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NumericalInvestigationofSteppedConcentricCrashTubesSubjectedtoAxialImpact:TheEffectsofNumberofTubes

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IstanbulTechnicalUniversity

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Numerical Investigation of Stepped Concentric

Crash Tubes Subjected to Axial Impact : The Effects

of Number of Tubes

Fatih Usta

Istanbul Technical University

Faculty of Aeronautics and Astronautics

Maslak, Istanbul, 34469, Turkey

ustaf@itu.edu.tr

Zana Eren

Istanbul Technical University

Faculty of Aeronautics and Astronautics

Maslak, Istanbul, 34469, Turkey

erenza@itu.edu.tr

Halit S. Türkmen

Istanbul Technical University

Faculty of Aeronautics and Astronautics

Maslak, Istanbul, 34469, Turkey

halit@itu.edu.tr

Zafer Kazancı

Aerospace Engineering Department

Turkish Air Force Academy

Yesilyurt, Istanbul, Turkey

z.kazanci@hho.edu.tr

Zahit Mecitoğlu

Istanbul Technical University

Faculty of Aeronautics and Astronautics

Maslak, Istanbul, 34469, Turkey

mecit@itu.edu.tr

Abstract—The purpose of this study is to examine the energy

absorption characteristics of stepped concentric crash tubes

subjected to an axial impact load. The stepped concentric tubes

with circular cross section are analyzed numerically by using LS-

DYNA. The total mass and volume are kept constant when the

number of tubes is increased. As the number of concentric tubes

is increased, it is observed a smooth transition of the peak forces

during the impact. Also increasing the number of tubes reduces

the maximum peak force and leads to a reduction of the initial

peak force due to lower wall thickness of the tubes.

Keywords—crash tubes, impact loading, crashworthiness,

energy absorption, peak force

I. INTRODUCTION

Impact phenomenon can be encountered in many field

such as automobile accident, debris impact on spacecraft vehicle, impact on a protection shield, etc. Because of having various types of this phenomenon, researchers have tried several ways to take precaution and reduce its harmful effects on people and vehicles. Traffic accidents kill an estimated 1.27 million people per a year globally according to a report

Support for this work has been provided by the Scientific and Technological Research Council of Turkey under Project Number 113M395.

(TUBITAK).

published by WHO [1]. Crash tubes have an important role to reduce harmful effects of accidents. Numerous studies have been done to enhance the crashworthiness characteristics of crash tubes at dynamic and quasi-static velocities.

In space, vehicles might be subjected to impact of meteoroids and debris particles or the loads acting during landing. Design of spacecraft shield gains more importance for protection of spacecraft’s structural integrity and crews’ health. Researchers generally focus on hypervelocity impact phenomenon due to being more common encountered problem. Bashurov et al. investigated the effects of debris impact to the spacecraft shield in between 500-6500 m/s velocity using numerical and experimental methods [2]. Various mass and dimensions of debris are tested, analyzed and obtained good agreement between experimental and numerical results. Taylor et al. test some samples of primary external wall structure which are exposed to the hypervelocity impact and search the ballistic limit of 47 mm thick structure [3]. They demonstrate that ballistic limit depends on not only impact energy but also projectile density.

There are several studies based on experiences of different geometrical parameters such as thickness and cross section of the crash box. Yamashita et al. investigate the different types of polygonal crash boxes and the effects of wall thickness and plastic hardening rate of material on the crush behavior [4]. As

39978-1-4799-7697-3/15/$31.00 ©2015 IEEE

long as corners of cross-sections increase, these results in raising crash strength of tube. It is observed apparently at smaller initial wall thicknesses. Also, strength of circular cross section is higher than square cross section tubes. Nia and Hamedani search crashworthiness characteristics of different geometrical shapes (cylindrical, square, hexagonal, conical, and hourglass) and different thicknesses (1 and 2 mm) of composite tubes under quasi-static loading conditions [5]. Conical circular tubes give higher SEA (specific energy absorption) and Ppeak (peak force) values than the other standard geometrical profiles. Abramowicz and Jones investigate the circular and square steel crash tubes under dynamic and static loading [6], [7]. Karagiozova and Jones search dynamic effects of cylindrical shells testing different types of materials numerically to show the influence of the material properties, shell geometry, boundary conditions and loading techniques on buckling and energy absorption [8]. It is shown that the fold length increases with shell thickness.

Steel, aluminum and composite materials are the most common used materials for crash boxes. Ince et al. investigate the energy absorption characteristics of hybrid crash tubes saving of %17.5 for total weight [9]. Fyllingen et al. study the influence of the element type and formulation for modeling aluminum profiles under axial loading using LS-DYNA and ABAQUS software program [10]. Kazancı and Bathe show that ADINA based on implicit time integration method can be a better alternative in such cases of quasi static impact loading on crash tubes [11]. Ergen investigates the ideal design of stepped concentric crash tubes. He searches energy absorption characteristics of crash tubes having different cross sections (square, circular and hexagonal) [12]. Goel examines the comparison of empty and foam filled single tubes with bi-tubular and tri-tubular empty and foam filled tubes. As a result of this examination, it is seen that energy absorption and final configuration of tubes can be improved [13].

The purpose of this study is to examine the energy absorption characteristics of stepped concentric crash tubes subjected to an axial impact load. The peak forces and the total deflection are also investigated. The stepped concentric tubes considered here have different lengths and different diameters. However, the total mass and volume are kept constant. The area of the impacting object is taken as greater than the maximum tube cross sectional area to prevent passing the impacting object through the tube hole.

II. PROBLEM DEFINITION

A. Problem Definition

The impact analyses of the four different types of stepped concentric crash tubes are performed. The samples are enumerated with the number of “n=1, 2, 3, 4” which have three, six, nine and twelve tubes, respectively. To observe the crashworthiness characteristics of these samples in same condition, all of them are limited to same total volume and same total mass. Total mass of the tubes considered here are 9.2033, 9.2075, 9.2049 and 9.2028 g, respectively and total volumes of four samples are kept constant. Maximum mean radius is equal to 10 mm and maximum length is 30 mm.

TABLE I. DIMENSIONS OF SAMPLE 1 AND 2

n=1 n=2

Tube

no

r_mean

(mm)

L

(mm)

t

(mm)

r_mean

(mm)

L

(mm)

t

(mm)

1 6 30 1 5 30 0.5

2 8 25 1 6 28 0.5

3 10 20 1 7 27 0.5

4 8 25 0.5

5 9 23 0.5

6 10 21 0.5

TABLE II. DIMENSIONS OF SAMPLE 3 AND 4

n=3 n=4

Tube

no

r_mean

(mm)

L

(mm)

t

(mm)

r_mean

(mm)

L

(mm)

t

(mm)

1 6 30 0.3 4.5 30 0.25

2 6.5 28.5 0.3 5 29.5 0.25 3 7 28 0.3 5.5 29 0.25 4 7.5 27 0.3 6 28.5 0.25 5 8 26 0.3 6.5 28 0.25 6 8.5 25 0.3 7 27 0.25 7 9 24 0.3 7.5 26 0.25 8 9.5 23 0.3 8 25 0.25 9 10 22.5 0.3 8.5 24 0.25

10 9 23 0.25 11 9.5 22 0.25 12 10 21 0.25

Other sizes are chosen in a way not to change total mass. Thicknesses of samples are determined as 1, 0.5, 0.3 and 0.25 mm, respectively. Tube lengths are reduced gradually from interior to exterior. All dimensions of samples are shown in Table 1 and 2.

B. Material Properties

All specimens are made of same material. The material uses here AL6063 which is a strain rate insensitive material, has

young modulus E= 78 GPa and density =2700 kg/m3. Material properties are listed in Table 3 and stress-strain curve shown in Fig. 1 is used to determine the material properties. Tubes are modeled with MAT024 PIECEWISE LINEAR PLASTICITY material model in LS-DYNA.

C. Finite Element Models

It is preferred to use mostly the explicit solver of the nonlinear finite element code LS-DYNA. So in this study, numerical analysis is made by using LS-DYNA software program. All tubes are modeled by using Belytschko-Tsay shell elements. After comparing the analysis of triple concentric tubes at different mesh qualities, optimum element size is defined as 0.4x0.4 mm. The bottom of all tubes is clamped and a rigid wall is defined 1 mm far from the top of the longest tube. It is crashed with an initial velocity in the axial direction. Mass of rigid wall is 100 g, and its initial velocity is 50 m/s. RIGIDWALL-PLANAR MOVING

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TABLE III. MATERIAL PROPERTIES OF AL6063

Density

kg/m3

Young

Modulus

(GPa)

Poison

Ratio

Yield

stress

(MPa)

Ultimate

tensile stress

(MPa)

2700 78 0.33 241 263

Fig. 1. Stress-Strain curve for AL6063

Fig. 2. Schematic of geometry with an example model and rigid wall

FORCES is used as model of the impactor. An example schematic for sample 1 and rigid wall are plotted together in Fig. 2.

In Fig. 3, It can be seen that front and section view of finite element models of four samples. AUTOMATIC SINGLE SURFACE contacts are identified for each sample, because they have possibility of lapping after deformation. Also, AUTOMATIC SURFACE TO SURFACE contacts are defined between surfaces of tubes. The static and dynamic friction coefficients are chosen as 0.2 for each contact definition.

III. RESULTS AND DISCUSSIONS

The amount of deformation, peak forces and energy

variation during impact are obtained from numerical alaysis in

order to characterize the crash response of the samples.

Appearences of all samples after deformation are

demonstrated in Fig 4. The deflections are 10.5902, 11.6217,

10.5847 and 11.1106 in milimeters and listed in Table IV. The

total deformation is almost obtained same for all samples. The

number of tubes did not effect the total deformation.

Kinetic and internal energy graphics of samples are taken

from LS-DYNA and shown in Fig. 5. Results demonstrate that

almost all kinetic energy is converted into internal energy

which is equal to 125 J. Every sample gives same results due

to partial deformation. The force variation of four samples is

Fig. 3. Front and top view of models: a) 3 concentric tube b) 6 concentric tube

c) 9 concentric tube d) 12 concentric tube

plotted with respect to time in same graphic shown in Fig. 6,

7, 8 and 9. Also, initial peak forces and maximum peak forces

are listed in Table IV. It can be seen that maximum peak

forces decreases and time of analysis takes longer except the

second sample. Maximum peak forces of samples 1 to 4 are

27597, 27699, 21634 and 19358 N, respectively.

Although the first and second values are too close, there are

noticeably reductions between other values. Besides, transition

from one peak force to the next peak force occurs smoother,

while the number of tubes is increased. Difference between

first and second sample can be result from the distances

between tubes of first sample. Because, it is seen that interior

tube of first sample doesn’t have contact with the next tube.

On the other hand, all tubes of other three samples can be

attained eachother, so they have surface to surface contact.

Contact algrotihm can bring about these small difference.

In addition to this, Fig. 6,7,8 and 9 give relationship

between initial peak forces which are 10772, 4141, 3171 and

3011 N. There is an appearent reduction between samples. It

can be resulted from the reduction in thicknesses of cross

section.

Fig. 4. Isometric, front and top view of all samples after deformation

processes a) n=1, b) n=2, c) n=3 and d) n=4

41

Fig. 5. Kinetic and internal energy of each sample

Fig. 6. Force versus time for sample 1

Fig. 7. Force versus time for sample 2

Fig. 8. Force versus time for sample 3

Fig. 9. Force versus time for sample 4

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TABLE IV. RESULTS

n

Impact

Mass

(g)

Velocity

(m/s)

Deflection

(mm)

Initial

Peak Force

(N)

Max. Peak

Force

(N)

1 100 50 10.5902 10772 27597

2 100 50 11.6217 4141 27699

3 100 50 10.5847 3171 21634

4 100 50 11.1106 3011 19358

IV. CONCLUSION

In this study, stepped concentric tubes made of AL6063 with circular cross section are analyzed numerically by using LS-DYNA. Total mass and volume of all samples are restricted to observe efficiency of crashworthiness properties such as peak crushing force and energy absorption capability. To see the energy absorption capability of samples, there is a need of analysis at higher impact energy.

As the number of concentric tubes is increased, it is observed a smooth transition of the peak forces during the impact. Also increasing the number of tubes reduces the maximum peak force and leads to a reduction of the initial peak force due to lower wall thickness of the tubes. It can reduce the inertial effect of peak forces on vehicles and people. These results show that increasing the number of stepped concentric tubes improves its crashworthiness properties in terms of peak forces. Furthermore, minimizing the size of concentric tubes can prevent or reduce the probability of penetration of impact objects.

Acknowledgment

Support for this work has been provided by the Scientific and

Technological Research Council of Turkey under Project

Number 113M395.

References [1] W.H. Organization, “WHO global status report on road safety 2013:

supporting a decade of action. 2013,” World Health Organization.

[2] V.V. Bashurov, G.V. Bebenin, G.V. Below, Y.N. Bukharev, V.I. Zhukov, A.G. Ioilev, N.V. Lapichev, A.L. Mikhailov, G.S. Smirnov, Y.A. Fateev and G.P. Schlyapnikov, “Experimental modelling and numerical simulation of high-and hypervelocity space debris impact to spacecraft shield protection,” International Journal of Impact Engineering, 1997. 20(1): p. 69-78.

[3] E.A. Taylor, M.K. Herbert, D.J. Gardner, L. Kay, R. Thomson and M.J. Burchall, “Hypervelocity impact on spacecraft carbon fibre reinforced plastic/aluminium honeycomb," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 1997. 211(5): p. 355-363.

[4] M. Yamashita, M. Gotoh, and Y. Sawairi, “Axial crush of hollow cylindrical structures with various polygonal cross-sections: Numerical simulation and experiment,” Journal of Materials Processing Technology, 2003. 140(1): p. 59-64.

[5] A.A. Nia, and J.H. Hamedani, “Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries,” Thin-Walled Structures, 2010. 48(12): p. 946-954.

[6] W. Abramowicz and N. Jones, “Transition from initial global bending to progressive buckling of tubes loaded statically and dynamically,” International Journal of Impact Engineering, 1997. 19(5): p. 415-437.

[7] W. Abramowicz and N. Jones, “Dynamic progressive buckling of circular and square tubes,” International Journal of Impact Engineering, 1986. 4(4): p. 243-270.

[8] D. Karagiozova and N. Jones, “Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact,” Thin-Walled Structures, 2001. 39(7): p. 583-610.

[9] F. İnce, H.S. Türkmen, Z. Mecitoğlu, N. Uludağ, İ. Durgun, E. Altınok, H. Örenel, "A numerical and experimental study on the impact behavior of box structures," Procedia Engineering, vol. 10, pp. 1736-1741, 2011.

[10] Ø. Fyllingen, O.S. Hopperstad, A.G. Hanssen, M. Langseth, “Modelling of tubes subjected to axial crushing,” Thin-Walled Structures, 2010. 48(2): p. 134-142.

[11] Z. Kazancı and K.J. Bathe, “Crushing and crashing of tubes with implicit time integration,” International Journal of Impact Engineering, 2012. 42: p. 80-88.

[12] T. Ergen, “Cok kademeli carpışma kutularında kutu şeklinin soğurulan enerjiye etkisinin incelenmesi,” Undergraduate Thesis, Aeronautical Engineering, Istanbul Technical University, 2013

[13] M.D. Goel, “Deformation, energy absorption and crushing behavior of single-, double- and multi-wall foam filled square and circular tubes”, Thin-Walled Structures, 2015: 1-11.

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