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2009 Tech Science Press SDHM, vol.098, no.1, pp.1-17, 2009

Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing

H. Ghasemnejad1, H. Hadavinia1,2, D. Marchant1and A. Aboutorabi1

Abstract: In this paper the crashworthiness ca-

pabilities of thin-walled corrugated crash boxes

in axial crushing relative to ﬂat sidewall boxes

from the same material are investigated. In order

to achieve this, various design of corrugated alu-

minium alloy 6060 temper T4 crash boxes were

chosen and their axial crushing behaviour under

impact loading was studied by developing a the-

oretical model based on Super Folding Element

theory and by conducting ﬁnite element analysis

using LS-DYNA in ANSYS. From the theoretical

and FE analysis the crush force efﬁciency, the spe-

ciﬁc energy absorption and the frequency and am-

plitude of ﬂuctuation of the dynamic crush force

of the corrugated crash boxes were calculated and

the results were compared with the reference un-

corrugated model. It was shown that the corru-

gated crash boxes have advantages of a lower ini-

tial collapse force, a lower crush force ﬂuctuation

frequency and amplitude relative to a ﬂat sidewall

box.

Keyword: Crashworthiness; Corrugation; Im-

pact; Aluminium; Theoretical analysis

Nomenclature

Amean area

Cwidth of extrusion

CFE crush force efﬁciency

ddepth of corrugates

D,qmaterial constants in

Cowper-Symonds equation

ˆ

Especiﬁc energy absorption

Fforce

Fmax initial maximum collapse force

1Faculty of Engineering, Kingston University, SW15 3DW,

UK

2Corresponding Author. Email:

h.hadavinia@kingston.ac.uk (H. Hadavinia), Tel: +44 20

8547 8864 Fax: +44 20 8547 7992

Fmd mean dynamic force

Hwall thickness

Lfree length of specimen

mmass of specimen

M0fully plastic bending moment

Nnumber of corrugations

SE stroke efﬁciency

Umembrane membrane energy

Ubending bending energy

Vimpact velocity

wcrush distance

ν

Poisson’s ratio

σ

0ﬂow stress

σ

yyield stress

σ

uultimate tensile strength

δ

magnitude of trigger

δ

0amplitude of trigger

ρ

density

λ

pitch distance

κ

effective crush distance

1 Introduction

The optimization technique plays an important

role in the crashworthiness design of automo-

tive structures. The use of a suitable geometrical

shape and material could give great payoffs such

as a lower weight, higher stiffness and a more

stable energy absorption process [Alkolose et al

(2003)]. Crashworthiness is deﬁned as the abil-

ity of a restraint system or component to with-

stand forces below a certain level and to reduce

the damage caused in those cases involving exces-

sive dynamic forces [Mahdi et al (2006)]. For the

automotive designers, it is a challenge to ﬁnd an

optimum design to maximise the safety. McGre-

gor et al. [McGregor et al (1993)] have stated the

principal stages involved in the design process of

an impact member as shown in Figure 1. Based on

this design philosophy, initially a preliminary ge-

ometry for the crash box is chosen, and then three

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2009 Tech Science Press SDHM, vol.098, no.1, pp.1-17, 2009

performance aspects forgood crashworthiness de-

signs practice, i.e. the collapse mode, average

collapse force and maximum collapse force, are

evaluated. The preliminary geometry can then be

modiﬁed to enhance the performance of the crash

box and the cycle of the design will be repeated

until the optimum design is obtained.

Assess Collapse

Mode

Assess Average

Collapse Force

Assess Maximum

Collapse Force

Select

Geometry

Design

Cycle

Figure 1: Design cycle for impact members [Mc-

Gregor et al (1993)].

The ﬁrst modern studies on the dynamic inelas-

tic behaviour of structures commenced about ﬁfty

years ago with the introduction of the rigid-plastic

idealisation [Jones (2003)]. Nowadays, car man-

ufacturers use numerical simulations to study the

crash behaviour of various vehicle structures. By

using numerical modelling, not only the num-

bers of prototypes testing are reduced but also

the numerical simulations enable new design and

materials to be evaluated without extensive and

expensive testing. These modelling also pro-

vide a benchmark platform for evaluating the new

knowledge gained through experiments and im-

provements in the theories of materials and struc-

tures [Langseth et al (1999)]. The majority of the

research and developments relating to crash zone

are to do with energy absorption by the frontal

and bending deformation of the metal structure

[Transportation Research Board and National Re-

search Council (1996)]. In principal, an efﬁcient

crashworthy design system should be able to: (i)

absorb the impact kinetic energy in a controlled

manner, (ii) after an impact, a sufﬁcient survival

space remain for the occupants, and (iii) the forces

and accelerations experienced by the occupants in

the vehicle are minimised and remain at a survival

level. The total energy absorption depends on

the governing deformation phenomena of all con-

stituent parts of the structure such as thin-walled

tubes, cones, frames and sections [Yamakazi and

Han (2000); Singace (1997) Mahdi et al (2003);

Abosbaia et al (2003)].

The structural crashworthiness requirement is

generally met by the use of crumple zones. These

zones exist in the front and rear of the car and

protect the passenger safety cell. In a crash,

these crumple zones absorb the vast majority of

the crash energy through plastic collapse. Jones

[Jones (1993)] has shown that an ideal energy

absorber should be lightweight and maintain the

maximum allowable retarding force throughout

the greatest possible crush displacement while

keeping the resulting axial crushing forces ﬂuc-

tuation frequency and amplitude relatively low.

Singace and El-Sobky [Singace and El-Sobky

(1997)] studied the energy absorption character-

istics of axially crushed corrugated metal tube.

They found that, for a controlled behaviour of

an energy absorption device, corrugated tubes

would be a favourable choice. Seitzberger et al.

[Seitzberger et al (2000)] have concluded that the

lower mean force for tubular member will be ad-

vantageous.

In this paper various corrugated aluminium alloy

6060 tempered T4 energy absorber square boxes

were designed and their effect on the crushing be-

haviour and crashworthiness were studied by de-

veloping a theoretical model based on Super Fold-

ing Element theory and by ﬁnite element software

LS-DYNA in ANSYS [Ghasemnejad et al (2007);

ANSYS documentation]. Parameters such as the

crush force efﬁciency, the energy absorption, the

stroke efﬁciency and the frequency and amplitude

of the resulting axial crushing force in each crash

box were obtained and the results were compared

with those from a ﬂat sidewall square crash box

hereafter referred to as the base model.

2 Design Aspect of Crash Box

There are three important parameters for the de-

sign of crash boxes. The ﬁrst is the crush force

efﬁciency (CFE) which is deﬁned as the ratio

between the maximum initial collapse force and

the mean dynamic force. An ideal absorber can

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Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing

3

exhibit a crush force efﬁciency of 100% with a

rectangular-shaped force-crush distance curve. It

means that initial collapse force and mean force

are equal but in practice the situation of a CFE

parameter equal to 1 is not achievable. The mean

dynamic force is a function of the impact velocity

while the mass of the striker has no noticeable in-

ﬂuence on it. The second important parameter is

the stroke efﬁciency (SE) which is the ratio of the

stroke (crushed distance) at the bottoming out to

the initial length of the absorber. High ratios in-

dicate efﬁcient use of the material. In such cases

the force-crush distance curves are cut at a point

where the force starts to increase steeply, and so

maximum displacement coincides with the stroke

length, and the deﬁnition of this cut-off point is

somewhat arbitrary. The reported stroke lengths

should be regarded only as approximate values.

The third parameter is speciﬁc absorbed energy

(ˆ

E) which is the area under the force-crush dis-

tance curve divided by the mass of the specimen.

Assuming that the contribution due to the elas-

tic deformation is negligible, the absorbed energy

can approximately be regarded as the energy dis-

sipated by plastic deformation.

In an impacted box, the force-crush distance curve

can be divided into three distinct regions as shown

in Figure 2. In region I, the force increases rapidly

and reaches a maximum (Fmax) before dropping.

In region II, the force ﬂuctuates around a mean

dynamic force (Fmd) while a series of folds form

successively in the tube so that a folded zone

grows progressively down the tube in a form of

mushrooming failure. In region III, all lobes touch

each other and the box stiffness to impacted ob-

ject increases and this will cause a rapid increase

in the force.

Generally, the speciﬁcation of the energy absorp-

tion component is dictated by the requirement of

the design e.g., the speciﬁcation for the struc-

tural design of a passenger carrying rail vehicle

ends by Railtrack [Railtrack Structural Require-

ments for Railway Group Standard (1994)] was

set at a minimum energy absorption of 1 MJ over

a distance not exceeding 1 m with a mean dy-

namic force of 3000 kN. Under these design re-

quirements the ideal energy absorber is a rectan-

gle with a mean dynamic force (Fmd) less than

3000 kN over a maximum allowable crush dis-

tance which absorbs the speciﬁed impact energy

as shown in Figure 2. Also in Figure 2 the crush-

ing behaviour of three possible realistic designs

are demonstrated. Case 1 design has the highest

initial maximum collapse force among the others

and hence it is discarded; though its Fmd is about

the ideal solution. Case 2 will absorb higher en-

ergy in the same crush distance but its mean dy-

namic force is higher than the ideal crush solu-

tion. Since biomedical loading caused by impact

will be experienced by the vehicle occupants, a

lower mean dynamic crush force is desirable as

long as the energy absorption criterion is satisﬁed.

In Case 3, initial collapse force is relatively low

and the mean crush force equal to the ideal crash

box which ﬂuctuates with low amplitude around

the ideal mean dynamic force. The amplitude of

ﬂuctuations in Case 3 is lower than Case 1. As

Case 3 satisﬁes all design requirements with least

minimum initial collapse force and least mean dy-

namic force with minimum amplitude of ﬂuctu-

ation about the mean force, it is the best design

amongst the designs presented in Figure 2.

3 Theoretical analysis of corrugated crash

box

The dynamic mean force for an uncorrugated

square box for a rigid-perfectly plastic material is

derived by Abramowicz and Jones [Jones (1993)]

as

Pm=13.05

σ

0H5

3C1

3n1+ (0.33V/CD)1

qo(1)

In the above equation because of strain rate in-

sensitivity of aluminium alloy, the strain harden-

ing effect is taken into account by assuming the

dynamic ﬂow stress is equal to static ﬂow stress

obtained from:

σ

0=

σ

y+

σ

u

2(2)

where

σ

yand

σ

uare yield stress, and ultimate ten-

sile strength of the box material, respectively.

A theoretical solution method (the so called Su-

per Folding Element method) for obtaining the

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2009 Tech Science Press SDHM, vol.098, no.1, pp.1-17, 2009

md

F

Force

Crush distance

Case 3

II

max

F

III

I

Ideal crush

Case 1

Case 2

Figure 2: Comparison of different scenario of force-crush distance curve during impact.

d

d

Ȝ /2

Ȝ /2

θ

θ

θ

θ

Ȝ

d

(a)

(b)

Corner

Ȝ

Ȝ

Figure 3: Presentation of dissipation in bending of a single corrugated unit with rotation angles.

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Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing

5

mean dynamic crush force in the axial pro-

gressive crushing of thin-walled square columns

was developed by Wierzbicki and Abramowicz

[Wierzbicki and Abramowicz (1983)]. In this

model by adopting a rigid-plastic material and

using the condition of kinematic continuity on

the boundaries between the rigid and deformable

zones, each corner is considered having three ex-

tensional/compressional triangular elements and

three stationary hinge lines. We extended this ap-

proach to the corrugated crash boxes.

From the energy balance of the system, for a

complete collapse of a single fold of corrugated

box, the external work done by compression of

the box has to be dissipated through the rota-

tional plastic deformation in bending and exten-

sional/compressional deformation of the mem-

brane walls, i.e.

2

λ

Fm

κ

=Ub+Um(3)

where

λ

is the corrugation pitch distance, Fmis

the mean force and

κ

≤1 is a correction factor for

effective crush distance. Uband Umare, respec-

tively, the energy dissipation in rotational bend-

ing and extension/compression due to the mem-

brane deformation. In the real structure, the cor-

rugated section isnever completely ﬂattened. The

effective crush distance is reported between 70-

75% of the folding wavelength in previous works

by Wierzbicki and Abramovicz [Wierzbicki and

Abramowicz (1983)]. In the present work, by

analysing the FEA results, the effective crush dis-

tance was found to vary linearly with the corruga-

tion pitch distance as

κ

=5.3

λ

+0.52 (4)

i.e. as the corrugation pitch distance decreases,

the effective crush distance also decreases and ap-

proach 0.52. In Eq. (4)

λ

is in meter.

The bending dissipated energy, Ub, was calculated

by summing up the energy dissipation at station-

ary hinge lines. In each corrugation unit, 6 hor-

izontal stationary hinge lines are developed, 3 at

the inner and 3 at the outer circumference (Figure

3a), hence

Ub= 3

∑

i=1M0

θ

iLc!extruded hinge line

+ 3

∑

i=1M0

θ

iLc!recessed hinge line (5)

where M0=2RH/2

0

σ

0tdt =

σ

0H2/4 is the fully

plastic bending moment of the ﬂange and

θ

is the

rotation angle at each hinge line. For simplicity, it

was assumed that the ﬂanges are completely ﬂat-

tened after the axial compression of 2

λ

(Figure

3b). In this situation, the rotational angles at the

hinge lines are

π

/2,

π

and

π

/2, respectively. The

Eq. (5) for dissipated energy in bending will sim-

plify to,

Ub=M0(2

π

LC1+2

π

LC2)(6)

whereLC1and LC2are the inner and outer circum-

ference of the corrugation.

H

Ȝ/4

Ȝ

45°

Corner line

Figure 4: Presentation of the membrane energy

dissipation in compression and extension.

The membrane dissipated energy, Um, during one

wavelength crushing in corner part was evaluated

by integrating the extensional and compressional

areas as shown in Figure 4,

Um=Z

S

σ

0H dS =

σ

0HNC1

2×

λ

4×

λ

4×8×2

=

σ

0H

λ

2NC

2(7)

where NCis the number of corners. For a square

corrugated unit NC=4.

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2009 Tech Science Press SDHM, vol.098, no.1, pp.1-17, 2009

0

50

100

150

200

250

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain

Stress (MPa)

True Engineering

Figure 5: Stress-strain curves for AA6060-T4.

0

10

20

30

40

50

0 20 40 60 80 100 120

Crush-distance (mm)

F (kN)

2x2 2.5x2.5 3x3 5x5

0

10

20

30

40

50

0 20 40 60 80 100 120

Crush-distance (mm)

F (kN)

NIP=3 NIP=5 NIP=9

(a)

(b)

Figure 6: Effect of (a) element sizes and (b) number of integration point on the force-crush distance be-

haviour.

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Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing

7

By substituting Eqs. (6) and (7) in Eq. (3), the

mean force is,

κ

Fm=

π

4

σ

0H2

λ

(LC1+LC2) +

σ

0H

λ

NC

4(8)

The mean force can be obtained by substituting

κ

from Eq. (4) in Eq. (8).

The static mean force obtained from Eq. (8) needs

to be corrected to take into account the dynamics

effect. This has been done according to the ratio

between dynamic and static progressive buckling

forces suggested by Jones [Jones (1993)],

Fmd

Fms = 1+0.33V

CD 1

q!(9)

The calculated dynamic mean forces obtained

from the above theoretical solution for all the

models are presented in Table 1. The discrepancy

between the theoretical results and FE results are

less than 3%.

4 Finite element studies

Nonlinear explicit ﬁnite element code

ANSYS/LS-DYNA was used to model the

axial crushing of the thin-walled aluminium

crash boxes. These energy absorbers were mod-

elled by the Belystchko-Lin-Tsay quadrilateral

four-node thin shell elements [Belytschko et al

(1984)]. These shell elements are available in the

element library of LS-DYNA. The Belystchko-

Lin-Tsay shell element is based on a combined

co-rotational and velocity-strain formulation

[Hallquist (1998)]. To simulate the quasi-static

condition, the constant velocity was applied to the

rigid striker. The real crushing speed is too slow

for the numerical simulation. The explicit time

integration method is only conditionally stable,

and therefore by using real crushing speed, very

small time increments was required to use. For

satisfying quasi-static condition, the total kinetic

energy has to be very small compared to the total

internal energy over the period of the crushing

process and also the crushing force-displacement

response must be independent from the applied

velocity.

4.1 Material modelling

In the present work, the crash boxes are made

from aluminium alloy with a Young’s modulus of

68.2 GPa, a yield stress of 80 MPa and a Poisson’s

ratio 0.3. The stress-strain relation of this material

is shown in Figure 3. The advantage of using alu-

minium in vehicle structure is reducing the weight

of the vehicle. It has been reported that savings in

the load-bearing structure of an aluminium vehi-

cle can be as much as 40–50% when compared to

steel. Aluminium alloys have approximately 1/3

the weight and 1/3 the elasticity modulus of steel,

and usually a lower strength. As an example, an

aluminium section with a 50% thicker wall rela-

tive to the same steel section have the same stiff-

ness but a lower weight [Meguid et al (2004)].

In LS-DYNA the aluminium was modelled by

a type 24 material which is deﬁned as MATE-

RIAL_PIECEWISE_LINEAR_PLASTICITY,

pertaining to the von Mises yield condition

with isotropic strain hardening, and strain rate-

dependent dynamic yield stress based on the

Cowper and Symonds model. The aluminium

alloy is known to be insensitive to high strain

rates and therefore strain rate effect was not

applied [Jones (2003)].

4.2 Sensitivity analysis of FE model

The sensitivity of the FE results to variation of el-

ement size, trigger position and the number of in-

tegration points (NIP) through the thickness was

studied to ﬁnd the optimum values of these pa-

rameters.

The effect of element sizes was studied by mod-

elling the base model using 2×2, 2.5×2.5, 3×3

and 5×5mm meshes. The trigger position was

located at C/8 (10mm from the top end of box)

and the NIP through the thickness was kept 3.

The results of force-crush distance of these mod-

els are compared in Figure 6a. The results show

that apart from 5×5mm coarse mesh, for the ﬁner

meshes from 2×2 to 3×3mm the results are very

similar and insensitive to element size.

Next the effect of NIP through the thickness was

studied on a model with element size of 2×2mm

and the same trigger position atC/8. NIP through

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2009 Tech Science Press SDHM, vol.098, no.1, pp.1-17, 2009

TP

L

C

Figure 7: Trigger position (TP) in the FE model

of the crash box at TP= C/16, C/8,C/4 and C/2.

the shell elements was varied at 3, 5 and 9. The

results are compared in Figure 6b and they are in-

sensitive to NIP in range of 3-9. Using higher in-

tegration points through the thickness increase the

computing cost and make the structure stiffer. For

further analysis NIP=3 is chosen.

The trigger position is shown in Figure 7. The

effect of trigger position at C/2 (40mm), C/4

(20mm), C/8(10mm) and C/16 (5mm) from top

end of box was investigated. The element size

of these models was 2×2mm and the NIP was

kept constant at 3. It was found that trigger po-

sition in the range of C/8 to C/2 from the top

end of box has no signiﬁcant effect on the re-

sponse of force-crush distance diagrams, (Fig-

ure 8a). In further study, the total length of

crash box was changed while keeping the element

size at 2×2mm with trigger position at C/8 and

NIP=3. The result shown in Figure 8b conﬁrmed

that the force-crush distance is not affected too

much by the total length of crash box. In con-

clusion, it is found that by choosing element size

between 2×2–3×3mm, trigger position between

C/8 (10mm) and C/2 (40mm) and NIP of 3 will

give an optimum FE parameters for modelling of

crash box. In the next part of this study an element

size of 3×3mm which gave lower CPU time in

comparison with other element sizes, trigger po-

sition of C/4 (20mm) with NIP=3 were chosen.

Using these parameters in our FE models, the

force-crush distance behaviour of the base model

is veriﬁed by comparing to those reported in

[Langseth et al (1999)] and [Zhang et al (2006)]

as shown in Figure 7. The discrepancy between

our base model and the results in [Langseth et al

(1999)] and [Meguid et al (2004)] were minimal.

There is no difference in mean dynamic force

and initial maximum collapsed force between the

models. Dynamic mean force obtained from the

FE result was also compared with the theoretical

solution given in Eq. (1). The calculated dynamic

mean force from the theoretical solution is 42 kN,

and from the FE analysis it is 47 kN, a difference

of 9%. The FE and theoretical results are com-

pared in Table 2.

4.3 FE modelling of corrugated crash box un-

der impact loading

The simulation of impact, especially at high im-

pact velocities requires very expensive equip-

ments such as a high speed impact machine, man-

ufacturing of specimens and a high-speed camera

to detect the crushing process which takes place

in fraction of a second. In this study ﬁnite ele-

ment simulation is used as an alternative method

to study the impact process.

A square tube under axial quasi-static or impact

condition can collapse in one of these distinct

crushing modes, symmetric mode, extensional

mode, asymmetric mixed mode or global buck-

ling during compression. Symmetric progressive

plastic buckling is the ideal crushing mode for

box like energy absorber. Extensive experimen-

tal studies [Jones (2003)] have shown that for the

combination of geometrical parameters, a sym-

metric progressive mode of collapse of a thin-

walled prismatic square column subjected to the

dynamic axial loading of an AA6060 aluminium

box regardless of the material temper condition

observed when 32 ≤C/H≤44.4. Furthermore,

the localisation of the lobes for temper T4 started

either at the impacted end of the specimens or at

the clamped support.

Four different corrugated models were studied. In

the ﬁnite element models, the free length of the

crash box was chosen at 310 mm with different

wall thicknesses while the total mass of all cor-

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Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing

9

Table 1: Comparison of the dynamic mean force from theoretical results and FE analysis for corrugated

crash boxes.

Model Wall Pitch Depth of WbWmFmd Fmd Error

thickness distance corrugates, (kJ) (kJ) (kN) (kN) %

H (mm)

λ

(mm) d (mm) FEA Theoretical

1 2.49 77.5 6 5.03 23.15 39 40.9 4.9

2 2.47 51.67 6 7.43 15.31 40 38.7 -3

3 2.34 25.83 6 13.34 7.25 42 42.3 0.7

4 2.20 19.38 6 15.71 5.1 44 45 2

0

10

20

30

40

50

0 20 40 60 80 100 120

Crush-distance (mm)

F (kN)

C /16 C /8 C /4 C /2

0

10

20

30

40

0 10 20 30 40 50 60 70 80 90 100

Crush distance (mm)

F (kN)

L310 L150

(b)

(a)

Figure 8: Effect of (a) trigger position and (b) the length of the crash box on the force-crush distance

behaviour.

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Table 2: Comparison of FE and analytical results of uncorrugated box under dynamic loading.

σ

0C H D[Singace and El-Sobky (1997)] q[Singace and El-Sobky (1997)] V Fmd (kN) Fmd (kN)

(MPa) (mm) (mm) (s−1) (m/s) FEA Analytical

120 80 2.5 6500 4 25 40 42

0

20

40

60

80

100

120

0 50 100 150 200 250

Crush-distance (mm)

F (kN)

Present analysis Base model [5]

1

1 2 3

4

4

2

3

0

10

20

30

40

50

0 20 40 60 80 100 120 140

Crush distance (mm)

F (kN)

Present analysis Base model [21]

1

4

3

2

1

2

3

4

Figure 9: Comparison of force-crush distance of the base model in the present study with those in [Langseth

et al (1999)] and [Zhang et al (2006)]. The inserts show von Mises stress distribution at various stages of

the impact.

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Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing

11

86

L=310

L=310 L=310

L=310

86

86 86

86

86

86

86

7474

74

74

λ

Model 1 Model 2

Model 3 Model 4

d

d

d

d

Figure 10: Isometric view of corrugated crash boxes (all dimensions in mm).

Table 3: Dimensions of the specimens.

Model Mean cross section Wall thickness Pitch distance Depth of corrugates,

(mm) H (mm)

λ

λ

λ

(mm) d (mm)

1 80×86 2.49 77.5 6

2 80×86 2.47 51.67 6

3 80×86 2.34 25.83 6

4 80×86 2.20 19.38 6

Base model 80×80 2.50 N/A -

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0

20

40

60

80

100

120

0 50 100 150 200 250

Crush distance ( mm )

F(kN)

Model 1 Base Model

23

4

1 4

2

3

1

Figure 11: Force-crush distance curve in Model 1 corrugated crash box. The inserts show von Mises stress

distribution at various stages.

0

20

40

60

80

100

120

0 50 100 150 200 250

Crush distance ( mm )

F(kN)

Model 2 Base Model

1

1

2

3

4

32

4

Figure 12: Force-crush distance curve in Model 2 corrugated crash box. The inserts show von Mises stress

distribution at various stages.

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0

20

40

60

80

100

120

140

0 50 100 150 200 250

Crush distance (mm)

F(kN)

Model 3 Base Model

1

2

3

4

1 2 3

4

Figure 13: Force-crush distance curve in Model 3 corrugated crash box. The inserts show von Mises stress

distribution at various stages.

0

20

40

60

80

100

120

0 50 100 150 200 250

Crush distance (mm)

F(kN)

Model 4 Base Model

4

4

1 2 3

1

2 3

Figure 14: Force-crush distance curve in Model 4 corrugated crash box. The inserts show von Mises stress

distribution at various stages.

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Model 1 Model 2

Model 3 Model 4

Figure 15: Symmetric collapse mode of corrugated crash boxes.

Table 4: Crashworthiness parameters of the corrugated models.

Model Fmax Fmd CFE SE ˆ

E

(kN) (kN) % % (kJ/kg)

1 105 39 37 80 14.6

2 100 40 40 80 15.1

3 74 42 57 79 15.8

4 64 44 69 79 16.6

Base model 113 47 41 80 17.6

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40

60

80

100

120

10 20 30 40 50 60 70 80

Pitch distance (mm)

Initial collapse force (kN)

Model 1

Model 3

Model 2

Model 4

35

40

45

50

10 20 30 40 50 60 70 80

Pitch distance (mm)

Mean dynamic force (kN)

Model 1

Model 3

Model 2

Model 4

Figure 16: Variation of initial maximum collapse force (Fmax) and mean dynamic force (Fmd ) with pitch

distance (

λ

).

rugated boxes were kept constant as in the base

model, i.e. 0.664 kg. The design information for

the four corrugated models and the base model are

presented in Figure 10 and Table 3. The speci-

mens were impacted at a velocity of 25 m/s with

a block of 50 kg which was modelled as a rigid

body. All degrees of freedom of the crash boxes

were ﬁxed at the bottom end and all the rotational

degrees of freedom were ﬁxed at the upper end

to avoid unrealistic deformation modes. The con-

tact between the striker and the specimens was

modelled using a nodes impacting surface with a

friction coefﬁcient of 0.25 to avoid lateral move-

ments. To account for the contact between the

lobes during deformation, a single surface contact

algorithm without friction was used. This contact

algorithm is used to prevent the penetration of the

deformed box boundary by its own nodes. In ac-

cordance with the mesh sensitivity studies in pre-

vious part, an element size of 3×3 was found to

be a suitable size which gave satisfactory results.

In the base model, a trigger mechanism with sine-

wave formulation [Langseth et al (1999)] was in-

serted on the sidewalls of the specimen at 130mm

from the end of the box to initiate the symmetric

deformation mode.

5 Results and discussion

The effects of corrugations on the crushing be-

haviour of crash boxes were investigated by ex-

tracting the force-crush distance behaviour from

FEA for each model. The force-crush distance re-

sults obtained from FEA simulations for all cor-

rugated models are shown in Figures 11-14 to-

gether with various stages of deformation of the

crash box during the deformation. In these Fig-

ures the behaviour of the base model has been

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2009 Tech Science Press SDHM, vol.098, no.1, pp.1-17, 2009

shown with dash line for comparison. In all sim-

ulations, the progressive symmetric deformation

mode was found for all specimens at impact as

shown in Figure 15. The FEA results show that

by decreasing the corrugation pitch distance, the

initial maximum collapse force (Fmax) decreases

from 113 kN in the base model to 64 kN in model

4 while at the same time the mean dynamic force

(Fmd) of all corrugated models was increased in

comparison with the base model (see Table 4 and

Figure 16). As discussed earlier the initial col-

lapse force is an important parameter for crash-

worthiness design. This gives an indication of the

required force to initiate collapse and the begin-

ning of the energy absorption process. The net re-

sults of changes in the mean dynamic force (Fmd)

and the initial maximum collapse force (Fmax) will

be observed in the CFE parameter. A maximum

CFE of about 70% has been achieved for model

4 as compared to 41% in the base model (see Ta-

ble 4). Model 3 and 4 both have higher CFE than

the base model while CFE in models 1 and 2 are

slightly lower than the base model. By increas-

ing the number of corrugations, the frequency and

amplitude of the mean crush force was also de-

creased, and this is another advantage of corru-

gating a crash box. However, the stroke efﬁciency

(SE) in all corrugated models remained nearly the

same as in the base model. As explained ear-

lier, this was related to our assumption for cut-off

point in the force-crush distance diagrams. These

trends are in accordance with guidelines for opti-

mum and efﬁcient crashworthiness designs. The

summary of the results for all the models are pre-

sented in Table 4.

6 Conclusions

In this paper, the effect of corrugating the sidewall

of aluminium crash box with various pitch dis-

tance on dynamic impact loading is investigated.

It is shown that the dynamic crushing of corru-

gated aluminium boxes is affected by the corru-

gated pitch. By decreasing the pitch distance (

λ

),

the initial collapse force decreases, and the energy

absorption process is started at a lower maximum

force compared to the base model. Also the crush

force efﬁciencies (CFE) increases signiﬁcantly as

the corrugation pitch distance decreases while by

decreasing the pitch distance, i.e. increasing the

number of corrugations, the frequency and ampli-

tude of mean forces are reduced. Decreasing the

pitch distance (

λ

) has minor effect on the speciﬁc

energy absorption. For all the models a progres-

sive symmetric deformation mode is found.

In summary, corrugated crash boxes have the ad-

vantages of a lower initial collapse force, hence

much higher crush force efﬁciency. They also

have a lower crush force ﬂuctuation frequency

and amplitude relative to a ﬂat sidewall box mak-

ing them a more efﬁcient design for automotive

application.

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