Thin-Walled Structures 67 (2013) 25–33

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Thin-Walled Structures

0263-82

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n Corr

E-m

journal homepage: www.elsevier.com/locate/tws

Crashworthiness design of vehicle side door beams under low-speedpole side impacts

Ali Ghadianlou n, Shahrir Bin Abdullah

Department of Mechanical and Materials Engineering, Faculty of Engineering, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

a r t i c l e i n f o

Article history:

Received 30 October 2012

Accepted 4 February 2013Available online 20 March 2013

Keywords:

Side door beam

Low speed impacts

Permanent damage

Reinforcing ribs

31/$ - see front matter & 2013 Elsevier Ltd. A

x.doi.org/10.1016/j.tws.2013.02.004

esponding author. Tel.: þ60 126394501.

ail address: ali.gh@eng.ukm.my (A. Ghadianlo

a b s t r a c t

In low speed collisions, insurance cost is a factor which is taken into account as a design criterion to

reduce structure damage and fixing cost. In this study, it is focused on the applied permanent damages

of vehicle frontal door caused by pole impacts. In the side impact, the side door beam is responsible to

absorb the most possible kinetic energy. Two significant parameters including material and geometry

of a side door beam are discussed here to reduce permanent damage of the door. To study the effect of

material as the first phase, six different sheets of material have been concerned to investigate the

rigidity of the structure. For the second phase, geometry modification of the side door beam has been

performed via creating new CAD-reinforcing ribs. Consequently, the strength in elasto-plastic mode,

maximum deflection and plastic strain of the equipped system representing the permanent damage is

obtained in order to achieve lower losses.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Side impacts are one of the awfully hazardous crashes causingdeath and injuries annually around the word. Global rate ofaccidents reveals that more than third of all accidents occursdue to the side impact of trees or posts showing the significanceof it comparing to frontal crash events. There are so manyresearch focusing on the ability of the vehicle structure to absorbthe impact energy and to reduce the crash pulse transferred tohuman in side impacts [1]. By the presence of new advancedmaterials such as composites and better comprehension ofcrashworthiness knowledge as well, occupant protection, passen-ger safety and structural weight have been developed in highspeed crash mode [2]. The main automotive part which under-goes impact stress caused by frontal crash either in low or highspeed mode is the bumper investigated by many researchers [3].In this respect, the design of this crucial element is very challen-ging as it is the first component experiencing the strike in frontalimpact. Therefore, it can be concluded that strengthening vehiclebody-door in side impacts demands more attention due to havingless impact zone area and lower rigidity compared with thebumper. From the other side, side impacts could lead to loss ofprofit further because of its high maintenance cost in painting andrepairing dents of the body. Generally, side impacts are dividedinto two diverse styles including pole impact and side to side car

ll rights reserved.

u).

impact which are examined by a round pole and a moveabledeformable barrier (MDB), respectively.

In this way, some car safety assessment standards like EuroNCAP and FMVSS have established specific full-scale proceduresin conducting side impact tests [4]. In the side impacts from thepole type, the test is performed by a narrow pole colliding withthe car so the side structure is stricken considerably and asizeable intrusion is created in the crash zone of the door. Sincethe side structure consists of the body plate and pillars, theirstiffness is much lower than that of the front bumper. It mightcome from the lack of space or reinforcing parts to strengthenthe door.

In low speed mode, the main goal has been to equip thesystem to have developed crashworthiness behavior and minimalgenerated damage [5]. This area of research studies have beenaccomplished very well in the past few decades by strengtheningcar bumpers in frontal crash using new manufacturing methodsand materials such as composites, foams, etc [6–10]. However,there are a few number of papers which could have been carriedout to reinforce the other parts of vehicles such as doors duringside impacts. Keeping the frontal door in the minimum possiblepermanent deformation in low speed collisions is the challengewe are looking for. Therefore, the objective of this research is toreinforce the side door beam geometrically and materially andevaluate the energy absorption distinctiveness of it achievingimproved crash behavior compared to the current structure. Thedevelopments are based on the body door-plate deflectionsrepresenting the insurance cost of accidental damage. Accord-ingly, the car must yield the crash with the least possible damage

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–3326

to satisfy the minimal fixing cost through particular insurancecategorization.

In this scenario, the side door beam plays a consequential rolein damping external forces and absorbing side impact energy byresisting bending in impact phenomena [11]. Consequently, it isnoticeably in need of improving crashworthiness to have bettercrash performance. In civil engineering, the term, beam, isreferred to any moderately long piece of a metal to yield in thedesign bending stress level. In impact problems, the bendingevent occurs per milliseconds dynamically so the beam should besufficient stiffness to withstand the bending momentum.

Numerous developments are carried out for thin-walled pro-files with various cross sections under impact loading [12–16].Automotive side door beam analyzed in this study is also made ofa thin-walled tube with cylindrical shape showing in Fig. 1 andthe whole model is obtained from a local car company which itsname is supposed to be confidential.

As the side door beam system should absorb most of thekinetic energy, the most valuable and expensive parts like thedoor plate ought not to receive plastic deformation seriously.For crashworthiness evaluating, nonlinear explicit FEA havehighly developed the dynamic modeling of the vehicle structures.In order to examine the door response in pole impacts, a simpli-fied real model including just the frontal door with its accessoriesis considered to analyze the real dynamic sequence of the side doorbeam and the door plate toward the mentioned above scopes.The computer aided design (CAD) data of the model is imported toLS-DYNA explicit finite element 3.1 Beta, LSTC Co. The wholestructure is meshed technically to have adaptively appropriatenodal coordination in the jointed regions which are constrained.

There are two strategic phases being studied here. The firstphase is derived from material investigation and the ability of amaterial to affect structure response and the generated move-ment of the door plate. In addition, form the point of claimingreduced weight to increase the vehicle fuel efficiency, the opera-tion characteristics in lightweight purpose are also discussed inthis section.

To clarify the function of material of the side door beam, theinfluence of module of elasticity and yield strength with the

Fig. 1. Three dimensional v

consideration of strain hardening behavior of the material isunder inquiry in this phase. As the second phase, geometrymodification of the side door beam is taken into concern byvarying thickness, i.e., how the thickness of the side door beamcan have effects on the door plate reactions, displacements andexisting crush forces.

Finalizing the geometry modification, modeling a set of sepa-rate reinforcing parts through integrated CAD and CAE process toextract the best impact behavior causing the door plate not to beundergone any significant plastic deformation. A great number ofreinforcing ribs are formed inside of the side door beams with avariety of cross-section areas to meet the fabrication features ofthe side door beams in automotive industry from the designaspect of low speed impacts.

2. Impact theory

To clear the basic principal of different impact algorithms,strain energy is defined from Eq. (1) meaning the potentiallyabsorbed energy corresponding to the work done accumulated ina material when is deformed. The integration is on the volume ofeach element based on the applied force, created elongation andstress distribution. Through lightweight scopes, specific energyabsorption parameter, SEA, is considered to consider the capabil-ity of a material to absorb the energy having less weight andachieving improved crash behavior or equal to the currentstructure from Eq. (2).

Ue ¼1

2

Zvs� e� dv¼

1

2Keq:d

2max ð1Þ

SEA¼Ue=Mass ð2Þ

Where s, e and v equal to stress tensor; strain tensor andelement volume respectively. Keq, an inherent characteristic of amaterial, is the stiffness of the body relating deflections (d) andthe resultant forces. In an event of a collision, it is quite importantto discriminate two types of impacts. In the perfectly elasticcollision, the masses could have different velocities after impact

iew of the side impact.

Table 1

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–33 27

and an insignificant amount of energy is transferred among them.However, objects could receive the same velocity after strikingtogether.

Automobile accidents include elasto-plastic deformationsdepending on the severity of the crash forces as this study impliesfor impacting of a rigid pole impactor to the car-door structure inlow-speed conditions. On the other hand, vehicle manufacturershave always struggled to strengthen the automotive componentsto prevent failure happening and plastic deflections. Havingdynamic kind of the problem causes nonuniform stress distribu-tion along the contact area of the door and the pole to be expectedwhich is in interest of analyzing in this study.

The foundation of energy conservation in an inelastic impactconditions implies that the masses must have the same convertedkinetic energy from the initiation of the movement up to themaximum deflection point and before the separation point.

1

2mpv2

p ¼v2

2ðmpþmdÞþ

1

2Keq:d

2max ð3Þ

Where mp is the mass of the pole impactor, md is the mass ofthe door; vp is the velocity of the imapactor before the crash andis the final same velocity of the two masses after the impact.In this study, the initial velocity of the door structure is supposedto be zero. The impulse-momentum change theorem infersthat the amount of momentum remains constant before and aftercollision expressed as follows:

mpvp ¼ ðmpþmdÞv ð4Þ

The equation of kinetic energy and momentum conservationafter the separation point could be specified as bellows:

1

2mpv2

p ¼1

2mpv0p2þ

1

2mdv0d2 ð5Þ

mpvp ¼mpv 0pþmdv 0d ð6Þ

Where v0p and v0d are the final velocities of the rigid pole andthe door from the initiation status up to the separation point.Another deterministic criterion in striking masses is the coeffi-cient of restitution abbreviated by COR which is the ratio of thespeed differences after and before striking.

COR¼v0p�v0dvp�vd

ð7Þ

Since in a crash event, the masses of the contactors cannot bechanged while the object’s velocities are varying quickly, thefactor COR is a useful parameter to check the converted energyand the generated deformation. The COR value of 1.0 representselastic collisions while the value of zero is for perfectly plasticimpacts explaining that the high amount of energy is converted toheat and deflections. It is necessary to mention that for the elasto-plastic impact of this study, the actual COR value is localizedsomewhere between this interval. The plastic strain energyrelating directly to the permanent damage of the door plate isobtained by deducting the kinetic energy of the door and the polebefore and after collision.

EPlastric ¼1

2mpv2

pþ1

2mdv2

d�1

2mpv0p2�

1

2mdv0d2 ð8Þ

Material properties of the side door beams.

Material Poisson’s

ratio, uYield stress,

Sy(MPa)

Density,

r (kg/m3)

Elasticity

modulus, E (GPa)

Magnesium

AZ31B-H24

0.350 136.3 1771 44.81

Aluminum

5050-H32 sheet

0.330 136.7 2684 68.94

Steel wrought 321 0.290 146.1 7888 193.05

3. Finite element approach

In order to analyze the precise impact performance of a frontvehicle door as near as possible to an actual fabricated door,a model from a local company is chosen to be tested numericallyshown in Fig. 1. To simulate the contact area between two masse,the type of automatic-single-surface contact is considered in

LS-DYNA finite element solver [17]. The CAE process is initiatedby importing the CAD data of the door and generating fittingsurfaces to be meshed satisfying the real constrained nodal rigidbodies as well. The aforementioned model consists of 21,172elements and 22,400 nodes associated by 17 shell parts withmostly the same material properties. The four node-quadrilateralelement, Belytschko-Tsay, is preferred to be applied because of itshighly suitable function in shell elements with the formulation of3 integration points. For a side door beam system to be analyzedaccurately, applying fine mesh resolution is vital and is appliedtechnically in the following investigations. To equip the doorunder any externally likelihood momentum, two cylindrical sidedoor beams with the same circular cross section and two diffe-rent arranging angles in the space toward the door plate areconsidered.

To simplify the impact occurring to this collection, it isassumed that a pole made of steel strikes to the stationary doorstructure with the velocity of 4 m/s. The crash is supposed to bevertically in all examples and in a straight line as illustrated in theFig. 1. The boundary conditions of the door movement areselected in the manner that lateral edges interfaced with thevehicle could travel along all directions except the directionwhich is perpendicular to the crash progress. The masses of thepole impactor and the door structure are 20 kg and approximately6 kg, respectively. Besides, there are no frictional losses betweenthe pole and the door’s surface.

For the connection type of the components, the effects of thespot-welded failure at jointed sheet-metals are neglected and it issupposed that any set of parts is constrained to each other in allsex degrees of freedom without modeling the mechanicalstrength of the coupled parts. The total termination time of theeach test is chosen to be 60 ms representing the enough timeduration to release kinetic energy completely.

4. Side door beam material

With the consideration of demanding minimum weight ofwhite-body to achieve higher fuel efficiency, deep-drawn sheetsof aluminum alloys are predominately being used for non-supporting parts such as doors, hoods and fenders [18]. Applyingaluminum kind of alloys caused the wall thickness of the parts tobe increased to satisfy the required stiffness and strength. In thisstudy, the door plate, door inner/outer panel and the side doorbeam are made of an aluminum alloy with reasonable corrosionresistance and weldability.

To simulate the material properties, Type 024, Piecewise-Linear-Plasticity, is used to model elasto-palstic materials with apredefined stress versus strain curve with many piecewise linearsegments. The used date includes 100 true stress–strain pointsobtained by other research developers experimentally such as[19] for each category of material selections in Tables 1 and 2. Thebasic principal of material selections in phase-1 is to includesimilar strain hardening behavior for each category. According to

Table 2Material properties of the side door beams.

Material Poisson’s

ratio, uYield stress,

Sy(MPa)

Density,

r (kg/m3)

Elasticity

modulus, E (GPa)

Aluminum

6063-O sheet

0.330 35.3 2712 68.94

Aluminum

5050-H32

sheet

0.330 136.7 2684 68.94

Aluminum

2219-T31 sheet

0.290 297.6 2823 73.08

0

50

100

150

200

250

0 0.01 0.02 0.03 0.04 0.05 0.06

Def

lect

ion

(mm

)

Time (s)

Mg.

Al.

St.

Fig. 2. Magnesium, steel and aluminum side door beam deflections.

0

10

20

30

40

50

60

70

80

90

0 0.01 0.02 0.03 0.04 0.05 0.06

Ene

rgy

(J)

Time (s)

Al.Mg.St.

Fig. 3. Internal absorbed energy of the side door beam materials.

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–3328

the relationship developed by Ramberg and Osgood [20], theelastic and plastic strain experienced by a material are assumedseparately and are added together to describe the non-linearrelationship between stress–strain as expressed in Eq. (9).Another useful factor to compare the plastic strain as thepermanent damage is the effective plastic strain (EPS) specifiedin Eq. (10).

s¼ Kenp-etotal ¼

sEþ

sk

� �ð1=nÞ

ð9Þ

Effective Plastic Strain ðEPSÞ ¼ total true strain �true stress

Eð10Þ

Where ep represents the plastic strain, K and n is calledstrength coefficient and strain hardening exponent correspond-ingly. To investigate the effects of material of the side door beams,the module of elasticity and the yield strength are changed in twoseparation parts 4.1 and 4.2. To emphasize the effects of thesetwo factors, it is needed to have equal strain hardening exponent(n), otherwise, in the plastic region; the materials could show anunanticipated result due to their dissimilar hardening works.

4.1. Elasticity modulus

To consider the effect of elasticity modulus, mechanical proper-ties of three sheets of materials with different elasticity modulushaving almost constant yielding points are assigned to the sidedoor beams. Table 1 shows these metal sheets as aluminum,magnesium and steel and their mechanical strength parameters.Other impact conditions are kept unchanged for the all case ofstudies. In addition, to signify the influence of E, the modulus ofelasticity, It is assumed that all categories of material conduct inthe same strain hardening conditions. Since their yield strength isalso near together, it can be concluded that their impact responsedepends only on their K-factor, strength coefficient.

Generally, there are two types of deformations which arediscussed in this study: First, the average longitudinal deflectionsof the side door beam-cylinders and second, the average displace-ments of the elements located at the middle of the door plate. Forthe first type, the deflections are not the actual displacementsoccurring to the side door beams since they are measured fromthe resultant rigid body displacement of the whole cylindersrepresenting the accumulation of all elements’ deflections in eachtime state. This type is useful if any strain energy is underinvestigation. For the second type, since the maximum damagetakes place in the middle of the body door-plate, the averagedisplacements of the door’s central elements are compared toeach other.

Fig. 2 shows the average longitudinal deflections of the twoside door beams made of magnesium, aluminum and steel alloys.The separation points occur approximately in 45, 42 and 35 msfor magnesium, aluminum and steel, respectively. It can be

concluded that the steel beam touched the pole impactor in theshortest time. In addition, the maximum deflection among thementioned cases belongs to the magnesium with the value of241 mm while the minimal deflection takes place for the steelside door beam in 157 mm. Both behaviors are attributed to thematerial rigidity and stiffness. In fact, steel stiffness is higher thanthat of aluminum and the aluminum stiffness are higher than thatof magnesium.

Fig. 3 illustrates the summation of the internal absorbedenergy of the two side door beams for the material cases. Thesteel side door beams could absorb the highest amount of energy,80 J, among the others in the shortest connection time. In otherwords, the integration of the stress and strain accumulated in themagnesium and aluminum could not catch the steel one. As it canbe seen in the graph, the energy rate becomes zero when theplastic deformation releases completely in the system and alsowith the initiation of the aforesaid separation time for eachmaterial from the group, their energy becomes constant as well.

Specific energy absorption, SEA in Eq. (2), is obtained bydividing the value of the energy to its own material weightdemonstrated in Fig. 4. The results show that since magnesiumhas the lowest density, it could attain the maximum SEA morethan three times of the steel’s SEA. Nevertheless the magnesiumbeam absorbs the maximum specific strain energy; it cannotachieve the current or improved crashworthiness of the steelstructure. Therefore, with the consideration of light weightpurpose, magnesium and aluminum have better performancethan the steel. However, they cannot absorb the impact energyas the steel does.

The next graph, Fig. 5, is to explain the permanent damagedoccurred to the door with different materials for the side doorbeams in low-speed crashes. Since the magnesium beams take

0

20

40

60

80

100

120

0 0.01 0.02 0.03 0.04 0.05 0.06

SE

A (J

/m)

Time (s)

Al.

Mg.

St.

Fig. 4. Specific energy absorption of the selected materials.

05

1015202530354045

0 0.01 0.02 0.03 0.04 0.05 0.06

Dis

plac

emen

t (m

m)

Time (s)

Al.

Mg.

St.

Fig. 5. Average displacement of the body door plate.

0

1000

2000

3000

4000

5000

6000

0 0.01 0.02 0.03 0.04 0.05 0.06

Forc

e (N

)

Time (s)

Mg.

Al.

St.

Fig. 6. Crush force distribution of the selected materials.

0

50

100

150

200

250

300

0 0.02 0.04 0.06

Def

lect

ion

(mm

)

Time (s)

Sy=298

Sy=35

Sy=137

Fig. 7. Various aluminum side door beam deflections.

0

10

20

30

40

50

60

70

0 0.02 0.04 0.06

Ene

rgy

(J)

Time (s)

Sy=298Sy=35Sy=137

Fig. 8. Internal absorbed energy of the aluminum materials.

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–33 29

the minimal amount of the energy to be deformed, the morekinetic energy can be transferred to the body so the door plateundergoes the maximum displacement of 47 mm and remainsconstant in the plastic deformation of 23 mm. In all cases, thedisplacements after collision do not become zero as the plasticdeformation takes place in the system. Steel door beams achievednot only the minimal peak-deflections of the door plate in 36 mmbut also the minimal plastic deformation of 5 mm. Thus, applyinghigh stiff materials like steel as the side door beam could lead tothe least permanent damage of the door in low-speed full sideimpacts.

Another significant factor is the crush distributed force whichmight be more highlighted in high-speed mode due to theimportance of passenger safety. This parameter is measured byadding a force transducer to assess the contact interface forcesproduced by the pole impactor as the master side and a subset ofthe door parts as the slave side. According to the Fig. 6, magne-sium beams produce the slightest peak force in 5.04 KN, alumi-num beams makes the intermediate peak force in 5.64 KN andthe steel beams generates the maximum force in 6.06 KN inthe system. Although using stiff materials such as steel reducedthe permanent damage and deformation of the door very well,producing the great amount of crash forces might be the negativepoint of their design and should be optimized to be taken place inthe limitations made by crash safety standards.

4.2. Yield strength

The differences between the yielding points of the threedifferent aluminum alloys are chosen to be studied in this sectionand listed in Table 2. This category of the materials acts alsoidentically in the strain hardening process and with roughlyequivalent yield strength. Fig. 7 shows the comparison of the side

door beam deflections made from a set of materials. As it can beseen, aluminum alloy whit higher yield strength is less deformedin both elastic and plastic regions. Moreover, low-strength alu-minums need more time to be separated (separation time) andalso more time to be bended up to the maximum possibledisplacement.

The accumulation of the individual side door beam’s strainenergy for the different aluminum alloys in Fig. 8 illuminates thataluminum 2219-T31 with the highest strength could absorb thepeak energy of the 77 J in the closest time. Furthermore, thisenergy was turned into the stable state earlier than the others inthe unbending process. Fig. 9 proves that using high stiff alumi-nums as the side door beam could decrease the permanentdamage or plastic deflection from 4 cm to less than 1 cm.

The maximum crash forces of aluminum beams are able to beanticipated from the last analysis, the effects of elasticity

0

10

20

30

40

50

0 0.02 0.04 0.06

Dis

plac

emen

t (m

m)

Time (s)

Sy=137Sy=35Sy=298

Fig. 9. Average displacement of the body door plate for different aluminums.

0

1000

2000

3000

4000

5000

6000

0 0.02 0.04 0.06

Forc

e (N

)

Time (s)

Sy=298

Sy=35

Sy=137

Fig. 10. Crush force distribution of different aluminums.

05

101520253035404550

0 0.02 0.04 0.06

Def

lect

ion

(mm

)

Time (s)

Thk 1 mmThk 2 mmThk 3 mmThk 4 mm

Fig. 11. Effects of thickness on side door beam deflections.

0

1000

2000

3000

4000

5000

6000

0 0.02 0.04 0.06

Forc

e (N

)

Time (s)

Thk 1 mm

Thk 2 mm

Thk 3 mm

Thk 4 mm

Fig. 12. Crush force by thickness variations.

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–3330

modulus. As shown in Fig. 10, low rigid materials such asaluminum 6063 results the smaller reaction forces between thepole and the body plate and has better crashworthiness behavior.

5. Side door beam thickness

Different side door beam thicknesses made of mediumstrength aluminum alloy with 134 MPa yield strength and theelasticity modulus of 70 GPa are assigned to assess the effects ofcylinder wall thickness of the side door beam. Carrying out thismaterial grade results the reduction of the empty weight and aconsequent raise in payload. The default fabricated thickness ofthe tubes is considered to be 2 mm.

The average displacement of the cylinders in the middleelements which are in contact with the pole from one side andthe body plate from another side are Figured out in the bellowgraph, Fig. 11. Therefore, the values are in kind of actual cases andare related proportionally to the damage occurred to the doorplate. It is obviously observed that by adding the wall thickness,the rigidity of the system goes up so the deflections of the sidedoor beams and body plate decrease. Meanwhile, the separationpoints and the peak-deflections of the thinner beams occur with adelay compared to the thickest wall of 4 mm.

The crash pulse transferred to the structure becomes strongerin Fig. 12 by increasing the side door beam’s thickness. To justifythis event, it can be said that; by increasing the rigidity throughmore thicknesses, the displacement amplitude of the doorresponse becomes less and it needs less time to be dampedcompletely. This event causes the acceleration to become raisedand affect directly the forces to become raised also.

6. Geometry modification

To reinforce the critical parts such as automobile bumpers andpillars, ribs are being prevalently used. This particular componenthas the average thickness of 2–4 mm and mainly placed in thepredesigned regions to prevent additional deflections andstrengthen the structural rigidity. To examine the role of reinfor-cing ribs on side impacts, various ribs with different shapes areemployed inside the side door beams whereas all of them havethe same material and thickness as the beams have. Efforts aretaken to produce the ribs CAD-data and mesh them to be basicallyhomogeneous with the cylinders. This task needs not only gen-erating the same mesh size for the ribs and cylinders but alsoreclassifying the elements’ coordinates to be compatible with thesupported regions at the ends of the cylinders.

For the first section, the cross-section of the cylinder beams isplaced under investigation by following two important questions.The first question is that; how many ribs could absorb the internalenergy usefully and affect impact conditions greatly. And thesecond question is that; how the ribs’ arrangement could modifythe beam deflections to reduce the permanent damage of thebody door plate. To answer these questions, four different shapesof the ribs are assumed to be applied showing in Fig. 13.

Fig. 14 shows the internal strain energy of the cylinder beamsequipped by different ribs. The results demonstrate that ribarrangements have preference to the number of the ribs, i.e.,the ribs with the number of the two (comprising 3 cells) assignedin horizontal direction could achieve the best impact response(type c). In other words, the three-cell horizontal ribs could

Fig. 13. Four different arrangements of the inside ribs: two-cell horizontal (a), two-cell vertical (b), three-cell horizontal (c) and three-cell vertical (d).

0

10000

20000

30000

40000

50000

60000

0 0.01 0.02 0.03 0.04 0.05 0.06

Ene

rgy

(mJ)

Time

Unribbed

2cells-Hor.

2cells-Ver.

3cells-Hor.

3cells-Ver.

Fig. 14. Internal absorbed energy of the beam equipped by different ribs.

020406080

100120140160180200

0 0.01 0.02 0.03 0.04 0.05 0.06

Def

lect

ion

(mm

)

Time (s)

3cells-Ver.2cells-Ver.3cells-Hor.2cells-Hor.Unribbed

Fig. 15. Average beam displacement equipped by different ribs.

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–33 31

absorb the maximum strain energy in the elastic region so it willresult the least deflection for the door plate. It can be observedthat almost in all cases, the energy is going to be stable around40 ms. Since less rigid models such as (type b) is deformed easily,their plastic deformation are more than that of stiff models andthis is the main reason why they have more strain energy inplastic mode. Door beams modeled with the higher rigidityopposing to the crash direction are deformed hardly as the nextFig. 15 proves it. In this way, (type a), achieved the best crashperformance after the three-cell horizontal ribs (type c). The ribswhich are parallel and set against to the crash normal-vector inthe horizontal direction are harder to be deformed and can lead tothe minimum permanent damage of the door plate.

In other words, the high deformation of the unequipped beams(unribbed beams) caused the door to be undergone severedamage. Vice versa, the beams reinforced technically such asthe type (a) and (c), experience a reduced amount of displacementalong the shorter separation point by absorbing more kinetic-energy. As it can be also seen, they experienced less plastic

deformation. Hence, the body door plates associated with theseribs would accompany less permanent damage.

For the second section of the geometry modification, more rib-arrangements are introduced beside the previous accomplisheddesign of the ribs from the last section (type c). The newintroduced rib-models are drawn in Fig. 16.

One of the useful factors to investigate the door permanentdamage is the strain energy accumulated in the door plate duringthe collision. According to Fig. 17, beams equipped byrectangular-crossover ribs (type h) caused the door-plate toreceive less absorbed energy. Actually, this type was the mostefficient method of reinforcing the side door beams since the lessenergy to be absorbed by the door, the less deformation itundergoes under the same impact conditions. Another importantoutcome is that the door equipped by the beam types of (e and g)could absorb more strain energy compared to the type (c).It indicates that curve-profile and crossover ribs are weakerthan three-cell horizontal ribs. Thus, for the consideration ofeasy manufacturing, type (c) is more suitable and would berecommended.

The actual deflection of the door equipped by the mosteffective rib (type h) among all case studies is compared to thanthat of the unequipped door lacking any reinforcing ribs in Fig. 18.Decreasing the permanent plastic deformation from 3.3 cm to0.6 cm is one of the advantageous aspects of this design. Besides,the peak-deflection of the door is dropped from 5.5 cm to 3.5 cmwhich could decrease the cost of painting damage as well.

Another significant factor to compare the permanent damageis the Effective Plastic Strain, EPS, specified in Eq. (10). In Fig. 19,the maximum EPS occurring to the door is illustrated for twosystems during the test. Consequently, there is not plastic straindetected until almost 10 ms in both systems. The equippedsystem by the ribs yields plastic deformation before than theunequipped system. Also, in the presence of the reinforcing ribsin the side door beams, the maximum steady EPS is reducedapproximately by one in fourth.

To understand the percent of improvement leading to the leastpossible permanent damage, it is effective to compare these twocases in the variation of velocities and momentums. Figs. 20 and21 are obtained to investigate how the kinetic energy of thewhole system can be and converted to the strain energy.

First, for the equipped system, the impactor is reflected bymore velocity 3.2 m/s during the shorter time of 20 ms indicatingthat the system is stiffer than the unequipped one. Second, bymeasuring the velocity differences at the initial sate and at theend state, the coefficient of restitution (COR), as in Eq. (7),between the pole and the door for the same termination time of60 ms can be calculated as 0.55. However, this factor for theunequipped system equals to 0.36. The exceptionally increasepercent of almost 50% of COR means that the value of kinetic-energy converted to the deformation decrease proportionally andthe new equipped system behaves elastically further.

The side door beams in the equipped system moved with thesame velocity as the pole’s motion when they are in straighttouch with it. At the time of separation, the door beams become a

Fig. 16. Another four different arrangements of the inside ribs: curve profile (e), rectangular (f), crossover (g) and rectangular-crossover (h).

18000

20000

22000

24000

26000

28000

30000

0.01 0.02 0.03 0.04 0.05

Inte

rnal

abs

orbe

d en

ergy

(mJ)

Time (s)

crossover-rectangular (h) crossover (g)

rectangular (f) curve profile (e)

3-cells Hor. (c)

Fig. 17. Internal energy of the door-plate equipped by different ribs.

0

10

20

30

40

50

60

0 0.02 0.04 0.06

Dis

plac

emen

t (m

m)

Time (s)

Uneqipped andunribbed system

Equipped system bycrossover-rectangular(h)

Fig. 18. Actual displacement of the door-plate for the unequipped system

(unribbed) and equipped system (ribbed by the type of ‘‘h’’).

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

4.00E-02

0 0.02 0.04 0.06

Effe

ctiv

e pl

astic

stra

in

Time (s)

Equipped systemUnequipped system

Fig. 19. Effective plastic strain of the door-plate for the unequipped system and

equipped system.

0500

10001500200025003000350040004500

0 0.01 0.02 0.03 0.04 0.05 0.06

Vel

ocity

(mm

/s)

Time (s)

Door Pole impactor

Fig. 20. Kinetic-energy transfer in the unequipped/unribbed system.

0500

10001500200025003000350040004500

0 0.01 0.02 0.03 0.04 0.05 0.06

Vel

ocity

(mm

/s)

Time (s)

Pole impactor Door side door beams

Fig. 21. Kinetic-energy transfer in the equipped system by the ribs.

020000400006000080000

100000120000140000160000180000

0 0.01 0.02 0.03 0.04 0.05 0.06

Ene

rgy

(mJ)

Time (s)

Kinetic Energy Internal EnergyTotal Energy

Fig. 22. Kinetic energy conversation to strain energy of the whole equipped

system.

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–3332

part of the door again and initiate to adjust themselves to thedoor structure. Fig. 22 illustrates the kinetic energy conversationto strain energy of the whole equipped structure showing the firstcontact up to the full separation and stress release.

A. Ghadianlou, S.B. Abdullah / Thin-Walled Structures 67 (2013) 25–33 33

7. Conclusion

In order to design the side door beam, there are two majorfactors which are basically considered. First of all, the internalabsorbed energy of the side door beams should be kept high. Inthe second place, any plastic displacement of the door plateshould be avoided as much as possible in low-speed mode. Thehighlighted improvements of the new side door beam design arelisted as below:

1.

The effects of the side door beam materials on the doordisplacement were analyzed. With the consideration of usingalmost the same strain hardening behavior, applying of mate-rials with low young module induces to low rigidity and use ofhigh-strength materials lead to accepted impact behaviorthrough least possible permanent damage of the door.

2.

Increasing the side door beam thickness causes a peak in thebeam rigidity and the crush forces. As a result, there is areduction in the side door beam deflections and consequentlyin the body door plate.

3.

Various rib arrangements are applied to the side door beams.Among them, the rectangular-crossover rib shape (type h)could achieve the highest percent of crashworthiness improve-ments. Also, it was showed that designing the side door beamswith the ribs installed opposite and parallel to the normalvector of the crash direction had better impact performance. Inaddition, the permanent deformation damage could bereduced dramatically.

4.

To compare the altered design of the side door beam, threemajor parameters were evaluated. First, the permanent defor-mation damage of the door was decreased by 80% from 3.3 cmto 0.6 cm and the peak-deflection of the door was reduced by36%. Second, by considering the velocity concept of COR; it wasshown that the energy conversion to the permanent deforma-tion was decreased around 50%. Last but not least, the newdeveloped side door beam design could show the one in forthdecrease of effective plastic strain for the whole doorstructure.

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