Energy Absorption of Thin-walled Corrugated Crash … Absorption of Thin-walled Corrugated Crash Box...

Copyright c© 2008 Tech Science Press SDHM, vol.4, no.1, pp.29-45, 2008

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

H. Ghasemnejad1, H. Hadavinia1,2, D. Marchant1 and A. Aboutorabi1

Abstract: In this paper the crashworthiness ca-pabilities of thin-walled corrugated crash boxesin axial crushing relative to flat sidewall boxesfrom the same material are investigated. In orderto achieve this, various design of corrugated alu-minium alloy 6060 temper T4 crash boxes werechosen and their axial crushing behaviour underimpact loading was studied by developing a the-oretical model based on Super Folding Elementtheory and by conducting finite element analysisusing LS-DYNA in ANSYS. From the theoreticaland FE analysis the crush force efficiency, the spe-cific energy absorption and the frequency and am-plitude of fluctuation of the dynamic crush forceof the corrugated crash boxes were calculated andthe 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 fluctuationfrequency and amplitude relative to a flat sidewallbox.

Keyword: Crashworthiness; Corrugation; Im-pact; Aluminium; Theoretical analysis

Nomenclature

A mean areaC width of extrusionCFE crush force efficiencyd depth of corrugatesD,q material constants in

Cowper-Symonds equationE specific energy absorptionF forceFmax initial maximum collapse force

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

2 Corresponding Author. Email:[email protected] (H. Hadavinia), Tel: +44 208547 8864 Fax: +44 20 8547 7992

Fmd mean dynamic forceH wall thicknessL free length of specimenm mass of specimenM0 fully plastic bending momentN number of corrugationsSE stroke efficiencyUm membrane energyUb bending energyV impact velocityw crush distanceν Poisson’s ratioσ0 flow stressσy yield stressσu ultimate tensile strengthδ magnitude of triggerδ0 amplitude of triggerρ densityλ half pitch distanceκ effective crush distance

1 Introduction

The optimization technique plays an importantrole in the crashworthiness design of automo-tive structures. The use of a suitable geometricalshape and material could give great payoffs suchas a lower weight, higher stiffness and a morestable 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 reducethe damage caused in those cases involving exces-sive dynamic forces [Mahdi et al (2006)]. For theautomotive designers, it is a challenge to find anoptimum design to maximise the safety. McGre-gor et al. [McGregor et al (1993)] have stated theprincipal stages involved in the design process ofan impact member as shown in Figure 1. Based onthis design philosophy, initially a preliminary ge-ometry for the crash box is chosen, and then three

30 Copyright c© 2008 Tech Science Press SDHM, vol.4, no.1, pp.29-45, 2008

performance aspects for good crashworthiness de-signs practice, i.e. the collapse mode, averagecollapse force and maximum collapse force, areevaluated. The preliminary geometry can then bemodified to enhance the performance of the crashbox and the cycle of the design will be repeateduntil the optimum design is obtained.

Assess Collapse Mode

Assess Average Collapse Force

Assess Maximum Collapse Force

Select Geometry

DesignCycle

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 fiftyyears ago with the introduction of the rigid-plasticidealisation [Jones (2003)]. Nowadays, car man-ufacturers use numerical simulations to study thecrash behaviour of various vehicle structures. Byusing numerical modelling, not only the num-bers of prototypes testing are reduced but alsothe numerical simulations enable new design andmaterials to be evaluated without extensive andexpensive testing. These modelling also pro-vide a benchmark platform for evaluating the newknowledge gained through experiments and im-provements in the theories of materials and struc-tures [Langseth et al (1999)]. The majority of theresearch and developments relating to crash zoneare to do with energy absorption by the frontaland bending deformation of the metal structure[Transportation Research Board and National Re-search Council (1996)]. In principal, an efficientcrashworthy design system should be able to: (i)absorb the impact kinetic energy in a controlledmanner, (ii) after an impact, a sufficient survivalspace remain for the occupants, and (iii) the forcesand accelerations experienced by the occupants inthe vehicle are minimised and remain at a survivallevel. The total energy absorption depends on

the governing deformation phenomena of all con-stituent parts of the structure such as thin-walledtubes, cones, frames and sections [Yamakazi andHan (2000); Singace (1997) Mahdi et al (2003);Abosbaia et al (2003)].

The structural crashworthiness requirement isgenerally met by the use of crumple zones. Thesezones exist in the front and rear of the car andprotect the passenger safety cell. In a crash,these crumple zones absorb the vast majority ofthe crash energy through plastic collapse. Jones[Jones (1993)] has shown that an ideal energyabsorber should be lightweight and maintain themaximum allowable retarding force throughoutthe greatest possible crush displacement whilekeeping 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 ofan energy absorption device, corrugated tubeswould be a favourable choice. Seitzberger et al.[Seitzberger et al (2000)] have concluded that thelower mean force for tubular member will be ad-vantageous.

In this paper various corrugated aluminium alloy6060 tempered T4 energy absorber square boxeswere 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 softwareLS-DYNA in ANSYS [Ghasemnejad et al (2007);ANSYS documentation]. Parameters such as thecrush force efficiency, the energy absorption, thestroke efficiency and the frequency and amplitudeof the resulting axial crushing force in each crashbox were obtained and the results were comparedwith those from a flat sidewall square crash boxhereafter 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 forceefficiency (CFE) which is defined as the ratiobetween the maximum initial collapse force andthe mean dynamic force. An ideal absorber can

Energy Absorption of Thin-walled Corrugated Crash Box in Axial Crushing 31

exhibit a crush force efficiency of 100% with arectangular-shaped force-crush distance curve. Itmeans that initial collapse force and mean forceare equal but in practice the situation of a CFEparameter equal to 1 is not achievable. The meandynamic force is a function of the impact velocitywhile the mass of the striker has no noticeable in-fluence on it. The second important parameter isthe stroke efficiency (SE) which is the ratio of thestroke (crushed distance) at the bottoming out tothe initial length of the absorber. High ratios in-dicate efficient use of the material. In such casesthe force-crush distance curves are cut at a pointwhere the force starts to increase steeply, and somaximum displacement coincides with the strokelength, and the definition of this cut-off point issomewhat arbitrary. The reported stroke lengthsshould be regarded only as approximate values.The third parameter is specific absorbed energy(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 energycan approximately be regarded as the energy dis-sipated by plastic deformation.

In an impacted box, the force-crush distance curvecan be divided into three distinct regions as shownin Figure 2. In region I, the force increases rapidlyand reaches a maximum (Fmax) before dropping.In region II, the force fluctuates around a meandynamic force (Fmd) while a series of folds formsuccessively in the tube so that a folded zonegrows progressively down the tube in a form ofmushrooming failure. In region III, all lobes toucheach other and the box stiffness to impacted ob-ject increases and this will cause a rapid increasein the force.

Generally, the specification of the energy absorp-tion component is dictated by the requirement ofthe design e.g., the specification for the struc-tural design of a passenger carrying rail vehicleends by Railtrack [Railtrack Structural Require-ments for Railway Group Standard (1994)] wasset at a minimum energy absorption of 1 MJ overa 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 than3000 kN over a maximum allowable crush dis-tance which absorbs the specified impact energyas shown in Figure 2. Also in Figure 2 the crush-ing behaviour of three possible realistic designsare demonstrated. Case 1 design has the highestinitial maximum collapse force among the othersand hence it is discarded; though its Fmd is aboutthe 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 impactwill be experienced by the vehicle occupants, alower mean dynamic crush force is desirable aslong as the energy absorption criterion is satisfied.In Case 3, initial collapse force is relatively lowand the mean crush force equal to the ideal crashbox which fluctuates with low amplitude aroundthe ideal mean dynamic force. The amplitude offluctuations in Case 3 is lower than Case 1. AsCase 3 satisfies all design requirements with leastminimum initial collapse force and least mean dy-namic force with minimum amplitude of fluctu-ation about the mean force, it is the best designamongst the designs presented in Figure 2.

3 Theoretical analysis of corrugated crashbox

The dynamic mean force for an uncorrugatedsquare box for a rigid-perfectly plastic material isderived by Abramowicz and Jones [Jones (1993)]as

Fm = 13.05σ0H53 C

13

{1+(0.33V/CD)

1q

}(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 thedynamic flow stress is equal to static flow stressobtained from:

σ0 =σy +σu

2(2)

where σy and σu are 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


mdF

Forc

e

Crush distance

Case 3

II

maxF

IIII

Ideal crush

Case 1

Case 2

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

(a)

Corner

(b)

d

d /2

/2

d

θ

θ θ

θ

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


mean dynamic crush force in the axial pro-gressive crushing of thin-walled square columnswas developed by Wierzbicki and Abramowicz[Wierzbicki and Abramowicz (1983)]. In thismodel by adopting a rigid-plastic material andusing the condition of kinematic continuity onthe boundaries between the rigid and deformablezones, each corner is considered having three ex-tensional/compressional triangular elements andthree stationary hinge lines. We extended this ap-proach to the corrugated crash boxes.

From the energy balance of the system, for acomplete collapse of a single fold of corrugatedbox, the external work done by compression ofthe 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.

2λ Fm κ = Ub +Um (3)

where λ is the corrugation pitch distance, Fm isthe mean force and κ ≤ 1 is a correction factor foreffective crush distance. Ub and Um are, 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 is never completely flattened. Theeffective crush distance is reported between 70-75% of the folding wavelength in previous worksby Wierzbicki and Abramovicz [Wierzbicki andAbramowicz (1983)]. In the present work, byanalysing the FEA results, the effective crush dis-tance was found to vary linearly with the corruga-tion pitch distance as

κ = 5.3λ +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 calculatedby summing up the energy dissipation at station-ary hinge lines. In each corrugation unit, 6 hor-izontal stationary hinge lines are developed, 3 atthe inner and 3 at the outer circumference (Figure

3a), hence

Ub =

(3

∑i=1

M0θiLc

)extruded hinge line

+

(3

∑i=1

M0θiLc

)recessed hinge line

(5)

where M0 = 2∫ H/2

0 σ0tdt = σ0H2/4 is the fullyplastic bending moment of the flange and θ is therotation angle at each hinge line. For simplicity, itwas assumed that the flanges are completely flat-tened after the axial compression of 2λ (Figure3b). In this situation, the rotational angles at thehinge lines are π /2, π and π /2, respectively. TheEq. (5) for dissipated energy in bending will sim-plify to,

Ub = M0 (2π LC1 +2π LC2) (6)

whereLC1 and LC2 are the inner and outer circum-ference of the corrugation.

H

/445°

Corner line

Figure 4: Presentation of the membrane energydissipation in compression and extension.

The membrane dissipated energy, Um, during onewavelength crushing in corner part was evaluatedby integrating the extensional and compressionalareas as shown in Figure 4,

Um =∫S

σ0H dS = σ0HNC

(12× λ

4× λ

4

)×8×2

=σ0Hλ 2NC

2(7)

where NC is the number of corners. For a squarecorrugated unit NC =4.


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

Stre

ss (M

Pa)

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 (k

N)

2x2 2.5x2.5 3x3 5x5

0

10

20

30

40

50

0 20 40 60 80 100 120

Crush-distance (mm)

F (k

N)

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.


By substituting Eqs. (6) and (7) in Eq. (3), themean force is,

κFm =π4

σ0H2

λ(LC1 +LC2)+

σ0Hλ NC

4(8)

The mean force can be obtained by substituting κfrom Eq. (4) in Eq. (8).

The static mean force obtained from Eq. (8) needsto be corrected to take into account the dynamicseffect. This has been done according to the ratiobetween dynamic and static progressive bucklingforces suggested by Jones [Jones (1993)],

Fmd

Fms=

(1+(

0.33VCD

) 1q

)(9)

The calculated dynamic mean forces obtainedfrom the above theoretical solution for all themodels are presented in Table 1. The discrepancybetween the theoretical results and FE results areless than 3%.

4 Finite element studies

Nonlinear explicit finite element codeANSYS/LS-DYNA was used to model theaxial crushing of the thin-walled aluminiumcrash boxes. These energy absorbers were mod-elled by the Belystchko-Lin-Tsay quadrilateralfour-node thin shell elements [Belytschko et al(1984)]. These shell elements are available in theelement library of LS-DYNA. The Belystchko-Lin-Tsay shell element is based on a combinedco-rotational and velocity-strain formulation[Hallquist (1998)]. To simulate the quasi-staticcondition, the constant velocity was applied to therigid striker. The real crushing speed is too slowfor the numerical simulation. The explicit timeintegration method is only conditionally stable,and therefore by using real crushing speed, verysmall time increments was required to use. Forsatisfying quasi-static condition, the total kineticenergy has to be very small compared to the totalinternal energy over the period of the crushingprocess and also the crushing force-displacementresponse must be independent from the appliedvelocity.

4.1 Material modelling

In the present work, the crash boxes are madefrom aluminium alloy with a Young’s modulus of68.2 GPa, a yield stress of 80 MPa and a Poisson’sratio 0.3. The stress-strain relation of this materialis shown in Figure 3. The advantage of using alu-minium in vehicle structure is reducing the weightof the vehicle. It has been reported that savings inthe load-bearing structure of an aluminium vehi-cle can be as much as 40–50% when compared tosteel. Aluminium alloys have approximately 1/3the weight and 1/3 the elasticity modulus of steel,and usually a lower strength. As an example, analuminium 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 bya type 24 material which is defined as MATE-RIAL_PIECEWISE_LINEAR_PLASTICITY,pertaining to the von Mises yield conditionwith isotropic strain hardening, and strain rate-dependent dynamic yield stress based on theCowper and Symonds model. The aluminiumalloy is known to be insensitive to high strainrates and therefore strain rate effect was notapplied [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 wasstudied 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, 3×3and 5×5mm meshes. The trigger position waslocated 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 showthat apart from 5×5mm coarse mesh, for the finermeshes from 2×2 to 3×3mm the results are verysimilar and insensitive to element size.

Next the effect of NIP through the thickness wasstudied on a model with element size of 2×2mmand the same trigger position at C/8. NIP through


TP

L

C

Figure 7: Trigger position (TP) in the FE modelof the crash box at TP= C/16, C/8, C/4 and C/2.

the shell elements was varied at 3, 5 and 9. Theresults 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 thecomputing cost and make the structure stiffer. Forfurther analysis NIP=3 is chosen.

The trigger position is shown in Figure 7. Theeffect of trigger position at C/2 (40mm), C/4(20mm), C/8(10mm) and C/16 (5mm) from topend of box was investigated. The element sizeof these models was 2×2mm and the NIP waskept constant at 3. It was found that trigger po-sition in the range of C/8 to C/2 from the topend of box has no significant effect on the re-sponse of force-crush distance diagrams, (Fig-ure 8a). In further study, the total length ofcrash box was changed while keeping the elementsize at 2×2mm with trigger position at C/8 andNIP=3. The result shown in Figure 8b confirmedthat the force-crush distance is not affected toomuch by the total length of crash box. In con-clusion, it is found that by choosing element sizebetween 2×2–3×3mm, trigger position betweenC/8 (10mm) and C/2 (40mm) and NIP of 3 willgive an optimum FE parameters for modelling ofcrash box. In the next part of this study an elementsize of 3×3mm which gave lower CPU time incomparison 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 modelis verified by comparing to those reported in[Langseth et al (1999)] and [Zhang et al (2006)]as shown in Figure 7. The discrepancy betweenour base model and the results in [Langseth et al(1999)] and [Meguid et al (2004)] were minimal.There is no difference in mean dynamic forceand initial maximum collapsed force between themodels. Dynamic mean force obtained from theFE result was also compared with the theoreticalsolution given in Eq. (1). The calculated dynamicmean force from the theoretical solution is 42 kN,and from the FE analysis it is 47 kN, a differenceof 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 camerato detect the crushing process which takes placein fraction of a second. In this study finite ele-ment simulation is used as an alternative methodto study the impact process.

A square tube under axial quasi-static or impactcondition can collapse in one of these distinctcrushing modes, symmetric mode, extensionalmode, asymmetric mixed mode or global buck-ling during compression. Symmetric progressiveplastic buckling is the ideal crushing mode forbox like energy absorber. Extensive experimen-tal studies [Jones (2003)] have shown that for thecombination of geometrical parameters, a sym-metric progressive mode of collapse of a thin-walled prismatic square column subjected to thedynamic axial loading of an AA6060 aluminiumbox regardless of the material temper conditionobserved when 32 ≤ C/H ≤ 44.4. Furthermore,the localisation of the lobes for temper T4 startedeither at the impacted end of the specimens or atthe clamped support.

Four different corrugated models were studied. Inthe finite element models, the free length of thecrash box was chosen at 310 mm with differentwall thicknesses while the total mass of all cor-


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

Model Wall Pitch Depth of Wb Wm Fmd Fmd Errorthickness 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 4.92 2.47 51.67 6 7.43 15.31 40 38.7 -33 2.34 25.83 6 13.34 7.25 42 42.3 0.74 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 (k

N)

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 (k

N)

L310 L150

(b)

(a)

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


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

σ0 C H D(1) Q(1) V Fmd (kN) Fmd (kN) Error(MPa) (mm) (mm) (s−1) (m/s) FEA Analytical (%)

120 80 2.5 6500 4 25 40 42 5

(1) [Singace and El-Sobky (1997)]

1

1 2 3

4

4

2

3

1

4

32

1

2

3

4

Figure 9: Comparison of force-crush distance of the base model in the present study with those in [Zhang(2006)] and [Langseth (1999)]. The inserts show von Mises stress distribution at various stages of theimpact.


86

L=310

L=310 L=310

L=310

86

86 86

86

86

86

86

7474

7474

λ

Model 1 Model 2

Model 3 Model 4

d

dd

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) λλλ (mm) d (mm)

1 80×86 2.49 77.5 62 80×86 2.47 51.67 63 80×86 2.34 25.83 64 80×86 2.20 19.38 6

Base model 80×80 2.50 N/A -


0

20

40

60

80

100

120

0 50 100 150 200 250

Crush distance ( mm )

F(kN

)

Model 1 Base Model

2 3

41 4

2

31

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

432

4



0

20

40

60

80

100

120

140

0 50 100 150 200 250

Crush distance (mm)

F(kN

)

Model 3 Base Model

1

23

4

1 2 3

4


0

20

40

60

80

100

120

0 50 100 150 200 250

Crush distance (mm)

F(kN

)

Model 4 Base Model

4

41 2 31

2 3



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

1 105 39 37 80 14.62 100 40 40 80 15.13 74 42 57 79 15.84 64 44 69 79 16.6

Base model 113 47 41 80 17.6


40

60

80

100

120

10 20 30 40 50 60 70 80

Pitch distance (mm)

Initi

al c

olla

pse

forc

e (k

N)

Model 1

Model 3

Model 2

Model 4

35

40

45

50

10 20 30 40 50 60 70 80

Pitch distance (mm)

Mea

n dy

nam

ic fo

rce

(kN

)

Model 1Model 3

Model 2

Model 4

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

rugated boxes were kept constant as in the basemodel, i.e. 0.664 kg. The design information forthe four corrugated models and the base model arepresented in Figure 10 and Table 3. The speci-mens were impacted at a velocity of 25 m/s witha block of 50 kg which was modelled as a rigidbody. All degrees of freedom of the crash boxeswere fixed at the bottom end and all the rotationaldegrees of freedom were fixed at the upper endto avoid unrealistic deformation modes. The con-tact between the striker and the specimens wasmodelled using a nodes impacting surface with afriction coefficient of 0.25 to avoid lateral move-ments. To account for the contact between thelobes during deformation, a single surface contactalgorithm without friction was used. This contactalgorithm is used to prevent the penetration of thedeformed 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 tobe 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 130mmfrom the end of the box to initiate the symmetricdeformation 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 fromFEA 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 thecrash box during the deformation. In these Fig-ures the behaviour of the base model has been


shown with dash line for comparison. In all sim-ulations, the progressive symmetric deformationmode was found for all specimens at impact asshown in Figure 15. The FEA results show thatby decreasing the corrugation pitch distance, theinitial maximum collapse force (Fmax) decreasesfrom 113 kN in the base model to 64 kN in model4 while at the same time the mean dynamic force(Fmd) of all corrugated models was increased incomparison with the base model (see Table 4 andFigure 16). As discussed earlier the initial col-lapse force is an important parameter for crash-worthiness design. This gives an indication of therequired 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) willbe observed in the CFE parameter. A maximumCFE of about 70% has been achieved for model4 as compared to 41% in the base model (see Ta-ble 4). Model 3 and 4 both have higher CFE thanthe base model while CFE in models 1 and 2 areslightly lower than the base model. By increas-ing the number of corrugations, the frequency andamplitude 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 thesame as in the base model. As explained ear-lier, this was related to our assumption for cut-offpoint in the force-crush distance diagrams. Thesetrends are in accordance with guidelines for opti-mum and efficient crashworthiness designs. Thesummary of the results for all the models are pre-sented in Table 4.

6 Conclusions

In this paper, the effect of corrugating the sidewallof 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 energyabsorption process is started at a lower maximumforce compared to the base model. Also the crushforce efficiencies (CFE) increases significantly as

the corrugation pitch distance decreases while bydecreasing the pitch distance, i.e. increasing thenumber of corrugations, the frequency and ampli-tude of mean forces are reduced. Decreasing thepitch distance (λ ) has minor effect on the specificenergy 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, hencemuch higher crush force efficiency. They alsohave a lower crush force fluctuation frequencyand amplitude relative to a flat sidewall box mak-ing them a more efficient design for automotiveapplication.

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