外文翻译原文.pdf

Short communication Lightweight design of automobile component using high strength steel based on dent resistance Yan Zhang *, Xinmin Lai, Ping Zhu, Wurong Wang School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, PR China Received 19 May 2004; accepted 14 September 2004 Abstract Lightweight and crashworthiness are two important aspects of auto-body design. In this paper, based on the shallow shell theory, the expression of dent resistance stiff ness of double curvatured shallow shell is obtained under the concentrated load condition. The critical loads resulting in the local trivial dent in the center of the shallow shell is regarded as the important index for the lightweight of the automobile parts. This rule is applied to the lightweight design of bumper system by using high strength steel instead of mild steel. 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 resistance 1. Introduction In recent years, the retaining number of automobiles has been increasing steadily, which has impacted the society and human life greatly. Such situation leads to many severe problems such as fuel crisis, environment pollution. The international association of aluminum stated that petrol consumption can decrease by 810% with 10% reduction of car weight 2. Thus, automobile lightweight is a basic way to fuel saving. In order to reduce the automobile weight, there are two important methods 3: One, automobile parts are redesigned to optimize the structure. By using thinning, hollowing, minitype, and compound parts, car weight can be reduced. The other, more and more lightweight materials, such as aluminum alloy, high strength steel, composite material, are widely used as lightweight mate- rials to replace the traditional materials like mild steel 4. These materials could reduce the weight remarkably. Material replacement is generally more eff ective in auto- mobile lightweighting than structure modifi cation. With the 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 automobile replacing the traditional material of mild steel. High strength steel sheet can be used in auto-body to improve components? impact energy absorption capacity and resistancetoplasticdeformation.Theautomobile weight can be reduced by use of high strength steel sheet of a thinner thickness to replace the mild steel sheet of body parts 1,3. Comparing with aluminum, magne- sium, and composite materials, high strength steel has better economy in that its raw material and fabrication cost are cheaper. Besides, high strength steel can be di- rectly used in product line including forming, wielding, assembling, and painting. The operating cost can be saved since there is no need adjusting the whole line. Outside of automobile body, there are several sheet metal Panels, most of which are shallow panels. Dent resistance is the ability to retain the shape against sunken defl ection and local dent under the external force. Dent 0261-3069/$ - 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 21 62933093. E-mail address: zytju (Y. Zhang). Materials and Design 27 (2006) 6468 Materials y:1 The following equations can be obtained because of the fl atness of the shell: oz ox ?2 ? 1; oz oy ?2 ? 1; oz ox ? oz oy ? ? ? ? ? ? ? ? ? 1:2 The curvature and torsion of mid surface can be approx- imated to: kx ? o2z ox2 ;ky ? o2z oy2 ;kxy ? o2z oxoy :3 The Lae coeffi cients of mid surface along a and b direc- tions are deduced: A ds1 da dx dx 1;B ds2 db dy dy 1:4 Applying concentrated force P along Z-axis and ignor- ing the infl uence of the transverse shear resultant forces, the balance diff erential equations of shallow shell are: oN1 ox oS oy 0; oN2 oy oS ox 0; ?kxN1 kyN2 oQ1 ox oQ2 oy Pd0;0 0;5 Q1 oM12 oy oM1 ox ; Q2 oM12 ox oM2 oy ; where d(0,0) is Dirac-d function. The compatibility equation of shallow shell is r2N1 N2 ? Etr2 kw 0; 6 where r2 o2 ox2 o2 oy2; r 2 k kx o2 ox2 ky o2 oy2: Expressing the moment resultants M1, M2and M12 by the function of transverse displacement w, the basic equations of shallow shell under concentrated transverse forces are: Dr2r2w kxN1 kyN2 Pd0;0; r2N1 N2 ? Etr2 kw 0; o2N1 ox2 o2N2 oy2 ; 7 where N1is the membrane stress resultant in X-direc- tion; N2, the membrane resultant in Y-direction; D, the bending stiff ness of shallow shell.Fig. 1. Double curvature shallow shell. Y. Zhang et al. / Materials and Design 27 (2006) 646865 It is very diffi cult to solve above equation. According to practical situation, sunken defl ection 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, N2 become to zero at infi n- ity. The following equations can be achieved by Fourier transformation to Eq. (7): Dn2 g2 w kxN1 kyN2 P; n2 g2N1N2 ? Etkyn2 kxg2 w 0; n2N1 g2N2; 8 where: Z 1 ?1 Z 1 ?1 Pd0;0e?inxe?igydx dy P; w 4 Z 1 0 Z 1 0 wcosnxcosgydx dy; N1 4 Z 1 0 Z 1 0 N1cosnxcosgydx dy; N2 4 Z 1 0 Z 1 0 N2cosnxcosgydx dy: 9 From Eq.(8), w can be obtained. Reverse Fourier trans- formation to w and polar coordinates transformation to n, g, w under polar coordinate system can be gained w P p2D Z p=2 0 Z 1 0 qcosqxcoshcosqy sinh q4 12 t2 kxcos2h kysin2h2 dq dh; 10 Put x = 0 and y = 0 in Eq.(8), the relationship between defl ection fpand concentrated force P of rectangle shal- low shell can be achieved as follows: P 4Et2 ffi ffi ffi ffi ffi ffi ffi ffiffi kxky p 1 ? l2 ffi ffiffi 3 p fp :11 Finally, dent resistance stiff ness of shallow shell K is obtained K P fp 4Et2 ffi ffi ffi ffi ffi ffi ffi ffiffi kxky p 1 ? l2 ffi ffiffi 3 p : 12 This equation explains synthetically the relationship be- tween the dent resistance stiff ness of double curvature shallow shell and all infl uencing factors including mate- rial properties, geometry parameters, which can be used to guide design, material select and manufacture. 2.2. Analysis of critical load causing local trivial dent For quantitative evaluation of critical load against lo- cal dent resistance of panels, several experience formulas have been brought forward by researchers. Based on large numbers of experiments, Dicellello 9 stated a for- mula that expresses minimum energy W causing visible trivial dent trace by thickness t, yield stress rsand basic dent resistance stiff ness K W C r2 st 4 K ;13 where C is proportional constant. From Eqs. (12) and (13), the critical load Pcrresulting in the local trivial dent in the center of the shallow shell can be achieved, which is defi ned as the evaluating index Pcr Crst2:14 From Eq. (14), there is a closely correlation between critical loads Pcrand thickness t, yield stress rs. The crit- ical load can be a rule to carry out lightweight design of automobile parts by using high strength steel instead of mild steel. 3. Example and crashworthiness analysis 3.1. FE model of full car and its crash simulation A detailed fi nite element model has been established based on a passenger car refi tted from a saloon car, which is showed in Fig. 2. To ensure the correctness and eff ectiveness of FE model, the following methods are adopted: 1. Since the goal is to simulate the frontal impact of the car, the meshing of front car body is denser than that of the rear car body. 2. Reduced integration method with hourglass control is taken for 4 noded shell element and 8 noded brick solid element to improve the effi ciency of simulation. 3. By using of the meshing and mass scaling technology, the characteristic length of the minimal element is ensured to improve the simulation effi ciency. 4. Materials constitutive with CowperSymonds strain rate item is used for steel parts. 5. Automaticsinglesurfacecontactalgorithmis adopted in the simulation aiming at complexity of car impact simulation. Fig. 2. Finite element model of full car. 66Y. Zhang et al. / Materials and Design 27 (2006) 6468 6. Spot weld element with failure rule that considering the couple of normal force and shear force is used to simulate the spot weld connection between auto parts. Explicit dynamic FEM software LS-DYNA Version 950isusedtosimulatethefrontalimpactofthecaragainst a rigid wall at the speed of 50 km/s according to the Na- tional Crash Legislation CMVDR294. A real car crash experiment is done at Car Crash Lab settled in TSing HuaUniversity.Bycomparingthetimehistoryofacceler- ation of certain position on the A pillar within 0.1 s, the simulationgivesareasonablefi ttotheexperimentresults, which guaranteesthecorrectness ofFEmodel andgives a nicer base for the next lightweighting optimized design. 3.2. Lightweighting design and crashworthiness analysis The use of high strength steel is one of the eff ective ways to reduce car weight. However, the performance (such as crashworthiness, stiff ness, and dent resistance) of part made of new material should be assured. For example, the front parts of a car are major energy absorption parts in the process of car crash, so energy absorption performance without aff ecting the safety of passengers should be assured in the design of front parts of a car. In this research, the bumper of the passenger car is studied under diff erent materials but remaining its dent resistance. The mechanical properties of mild steel and high strength steel are listed below (see Table 1). The evaluation index of dent resistance for bumper using mild steel is Pcr1 C1rs1t2 1: 15 When high strength steel is used to replace the mild steel remaining its primary shape and dent resistance per- formance, the new thickness t2of high strength steel can be achieved t2 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi C1rs1 C2rs2 t1 r :16 From (16), the thickness of bumper that uses high strength steel is gained and updated in the full car FE model. The deformation history of bumper using new material is achieved after the car crash is re-simulated with updated part thickness (see Fig. 3). By simulation, the deformations of bumper made of two diff erent kinds of material are similar in that plastic hingeandtensionalplasticdeformationappearinthemid- dle part of bumper. And the energy absorption history is shown in the following for beam of the bumper. From Fig. 4 the diff erence of the energy absorption between Table 1 Mechanical properties of two materials MaterialDensity (g/cm3)E (GPa)lrs(MPa) Mild steel7.82100.3166 High strength steel7.82100.3220 Fig. 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) 646867 twomaterialsissmall,about4.1%forbeamofthebumper, from which a conclusion can be drawn that itis feasible to reducethethicknessofthebumperpanelbasedonthedent resistance evaluation index studied in this research. 4. Conclusion Dent resistance performance of small curvature shal- low shell parts in automobile is studied in this paper, which enables the follows: 1. Dent resistance stiff ness under concentrated force is given for such parts. 2. The critical load resulting in the local trivial dent in the center of the shallow shell has been deduced, which in turn becomes the index to evaluate the dent resistance of automobile parts. 3. The validity of evaluating index is proven by applying the developed rule to the lightweight design of bum- per system using high strength steel instead of mild