The Energy Absorption Characteristics of Square Mild Tubes with Multiple Induced circular hole...

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S. B. Bodlani

S. Chung Kim Yuen1

e-mail: [email protected]

G. N. Nurick

Blast Impact and Survivability Research Unit(BISRU),

Department of Mechanical Engineering,University of Cape Town,

Private Bag,Rondebosch, 7700, South Africa

The Energy AbsorptionCharacteristics of Square MildSteel Tubes With MultipleInduced Circular HoleDiscontinuities—Part I:ExperimentsThis two-part article reports the results of experimental and numerical works conductedon the energy absorption characteristics of thin-walled square tubes with multiple circu-lar hole discontinuities. Part I presents the experimental tests in which dynamic andquasistatic axial crushings are performed. The mild steel tubes are 350 mm in length, 50mm wide, and 1.5 mm thick. Circular hole discontinuities, 17 mm in diameter, are later-ally drilled on two or all four opposing walls of the tube to form opposing hole pairs. Thetotal number of holes varies from 2 to 10. The results indicate that the introduction ofholes decreases the initial peak force but an increase in the number of holes beyond 2holes per side does not further significantly decrease the initial peak force. The findingsshow that strategic positioning of holes triggers progressive collapse hence improvingenergy absorption. The results also indicate that the presence of holes may at timesdisrupt the formation of lobes thus compromising the energy absorption capacity of thetube. In Part II, the finite element package ABAQUS/EXPLICIT version 6.4–6 is used tomodel the dynamic axial crushing of the tubes and to investigate the action of the holesduring dynamic loading at an impact velocity of 8 m/s. �DOI: 10.1115/1.3114971�

Keywords: square tubes, imperfections, multiple hole cut-outs, energy absorption

IntroductionHigh impact events such as transport-related accidents can re-

ult in life-changing injuries or loss of life to vehicle occupants.ttempts to minimize this damage primarily require the absorp-

ion of the kinetic energy of the crash in an effort to attain what isermed good vehicle crashworthiness �1–3�. Improving vehiclerashworthiness is of specific importance in the light of an ever-ncreasing number of vehicles on the road and the subsequentncrease in vehicular accident deaths. According to the 2004

orld Health Organization report �4�, on average, 3000 people areilled daily in road accidents. Such statistical figures have ensuredhat the subject of vehicle crashworthiness continues to draw thettention of academic and industrial researchers worldwide5–11�.

In order to achieve good vehicle crashworthiness the commongreement among researchers �1,2,5–15� is to have an energy ab-orption device that achieves one or both of the following: de-rease the initial peak force and/or absorb as much energy asossible. In fulfilling these criteria the device will enable a reduc-ion in the acceleration perceived by vehicle occupants and themount of energy transferred from the vehicle to its occupants incrash. Crush force efficiency �CFE� and stroke energy �SE�,

iven in Eqs. �1� and �2�, are typical parameters used to assess theerformance of these energy absorbing devices in achieving theseriteria.

1Corresponding author.Contributed by the Applied Mechanics Division of ASME for publication in the

OURNAL OF APPLIED MECHANISMS. Manuscript received October 2, 2007; final manu-cript received November 2, 2007; published online April 27, 2009. Review con-
ucted by Robert M. McMeeking.
ournal of Applied Mechanics Copyright © 20

ded 28 Apr 2009 to 137.158.152.210. Redistribution subject to ASM

CFE =Pm

Pi�1�

SE =�

L�2�

The ideal value for CFE is unity �5�. The CFE parameter is usefulin determining the extent to which a constant deceleration isachieved, thus a value of unity would indicate that the device hasreduced the initial peak force �Pi�, also referred to as ultimatepeak force, sufficiently to enable a smooth deceleration duringimpact. The ideal value that would indicate maximum energy ab-sorption for SE is 100%. Due to the compaction of the tubeshowever, this is not physically possible. Abramowicz and Jones�6� found that the maximum attainable value of SE for squaretubes is 73%.

Various studies �2,3,5–11� have been conducted on the axialcompression of thin-walled tubes and have enabled the character-ization of the manner in which they fail, namely, Euler and pro-gressive bucklings. Euler buckling is characterized by a smalldeformation after loading begins followed by a very large globalbending such that the tube can no longer sustain further axialloading �5,7�. Progressive buckling is associated with an initialpeak force followed by a lower periodic force with relatively con-stant amplitude for the remainder of the load application event�5,7�. Progressive buckling proceeds through the development offolds or lobes resulting in extensive plastic strain. This strain isthe mechanism through which progressive buckling absorbs sig-nificantly more energy than Euler buckling �2,5,8�. Furthermore,the incidence of either Euler or progressive mode is governed by
the tube geometry of the tube. Abramowicz and Jones �9� found
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hat the length to width ratio �L /C� at which progressive collapseransitioned to Euler increased with an increase in the width tohickness ratio �C / t�.

This ability to effectively dissipate energy makes thin-walledubes an ideal manner of improving vehicle crashworthiness1,2,5–9�. Consequently they are widely used in the constructionf the mainframes of cars �2,3�. These thin-walled tubes are joinedogether to form a hollow frame commonly known as the space-rame. Various studies �1–3,5–18� have investigated the mannerhrough which thin-walled tubes dissipate energy and the optimi-ation of that energy absorption. This allows thin-walled tubes toe applied in a manner that fully exploits their energy absorbingapabilities �5�.

One of the ways to improve energy absorption is to insert im-erfections, also known as triggers or initiators or discontinuities,nto the tube wall. These discontinuities can be geometrical inorm such as dents and through-hole circular, elliptical, or slottedut-outs or material changes. Chung Kim Yuen and Nurick �11�rovided an extensive review of the application of induced geo-etric and material modifications to the improvement of energy

bsorption in thin-walled structures. It was noted that these effortso improve energy absorption must ensure that tubes are able toeform in a predictable manner when their energy absorbingualities are required. More particularly, these induced imperfec-ions can decrease the initial peak force and control the particular

ode of buckling induced in the tube. Studies �5,7,13,14� inves-igating the effect of a single discontinuity pair inserted at mid-eight have concluded that the introduction of discontinuities intohe tube wall does decrease the initial peak force. Furthermore,hese discontinuities “trigger” the collapse of the tube. This is asiscussed by Abramowicz �2� who stressed the need for the rel-vant absorber to be “triggered” in such a way that the formationf natural folds is promoted. The formation of natural folds en-ourages progressive buckling and energy absorption is maxi-ized.The prevailing conclusion among Refs. �5,7,13,14� is that for

ircular discontinuities an increase in hole diameter results in anncrease in the reduction in the initial peak force. There is how-ver a limit beyond which increasing the discontinuity severityill have an adverse effect on energy absorption. For example,rnold and Altenhof �7� and Marshall and Nurick �13� found thatdiscontinuity of hole diameter larger than 32 mm in 50 mm wide

quare tubes caused splitting.Gupta and Gupta �14� investigated the effect of multiple circu-

ar holes on the energy absorption characteristics of circular tubes.he specimens used contained two or four opposing circular holeiscontinuities laterally drilled on one, two, or three planes spacedymmetrically along the length of the tube. The results indicatehat the introduction of more than two opposing holes did notecrease the initial peak force significantly further than thatchieved by just two opposing holes. Furthermore, Gupta andupta �14� reported that buckling was triggered at the location of

he holes in one of the planes and the collapse mode varied de-ending on the number of planes.

Montanini et al. �10� noted that both the size and the position-ng of the trigger need to be taken into account for effective crushnitiation. Lee et al. �15� furthermore found that if induced discon-inuities were not located at the natural hinges of lobes then theyould cause irrevocable disturbances to the collapse mode thateveloped and lead to global bending even if the geometry of theube was such that it would have otherwise buckled in progressive

ode. Consequently, a strategic placement of holes in the zoneshere the lobe hinges are expected to fall when the tube under-oes progressive buckling is required. Montanini et al. �10� sug-ested the application of theoretical findings to calculate the po-itioning of the triggers. Abramowicz and Jones �6,16� proposednalytical predictions for the wavelength of a single lobe in therogressive buckling of square tubes, in that the original �before
obe formation� height of the lobe is given as
41012-2 / Vol. 76, JULY 2009


l/t = 0.99�C/t�2/3 �3�The work described in this paper extends the knowledge describedabove by investigating the effect of multiple circular discontinui-ties as crush initiators in the collapse mode progression. Since theaim is that the discontinuities act as points of crush initiation atwhich lobes are induced, the spacing of successive hole pairsrelative to one another is considered carefully. Furthermore, theeffect of placing holes on both or all four tube walls is also re-ported. For the quasistatic tests the manner by which collapse istriggered and progresses during axial loading is closely examined.The nature of the dynamic tests precludes similar observationsand consequently a validated numerical model is presented in PartII �17� to observe the role of the discontinuities in triggering col-lapse during dynamic axial loading.

2 Experimental Program

2.1 Test Specimens. Mild steel industrial seam weld tubeswith nominal width �C� 50 mm, thickness �t� 1.5 mm, and length�L� 350 mm are used. These dimensions give geometrical ratios ofL /C and C / t corresponding to progressive buckling �L /C�10 for5.5�C / t�38� as described by Abromowicz and Jones �6,16�.Using Eq. �3�, the wavelength �2l� for the tubes in this papershould be 32 mm. However, on the measurement of the actuallobe wavelength of as-received tube �plain with no discontinui-ties� of the above dimensions, the theoretical prediction appears tounderestimate the actual lobe wavelength, which is approximately50 mm. The objective is to place discontinuities at regular inter-vals of 50 mm in order to attempt to trigger lobe formation wherethe lobe would naturally form in the absence of holes. Opposinghole pairs of diameter 17 mm are laterally drilled midwidth of thewalls of the tube. The specimen configurations are illustrated inFig. 1. Specimen group A has holes on two tube walls and speci-men groups B_H50 and B_HEq have holes on all four tube walls.In group A, illustrated in Fig. 1�a�, the hole are spaced 50 mmapart where there are multiple holes per sides. In group B_H50,illustrated in Fig. 1�b�, the holes are also 50 mm apart on eachtube wall and adjacent hole pairs are placed on alternating walls.Group B_HEq, illustrated in Fig. 1�c�, contains hole pairs spacedsymmetrically along the length of the tube with adjacent holepairs being on alternating tube walls. A number is appended afterthe letters “A” or “B” in each group name to indicate the numberof holes present in the particular specimen.

2.2 Quasistatic Axial Crush Testing. Quasistatic axial crush-ing is performed in a Zwick hydraulic load cell with a maximumcapacity of 200 kN. The bottom 50 mm of the tube is fixed by aclamp during testing. All tubes are crushed at a cross head speedof 30 mm/min �strain rate 1.7�10−3 s−1� for a distance of 220mm to correspond to the maximum tube compaction of 73% �6�.Data acquisition software, connected to the load cell and a com-puter, records the force-displacement history of the crushingevent. The energy absorbed �Ea

s� and mean crushing force �Pm�are calculated using Eqs. �4� and �5�. Equation �4� applies thetrapezium rule for integrating the area under the force-displacement graph and represents the energy absorbed during theentire quasistatic axial crushing event.

Eas = �

j=2

N

0.5�Pi + Pi−1��i − �i−1� �4�

Pm =Ea

s

��5�

2.3 Dynamic Axial Crush Testing. The dynamic crush testsare performed in a drop hammer rig. The specimen is clamped fora length of 50 mm at its base and placed on the anvil of the rig.
The mass is raised to the desired height and released to impact the
Transactions of the ASME


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ube in an axial direction. The energy absorbed �Ead� during the

ynamic loading event is calculated using Eq. �6�, assuming noosses to friction, in which the crushed distance �� is measuredor each specimen.

Ead = Mg�h + �� 6�

eplacing energy absorbed in the quasistatic tests �Eas� in Eq. �5�

ith Ead yields the mean force for the dynamic tests. The drop

ammer rig used is not equipped with data acquisition equipmentnd hence force-displacement histories are not recorded. A finitelement model is validated and used to analyze the force-isplacement histories of the dynamic tests and is reported in Ref.17�.

Experimental Results and Observations

3.1 Quasistatic Tests. Table 1 presents the results of the qua-istatic axial crush tests. The letter “S” is prefixed to the specimename to indicate the quasistatic test and a number is suffixed toistinguish between different specimens of the same configura-

Fig. 1 Test spec

ion. Furthermore, specimens without holes are referred to as

ournal of Applied Mechanics


“plain_tube” and where the diameter of discontinuities present inthe specimen differs from the standard 17 mm, the diameter isincluded in the specimen name preceded by the letter “d.” Twofailure modes are observed in the quasistatic tests, namely, pro-gressive collapse �PS� and mixed mode �MM�, and are illustratedin Fig. 2. Mixed mode refers to a collapse mode that is a combi-nation of progressive collapse and Euler buckling. The test isstopped if MM collapse mode develops.

3.1.1 Specimen Group A

3.1.1.1 Configuration A2. As expected, the introduction of anopposing hole discontinuity pair at midheight causes a reductionin initial peak force. The initial peak force for specimen SA2_1 is10% lower than that for the specimens without holes �splain-_tube_1 and splain_tube_2�. Furthermore a specimen of diameter17 mm �SA2_1� results in a lower initial peak force than one ofdiameter 12.5 mm �SA2_d12.5_1�. This result is concurrent withliterature �5,14� in which the understanding is that the larger thehole diameter, the lower the initial peak force. This reduction inforce is due to the localization of deformation at the hole discon-

n configurations

tinuity. The discontinuities act as stress raisers within the area in

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hich they are placed allowing the area to fail at a comparativelyower applied force than it would in the absence of discontinuities5�. Photographs taken during the crushing event are given in Fig.�a� for specimen SA2_d12.5_1. The letters below each photo-raph correspond to those in Fig. 3�b�, which illustrates the cor-esponding force-displacement curve together with that of a plainube �splain_tube_2�. Specimen SA2_1 displays similar crushingehavior to SA2_d12.5_1 but with a larger reduction in initialeak force. The crushing event for specimen SA2_1 is illustratedn Fig. 4.

Although specimen SA2_1 collapsed in the PS mode, a skewnitial lobe is observed in point �b� of Fig. 4. This is characterizedy an upturning of the outer hinge of the lobe such that it contactshe tube wall above it and interferes with the subsequent lobeormation adjacent to it. This is visible at points �c�, �d�, and �e� ofig. 4. The incidence of a skew lobe for the initial lobe appears toe a random occurrence since it is observed for some initial lobesut not all.

3.1.1.2 Configuration A4 and A6. Increasing the number ofoles from two to six holes affords a slight decrease in the initial

Table 1 Results for quasistatic axial crusdiscontinuities

Specimen namePi

�kN�Pm

�kN�

splain_tube_1 101.7 32.0splain_tube_2 101.6 31.4SA2_d12.5_1 94.8 32.7SA2_1 91.3 33.4SA4_1 86.9 31.9SA4_2 90.2 34.6SA6_1 89.4 33.4SA6_2 91.0 35.1SB4_H50_1 84.0 32.2SB6_H50_1 81.6 33.3SB8_H50_1 80.5 32.1SB10_H50_1 79.6 33.6SB10_H50_2 79.9 32.6SB4_HEq_1 86.6 29.9SB6_HEq_1 89.3 31.62SB8_HEq_1 86.9 34.02

ig. 2 Photographs of quasistatically crushed tubes, which
ollapsed in „a… MM and „b… PS modes
41012-4 / Vol. 76, JULY 2009


peak force. The average initial peak force for the specimens offour and six holes is 89.34 kN. Increasing the number of holesdoes however produce a change in the collapse mode from pro-gressive collapse in specimens of configuration A2 to mixed modein A4 and A6 specimens. The crushing event for SA4_1 is illus-trated in Fig. 5. It is illustrated that one pair of opposing holes inSA4_1 act as crush initiators. After the initial lobe is formed, asimilar incidence of skew lobe formation as observed in specimenSA2_1 �Fig. 4� is observed at point �c� of Fig. 5. This skew loberesults in a destabilization of the subsequent lobes forming aboveit and the collapse mode of the tube is compromised as illustratedby points �d�–�f� in Fig. 5. The centerline of the tube shifts side-ways resulting in an offset in the axis through which the load isbeing applied as seen at points �e� and �f� at which point the tubecan no longer sustain further axial loading. This collapse mode isdefined as MM since progressive collapse is first observed fol-lowed by the global bending of the tube. MM collapse is alsoobserved in specimens SA4_2 and SA6_2. Specimens SA4_1 andSA4_2 are illustrated in Fig. 6.

3.1.2 Specimen Group B_H50 and B_HEq

3.1.2.1 Group B_H50. The average initial peak force for allgroup B_H50 specimens is 81 kN. This represents a 20% reduc-tion in the initial peak force of a plain tube. Furthermore, in Table1 it is observed that there is a slight decrease in initial peak forceas the number of holes is increased from four to ten. The crushingevent for specimen SB6_H50_1 is illustrated in Fig. 7. The pro-gressive collapse in specimens of group B_H50 is triggered bytwo pairs of opposing holes simultaneously. The arrows at point�b� of Fig. 7 indicate the triggers that concurrently initiate the firstlobe. Subsequent collapse continues progressively first below andthen above the initial lobe. Most specimens in group B_H50 aresubject to a skew initial lobe but the lobes forming subsequentlyare able to straighten the initial lobe and progressive collapsecontinues undisturbed, except in specimen SB10_1 whose crush-ing event is illustrated in Fig. 8.

To illustrate the lobe initiation role that hole discontinuities playin the progressive collapse of tubes, the crushing process forspecimen SB10_H50_1, which failed in MM collapse, is given bythe photographs in Fig. 8. As noted for group B_H50 specimens,two sets of opposing holes simultaneously trigger the initiation ofthe first lobe visible at point �b� of Fig. 8. The skew lobe forma-tion that occurs in specimen SB10_H50_1 is more severe than thatobserved in the other group B_H50 specimens. The initial loberotates to contact the tube wall as indicated at point �d� of Fig. 8.

g of square tubes with and without hole

aJ� CFE

SE�%� Failure mode

0 0.32 73.3 PS9 0.31 73.3 PS1 0.34 73.3 PS3 0.37 73.3 PS4 0.37 35.5 MM7 0.38 35.8 MM3 0.37 73.3 PS8 0.39 35.6 MM0 0.38 73.33 PS3 0.41 73.33 PS0 0.4 73.33 PS5 0.42 34.6 MM2 0.41 73.3 PS6 0.35 73.3 PS0 0.35 73.3 PS5 0.39 73.3 PS

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The hole discontinuity marked with an arrow displaces the action



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f the skew lobe and enforces the initiation of another lobe, whichubsequently prevents the specimen from bending further to theight as illustrated by points �d�–�f�. It appears that the impactionf the skew lobe on the tube wall is severe enough to cause theube to bend in the opposite direction as shown in point �g� result-ng in MM collapse, even after the hole discontinuity straightenshe tube in point �e�. Figures 7 and 8 illustrate that the hole dis-ontinuities fall at the hinges of the lobes for group B_H50.

3.1.2.2 Group B_HEq. The initial peak force for all group_HEq specimens averages 88 kN, a 13% reduction from that ofplain tube, with no significant change with increasing number ofoles. All specimens collapsed in the PS mode. In specimenB4_HEq_1, crushing commences at the top pair of opposingoles, progressing in a steady manner above the initial lobe.

Fig. 3 „a… Photographs of the quasistatic crushincurve for the quasistatic crushing of specimens

Fig. 4 Photographs of the transie
SA2_1


Crushing continues below the initial lobe down the length of thetube in a steady manner as for a tube without hole discontinuities.The same crush behavior was observed for specimenSB6_d17_HEq_1. Some hole discontinuities fall at the lobehinges and some do not for both specimens. Photographs of thefinal crushed specimens are given in Fig. 9 for specimensSB4_HEq_1 and SB6_HEq_1. The force-displacement curve andthe crushing process for specimen SB8_HEq_1 is given in Figs.10 and 11, respectively. The buckling of specimen SB8_HEq_1initiates at one of the hole discontinuity pairs as shown by point�b� of Fig. 11. Progressive buckling occurs in an upwards direc-tion. Once crushing finishes above the initial lobe, another lobe istriggered at a hole discontinuity located further down the tube.This leads to the formation of a relatively large lobe as shown in

f specimen SA2_d12.5_1; „b… force-displacement2_d12.5_1 and splain_tube-2

quasistatic crushing of specimen

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points �g�–�i�. The positioning of the hole pairs at different dis-tances relative to one another thus imposes a certain lobe wave-length on the tube.

3.2 Dynamic Tests. The results of all specimens tested dy-namically are presented in Table 2. The letter “D” is prefixed tothe specimen name to indicate the dynamic test and, as before, anumber is suffixed to distinguish between different specimens. Allspecimens failed in PS mode except the three marked with anasterisk � �� in Table 2, which failed in MM. Velocity is calculatedby Eq. �7�, which assumes zero friction losses and applies conser-vation of energy.

V = �2g�h + �� 7�

3.2.1 Specimen group A

3.2.1.1 Configuration A4. The specimens of configuration A4tested at different heights are shown in Fig. 12. Expectedly, anincrease in height and hence impact velocity results in an increasein stroke efficiency, which is visible by the increase in crusheddistance in Fig. 12. The collapse mode appears to develop in a



Fig. 9 Photographs of specimens „a… SB4_HEq_1 and „b…SB6_HEq_1 at the end of quasistatic crushing

ig. 5 Photographs of the transient quasistatic crushing ofpecimen SA4_1

ig. 6 Photographs of specimens SA4_1 and SA4–2 at the end

Fig. 7 Photographs of the transientSB6_H50_1

Fig. 8 Photographs of the transient



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teadier manner with increasing height as illustrated by the lack ofisible disturbances in the formation of lobes for specimenA4_3 in photograph �c� of Fig. 12 as opposed to the other two

pecimens �photographs �a� and �b��.

3.2.1.2 A6. Specimens DA6_1, DA6_2, and DA6_3 are illus-rated in Fig. 13. The mean force is slightly higher for specimensith six holes �Fig. 13� than for those with four holes �Fig. 12�,hile those with four holes have a slightly better stroke efficiency

esulting in an overall equivalent amount of energy absorption.or a height of 3.3 m, specimen DA4_1 has a stroke efficiency of4.4%, while DA6_1 has a stroke efficiency of 61.6%; the energybsorbed is 11.2 kJ and 11.1 kJ, respectively.

3.2.2 Specimen Group B_H50 and B_HEq

3.2.2.1 Group B_H50. All group B_H50 specimens tested dy-amically buckled in the PS mode. Specimens tested at heights of.5 m and 3.3 m, respectively, are given in Fig. 14. The figurellustrates that specimens of group B_H50 are characterized by a

Fig. 10 Force-displacement curve for the

ig. 11 Photographs of the transient quasistatic crushing of
pecimen SB8_HEq_1


steady and repeatable mode of collapse. Figure 14 also illustratesthat there is a random cluster of lobes formed at either the impactend, nonimpact end, or the middle of the tube. No significantchanges in mean force, stroke efficiency, or energy absorption arenotable for an increase in the number of holes within the speci-mens tested at the same height. The average values for meanforce, stroke efficiency, and energy absorbed for specimens testedat 4m are 57.4 kN, 79.8%, and 13.7 kJ, respectively. These valuesare similar to those for the plain tube, d_plain_tube_2, tested atthe same height; a mean force of 57.5 kN, a stroke efficiency of79.6%, and an energy absorption of 13.7 kJ. This indicates that theaddition of holes has no quantitative effect on the energy absorp-tion parameters of a plain tube. The absence of collapse in Eulerbending or MM in this group indicates that the addition of holes inthe specified configuration ensures the development of progres-sive collapse. A definite occurrence of progressive collapse is adesirable feature in energy absorbing devices in which progressivecollapse is required to provide the necessary energy absorbingattributes. Figure 15 further illustrates the repeatability achievedby specimen group B_H50 where configuration B6_H50 speci-mens both tested at 3.3 m produce similar collapse profiles.

3.2.2.2 Group B_HEq. Specimen group B_HEq is character-ized by the formation of lobes of different sizes within the samespecimen. Though the overall collapse mode remains progressive,the change in the lobe size compromises the overall stability ofthe collapse mode in some specimens. Figures 16–18 illustratephotographs of the specimens of group B_HEq after dynamicaxial crushing at the indicated heights.

The irregular lobes formed in group B_HEq specimens are im-posed by the distances between successive discontinuities andhave wavelengths larger than that would develop in a plain tube.The result is an uneven distribution of lobes such that these ir-regular lobes destabilize the collapse causing the tube to tilt to oneside as viewed in photograph �b� of Figs. 16 and 17, respectively.The collapse mode is compromised because these irregular lobesresult in the tube leaning over precariously as if about to collapsein mixed mode. It is noted earlier for the quasistatic tests thatspecimen configuration B6_HEq is characterized by regular sizedlobes similar to those present in a plain tube. For the dynamic

sistatic crushing of specimen SB8_HEq_1

tests, the same observation is made for specimen DB6_HEq_3,

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llustrated in Fig. 19. The mean force, energy absorbed and strokefficiency for specimen DB6_HEq_3 are 57.5 kN, 13.7 kJ, and9.5%, respectively. These values are similar to those of d_plain-tube_2 also tested at 3.3 m, which are 57.5 kN, 13.7 kJ, and9.6%, respectively.

Discussion of Experimental Findings

4.1 Initial Peak Force. The reduction in initial peak forceelative to a plain tube is illustrated in Fig. 20 for each specimenonfiguration. Figure 20 illustrates that group B_H50 results in theighest reduction in initial peak force. The reduction in initialeak force for group B_HEq is generally similar to that of group

Table 2 Test results for square tub

Specimen nameh

�m�V

�m/s�

d_plain_tube_1 3.3 8.0d_plain_tube_2 4.0 8.9DA2_1 3.3 8.0DA2_2 3.3 8.0DA2_3 3.3 8.0DA4_1 3.3 8.0DA4_2� 3.3 8.0DA4_3 4.0 8.9DA4_4 2.5 7.0DA6_1 3.3 8.0DA6_2 4.0 8.9DA6_3� 2.5 7.0DB4_H50_1 3.3 8.0DB4_H50_2 3.3 8.0DB4_H50_3 4.0 8.9DB4_50_4 2.5 7.0DB6_H50_1 3.3 8.0DB6_H50_2 3.3 8.0DB6_H50_3 4.0 8.9DB6_H50_4 2.5 7.0DB8_H50_1 3.3 8.0DB8_H50_2 4.0 8.9DB8_H50_3 2.5 7.0DB10_H50_1 3.3 8.0DB10_H50_2 4.0 8.9DB10_H50_3 2.5 7.0DB4_Heq_1 3.3 8.0DB4_Heq_2 2.5 7.0DB4_Heq_3� 4.0 8.9DB6_Heq_1 3.3 8.0DB6_Heq_2 2.5 7.0DB6_Heq_3 4.0 8.9DB8_Heq_1 3.3 8.0DB8_Heq_2 2.5 7.0DB8_Heq_3 3.3 8.0

ig. 12 Photographs of specimens „a… DA4_4, „b… DA4–1, andc… DA4_3 after loading at heights of 2.5 m, 3.3 m, and 4 m,
espectively
41012-8 / Vol. 76, JULY 2009


A. This implies that not only is having holes on all four sides ofthe tube better for initial peak force reduction but also fixing holespacing appropriately as group B_H50 is better than the sym-metrical spacing of group B_HEq. This confirms that having thediscontinuities at the estimated tube wavelength improves crash-worthiness as suggested by Montanini et al. �10� and Lee et al.�15�.

4.2 Collapse Mode. Group B_H50 has the most stable col-lapse mode, which was not prone to mixed mode collapse. Speci-men group A is the most unstable. Of the 11 group A specimenstested dynamically and quasistatically, 5 collapsed in mixed mode,

subjected to dynamic axial loading

��mm�

Ea�kJ�

Pm�kN�

SE�%�

210.0 11.2 53.5 70.0238.7 13.7 57.5 79.6172.0 11.1 64.6 57.3176.1 11.1 63.1 58.7209.3 11.2 53.7 69.8193.3 11.2 57.9 64.4

- - - -241.8 13.8 56.9 80.6155.8 8.6 55.2 52.0184.6 11.1 60.3 61.6235.5 13.7 58.3 78.5

- - - -193.6 11.2 57.6 64.6199.4 11.2 56.2 66.5240.8 13.8 57.1 80.3154.5 8.6 55.6 51.5190.5 11.2 58.5 63.5200.1 11.2 56.1 66.7237.4 13.7 57.8 79.1167.5 8.6 51.5 55.8201.4 11.2 55.6 67.1239.8 13.7 57.3 79.9167.2 8.7 51.7 55.7192.1 11.2 58.2 64.0239.1 13.7 57.4 79.7158.6 8.6 54.4 52.9184.7 11.2 60.4 61.6180.6 8.7 48.0 60.2

- - - -179.5 11.1 62.1 59.8181.9 8.7 47.7 60.6238.4 13.7 57.5 79.5216.0 11.3 52.1 72.0177.9 8.7 48.7 59.3203.4 11.2 55.2 67.8

Fig. 13 Photographs of specimens „a… DA6_3, „b… DA6_1, and„c… DA6_2 after load at heights of 2.5 m, 3.3 m, and 4 m,

es

respectively



3BwlB

Fi

Fa

Fa

J

Downloa

of which were tested dynamically. Both groups B_H50 and_HEq exhibit mostly progressive collapse mode but the lobesere of significantly different shapes. Group B_H50 produces

obes of regular sizes much like those of a plain tube. In group_HEq however, the lobes induced are of a nonuniform size.

ig. 14 Photographs of specimens of group B-H50 after load-ng at heights of „a… 2.5 m and „b… 3.3 m

ig. 15 Photographs of specimens of configuration B6_H50fter loading at a height of 3.3 m

ig. 16 Photographs of specimens of configuration B4_HEq
fter loading at heights of „a… 2.5 m and „b… 3.3 m


4.3 Crush Force Efficiency. The crush force efficiency forgroups B_H50 and B_HEq is illustrated in Fig. 21. Within eachspecimen group, CFE fluctuates about some average for an in-crease in the number of holes. The average CFE for group A,B_H50, and B_HEq is 0.38, 0.40, and 0.36, respectively. The

Fig. 17 Photographs of specimens of configuration B6_HEqafter loading at heights of „a… 2.5 m, „b… 3.3 m, and „c… 4 m

Fig. 18 Photographs of specimens of configuration B8_HEqafter loading at a height of 3.3 m

Fig. 19 Photograph of specimen DB6_HEq_3 after loading at a
height of 4 m
JULY 2009, Vol. 76 / 041012-9


at

macT

of

0

Downloa

verage CFE for group B_H50 is 27% higher than that of the plainubes, which averages 0.31 for plain tubes tested quasistatically.

4.4 Stroke Efficiency. The stroke efficiencies for all speci-ens of group A, group B_H50 and B_HEq crushed dynamically

t height of 3.3m averaged 65%. This is less than the stroke effi-iency of a plain tube crushed at the same height which is 70%.his better stroke efficiency does not necessarily imply that the

Fig. 20 Reduction in initial peak force for specimens

Fig. 21 Crush force efficiency for groups B_H50 an

41012-10 / Vol. 76, JULY 2009


introduction of holes is futile since it has been shown that groupswith holes �B_H50� improve other energy absorption parameters�CFE�.

5 ConclusionsDynamic and quasistatic axial crush tests are performed on

mild steel tubes of various hole configurations. The presence of

groups A, B_ HEq, and B_H50 crushed quasistatically

d B_HEq for specimens crushed quasistatically



hngaBostgvpptmti

A

Mt

N

R

J

Downloa

oles decreases the initial peak force at all times; this is howeverot improved by an increase in the number of holes. Specimenroup B_H50 significantly improves the crush force efficiency ofplain tube. The mode of crush initiation that develops in group_H50 is associated with lower initial peak forces. The locationf holes at points corresponding to the natural hinges of lobes, aseen in group B_H50, appears to greatly improve energy absorp-ion by ensuring that progressive collapse mode is repeatedly trig-ered. This repeatability is important for energy absorption de-ices as it means that this group can be expected to crush in thereferred progressive mode at most times. Specimen group A dis-lays both progressive and mixed mode collapse in specimens ofhe same hole configuration. This means that hole discontinuities

ay have a negative effect on the energy absorption characteris-ics if unfavorably positioned. Group A specimens, however, showmproved performance under dynamic loading.

cknowledgmentThe authors wish to thank Glen Newins and Dylan Jacobs at theechanical Engineering Workshop, UCT for manufacturing the

est specimens.

omenclatureC � width of side of square tubed � hole diameter

Ead � energy absorbed �dynamic�

Eas � energy absorbed �quasistatic�

H � initial height of massl � half the wavelength of a single lobe

L � initial length of tubem � massPi � initial peak force

Pm � mean crushing forcet � wall thickness

V � impact velocity� � crushed distance �stroke�

eferences�1� Lu, G., and Yu, T., 2003, Energy Absorption of Structures and Materials,

Woodhead, Cambridge.�2� Abramowicz, W., 2003, “Thin-Walled Structures as Impact Energy Absorb-



ers,” Thin-Walled Struct., 41, pp. 91–107.�3� Langseth, M., and Hopperstad, O. S., 1996, “Static and Dynamic Axial Crush-

ing of Square Thin-Walled Aluminium Extrusions,” Int. J. Impact Eng., 18�7–8�, pp. 949–968.

�4� World Health Organization and World Bank, 2004, “World Report on RoadTraffic Injury Prevention,” Prevention, World Health Organization, Geneva.

�5� Cheng, Q., Altenhof, W., and Li, L., 2006, “Experimental Investigations on theCrush Behaviour of AA6061-T6 Aluminium Square Tubes With DifferentTypes of Through-Hole Discontinuities,” Thin-Walled Struct., 44, pp. 441–454.

�6� Abramowicz, W., and Jones, N., 1984, “Dynamic Axial Crushing of SquareTubes,” Int. J. Impact Eng., 2, pp. 179–208.

�7� Arnold, B., and Altenhof, W., 2004, “Experimental Observations on the CrushCharacteristics of AA6061 T4 and T6 Structural Square Tubes With and With-out Circular Discontinuities,” Int. J. Crashworthiness, 9�1�, pp. 73–87.

�8� Tarigopula, V., Langseth, M., Hopperstad, O. S., and Clausen, A. H., 2006,“An Experimental and Numerical Study of Energy Absorption in Thin-WalledHigh-Strength Steel Sections,” Int. J. Impact Eng., 32�5�, pp. 847–882.

�9� Abramowicz, W., and Jones, N., 1997, “Transition From Initial Global Bend-ing to Progressive Buckling of Tubes Loaded Statically and Dynamically,” Int.J. Impact Eng., 19�5–6�, pp. 415–437.

�10� Montanini, R., Belingardi, G., and Vadori, R., 1997, “Dynamic Axial Crushingof Triggered Aluminium Thin-Walled Columns,” 30th International Sympo-sium on Automotive Technology & Automation, Florence, Italy, Jun. 16–19,pp. 437–444.

�11� Chung Kim Yuen, S., and Nurick, G. N., 2008, “The Energy Absorbing Char-acteristics of Tubular Structures With Geometric and Material Modifications:An Overview,” Appl. Mech. Rev., 61�2�, p. 020802.

�12� Langseth, M., and Hopperstad, O. S., 1997, “Local Buckling of Square Thin-Walled Aluminium Extrusions,” Thin-Walled Struct., 27�1�, pp. 117–126.

�13� Marshall, N. S., and Nurick, G. N., 1998, “The Effect of Induced Deforma-tions on the Formation of the First Lobe of Symmetric Progressive Buckling ofThin Walled Square Tubes,” Structures Under Shock and Impact �SUSI 98�,Thessaloniki, Greece, Jun. 24–26, N. Jones, D. G. Talaslidis, C. A. Brebbia,and G. D. Manolis, eds., pp. 155–168.

�14� Gupta, N. K., and Gupta, S. K., 1993, “Effect of Annealing, Size and Cut-Outson Axial Collapse Behaviour of Circular Tubes,” Int. J. Mech. Sci., 35�7�, pp.597–613.

�15� Lee, S., Hahn, C., Rhee, M., and Oh, J., 1999, “Effect of Triggering on theEnergy Absorption Capacity of Axially Compressed Aluminum Tubes,” Mater.Des., 20�1�, pp. 31–40.

�16� Abramowicz, W., and Jones, N., 1986, “Dynamic Progressive Buckling ofCircular and Square Tubes,” Int. J. Impact Eng., 4�4�, pp. 243–270.

�17� Bodlani, S. B., Chung Kim Yuen, S., and Nurick, G. N., 2009, “The EnergyAbsorption Characteristics of Square Mild Steel Tubes With Multiple InducedCircular Hole Discontinuities—Part II: Numerical Simulations,” ASME J.Appl. Mech., 76, p. 041013.

�18� Otubushin, A., 1998, “Detailed Validation of a Non-Linear Finite ElementCode Using Dynamic Axial Crushing of a Square Tube,” Int. J. Impact Eng.,21�5�, pp. 349–368.

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