car frontal impact

International Journal of Impact Engineering 30 (2004) 1055–1079

Design of an aluminium-based vehicle platform for frontimpact safety

A. Deba,*, M.S. Mahendrakumara, C. Chavana, J. Karvea,D. Blankenburgb, S. Storenb

aCentre for Product Design & Manufacturing, Indian Institute of Science, Bangalore 560012, IndiabDepartment of Machine Design and Materials Technology, NTNU, N-7491 Trondheim, Norway

Received in revised form 5 April 2004; accepted 6 April 2004

Available online 26 June 2004

Abstract

The current paper examines the design of an aluminium-intensive small car platform for desirable frontimpact safety performance. A space frame-type architecture comprised of extruded aluminium memberswith welded joints is considered for inherent structural rigidity, and low investment in terms of tooling. Afinite element model of the vehicle is employed for crash analysis using the explicit code LS-DYNA.Confidence in analysis is established at the component level by benchmarking finite element models ofwelded joints against experimental data, and axial crushing of aluminium tubes against published numericalresults and theoretical prediction. A numerical design of experiments is conducted for arriving at a front-end design that will yield desirable safety performance during impact against a rigid barrier at 30mph(FMVSS 208 condition). For comparable new car assessment program performance at a higher speed of35mph, a lumped parameter idealization is used to identify the principal design changes that may benecessary. The current approach of component level testing combined with finite element and lumpedparameter-based simulations can be regarded as an effective and time-saving procedure in the crash safetydesign of new vehicles.r 2004 Published by Elsevier Ltd.

Keywords: Aluminium; Vehicle; Front impact

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*Corresponding author. Tel.: +91-80-2293-2922; fax: +91-80-2360-1975.

E-mail address: [email protected] (A. Deb).

0734-743X/$ - see front matter r 2004 Published by Elsevier Ltd.

doi:10.1016/j.ijimpeng.2004.04.016

1. Introduction

In order to design a successful battery-powered electric vehicle, its weight should be as low aspossible. Even for conventional IC engine-based powertrain, savings in weight using lightweightmaterials such as aluminium can lead to increased fuel economy and reduction in pollution. Indeveloping countries like India, air-pollution arising mainly from traffic exhaust emissions issignificantly affecting the health and well-being of the dwellers in urban areas. There is thus a needfor designing lightweight vehicle platforms without sacrificing market requirements. Aluminiumalloys stand out as attractive material for body construction being about one-third lighter thansteel but possessing comparable strength to weight ratio as steel. Aluminium also has superiorcorossion-resistance and recyclability when compared to mild or high strength steel. Usage ofaluminium would, however, undoubtedly have a negative impact on cost; although it may bepossible to meet the cost objectives by using extruded members, optimizing design by usingcomputer-aided engineering, and minimizing expenses related to manufacturing. It is noted thatonly a few aluminium-intensive vehicles are available in the world automotive market today. AudiA8 is one such vehicle in which sheet-metal and casting-based body parts are used predominantly.The space frame body configuration for this vehicle is shown in Fig. 1. Think City is a smallaluminium-intensive electric car sold in some European countries such as Norway. The upperbody of this car is made from aluminium extrusion members mated with a steel chassis. ThinkCity can accommodate two passengers only including the driver.The vehicle body studied in the current paper is unique in terms of having an integrated upper

body and chassis made completely from extruded members some of which need to be bent usingsecondary processes to achieve an aesthetic exterior form. The members are connected at jointsusing inert gas metal arc welding. Non-structural body panels acting as vehicle skin are notincluded in the vehicle frame analyzed. The design of the proposed platform involves variousconsiderations [1], however, the focus of the work reported here is on front impact safety. Forassessment of the current vehicle platform for full frontal impact, the mandatory Federal MotorVehicle Safety Standards (FMVSS 208) [2] regulation for new vehicles in USA is considered.According to this requirement, a vehicle is crashed against a rigid barrier with a speed of 48 kph(30mph). This is somewhat equivalent to head-on collision between two identical vehicles, onebeing stationary and the other approaching it with a speed of 96 kph. A scrutiny of the spaceframe body discussed in the next section will reveal that welded joints and axial members such as

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Fig. 1. Audi A8 aluminium space frame [10].

A. Deb et al. / International Journal of Impact Engineering 30 (2004) 1055–10791056

front rails are principal components contributing to energy-absorption during a frontal collision.As finite-element-based simulation using the explicit code LS-DYNA is employed for impactanalysis of the vehicle, it is important that the body components mentioned above are modeledsatisfactorily. The predictability of two separate finite element models of a welded T-joint isverified at first against a physical test carried out by the authors. This is followed by comparisonof finite-element analysis of axial crushing of an extruded aluminium tube against simulationresults given in [3] and theoretical mean crush load prediction [7]. After establishing confidence inthe modeling of the components described, a finite-element model of the complete vehicle bodywith wheels, axles, suspension and electric motor is used for full frontal impact safety evaluation.Finally, a computationally inexpensive spring-mass model is employed for assessment of thecurrent platform for NCAP condition with a higher impact speed of 35mph and necessary designchanges are suggested for improved safety.

2. A space frame-based vehicle concept

The work reported in the current paper is a subset of a design project that aimed at creating aprototype for a robust and lightweight small car ‘‘platform’’ for the Indian market. As the projectwas of investigative nature and not a commercial one, it was decided that emphasis would beplaced on usage of extruded aluminium components for building the body. Initial cost analysissuggested that it would be economic to choose a space frame configuration for a fully aluminium -based chassis and upper body. Commercially available wheels, axles, suspension and steeringsystems, and electric motor made predominantly of steel were integrated with the vehicle frame.Weightage was given to aesthetics and ergonomics in the design of the computer-based concept.Body panels made of lightweight materials such as composites can be attached to the skeletalframe; however, these are unlikely to contribute in a significant manner to body rigidity andcrashworthiness. The overall body dimensions for the vehicle were chosen based on CompetitiveVehicle Benchmarking, i.e. an analysis of vehicles already available in the relevant segment of thetarget market. For example, the target length and width of the vehicle (referred to as the ‘‘CPDMModel’’ in Figs. 2 and 3) were chosen as 3000 and 1400mm, respectively. These dimensions arehigher than those of the nearest small vehicles in India, namely the Bajaj Autorickshaw and an

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Fig. 2. Overall length of the present vehicle concept vs. those for competing vehicles.

A. Deb et al. / International Journal of Impact Engineering 30 (2004) 1055–1079 1057

electric car named Reva, but are less than those for the popular Maruti 800 (Figs. 2 and 3). Theenvisioned CPDM car thus finds a place between the ubiquitous three-wheeler commuter taxi, i.e.the autorickshaw and the highest sold small retail car, i.e. Maruti 800.The design began with a computer-aided design (CAD) model of the space frame architecture

(Fig. 4) for the concept vehicle. One may consider this basic design as realistic and substantivewhen compared to production vehicles (as can be seen by comparing Figs. 2 and 4). The term‘‘platform’’ used earlier is intended to signify that variants such as vans and sedans can begenerated without major modifications to the current design. A finite element model reflecting thefinal concept is shown in Fig. 5. The model employs a nearly uniform mesh for the whole vehicle.The body-in-white static and vibration frequency targets were met after making suitable changesto the initial concept. Before undertaking the frontal impact analysis against a rigid barrier as perthe FMVSS 208 test set-up, validation of finite-element modeling of welded joints and axialcrushing of components is carried out as described in the next two sections.

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Fig. 3. Overall width of the present vehicle concept vs. those for competing vehicles.

Fig. 4. Aluminium extrusion-based space frame vehicle concept.


3. Behavior of welded aluminium joints

The joints between extruded members in the vehicle modeled in Fig. 5 are proposed to be madewith MIG welding. Truly speaking, weld fillets should be modeled with 3D elements [12] havingappropriate material properties, and the effect of heat-affected zone (HAZ) surrounding a weldshould be taken into account. However, it is difficult to know weld properties directly. Althoughgood correlation is obtained in [12] between experimental and finite-element results, details ofmesh size used or material properties applied to the weld fillets and HAZ are not given. As usageof small 3D elements in every joint poses severe demands on computational time in a large crashmodel and as the extruded aluminium components are represented with shell elements, it wasdecided that two approaches will be studied for simulation of the failure of a welded T-joint underbending load applied on one of its legs (see Fig. 6 below for the test set-up): (1) monolithicconnection between the two mating components (as shown in Fig. 7), and (2) shell elements(shown in a dark shade in Fig. 8) with modified properties for modeling the weld zone. Thealuminium extrusions used in the test were made from SAPA 6060 T6 alloy. The cross-sectionaldimensions of each component were 100mm� 50mm with a wall thickness of 3.4mm.The properties of aluminium (SAPA 6060 T6) used were obtained from the material supplier’s

manual [10] and are given below:

Young’s modulus ðEÞ : 70 GPa; ð1aÞ

Poisson’s ratio ðvÞ : 0:33; ð1bÞ

Ultimate tensile stress ðsuÞ : 0:17 GPa; ð1cÞ

Yield stress ðsyÞ : 0:14 GPa; ð1dÞ

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Fig. 5. Finite-element model of prototype space frame.


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Fig. 6. Test set-up for studying load–deformation behavior of a welded T-joint.

Fig. 7. Model with monolithic joint.


Failure strain ðef Þ : 8%; ð1eÞ

Density ðrÞ : 2:7E� 06 kg=mm3; ð1fÞ

Tangent modulus ðETÞ : 385GPa: ð1gÞ

It is noted that three tensile tests performed with coupons obtained from the walls of extrudedmembers of grade 6060 T6 confirmed the yield and tensile strengths as well failure strain assumedabove. In order to simulate quasi-static loading with minimal inertial forces, the rigid cylindricalrod shown in Fig. 6 is moved downward with a uniform speed of 2m/s. The automatic contactalgorithm with key word CONTACT AUTOMATIC GENERAL is chosen for analysis with LS-DYNA. The material model used is of type 24 (defined by the key word MATERI-AL PIECEWISE LINEAR PLASTICITY in LS-DYNA) pertaining to Von Mises yieldcondition with isotropic strain hardening, and strain rate-dependent dynamic yield stress basedon Cowper and Symonds model. The progression of stress beyond yield (according to scalingalgorithm) for this model is given below:

s ¼ ðsy þ ETepeff Þ 1þ

’epeffD

� �1=p" #

; ð2Þ

where,

epeff ; ’epeff are the effective plastic strain and strain rate; respectively; and ð2aÞ

D and p are material constants: ð2bÞ

The aluminium alloy being considered here is known to be relatively insensitive to high strainrates [8]. Hence in the current study, the term within square brackets in the right side of Eq. (2) istaken as unity signifying that the scaling of static yield stress due to strain rate effect is notapplied.

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Fig. 8. Model with distinct shell element properties for the weld zone.


In the test set-up in Fig. 6, the vertical load applied on the horizontal leg of the welded T-joint istracked along with the downward displacement of the load applicator. The recorded load–deformation behavior is given in Fig. 9. Initially, analysis has been done with the monolithic jointmodel shown in Fig. 7 the result for which is superimposed with the test result in Fig. 9. It isobserved that the monolithic joint simulation yields a peak load that is about 30% higher than thetest peak load. After computing the area under a given force–deformation curve, it is seen that themonolithic joint simulation also over-predicts energy absorption during the entire history ofdeformation by 10.5%. The obtained results make it obvious that for better correlation betweensimulation and test behaviors, elements with special properties in the joint area may be necessary.It is not readily apparent, however, as to what values of material parameters for the shadedelements in Fig. 8 will yield a load–deformation variation close to the test response. A study istherefore carried out in the form of a design of experiments (DOE) to determine the weld materialproperties that would ensure minimum variations in peak load and energy absorption with respectto the experimental values. In order to achieve the stated optimization in weld simulation, thefollowing objective function Ow is defined:

Ow ¼ ðDPÞ2 þ ðDEÞ2; ð3Þ

subject to the following constraints:

jDPjp10%; ð3aÞ

jDEjp10%; ð3bÞ

where,

DP is the percent variation in peak load with respect to the test value of 13:2 kN; and

ð3cÞ

DE the percent variation in energy absorption with respect to the test value of 338 J:

ð3dÞ

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Fig. 9. A comparison of test and simulation results for bending of welded T-joint.


(Note: the absorbed energy is computed as the area under a given load–deformation curve untilthe load drops to zero).The material parameters varied were sy, ef and ET. Twenty-seven (3� 3� 3) cases were

analyzed with combinations of sy, ef and ET from values given in the Table 1.It is noted that in Table 1, values of sy considered are 10–30% lower than the baseline value for

the current aluminium alloy given in (1d) in anticipation of the weakened strength of HAZ in theweld region. The other two parameters (i.e ef and ET ) are taken as equal to, above and below theircorresponding baseline values given by (1e) and (1 g). The variation of the computed objectivefunction Ow for the twenty-seven DOE cases is shown in Fig. 10.It is seen from Fig. 10 that the best correlation between test and weld element-based analysis is

achieved for case 14 for which Ow is a minimum. A summary of peak load and energy absorptiondata showing highly improved correlation between test and weld element-based analysis (case 14)is given in Table 2. The values of design variables for case 14 are: sy ¼ 0:098GPa, ef ¼ 10% andET ¼ 0:385GPa. It is observed that the weld yield strength in case 14 is 30% lower than that givenby (1d) for the tube alloy.In the finite element models of Figs. 7 and 8, an average element size of 15mm is assumed for

compatibility with the mesh density used in the full vehicle model (Fig. 5). A finer mesh for thevehicle model would place severe burden on available computational resource and theoptimization study described later could not be carried out in a reasonable time frame. Withthe current state of CAD, finite-element pre-processing, and data management technologies, the

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Table 1

Values of material parameters considered in weld simulation optimization

sy (GPa) ef (%) ET (GPa)

0.098 6 0.347

0.112 8 0.385

0.126 10 0.424

Fig. 10. Variation of objective function for weld optimization.


present procedure of ‘‘tuning’’ finite-element modeling for predicting test behavior is also followedin designing production vehicles. The width of the weld zone (including a weld fillet of ap-proximately 5mm width all around the junction between the two rectangular members)considered in Fig. 8 is 30mm in the vertical leg and 45mm in the cantilever member on which loadis applied. These weld zone widths are in the same range as the recommended width of HAZ givenin [11], viz. 25mm (1 in), and the width of HAZ used in finite element models in [12], i.e. 38mm. In[10], the reductions in ultimate strength in weld fillet and in HAZ are reported as 25% and 40%,respectively. In [13], the authors found a drop in yield strength of 40–50% in coupon specimenscut from HAZ areas in welded plates. The current reduction of 30% in yield and ultimatestrengths for combined weld fillet and HAZ areas represented by shell elements in Fig. 8 is thusconsistent with the quoted findings in [10,13].The deformed shapes yielded by the finite element runs after the cylindrical load-head has

moved downward by about 28mm are shown in Figs. 11 and 12. It is seen that due to symmetrical

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Fig. 11. Failure pattern for monolithic joint simulation.

Table 2

A comparison of absorbed energy and peak load for simulation and test cases

Case Energy absorbed (J) Peak load (kN) Difference in

energy absorption

between analysis

and test (%)

Difference in peak

load between

analysis and test

(%)

Physical test 337.7 13.2 N/A N/A

Monolithic joint

analysis (Fig. 7)

377.3 18.9 10.5 30.2

Weld element analysis

(Fig. 8, DOE case 14)

349.8 14.0 3.9 6.4


nature of tensile and compressive stresses in the joint exerted by the outstanding leg, failure takesplace at both the top and bottom vertical edges of the joint. Separation of the cantilever leg fromthe joint also takes place at the top and bottom horizontal edges. In the tested joint component inFig. 6, failure in the weld was initiated at the top corners of the joint (i.e. in the tension zone) andpropagated to result in complete tearing along a horizontal direction in the HAZ as predicted inthe finite element model. In the compression zone, cracks developed in the vertical weld fillets;however, no through crack or tearing of extrusion wall in the HAZ in the horizontal direction wasobserved. The lack of symmetry in the failure of top and bottom horizontal edges in the testedcomponent can be attributed to the fact that the lower edge of the cantilever leg is supported incompression on the vertical member which prevents complete failure in the bottom horizontalweld fillet. In the finite element model, on the other hand, the load from the cantilever leg istransferred through the weld elements only to the vertical member. In order to obtain a closercorrelation of predicted failure pattern with observed behavior, the weld fillets should be modeledwith 3D elements as remarked earlier to connect the two extrusion members while the lattershould not be directly connected to each other. The current approach of using modified shellelements (Fig. 8) to represent the weld zone, however, leads to a load–deformation behavior (Fig.9) that can be considered as sufficiently close to the experimental curve and hence can be adoptedin full vehicle simulation.

4. Axial crushing of an extruded aluminium component

A key mode of failure of the vehicle frame components in front impact is in the form ofprogressive buckling of front rails. Axial collapse of steel and aluminium columns has beenpreviously studied by a number of investigators (notably, [3–8]). Usually, a limit state of plasticityapproach will analytically yield the peak and average values of load generated during axial

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Fig. 12. Failure pattern for joint with welded elements.


crushing. However, to obtain the entire history of deformation, nonlinear finite-element methodwith robust contact algorithms would be most useful. The information obtained here through LS-DYNA-based analysis of a square aluminium tube will be compared against PAM-CRASH-basedresults previously reported in [3] and theoretically predicted mean crush load [7] for the given tubematerial and geometrical properties.The problem considered is the progressive buckling of a square column of sides 80mm,

thickness 1.88mm, and length 245mm as given in [3]. The column is assumed to be madeof AA 6063 T7 alloy for which the elasto-plastic properties are taken from [3]. The constitutivemodel used in the present LS-DYNA-based simulation is MAT PIECEWISE LINEARPLASTICITY in which values of effective stresses corresponding to effective plastic strainsare defined. The finite-element model of the component with an element size of 5mm is shown inFig. 13. It is fixed at the base and is subject to gradual compression with a rigid flat platepositioned on the top. In the beginning, a small initial gap is maintained between the plate and thecolumn to avoid initial penetrations. The plate is applied a uniform velocity of 2m/s along thecolumn axis giving rise to its progressive failure by formation of folds as shown in Fig. 14.

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Fig. 13. Finite-element model for axial compression simulation.

Fig. 14. Side view of simulated tube collapse after full compression.


It is pointed out that the manner of load application on the extrusion component is differentfrom what was followed in [3], although this is not expected to cause a significant difference inresults. In [3], velocity boundary condition is applied to the top of the column and the velocity isramped during the first 50ms until a steady-state velocity of 2m/s is reached. In the present case,load is applied with a plate as this approach would be perhaps closer to an actual physicalexperiment.The load–deformation curve for the square tube obtained from LS-DYNA analysis is given in

Fig. 15. It has been filtered with SAE 1000-9 in LS-POST. The peak load of 62 kN obtained fromthe present analysis agrees excellently with the value of 63 kN reported in [3]. The mean crush loadof 20 kN (for a total axial deformation of 180mm after which the tube bottoms out) obtained hereis about 18% higher compared to a value of 16.9 kN reported in [3]. However, the current meanload agrees excellently with a value of 20.6 kN yielded by the following theoretical relation due toAbramowicz and Jones [7]:

Fmean ¼ 13:06s0b1=3m h5=3; ð4Þ

where

s0 ¼1

2sy þ su� �

; ð4aÞ

sy ¼ 0:08694GPa ½3; ð4bÞ

su ¼ 0:171GPa ½3; ð4cÞ

bm ¼ b � h ðmean width of square tubeÞ; ð4dÞ

b ¼ 80 mm ðwidth of square tubeÞ; and ð4eÞ

h ¼ 1:8 mm ðthickness of square tubeÞ: ð4fÞ

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Fig. 15. Axial load vs. displacement behavior of square column.


It may be noted that a mesh size sensitivity study was carried out by considering two coarser meshconfigurations, however, the 5mm size mesh (Fig. 13) yielded most satisfactory correlation withthe theoretically predicted mean load given by (4) above.

5. Frontal impact simulation against a rigid barrier

The results presented in the previous sections on bending of a welded T-joint and progressiveaxial collapse of an aluminium tube lead to a fair degree of confidence on finite-element modelingprocedures followed here. Using the same general approach for components, one could perform afinite-element-based assessment of frontal impact safety of the full vehicle concept. The finite-element model employed for impact simulation against a rigid barrier with a speed of 48 kphconforming to the mandatory FMVSS 208 regulation in USA is shown in Fig. 5. The aluminiummembers of the vehicle frame are assumed to be made of SAPA 6060 T6 alloy. All members are ofthickness 3.0mm except the front fore-rails (comprising crush box and mid-rail shown in Fig. 16)which have a thickness of 2.0mm. The front fore-rails, which are the principal load-carrying andenergy-absorbing members in front impact, have cross-sectional dimensions of 100mm� 50mm.The mass of the vehicle is 620 kg including power train (i.e. a 72V DC motor with front wheeldrive transmission system and a pack of twelve 6V batteries).The full vehicle front impact simulation is initially carried out (a) with all frame joints being

considered as monolithic, and (b) using weld elements (as in Fig. 17) at joints with optimizedproperties obtained earlier. Overall vehicle deceleration responses obtained for cases (a) and (b)when the vehicle is impacted against a rigid wall with an initial forward speed (in the negative x

direction in Fig. 17) of 48 kph (13.33m/s) are shown in Fig. 18 (after processing with SAE 60filter). This deceleration history can be looked upon as an average for the entire vehicle and is

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Fig. 16. Vehicle front structure with segments of rail.


directly obtained in the LS-DYNA post-processor. Alternatively, vehicle response (sometimesreferred to as front ‘‘crash pulse’’) could be studied at locations such as B-pillar-and-rocker jointor under the rear seat (Fig. 22). The responses in Fig. 18 have a desirable square-type shapeindicating efficient energy absorption by the front structure. An important outcome of the currentanalyses is that the peak decelerations as seen in Fig. 18 are not significantly different. The peakdeceleration turns out to be lower and energy absorption higher (as per Figs. 18 and 19) whenjoints are represented with weld elements because of increased overall compliance in the structurewhen compared to monolithic joint modeling. It needs to be mentioned that full front impactagainst a rigid barrier is primarily an axial phenomenon while the component joint study

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Fig. 18. Acceleration histories for front impact simulation cases (a) and (b).

Fig. 17. Full vehicle finite-element model with all joints represented with weld elements.


conducted in an earlier section corresponded to bending loading in which shear force carryingcapacity of the weld section is almost completely lost after failure of a few elements. This mayexplain the general agreement between welded and monolithic joint representation results in fullfrontal impact simulations as carried out here.Snap-shots of vehicle deformation along with close-up views of the front structure are shown in

Fig. 20. It is seen that until 5ms, no significant deformation in the front of the vehicle hastaken place. However by 12ms, a major part of the crush boxes for both front rails hascollapsed. Referring to Fig. 18, the occurrence of first deceleration peak in both monolithicand welded joint-based analyses at around 16–18ms is likely to signify the complete collapseof the left and right crush boxes (as observed in the deformation snap-shots). The occurrence ofanother peak in Fig. 18 at 30ms for either joint modeling approach indicates the formation ofone plastic hinge each in left and right mid-rail segments. The continuous drop in decelerationfrom 45ms (Fig. 18) corresponds to the beginning of rebound phase in the impact event underconsideration.The majority of the elements in the front of the structure (Figs. 5 and 17) considered in the

previous analyses vary between 17 and 20mm in size. This configuration is referred to as ‘‘uniformvehicle mesh’’ for subsequent reference. The desired mesh size for predicting progressive bucklingof component rectangular tubes was earlier found to be 5mm. In order to assess the effect of thissmaller element size, the leading portions of the vehicle front end including the fore-rails were re-meshed with an average of 5mm size elements and a complete vehicle front crash analysis wascarried out (Fig. 21). A comparison of the crash pulses between the nearly uniform and refinedfront-end vehicle models at the rear of the vehicle (i.e. the zone in which NHTSA reports NCAPtest deceleration histories of new vehicles) is given in Fig. 22. It is observed that although there aredifferences in the shapes of the acceleration curves, the magnitudes of peak and averagedeceleration for the two cases are not significantly different. As these are the parameters that areconsidered in the optimization of the vehicle design for front impact safety (to be describedlater), the use of a coarser mesh is not likely to significantly affect the conclusions of the present

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Fig. 19. Energy plots for front impact simulation cases (a) and (b) (Note. KE—kinetic energy; IE—internal energy;

TE—total energy).


study. The uniform mesh vehicle model (with 74,000 shell elements) is highly advantageouscomputationally as it requires 14 h less for analysis compared to the refined vehicle model (with1,14,000 shell elements) on a personal computer equipped with an AMD Athlon XP 2000+processor and Windows 2000 operating system.

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Fig. 20. Vehicle snap-shots on the left and close-up views of front structure on the right during front impact simulation

against a rigid wall. (a) At analysis time = 5ms (no significant deformation has taken place). (b) At analysis time =

12ms (damage in bumper beam, collapse of a significant part of crush box, and plastic deformation in mid-rail). (c) At

analysis time = 30ms (complete collapse of crush box, partial collapse of mid-rail, and severe damage in the curved

part of upper longitudinal member).


6. Assessment of occupant injury

In order to ensure occupant safety, it is essential that the front passenger compartmentdeformation is kept to a minimum following impact and that peak deceleration is withinreasonable limits. Changes in horizontal (L1 in Fig. 5) and diagonal (L2 in Fig. 5) front left doorapertures are shown in Fig. 23 for analysis cases (a) and (b). While change in L1 is insignificant,that in L2 is also less than 10mm for both cases. Thus the chance of leg injury at the given testmode appears to be minimal. The peak vehicle decelerations in Fig. 18 are seen to be 40 g for case(a) and 38 g for case (b). Test deceleration curves (after processing with SAE 60 filter) for anumber of body-on-frame type sport utility vehicles sold in USA are shown in Fig. 24. Thereferred tests were carried out by National Highway Traffic Safety Administration (NHTSA) inUSA for NCAP rating for which the impact speed was 56 kph (15.6 m/s), i.e. 8 kph higher than

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Fig. 22. Comparison of decelerations at the middle of first cross-member under the rear seat.

Fig. 21. Refined vehicle front end mesh.


that in the regulatory FMVSS 208 test. It is seen that peak deceleration for these tests is in therange of 30–65 g. Since all of these vehicles perform well in terms of occupant injury criteria (i.e.chest deceleration and Head Injury Criterion (HIC) and receive a minimum of 3-star rating, thepeak deceleration of 38–40 g obtained in the current simulations can be considered as acceptablefor the case of FMVSS 208 test configuration if the steering column and restraint systems (i.e. seatbelts and airbags) are properly designed. It may be possible to further reduce the peakdeceleration for the considered test mode by effecting changes in the crush box as demonstrated inthe next section.

7. Optimization of front impact performance

In order to achieve further reduction in deceleration level for an impact speed of 30mph(13.33m/s), a procedure similar to that followed for weld property optimization is adopted. As

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Fig. 24. Responses obtained from NCAP tests for various sport utility vehicles.

Fig. 23. Changes in horizontal and diagonal front door apertures during impact.


peak deceleration and door intrusion yielded by each of the simulation cases (a) and (b) did notdiffer appreciably (Figs. 18 and 23), the monolithic joint representation is followed in the DOE-type study to be carried out. The parameters varied for investigating possible reduction indeceleration are the length (lcb) and wall thickness (tcb) of crush box, as well as the wall thickness(tmr) of mid-rail. The crush box and the mid-rail segments of front rails are shown in Fig. 16.Eighteen DOE cases are considered and the various combinations of values of lcb, tcb and tmr aregiven in Table 3.In order to assess the relative performance of design options, a time-average of the acceleration

response history is used here in conjunction with an intrusion-related parameter. For example, fora DOE case (designated as case 10) in which the crush box length is increased by 50mm comparedto the baseline, and crush box and mid-rail gages are both 2.0mm, the filtered vehicle accelerationand its time-average responses are shown in Fig. 25. The concept of average acceleration alsoprovides a convenient paradigm for application of the lumped parameter-based approachdiscussed in the next section for further safety improvement at a higher impact speed. The goal ofobtaining an enhanced design in the vicinity of the baseline solution is assumed to be met with theminimization of the following objective function:

Ov ¼ aavg þ d1; ð5Þ

where

aavg ¼ average deceleration in g’s ðas in Fig: 25 but with sign reversedÞ; ð5aÞ

d1 ¼ DL1=L1 � 100 ¼ percentage reduction in door lateral dimension ðsee Fig: 5Þ: ð5bÞ

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Table 3

Combinations of values of front rail design variables for DOE study

lcb (mm) tcb (mm) Tmr (mm) Remarks

207 2 2 Baseline, case (a) in Section 5 as well as DOE case 12

207 2 2.5 DOE case 1

207 2 3 DOE case 3

207 2.5 2.5 DOE case 7

207 2.5 3 DOE case 16

207 3 3 DOE case 13

232 2 2 25mm increase in baseline value of lcb, DOE case 11

232 2 2.5 25mm increase in baseline value of lcb, DOE case 2












The results of the DOE study are given in Fig. 26. It is seen from the variation of Ov in Fig. 26that case 10 which has been described earlier yields the optimum safety solution. The maximumchange in vehicle weight for the various DOE options is negligible as only stretching of hollowfront rails up to a maximum of 100mm is considered. Furthermore, it is noted that the optimumsafety solution for which the peak deceleration is 38 g is only 2 g lower than the peak decelerationof 40 g obtained in the baseline monolithic joint-based response given in Fig. 18. It is noted that inthe DOE cases analyzed, the first lateral cross-member (located at the rear of the bumper beam)is kept unchanged in position relative to the fire-wall. Hence, increasing the length of crushbox beyond 75mm initiates its global buckling and does not lead to any advantage in safetyperformance.

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Fig. 26. Variation of objective function for front impact safety optimization.

Fig. 25. Analysis-based acceleration response for FMVSS 208-optimized case 10 and its time-average representation.


8. Lumped parameter idealization for NCAP evaluation

As a logical next step in the front crash safety design of the current vehicle platform, an NCAPevaluation is made with the help of a lumped parameter model (LPM) of the FMVSS 208-optimized solution represented by case 10 in Fig. 26. The generic spring–mass model employed isshown in Fig. 27 in which the vehicle is lumped as a single mass m and the front-end stiffnessproperties of the vehicle are idealized by a nonlinear spring with force–deformation behaviorgiven in Fig. 28. The LPM of Fig. 27 has been previously applied [9] in the context of headformsafety impact design with closed-form dynamic solutions for an initial velocity of m given by v0.The same computational procedure is also adopted here.

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Fig. 28. Behavior of idealized spring [9].

Fig. 27. A lumped parameter idealization of front impact.


In the idealized vehicle front end behavior represented in Figs. 27 and 28, the followinginterpretations are made of the various parameters shown:

Fy ¼ average force sustained by the vehicle front structure; ð6aÞ

Ke ¼ elastic stiffness of the vehicle front; ð6bÞ

Ku ¼ stiffness characterization of the back-up structure after front end deformation

bottoms out sf � Ke ðwhere sf is an assumed stiffness factorÞ;ð6cÞ

ls ¼ total length of the crushable front end

ðin the current case; sum of lengths of crush box and mid-railÞ and ð6dÞ

du ¼ maximum crush that can be realized ¼ cf � ls

ðwhere cf can be referred to as a compaction factor ½9Þ: ð6eÞ

Before the LPM of Fig. 27 can be used for NCAP safety assessment of the current platform, itsapplicability to FMVSS 208 simulation should be established. To this end, the following values ofpertinent spring–mass properties are assumed for representing the average acceleration version ofcase 10 in Fig. 25 (noting that te, tm and tf in Fig. 25, respectively, denote the end of elastic phase,beginning of unloading and end of impact event; and, the average deceleration is 26.3 g) :

m ¼ 620 kg ðfrom full vehicle finite element model of Fig: 5Þ; ð7aÞ

v0 ¼ 30 mph ¼ 13:33 mm=ms; ð7bÞ

duE383mm; dynamic crush from finite element analysis of case 10; ð7cÞ

FyEm � 26:3g ¼ 160 kN; ð7dÞ

teE5 ms; tmE49ms; tfE70ms; ð7eÞ

cfEtm

tf¼ 0:7; ð7fÞ

deEte

tfdu ¼ 27:4 mm; ð7gÞ

KeEFy

de¼ 5:85 kN=mm; ð7hÞ

lsEdu

cf¼ 547 mm and ð7iÞ

sf ¼ 0:15: ð7jÞ

Analysis using the current LPM requires as input the quantities given by Eqs. (7a), (7b), (7d), (7f)and (7h)–(7j). It is noted that the value of sf in Eq. (7j) is chosen using a tri-and-error approach toensure that the current LPM is able to reproduce the equivalent uniform crash pulse in Fig. 25without the bottoming out of the front structure. The acceleration history obtained after analysis

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is given in Fig. 29 and a constant deceleration of 26.3 g corresponding to phase (II) deformation inFig. 28 is obtained. Thus the LPM-based response exactly matches the average deceleration ofFig. 25. Hence, the validity of the estimated input spring properties given above is grosslyestablished. The LPM is now re-analyzed for the NCAP test speed of 35mph (i.e. v0 ¼ 15:56mm/ms). In this case, complete crush of the fore-rail comprising crush box and mid-rail takes placeresulting in a higher peak deceleration of 38 g and an average deceleration of approximately 32 g.It is known from prior experience with the LPM for the case of headform impact safety (which isreally a scaled counterpart of vehicle front impact in terms of energy content) that the parameter ls(and hence du via (6e)) plays the most significant role in reducing deceleration. After carrying outseveral trial-and-error runs with the LPM, it was found that, if the front-end stiffness and loadcarrying capacity of the vehicle are held as approximately constant, the dynamic crush ( i.e. du)needs to be increased to 518mm (from a previous value of 383mm, (7c)) so that the uniformdeceleration of 26.3 g of case 10 for the lower test speed of 30mph can be obtained. The pertinentLPM-based acceleration response with cross marks is shown in Fig. 29. In terms of ls, therequirement would be to increase the length of fore-rail to 740mm (for cf ¼ 0:7). However, if thecrushability of front rail can be raised to more than 70% (cf > 0:7), a lower value of ls will suffice.The directional design guidance provided by the LPM-based analysis has been verified in a finiteelement model corresponding to case 10 in which the front fore-rails have been lengthened to740mm. There is scope for reducing this length by increasing crushability of mid-rail and aft-railshown in Fig. 16. In the absence of the valuable insight provided by the present LPM, it wouldhave been much more time consuming and expensive to obtain the same conclusions by applyingfull vehicle finite-element analysis.

9. Conclusions

The current paper illustrates a systematic simulation-driven approach towards designing alightweight vehicle platform with aluminium extrusion-based components. A space frame-typevehicle architecture is introduced and evaluated for front impact safety. Benchmarking of jointanalysis results against a physical test carried out in the present study, and of axial collapse of asquare aluminium column against published numerical results and theoretical prediction add

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Fig. 29. Acceleration responses yielded by LPM of Fig. 27.


credibility to subsequent full vehicle finite-element modeling and analysis. A finite-element-driven,DOE-based optimization approach has been followed in deriving weld element properties thatwould yield close correlation to test behavior. A similar approach has also been adopted foroptimization of full vehicle front impact crashworthiness for the 30mph impact speed conformingto the FMVSS 208 standard of NHTSA in USA. By applying an efficient LPM-based approach,insight on necessary change to front end crush space is obtained for the tougher NCAP standardcorresponding to an impact speed of 35mph. The present design approach effectively combinescomponent testing, detailed finite-element-based analysis, and lumped parameter idealizationleading to shortened design cycle and reduced development costs. Based on the results obtained,the current vehicle design, which is lightweight and eco-friendly when compared to a steel bodiedvehicle of similar dimensions and has been prototyped, holds out promise in terms ofcrashworthiness.

Acknowledgements

The authors would like to thank the Altech Program involving Hydro Aluminium (Norway),IISc (Bangalore, India) and NTNU (Trondheim, Norway) for providing impetus to the presenteffort. Thanks are also due to Prof. D.H. Sastry, Coordinator of the Altech Program at IISc, forhis interest and support, and to Prof. T. Welo, Department of Machine Design and MaterialsTechnology, NTNU, Trondheim for his valuable advice.

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http://www.nhtsa.dot.gov/cars/rules/standards/safstan2.htm

http://www.sapagroup.com

car frontal impact

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