.3

42172.4 40548.4 37140.4 32626.4 28304.6 31404.4 34568.7 40209.5 45917.5 11123.6 39242.0 54164.0 73388.6 80076.1

2.70 2.60 2.38 2.10 1.81 1.87 1.87 1.94 1.97 1.34 2.15 2.59 3.10 2.10


Note: Case 5 is a baseline result with fully deploying; case 14 is multi-block result.

observed at the outermost cells in Figure 8, which have less contribution to the energy dissipation. However, outermost cells of FDEA may benefit under oblique impact condition, such as car side collision [12,27] and helicopter rollover accident [29]. In these cases, outermost cells become primary energy absorbing components as the oblique load angle is decreased. Figure 9 shows the crushing load versus stroking distance curve, which is obtained from the reaction force of rigid fuselage with respect to its displacement. The peak load is achieved in the initial state of buckling deformation and then the load values oscillate between local peak loads and local minimum loads. After the stroking distance beyond 50 mm, the crushing load is gradually increased. When the stroking distance reaches 250 mm, the FDEA is compacted and the crushing load is increasing sharply. Mean crushing load (as plotted in Figure 9) is obtained by dividing the absorbed energy by the stroking distance. It can be observed that the difference between the peak load and mean crushing load is not significant.

This can be attributed to the fact that the side cells are crushed successively with the increase of oblique load angle, leading to relatively steady crushing load. To guide the design of FDEA structure, it is necessary to understand the effect of geometry parameters on the crushing characteristic of FDEA structure. Actually as for thin-walled tubes, the influence of section geometry parameters, such as thickness, length, web width and so on, already have been thoroughly studied in previous studies [12,27]. Instead, the emphasis of this paper is focused on effects of deployment angle, hinge radius and wall thickness of middle cells. Furthermore, a numerical model of multi-block FDEA is developed and then the comparison is made with one-block FDEA model. A total of 14 cases are analysed, with results summarised in Table 2.

Figure 10. The FE model of FDEA with the deployment angle b from 30 to 90 in increments of 15 .

Figure 11. The collapse modes of the FE model of FDEA with the deployment angle b from 30 to 90 in increments of 15 .



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Figure 12. The curve of crushing load versus stroking distance with the deployment angle b from 30 to 90 in increments of 15 .

3.2.

Effect of deployment angle on energy absorption capability of FDEA To investigate the effect of deployment angle on energy absorption capability, five FE models are developed with the angle varying from 30 to 90 in increments of 15 , as shown in Figure 10. The section shape of a single cell is changed from re-entrant regular hexagon to square when deployment angle is varied. The deformed modes of each model are depicted in Figure 11. It can be observed that all models exhibit similar progressive crushing modes and show a tendency to slide sideways slightly in horizontal direction. Figure 12 shows the crushing load versus stroking distance curve. It can be seen from Figure 12 that the crushing load of 30 is higher than that of other angles. The relationship between the deployment angle and specific energy absorption can be fitted with a parabolic curve, as shown in Figure 13. For a small deployment angle, most of the cells subjected to approximate axial load exhibit symmetrical collapse mode, while only the less outermost cells show global bending collapse mode due to oblique load, and vice versa [27]. From the numerical results, it could be concluded that the deployment angle could significantly affect the energy absorption capability in quasi-static crushing condition. Based on the above analysis, it is reasonable to adopt a small deployment angle in design. However, for real crash conditions, loading is seldom purely axial in nature, rather comprises oblique loads. Consequently, the deployment

angle of 90 with better omnidirectional capability is recommended to achieve a compromising performance of energy absorption. 3.3.

Effect of hinge radius on energy absorption of FDEA

The hinge is one of the most important components in the FDEA structure. It is also crushed accompanying with cell walls buckling, with the large plastic deformation in

Figure 13. The effect of the deployment angle b on specific energy absorption.


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Figure 14. The curve of crushing load versus stroking distance with hinge radius from 1 to 3 mm in increments of 0.5 mm.

Figure 15. The effect of hinge radius on specific energy absorption.


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radius. The specific energy absorption (SAE) increases linearly with the increase of hinge radius, as shown in Figure 15. However, a peak load occurs for the radius of 3.0 mm, which is negative to the EA. Therefore, the optimisation design of FDEA is to balance the energy absorption and peak load.

3.4.


Figure 16. The schematic diagram of thickness variation of FDEA.

the hinge contributing to the energy absorption. Moreover, stiffness of the hinge may also lead to higher peak load, which may result in structure failure. To investigate the effect of hinge dimension on energy absorption capability, five FE models are developed with the radius of hinge adjusting from 1 to 3 mm in increments of 0.5 mm. The crushing load versus stroking distance curve is illustrated in Figure 14, in which it can be observed that the crushing load increases with the hinge

Effect of middle cell thickness on energy absorption of FDEA As mentioned in Section 3.1, the middle cells of FDEA first contact with the rigid impact surface and produce a symmetrical collapse mode, absorbing a large portion of energy. Based on this reason, it is effective to improve the energy absorption capability by adjusting the geometry parameters of middle cells. Figure 16 indicates the FE model with wall thickness variation. The wall thickness of middle cells is varied from 0.5 to 2.5 mm in increments of 0.5 mm. Figure 17 shows the crushing load versus stroking distance curve. It can be observed the crushing load is improved significantly with the increase of the thickness. The results of SAE versus wall thickness are also depicted in Figure 18. It can be found that SAE increases linearly with the thickness. Therefore, the wall thickness of middle cells plays an important role in the energy absorption capability of FDEA.

Figure 17. The curve of crushing load versus stroking distance with thickness from 1 to 3 mm in increments of 0.5 mm.


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Figure 18. The effect of thickness on specific energy absorption.

3.5.

Effect of multiple cells on energy absorption of FDEA The above analysis is carried out about the crushing characteristics of one-block FDEA. In fact, a multi-block structure is commonly used in real structures. Figure 19 shows the FE model of multi-block FDEA. To avoid data confusion, the representation of single-block and multiblock FDEA are also depicted in Figure 19. The three-single-block model indicates model consisted of three separated blocks, and the crushing load and absorbed energy can be obtained by trebling those of single-block.

Figure 19. The FE model of multi-block FDEA.

The deformed mode under quasi-static crushing condition is illustrated in Figure 20, in which symmetrical collapse can be observed in most of the cells. Figure 21 shows the crushing load comparison between multi-block model and three-single-block. It can be found that the crushing load of multi-block model is slightly lower. Same trend can also be found in the comparison of energy absorption. The crushing load for the multi-block model is steadier than that of three-single-block model. Comparison on the specific energy absorption shows that the multiblock is higher than three-single-block as shown in


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Figure 20. The collapse mode of multi-block.

absorption capability, such as the deployment angle, hinge radius and wall thickness of middle cells. Based on the numerical results, it is found that these factors play an important role in affecting energy absorption characteristics of the FDEA as following:

Figure 21. Comparison of crushing load between multi-block and single-block.

Table 2. These can be attributed to the interaction between multiple blocks. 4. Conclusions In the present paper, a design of an external FDEA is proposed to overcome the stroking distance limitation of EA in the event of automotive and aircraft crash. An FE model is developed to study the crushing characteristic of FDEA using a general nonlinear FE software ABAQUS. The crush pattern of FDEA can be divided into three typical crush zones, with zones 1, 2 and 3 exhibiting progressive symmetrical collapse, progressive to global bending collapse transition, and global bending collapse, respectively. The collapse modes can lead to different contribution to the absorbed energy and crushing load. Furthermore, to guide a design of FDEA structure, parametric studies are also carried out to investigate the influence of the geometry parameters on the energy

(1) Both the crushing load and specific absorbed energy decrease with the increase of the deployment angle. The relationship between the deployment angle and specific absorbed energy can be fitted by a parabolic function. (2) The crushing load and specific absorbed energy is improved with the increase of hinge radius from 1.0 to 3.0 mm. The SAE increases linearly with the increase of hinge radius. (3) The crushing load and specific absorbed energy are improved significantly with the increase of the wall thickness of middle cells. The SAE increases linearly with the thickness. In addition, a FE model of multi-block FDEA is set up and the comparison is made with single-block FDEA model. The results demonstrate that the crushing load and absorbed energy of the multi-block are slightly lower than those of three-single-block model. The crushing load for the multi-block model is steadier than that of three-singleblock model, and the specific energy absorption of the multi-block model is higher, which can be attributed to the interaction between multiple blocks. It should be noted that only axial load condition is investigated in this paper, while for oblique load condition, the phenomena may be different. Therefore, it is highly desirable to develop an adjustable deployment mechanism allowing FDEA to become an adaptive EA, which can be deployed with various deployment angles according to complicated load conditions. But the design of deployment mechanism is a very challenging work due to its complex and still needs to be studied in future.

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Funding The work described in this paper is financially supported by the National Natural Science Foundation of China under [grant number 11032001], [grant number 11102017], [grant number 11002011]. The authors wish to gratefully acknowledge these supports.


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