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Short communicationLightweight design of automobile component usinghigh strength steel based on dent resistanceYan Zhang*, Xinmin Lai, Ping Zhu, Wurong WangSchool of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, PR ChinaReceived 19 May 2004; accepted 14 September 2004AbstractLightweight and crashworthiness are two important aspects of auto-body design. In this paper, based on the shallow shell theory,the expression of dent resistance stiffness of double curvatured shallow shell is obtained under the concentrated load condition. Thecritical loads resulting in the local trivial dent in the center of the shallow shell is regarded as the important index for the lightweightof the automobile parts. This rule is applied to the lightweight design of bumper system by using high strength steel instead of mildsteel. The crashworthiness simulation of the lightweight part proves the validity of the lightweighting process.? 2004 Elsevier Ltd. All rights reserved.Keywords: High strength steel; Lightweight; Dent resistance1. IntroductionIn recent years, the retaining number of automobileshas been increasing steadily, which has impacted thesociety and human life greatly. Such situation leads tomany severe problems such as fuel crisis, environmentpollution. The international association of aluminumstated that petrol consumption can decrease by 810%with 10% reduction of car weight 2. Thus, automobilelightweight is a basic way to fuel saving.In order to reduce the automobile weight, there aretwo important methods 3: One, automobile parts areredesigned to optimize the structure. By using thinning,hollowing, minitype, and compound parts, car weightcan be reduced. The other, more and more lightweightmaterials, such as aluminum alloy, high strength steel,composite material, are widely used as lightweight mate-rials to replace the traditional materials like mild steel4. These materials could reduce the weight remarkably.Material replacement is generally more effective in auto-mobile lightweighting than structure modification. Withthe introduction of automobile safety legislation, crash-worthiness and safety should be considered as precondi-tions in lightweighting design of auto-body.High strength steel is widely used in automobilereplacing the traditional material of mild steel. Highstrength steel sheet can be used in auto-body to improvecomponents? impact energy absorption capacity andresistancetoplasticdeformation.Theautomobileweight can be reduced by use of high strength steel sheetof a thinner thickness to replace the mild steel sheet ofbody parts 1,3. Comparing with aluminum, magne-sium, and composite materials, high strength steel hasbetter economy in that its raw material and fabricationcost are cheaper. Besides, high strength steel can be di-rectly used in product line including forming, wielding,assembling, and painting. The operating cost can besaved since there is no need adjusting the whole line.Outside of automobile body, there are several sheetmetal Panels, most of which are shallow panels. Dentresistance is the ability to retain the shape against sunkendeflection and local dent under the external force. Dent0261-3069/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2004.09.010*Corresponding author. Tel.: +86 21 62932964; fax: +86 2162933093.E-mail address: zytju (Y. Zhang)./locate/matdesMaterials and Design 27 (2006) 6468Materials& DesignResistance of automobile panels becomes an importantissue and quality criterion. Therefore, dent resistancestiffness of automobile panels should be tested and eval-uated in the process of panel design and manufacture.Some reported methods of testing are listed below 68:1. Test the displacement of sunken deflection fpunderfixed external force.2. Test the external force f to obtain fixed displacementof sunken deflection.3. Test the slope of forcedisplacement curve underexternal load.In this study, the second method will be used. The restof this paper is organized as follows: In Section 2, theexpression of dent resistance stiffness of double curva-tured shallow shell is obtained under the concentratedload condition based on the shallow shell theory. Thecritical load resulting in the local trivial dent in the centerof the shallow shell is regarded as the important evaluat-ing index for the dent resistance of the automobile parts.This rule is applied in Section 2 to the lightweighting de-sign of bumper system by using high strength steel in-stead of mild steel with crashworthiness simulation.2. Dent resistance analysis of double curvatured shallowshell2.1. Dent resistance stiffness analysis of shallow shellShell with mid surface can be characterized into threefeatures: thickness h, mid surface dimension L, curva-ture radius r, which satisfies h/r ? 1. When there existsh/L ? 1, the shell can be defined as thin shell. If L/r ? 1 is added besides the above two conditions, thethin shell is regarded as shallow shell 10.As Fig. 1 shows, the plane xy is the projection of themid surface of shallow shell along the z-axis. SupposingM is an arbitrary point on mid surface, two planesQMN & PMN are made paralleling to coordinate planeOYZ and OXZ, respectively. The two edges PM andQM can be regarded approximately as vertical becauseof mid surface?s flatness. At the same time, the lineMN is normal to mid surface. Thus, MN, QM, PMcan constitute a perpendicular reference frame MPQN,whose difference from orthogonal coordinate systemOXYZ can be ignored. And PM and QM are denotedby a and b, the curvilineal coordinate of MPQN.Assuming the Z coordinate of the point M is z, theanalytical equation of mid surface is expressed asfollows:z Fx;y:1The following equations can be obtained because of theflatness of the shell:ozox?2? 1;ozoy?2? 1;ozox?ozoy? 1:2The curvature and torsion of mid surface can be approx-imated to:kx ?o2zox2;ky ?o2zoy2;kxy ?o2zoxoy:3The Lae coefficients of mid surface along a and b direc-tions are deduced:A ds1dadxdx 1;B ds2dbdydy 1:4Applying concentrated force P along Z-axis and ignor-ing the influence of the transverse shear resultant forces,the balance differential equations of shallow shell are:oN1oxoSoy 0;oN2oyoSox 0;?kxN1 kyN2 oQ1oxoQ2oy Pd0;0 0;5Q1oM12oyoM1ox; Q2oM12oxoM2oy;where d(0,0) is Dirac-d function.The compatibility equation of shallow shell isr2N1 N2 ? Etr2kw 0;6where r2o2ox2o2oy2; r2k kxo2ox2 kyo2oy2:Expressing the moment resultants M1, M2and M12by the function of transverse displacement w, the basicequations of shallow shell under concentrated transverseforces are:Dr2r2w kxN1 kyN2 Pd0;0;r2N1 N2 ? Etr2kw 0;o2N1ox2o2N2oy2;7where N1is the membrane stress resultant in X-direc-tion; N2, the membrane resultant in Y-direction; D, thebending stiffness of shallow shell.Fig. 1. Double curvature shallow shell.Y. Zhang et al. / Materials and Design 27 (2006) 646865It is very difficult to solve above equation. Accordingto practical situation, sunken deflection will only con-centrate on a small area around external force P, so infi-nite large shallow shell 5 is assumed in this study.Because w, N1, N2are symmetric about x-, y-axis, all or-ders of derivatives of w, N1, N2become to zero at infin-ity. The following equations can be achieved by Fouriertransformation to Eq. (7):Dn2 g2 w kxN1 kyN2 P;n2 g2N1N2 ? Etkyn2 kxg2 w 0;n2N1 g2N2;8where:Z1?1Z1?1Pd0;0e?inxe?igydx dy P; w 4Z10Z10wcosnxcosgydx dy;N1 4Z10Z10N1cosnxcosgydx dy;N2 4Z10Z10N2cosnxcosgydx dy:9From Eq.(8), w can be obtained. Reverse Fourier trans-formation to w and polar coordinates transformation ton, g, w under polar coordinate system can be gainedw Pp2DZp=20Z10qcosqxcoshcosqy sinhq412t2kxcos2h kysin2h2dq dh;10Put x = 0 and y = 0 in Eq.(8), the relationship betweendeflection fpand concentrated force P of rectangle shal-low shell can be achieved as follows:P 4Et2ffiffiffiffiffiffiffiffiffikxkyp1 ? l2ffiffiffi3pfp:11Finally, dent resistance stiffness of shallow shell K isobtainedK Pfp4Et2ffiffiffiffiffiffiffiffiffikxkyp1 ? l2ffiffiffi3p :12This equation explains synthetically the relationship be-tween the dent resistance stiffness of double curvatureshallow shell and all influencing factors including mate-rial properties, geometry parameters, which can be usedto guide design, material select and manufacture.2.2. Analysis of critical load causing local trivial dentFor quantitative evaluation of critical load against lo-cal dent resistance of panels, several experience formulashave been brought forward by researchers. Based onlarge numbers of experiments, Dicellello 9 stated a for-mula that expresses minimum energy W causing visibletrivial dent trace by thickness t, yield stress rsand basicdent resistance stiffness KW Cr2st4K;13where C is proportional constant. From Eqs. (12) and(13), the critical load Pcrresulting in the local trivial dentin the center of the shallow shell can be achieved, whichis defined as the evaluating indexPcr Crst2:14From Eq. (14), there is a closely correlation betweencritical loads Pcrand thickness t, yield stress rs. The crit-ical load can be a rule to carry out lightweight design ofautomobile parts by using high strength steel instead ofmild steel.3. Example and crashworthiness analysis3.1. FE model of full car and its crash simulationA detailed finite element model has been establishedbased on a passenger car refitted from a saloon car,which is showed in Fig. 2. To ensure the correctnessand effectiveness of FE model, the following methodsare adopted:1. Since the goal is to simulate the frontal impact of thecar, the meshing of front car body is denser than thatof the rear car body.2. Reduced integration method with hourglass control istaken for 4 noded shell element and 8 noded bricksolid element to improve the efficiency of simulation.3. By using of the meshing and mass scaling technology,the characteristic length of the minimal element isensured to improve the simulation efficiency.4. Materials constitutive with CowperSymonds strainrate item is used for steel parts.5. Automaticsinglesurfacecontactalgorithmisadopted in the simulation aiming at complexity ofcar impact simulation.Fig. 2. Finite element model of full car.66Y. Zhang et al. / Materials and Design 27 (2006) 64686. Spot weld element with failure rule that consideringthe couple of normal force and shear force is used tosimulate the spot weld connection between auto parts.Explicit dynamic FEM software LS-DYNA Version950isusedtosimulatethefrontalimpactofthecaragainsta rigid wall at the speed of 50 km/s according to the Na-tional Crash Legislation CMVDR294. A real car crashexperiment is done at Car Crash Lab settled in TSingHuaUniversity.Bycomparingthetimehistoryofacceler-ation of certain position on the A pillar within 0.1 s, thesimulationgivesareasonablefittotheexperimentresults,which guaranteesthecorrectness ofFEmodel andgives anicer base for the next lightweighting optimized design.3.2. Lightweighting design and crashworthiness analysisThe use of high strength steel is one of the effectiveways to reduce car weight. However, the performance(such as crashworthiness, stiffness, and dent resistance)of part made of new material should be assured. Forexample, the front parts of a car are major energyabsorption parts in the process of car crash, so energyabsorption performance without affecting the safety ofpassengers should be assured in the design of front partsof a car. In this research, the bumper of the passengercar is studied under different materials but remainingits dent resistance.The mechanical properties of mild steel and highstrength steel are listed below (see Table 1).The evaluation index of dent resistance for bumperusing mild steel isPcr1 C1rs1t21:15When high strength steel is used to replace the mild steelremaining its primary shape and dent resistance per-formance, the new thickness t2of high strength steelcan be achievedt2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC1rs1C2rs2t1r:16From (16), the thickness of bumper that uses highstrength steel is gained and updated in the full car FEmodel. The deformation history of bumper using newmaterial is achieved after the car crash is re-simulatedwith updated part thickness (see Fig. 3).By simulation, the deformations of bumper made oftwo different kinds of material are similar in that plastichingeandtensionalplasticdeformationappearinthemid-dle part of bumper. And the energy absorption history isshown in the following for beam of the bumper. FromFig. 4 the difference of the energy absorption betweenTable 1Mechanical properties of two materialsMaterialDensity (g/cm3)E (GPa)lrs(MPa)Mild steel7.82100.3166High strength steel7.82100.3220Fig. 3. The deformation history of bumper using high strength steel.Fig. 4. Energy absorption time history of bumper beam.Y. Zhang et al. / Materials and Design 27 (2006) 646867twomaterialsissmall,about4.1%forbeamofthebumper,from which a conclusion can be drawn that itis feasible toreducethethicknessofthebumperpanelbasedonthedentresistance evaluation index studied in this research.4. ConclusionDent resistance performance of small curvature shal-low shell parts in automobile is studied in this paper,which enables the follows:1. Dent resistance stiffness under concentrated force isgiven for such parts.2. The critical load resulting in the local trivial dent inthe center of the shallow shell has been deduced,which in turn becomes the index to e