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Crashworthiness assessment of front side members in an auto-body considering the fabrication histories
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International Journal of Mechanical Sciences 45 (2003) 1645 – 1660
Crashworthiness assessment of front side members in an auto-body considering the fabrication histories H. Huha;∗ , K.P. Kima , S.H. Kima , J.H. Songa , H.S. Kimb , S.K. Hongb a
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Gusongdong, Science Town, Daejon 305-701, South Korea b Research and Development Division for Hyundai Motor Company and Kia Motors Corporation, Namyang-myun, Whasung-gun, Kyunggi-do 445-706, South Korea Received 12 June 2003; received in revised form 29 September 2003; accepted 27 November 2003
Abstract This paper is concerned with crash analysis of a front side member in an auto-body considering the e1ect of fabrication. The front side member is fabricated with sheet metal forming processes that induce forming histories such as plastic work hardening and non-uniform thickness distribution. Numerical simulation is carried out with LS-DYNA3D in order to identify the forming e1ect on the crashworthiness. The result shows that the crash analysis of the front side member with considering the forming history leads to a di1erent result from that without considering the forming e1ect. The analysis calculated the crash mode, the reaction force and the energy absorption for crashworthiness assessment with the forming e1ect. The analysis results demonstrate that the design of auto-body members should be carried out considering the forming history for accurate assessment of crashworthiness. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Crashworthiness assessment; Crash analysis; Sheet forming analysis; Draw-bead analysis; Forming e1ect; Front side member
1. Introduction The crashworthiness of a car has to be evaluated with the load-carrying capacity and the crash mode at the initial stage of auto-body design. Auto-body members such as a front side member should be designed to e9ciently absorb the kinetic energy during the car crash in order to secure occupants from the impact and penetration. The estimation of the energy absorption e9ciency of auto-body members requires the accurate crash analysis for the load-carrying capacity and the ∗
Corresponding author. Tel.: +82-42-869-3222; fax: +82-42-869-3210. E-mail address: [email protected] (H. Huh).
0020-7403/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmecsci.2003.09.022
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crash mode. In order to accomplish reliable crash simulation, crashworthiness of auto-body members should be evaluated considering the e1ect of stamping and forming as well as the dynamic properties of materials. As most load-carrying members of an auto-body are fabricated from the sheet metal forming process, they could possess wrinkling and thinning induced from forming as well as non-uniform distributions of the e1ective plastic strain and the thickness strain according to the forming condition and their Cnal shapes. Many crash analyses have been, however, carried out neglecting the forming e1ect induced by stamping and forming processes for estimation of the crashworthiness of an auto-body, providing erroneous results in the crash mode and the amount of crash. Recently, the crash analysis has been performed for auto-body members considering forming e1ect such as the strain hardening and the non-uniform thickness distribution [1–6]. These studies insisted that the crash analysis of auto-body structures should be carried out considering forming e1ects for the purpose of reliable assessment. Dutton et al. evaluated the crashworthiness of the side-rail considering variations of thickness, plastic strain and residual stress obtained from the hydro-forming analysis [1,2]. Lee et al. carried out the crash analyses of a sheet formed S-rail and a hydro-formed tube considering the e1ect of the mesh conCguration as well as the thickness, the plastic strain and the residual stress [3]. Kim and Huh considered not only e1ects of the thickness variation and the e1ective plastic strain but also the e1ect of the Cnal formed shape in the collapse analysis of an S-rail structure using the Cnite element limit analysis [4,5]. Mikami et al. carried out the frontal crash analysis of a car considering the thickness variation and the plastic strain for the front side member and the under frame [6]. In this paper, the forming histories of a front side member are obtained from simulation of stamping and forming processes so that they can be considered in the estimation of its crashworthiness. Since front side members should play an important role in absorption of the kinetic energy during the front crash, they are fabricated from sheet metals. Forming analysis of each panel of the front side member is carried out with an explicit elasto-plastic Cnite element analysis code, LS-DYNA3D. Non-uniform distributions of the e1ective plastic strain and the thickness strain in formed panels are obtained as the forming history from simulation of sheet metal forming. As the Crst step, draw-bead analysis is performed for calculation of the restraining force of draw-beads with an implicit elasto-plastic Cnite element analysis code, ABAQUS/Standard. Secondly, the calculated restraining force is applied to forming simulation of each panel as the equivalent restraining force on the Iange region. The thickness strain of the inner panel, frame-frt-in, is compared with the thickness strain in a real product for veriCcation of the analysis result. Crash analysis of the front side member is carried out imposing the forming analysis result on the initial condition. Numerical simulation is performed with LS-DYNA3D in order to evaluate the crashworthiness of the front side member. In order to consider the non-uniform distributions of the e1ective plastic strain and the thickness as the condition for crash analysis, the forming histories are mapped into the new Cnite element mesh system. The crash analysis results of the front side member considering the forming histories are compared with that without the forming e1ect. The forming e1ect on the crashworthiness is investigated for non-uniform distribution of the thickness and the e1ective plastic strain separately. The crash analysis results well demonstrate that these forming histories greatly change the crash mode, the load-carrying capacity and the energy absorption e9ciency of the front side member. It is noted from the results that design of auto-body members needs to consider the forming e1ects for a proper and accurate evaluation of the crashworthiness of a car with fabricated members.
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2. Forming analysis of the front side member A front side member is composed of seven panels as shown in Fig. 1: frame-frt-in; frame-frt-out-A; frame-frt-out-B; reinf-frt-frame-A; reinf-frt-frame-C; reinf-frt-frame-D; and hook-tie-down. The forming histories are calculated with the direct forming analysis for four panels that have great inIuence on the behavior of the front crash. For the sake of the computational e9ciency, the restraining forces of draw-beads in the dies are calculated with an implicit elasto-plastic Cnite element code, ABAQUS/Standard. The forming analysis is then carried out for four panels, imposing the calculated restraining forces as boundary conditions of the equivalent draw-bead [7–11]. The forming analysis, which is made up of the binder wrap process and the punch forming process, is performed with explicit elasto-plastic Cnite element code, LS-DYNA3D. Calculated forming results are applied to the crash simulation as the initial condition. 2.1. Draw-bead analysis The punch and die proCles for the Cnite element analysis of the draw-bead forming process are extracted from the geometric data of the tool-set as shown in Fig. 2 for frame-frt-in. Draw-beads are employed with di1erent shape and size according to each panel. The binder wrap analysis as well as the drawing analysis of the draw-bead is performed to calculate the restraining force of draw-beads for accurate forming simulation. Calculated equivalent draw-bead forces are applied to the forming analysis of the front side member. Fig. 3 explains geometric shapes of the circular and rectangular draw-beads for the simulation. The dimensions of circular draw-beads employed in forming of four
Fig. 1. Finite element model of seven parts of a front side member.
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Fig. 2. Location of draw-beads in the sheet metal forming die for a front frame.
Fig. 3. Geometric shapes of draw-beads in the front side member: (a) circular draw-bead; (b) rectangular draw-bead. Table 1 Dimensions of circular draw-beads in the front side member (unit = mm) Part
Bead type
R
r
H
Frame-frt-in Frame-frt-out-A Reinf-frt-frame-A
Circular Circular Circular Circular Circular Circular Circular
4.8 4.0 4.5 4.5 6.5 6.5 6.5
6.2 5.2 3.8 3.8 4.7 4.7 4.7
3.0 6.0 3.2 5.2 3.0 5.0 6.0
Reinf-frt-frame-C
bead bead bead bead bead bead bead
1 2 1 2 3
panels are explained in Table 1. The dimension of the rectangular draw-bead in the reinf-frt-frame-A is H = 6 mm, L = 7:65 mm, r1 = 2:18 mm and r2 = 1:5 mm. Table 2 shows the initial sheet thickness and material properties for forming simulation of four panels. The Cnite element model of an initial blank sheet has four layers of Cnite elements for accurate description of bending deformation. Figs. 4 and 5 show deformed shapes during the bead formation process with a circular draw-bead in the frame-frt-in for the binder wrap process and for the drawing process, respectively, and Figs. 6 and 7 show deformed shapes during the bead formation process with a rectangular draw-bead in the reinf-frt-frame-A for the binder wrap process and for the drawing process, respectively. The strain distribution during the bead formation process and the drawing process is very complicated and well explained in the previous work [9]. Although it is not shown in this paper, the strain distribution with a circular draw-bead is quite di1erent from that with a rectangular draw-bead. Draw-bead analyses of other panels are simulated with the same procedures.
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Table 2 Material properties and initial thickness of panels in the front side member Part (Material)
Sheet thickness and Iow stress curve
Frame-frt-in (SPRC40) Frame-frt-out-A (SPRC40) Reinf-frt-frame-A (SAPH38) Reinf-frt-frame-C (SPRC45)
Initial sheet thickness: 1:6 mm M = 734:7(0:01 + ) M 0:245 (MPa) Initial sheet thickness: 1:2 mm M = 734:7(0:01 + ) M 0:245 (MPa) Initial sheet thickness: 0:9 mm M = 768:5(0:023 + ) M 0:285 (MPa) Initial sheet thickness: 2:0 mm M = 823:8(0:012 + ) M 0:229 (MPa)
Fig. 4. Deformed shapes of the blank during the bead formation process with a circular draw-bead in frame-frt-in.
Fig. 5. Deformed shapes of the blank during the drawing process with a circular draw-bead in frame-frt-in.
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Fig. 6. Deformed shapes of the blank during the bead formation process with a rectangular draw-bead in Reinf-frt-frame-A.
Fig. 7. Deformed shapes of the blank during the drawing process with a rectangular draw-bead in Reinf-frt-frame-A.
Fig. 8 shows the calculated restraining force with respect to the drawing length for the circular and rectangular draw-beads. Since the rectangular draw-bead restrains the draw-in of sheet metal more than the circular draw-bead, the restraining force with the rectangular draw-bead gradually increases with the drawing length while the restraining force with the circular draw-bead reaches to the steady-state value. Table 3 shows the restraining forces that are obtained at the steady state for each draw-bead as the equivalent force in forming simulation. A rectangular draw-bead is employed in forming the reinf-frt-frame-A in order to control the material Iow the sheet with less draw-in with the large restraining force.
300
300
250
250
Restraining Force(N/mm)
Restraining Force(N/mm)
H. Huh et al. / International Journal of Mechanical Sciences 45 (2003) 1645 – 1660
200 150 100 50
200 150 100 50 0
0 0
2
(a)
4
6
8
0
10
350
300
300
250 200 150
Circular 1 Circular 2 Rectangular
50
4
6
8
10
Drawing Length (mm)
350
100
2
(b)
Drawing Length (mm)
Restraining Force(N/mm)
Restraining Force(N/mm)
1651
250 200 150 100
Circular 1 Circular 2 Circular 3
50 0
0 0
(c)
2
4
6
8
0
10
Drawing Length (mm)
(d)
2
4
6
8
10
Drawing Length (mm)
Fig. 8. Restraining force with respect to the drawing length: (a) frame-frt-in; (b)frame-frt-in; (c) reinf-frt-frame-A ; (d) reinf-frt-frame-C. Table 3 Restraining forces of draw-beads in the front side member Part
Bead type
Restraining force (N/mm)
Frame-frt-in Frame-frt-out-A Reinf-frt-frame-A
Circular bead Circular bead Circular bead 1 Circular bead 2 Rectangular bead Circular bead 1 Circular bead 2 Circular bead 3
226 243 246 271 294 217 235 278
Reinf-frt-frame-C
2.2. Forming analysis Direct forming analyses have been carried out for four panels of the front side member. A commercial explicit Cnite element code, LS-DYNA3D is employed in forming simulation for computational e9ciency since it requires tremendous calculation time to simulate forming processes with
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Fig. 9. Initial setting of tools and the blank for the numerical analysis of the frame-frt-in in the front side member.
Fig. 10. Final forming results of the frame-frt-in: (a) distribution of the e1ective plastic strain; (b) distribution of the thickness strain.
the implicit Cnite element method. The initial sheet thickness and material properties are shown in Table 2. The coulomb friction coe9cient is 0.15 between the sheet and tools. The blank holding force of 100 kN are applied to the blank holder. The binder wrap analysis and the punch forming analysis are carried out with calculated equivalent draw-bead forces listed in Table 3 as boundary conditions. The die, the punch and the blank holder are modeled with Cnite element patches for forming simulation of each panel. Fig. 9 shows the tooling system for the analysis of the frame-frt-in. Draw-beads are expressed with curved lines and attached to the blank holder as shown in Fig. 2. An r-type adaptive mesh system is adopted for the precise description of the formed shape. Fig. 10 shows the e1ective plastic strain distribution and the thickness distribution in the frame-frt-in after forming simulation. The thickness distribution calculated has been compared with that in the real part for the frame-frt-in. Fig. 11 shows the quantitative comparison of the thickness variation along the designated line between the real product and the Cnite element simulation result. The Cgures show very close coincidence between the measured results and the calculated results. The comparison fully demonstrates that the result from Cnite element forming simulation of the front frame member is highly reliable and its result of the e1ective plastic strain distribution and the thickness distribution
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Fig. 11. Comparison of thickness distribution of the frame-frt-in: (a) measured section; (b) section A–A ; (c) section B–B ; (d) section C–C .
can be applied to the crash analysis as the initial condition for better description of the real crash behavior. Forming analyses of other panels were also carried out with the same procedures in order to obtain the e1ective plastic strain distribution and the thickness distribution as the forming histories that are to be considered as forming e1ects in the crash simulation. Distributions of the e1ective plastic strain and the thickness were mapped into new Cnite element mesh systems for the crash simulation. Fig. 12 shows the e1ective plastic strain distribution and the thickness distribution mapped from the simulation results for each part. 3. Crash analysis of the front side member A Cnite element model of the assembled front side member for the crash analysis is shown in Fig. 13. The total mesh system consists of 29842 four-node shell elements and 30788 nodal points. The welding points for assembling seven parts are 93 points that are also modeled in simulation. Finite element models of seven panels that compose the front side member are illustrated in Fig. 1 with the number of nodes and elements speciCed for each panel. The panels are obtained from the formed ones by trimming. Forming histories obtained from the forming analysis in the previous section are utilized as the initial condition of the crash analysis for accurate assessment of crashworthiness. The material speciCcation and the thickness for seven panels of the front side member are shown in Table 4. The dynamic behavior of materials is described with the Johnson–Cook constitutive
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Fig. 12. Distribution of the e1ective plastic strain and the thickness, respectively in parts of the front side member: (a) frame-frt-in; (b) frame-frt-out-A; (c) reinf-frt-frame-A; (d) reinf-frt-frame-C.
relation as shown in Eq. (1) which has Cve material constants: A; B; n; C and m [12,13]. M˙ m n [1 − T ∗ ]; M = [A + BM ] 1 + C ln M˙0
(1)
where T∗ =
T − Troom ; Tmelt − Troom
M˙0 = 1=s:
(2)
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Fig. 13. Finite element model of the front side member for crash analysis. Table 4 Materials with the initial thickness for each part of the front side member Part
Material
Thickness (mm)
Frame-frt-in Frame-frt-out-A Frame-frt-out-B Reinf-frt-frame-A Reinf-frt-frame-C Reinf-frt-frame-D Hook-tie-down
SPRC40 SPRC40 SPRC40 SAPH38 SPRC45 SPRC45 SPRC45
1.6 1.2 1.2 0.9 2.0 1.6 2.0
Table 5 Material constants in the Johnson–Cook constitutive relation for the dynamic material properties Material constant
SAPH38
SPRC40
SPRC45
A (MPa) B (MPa) n C m
295.5 550.39 0.576 0.039 0.43
294.1 667.5 0.622 0.06 0.375
345.1 703.2 0.6 0.046 0.33
The constants for three materials of the front side member are obtained from the static and dynamic tensile test with Instron 5500, Instron 8032, and a tension split Hopkinson bar apparatus [13]. The experimental results are tabulated in Table 5. Simulation conditions for the crash analysis of the front side member are explained in Fig. 14. One end of the front side member is Cxed and the other end is crashed by a moving rigid wall. The mass of the rigid wall is 200 kg and its initial velocity is 13:3 m=s.
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Fig. 14. Schematic diagram for crash analysis of the front side member.
Fig. 15. Deformed shapes of the front side member at 30 ms: (a) without forming histories; (b) with the thickness distribution; (c) with the e1ective plastic strain distribution; (d) with all forming histories.
Crash analysis of the front side member is carried out considering the forming histories obtained from the forming analysis. The crash analysis has been carried out for 30 ms. The analysis result is compared with the one without considering forming e1ects. The thickness distribution and the e1ective plastic strain distribution are considered separately or all together as the initial condition of the crash analysis of the front side member. Fig. 15 shows deformed shapes of the front side member in four di1erent cases of simulation: The Crst one is without considering the forming e1ect; the second one is with considering the thickness
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Fig. 16. Comparison of deformed shapes of the front side member: (a) without forming histories; (b) with all forming histories.
distribution; the third one is with considering the e1ective plastic strain distribution; and the fourth one is with considering all forming histories. The deformation proceeds from the struck end since the end region has several grooves to induce axial folding. After the front region is crushed with folding, the deformation proceeds to the rear region absorbing more kinetic energy. The results show that the Crst and second ones deform more than the third and forth ones and the third one with considering the e1ective plastic strain distribution is the strongest while the second one with considering the thickness distribution is the weakest. It is because the e1ective plastic strain distribution plays a role in crash as reinforcements with the increased Iow stress and the thickness distribution plays a role in crash as defects stemming from thinning due to stamping. When the e1ective plastic strain is considered as the forming history, the deformation proceeds less and slower than others. When the thickness is considered, deformation is concentrated on dimples in the grooved region and thus the energy is absorbed less than others. Fig. 16 demonstrates that the deformed shape with all forming histories considered is di1erent from the one of the designed front side member that did not consider any forming e1ect. The region with dimples undergoes severer deformation when the forming e1ect is not considered than when the forming histories are considered. The middle region undergoes more remarkable bending when the forming e1ect is not considered than the one with all forming histories considered. It is because the bending in the middle region is delayed when the e1ective plastic strain distribution is considered as the forming histories. These results show that the deformation mode is greatly changed when forming histories are considered in the crash analysis. The most inIuencing factor is the non-uniform distributions of the e1ective plastic strain and the thickness. The comparison fully demonstrates that the forming histories have to be considered in the crash analysis for accurate assessment of crashworthiness. The reaction forces normal to the wall are plotted with respect to the crushing distance in Fig. 17. The curves were obtained by Cltering the original curves from the crash analysis with
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H. Huh et al. / International Journal of Mechanical Sciences 45 (2003) 1645 – 1660 180 without forming effects with only thickness distribution with only strain distribution with all forming effects
Reaction force (kN)
150 120 90 60 30 0 0
50
100
150
200
250
300
Displacement (mm)
Fig. 17. Reaction force during the crash of the front side member.
Internal energy (kJ)
16 without forming effects with only thickness distribution with only strain distribution with all forming effects
12
8
4
0 0
50
100
150
200
250
300
Displacement (mm)
Fig. 18. Comparison of the energy absorption with respect to the displacement in the front side member during the crash for 30 ms.
the SAE600 Clter. The initial peak load is 138:3 kN when the forming e1ect is not considered and 155:6 kN when all forming histories are considered. The initial peak load increases by 13% when only the e1ective plastic strain is considered and decreases slightly when only the non-uniform thickness is considered compared to the one without the forming e1ect. The reaction force tends to increase more with deformation in the case of the analysis considering the e1ective plastic strain than without considering the e1ective plastic strain. The results explain that the strain hardening with the e1ective plastic strain from forming processes makes the maximum load increase and the non-uniform thickness distribution with the thinned region can be considered as the initial defect of the front side member. The absorbed energy during deformation is plotted in Fig. 18. The Cgure also demonstrates that energy absorption increases remarkably when the e1ective plastic strain is considered and decreases slightly when the non-uniform thickness distribution is considered. The energy absorption of the front side member has a larger value when all forming e1ects are considered than the one without forming
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e1ect. The di1erence is 5.3% at the crushing distance of 100 mm, 10.2% when the crushing distance is 200 mm, and 17.3% when the crushing distance is 250 mm. The most important phenomenon is that the energy absorption rate increases with deformation when the e1ective plastic strain is considered in the analysis, while the energy absorption rate decreases with deformation when the e1ective plastic strain is not considered. It is because the deformation is delayed with the sti1ened body when the e1ective plastic strain is considered. The Cgure shows that the displacement after 30 ms is 275:8 mm when the forming e1ect is not considered and 262:1 mm when all forming histories are considered. These results demonstrate that the strain hardening resulted from forming processes is dominant in calculation of the reaction force and energy absorption. It is noted from the results that the crash analysis of the front side member has to be carried out considering the forming e1ect, especially, the e1ective plastic strain, for accurate assessment of crashworthiness. 4. Conclusion Crash analysis of a front side member has been carried out in order to evaluate the crashworthiness accurately considering the forming history. The analysis investigated the di1erence of the crash mode, the reaction force and the energy absorption between the results with considering the forming history and without considering the forming e1ect. Forming analyses of parts of the front side member have been carried out to obtain the distribution of the thickness and the e1ective plastic strain as the forming history that were considered as the initial condition in the crash analysis. Forming analysis includes draw-bead formation and drawing analysis as the equivalent condition in the binder wrap process and the punch forming process. The crash analysis results considering the forming history were compared with that without the forming e1ect. The comparison explains that the e1ective plastic strain is dominant in the calculation of the crash mode, the reaction force and the energy absorption due to strain hardening. The analysis results fully demonstrated that the forming history should be considered for accurate assessment of crashworthiness at the design stage of auto-body members. References [1] Dutton T, Iregbu S, Sturt R, Kellicut A, Cowell B, Kavikondala K. The e1ect of forming on the crashworthiness of vehicles with hydroformed frame siderails. SAE paper 1999-01-3208, 1999. [2] Kellicut A, Cowell B, Kavikondala K, Dutton T, Iregbu S, Sturt R. Application of the results of forming simulation in crash models. Proceedings of NUMISHEET’99, BesanScon, France, 1999. p. 509 –14. [3] Lee S-H, Han C-S, Oh S-I, Wriggers P. Comparative crash simulations incorporating the results of sheet forming analyses. Engineering Computations 2001;18(5/6):744–58. [4] Kim KP, Huh H. Collapse analysis of an auto-body structure by a Cnite element limit method. Proceedings of the Sixth USNCCM, Dearborn, USA, 2003. p. 737– 42. [5] Kim KP, Huh H. Collapse analysis of auto-body structures considering the e1ect of fabrication. Key Engineering Materials 2003;233–236:737–42. [6] Mikami H, Suzuki H, Ishizawa M, Matsuoka Y. Crash simulation considered inIuence of stamping. Proceedings of HANPAM’99, Seoul, Korea, 1999. p. 187–200. [7] Huh H, Han SS. Numerical simulation of rectangular cup drawing process with draw-beads. Proceedings of NUMIFORM’95, Ithaca, USA, 1995. p. 723–8.
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[8] Cao J, Boyce MC. Drawbead penetration as a control element of material Iow. SAE paper 930517, Detroit, USA, 1993. [9] Choi TH, Huh H, Chun BK, Lee JH. Draw-bead simulation by an elasto-plastic Cnite element method with directional reduced integration. Journal of Materials Processing Technology 1997;63:666–71. [10] Meinders T, Geijselasers HJM, HuTetink J. Equivalent drawbead performance in deep drawing simulations. Proceedings of NUMISHEET’ 99, Besancon, France, 1999. p. 243–8. [11] Sunaga H, Kawa M, Makinouchi A. Drawbeads-simulation models and experimental veriCcation in sheet metal forming processes. Proceedings of NUMIFORM’98, Enschede, Netherlands, 1998. p. 917–23. [12] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the Seventh International Symposium on Ballistics, Hague, Netherlands, 1983. p. 541–7. [13] Kang WJ, Huh H. VeriCcation of tension split Hopkinson bar to identify the dynamic behavior of sheet metals. Experimental Mechanics 2002;42(1):8–17.
International Journal of Mechanical Sciences 45 (2003) 1645 – 1660
Crashworthiness assessment of front side members in an auto-body considering the fabrication histories H. Huha;∗ , K.P. Kima , S.H. Kima , J.H. Songa , H.S. Kimb , S.K. Hongb a
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Gusongdong, Science Town, Daejon 305-701, South Korea b Research and Development Division for Hyundai Motor Company and Kia Motors Corporation, Namyang-myun, Whasung-gun, Kyunggi-do 445-706, South Korea Received 12 June 2003; received in revised form 29 September 2003; accepted 27 November 2003
Abstract This paper is concerned with crash analysis of a front side member in an auto-body considering the e1ect of fabrication. The front side member is fabricated with sheet metal forming processes that induce forming histories such as plastic work hardening and non-uniform thickness distribution. Numerical simulation is carried out with LS-DYNA3D in order to identify the forming e1ect on the crashworthiness. The result shows that the crash analysis of the front side member with considering the forming history leads to a di1erent result from that without considering the forming e1ect. The analysis calculated the crash mode, the reaction force and the energy absorption for crashworthiness assessment with the forming e1ect. The analysis results demonstrate that the design of auto-body members should be carried out considering the forming history for accurate assessment of crashworthiness. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Crashworthiness assessment; Crash analysis; Sheet forming analysis; Draw-bead analysis; Forming e1ect; Front side member
1. Introduction The crashworthiness of a car has to be evaluated with the load-carrying capacity and the crash mode at the initial stage of auto-body design. Auto-body members such as a front side member should be designed to e9ciently absorb the kinetic energy during the car crash in order to secure occupants from the impact and penetration. The estimation of the energy absorption e9ciency of auto-body members requires the accurate crash analysis for the load-carrying capacity and the ∗
Corresponding author. Tel.: +82-42-869-3222; fax: +82-42-869-3210. E-mail address: [email protected] (H. Huh).
0020-7403/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmecsci.2003.09.022
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crash mode. In order to accomplish reliable crash simulation, crashworthiness of auto-body members should be evaluated considering the e1ect of stamping and forming as well as the dynamic properties of materials. As most load-carrying members of an auto-body are fabricated from the sheet metal forming process, they could possess wrinkling and thinning induced from forming as well as non-uniform distributions of the e1ective plastic strain and the thickness strain according to the forming condition and their Cnal shapes. Many crash analyses have been, however, carried out neglecting the forming e1ect induced by stamping and forming processes for estimation of the crashworthiness of an auto-body, providing erroneous results in the crash mode and the amount of crash. Recently, the crash analysis has been performed for auto-body members considering forming e1ect such as the strain hardening and the non-uniform thickness distribution [1–6]. These studies insisted that the crash analysis of auto-body structures should be carried out considering forming e1ects for the purpose of reliable assessment. Dutton et al. evaluated the crashworthiness of the side-rail considering variations of thickness, plastic strain and residual stress obtained from the hydro-forming analysis [1,2]. Lee et al. carried out the crash analyses of a sheet formed S-rail and a hydro-formed tube considering the e1ect of the mesh conCguration as well as the thickness, the plastic strain and the residual stress [3]. Kim and Huh considered not only e1ects of the thickness variation and the e1ective plastic strain but also the e1ect of the Cnal formed shape in the collapse analysis of an S-rail structure using the Cnite element limit analysis [4,5]. Mikami et al. carried out the frontal crash analysis of a car considering the thickness variation and the plastic strain for the front side member and the under frame [6]. In this paper, the forming histories of a front side member are obtained from simulation of stamping and forming processes so that they can be considered in the estimation of its crashworthiness. Since front side members should play an important role in absorption of the kinetic energy during the front crash, they are fabricated from sheet metals. Forming analysis of each panel of the front side member is carried out with an explicit elasto-plastic Cnite element analysis code, LS-DYNA3D. Non-uniform distributions of the e1ective plastic strain and the thickness strain in formed panels are obtained as the forming history from simulation of sheet metal forming. As the Crst step, draw-bead analysis is performed for calculation of the restraining force of draw-beads with an implicit elasto-plastic Cnite element analysis code, ABAQUS/Standard. Secondly, the calculated restraining force is applied to forming simulation of each panel as the equivalent restraining force on the Iange region. The thickness strain of the inner panel, frame-frt-in, is compared with the thickness strain in a real product for veriCcation of the analysis result. Crash analysis of the front side member is carried out imposing the forming analysis result on the initial condition. Numerical simulation is performed with LS-DYNA3D in order to evaluate the crashworthiness of the front side member. In order to consider the non-uniform distributions of the e1ective plastic strain and the thickness as the condition for crash analysis, the forming histories are mapped into the new Cnite element mesh system. The crash analysis results of the front side member considering the forming histories are compared with that without the forming e1ect. The forming e1ect on the crashworthiness is investigated for non-uniform distribution of the thickness and the e1ective plastic strain separately. The crash analysis results well demonstrate that these forming histories greatly change the crash mode, the load-carrying capacity and the energy absorption e9ciency of the front side member. It is noted from the results that design of auto-body members needs to consider the forming e1ects for a proper and accurate evaluation of the crashworthiness of a car with fabricated members.
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2. Forming analysis of the front side member A front side member is composed of seven panels as shown in Fig. 1: frame-frt-in; frame-frt-out-A; frame-frt-out-B; reinf-frt-frame-A; reinf-frt-frame-C; reinf-frt-frame-D; and hook-tie-down. The forming histories are calculated with the direct forming analysis for four panels that have great inIuence on the behavior of the front crash. For the sake of the computational e9ciency, the restraining forces of draw-beads in the dies are calculated with an implicit elasto-plastic Cnite element code, ABAQUS/Standard. The forming analysis is then carried out for four panels, imposing the calculated restraining forces as boundary conditions of the equivalent draw-bead [7–11]. The forming analysis, which is made up of the binder wrap process and the punch forming process, is performed with explicit elasto-plastic Cnite element code, LS-DYNA3D. Calculated forming results are applied to the crash simulation as the initial condition. 2.1. Draw-bead analysis The punch and die proCles for the Cnite element analysis of the draw-bead forming process are extracted from the geometric data of the tool-set as shown in Fig. 2 for frame-frt-in. Draw-beads are employed with di1erent shape and size according to each panel. The binder wrap analysis as well as the drawing analysis of the draw-bead is performed to calculate the restraining force of draw-beads for accurate forming simulation. Calculated equivalent draw-bead forces are applied to the forming analysis of the front side member. Fig. 3 explains geometric shapes of the circular and rectangular draw-beads for the simulation. The dimensions of circular draw-beads employed in forming of four
Fig. 1. Finite element model of seven parts of a front side member.
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Fig. 2. Location of draw-beads in the sheet metal forming die for a front frame.
Fig. 3. Geometric shapes of draw-beads in the front side member: (a) circular draw-bead; (b) rectangular draw-bead. Table 1 Dimensions of circular draw-beads in the front side member (unit = mm) Part
Bead type
R
r
H
Frame-frt-in Frame-frt-out-A Reinf-frt-frame-A
Circular Circular Circular Circular Circular Circular Circular
4.8 4.0 4.5 4.5 6.5 6.5 6.5
6.2 5.2 3.8 3.8 4.7 4.7 4.7
3.0 6.0 3.2 5.2 3.0 5.0 6.0
Reinf-frt-frame-C
bead bead bead bead bead bead bead
1 2 1 2 3
panels are explained in Table 1. The dimension of the rectangular draw-bead in the reinf-frt-frame-A is H = 6 mm, L = 7:65 mm, r1 = 2:18 mm and r2 = 1:5 mm. Table 2 shows the initial sheet thickness and material properties for forming simulation of four panels. The Cnite element model of an initial blank sheet has four layers of Cnite elements for accurate description of bending deformation. Figs. 4 and 5 show deformed shapes during the bead formation process with a circular draw-bead in the frame-frt-in for the binder wrap process and for the drawing process, respectively, and Figs. 6 and 7 show deformed shapes during the bead formation process with a rectangular draw-bead in the reinf-frt-frame-A for the binder wrap process and for the drawing process, respectively. The strain distribution during the bead formation process and the drawing process is very complicated and well explained in the previous work [9]. Although it is not shown in this paper, the strain distribution with a circular draw-bead is quite di1erent from that with a rectangular draw-bead. Draw-bead analyses of other panels are simulated with the same procedures.
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Table 2 Material properties and initial thickness of panels in the front side member Part (Material)
Sheet thickness and Iow stress curve
Frame-frt-in (SPRC40) Frame-frt-out-A (SPRC40) Reinf-frt-frame-A (SAPH38) Reinf-frt-frame-C (SPRC45)
Initial sheet thickness: 1:6 mm M = 734:7(0:01 + ) M 0:245 (MPa) Initial sheet thickness: 1:2 mm M = 734:7(0:01 + ) M 0:245 (MPa) Initial sheet thickness: 0:9 mm M = 768:5(0:023 + ) M 0:285 (MPa) Initial sheet thickness: 2:0 mm M = 823:8(0:012 + ) M 0:229 (MPa)
Fig. 4. Deformed shapes of the blank during the bead formation process with a circular draw-bead in frame-frt-in.
Fig. 5. Deformed shapes of the blank during the drawing process with a circular draw-bead in frame-frt-in.
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Fig. 6. Deformed shapes of the blank during the bead formation process with a rectangular draw-bead in Reinf-frt-frame-A.
Fig. 7. Deformed shapes of the blank during the drawing process with a rectangular draw-bead in Reinf-frt-frame-A.
Fig. 8 shows the calculated restraining force with respect to the drawing length for the circular and rectangular draw-beads. Since the rectangular draw-bead restrains the draw-in of sheet metal more than the circular draw-bead, the restraining force with the rectangular draw-bead gradually increases with the drawing length while the restraining force with the circular draw-bead reaches to the steady-state value. Table 3 shows the restraining forces that are obtained at the steady state for each draw-bead as the equivalent force in forming simulation. A rectangular draw-bead is employed in forming the reinf-frt-frame-A in order to control the material Iow the sheet with less draw-in with the large restraining force.
300
300
250
250
Restraining Force(N/mm)
Restraining Force(N/mm)
H. Huh et al. / International Journal of Mechanical Sciences 45 (2003) 1645 – 1660
200 150 100 50
200 150 100 50 0
0 0
2
(a)
4
6
8
0
10
350
300
300
250 200 150
Circular 1 Circular 2 Rectangular
50
4
6
8
10
Drawing Length (mm)
350
100
2
(b)
Drawing Length (mm)
Restraining Force(N/mm)
Restraining Force(N/mm)
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250 200 150 100
Circular 1 Circular 2 Circular 3
50 0
0 0
(c)
2
4
6
8
0
10
Drawing Length (mm)
(d)
2
4
6
8
10
Drawing Length (mm)
Fig. 8. Restraining force with respect to the drawing length: (a) frame-frt-in; (b)frame-frt-in; (c) reinf-frt-frame-A ; (d) reinf-frt-frame-C. Table 3 Restraining forces of draw-beads in the front side member Part
Bead type
Restraining force (N/mm)
Frame-frt-in Frame-frt-out-A Reinf-frt-frame-A
Circular bead Circular bead Circular bead 1 Circular bead 2 Rectangular bead Circular bead 1 Circular bead 2 Circular bead 3
226 243 246 271 294 217 235 278
Reinf-frt-frame-C
2.2. Forming analysis Direct forming analyses have been carried out for four panels of the front side member. A commercial explicit Cnite element code, LS-DYNA3D is employed in forming simulation for computational e9ciency since it requires tremendous calculation time to simulate forming processes with
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Fig. 9. Initial setting of tools and the blank for the numerical analysis of the frame-frt-in in the front side member.
Fig. 10. Final forming results of the frame-frt-in: (a) distribution of the e1ective plastic strain; (b) distribution of the thickness strain.
the implicit Cnite element method. The initial sheet thickness and material properties are shown in Table 2. The coulomb friction coe9cient is 0.15 between the sheet and tools. The blank holding force of 100 kN are applied to the blank holder. The binder wrap analysis and the punch forming analysis are carried out with calculated equivalent draw-bead forces listed in Table 3 as boundary conditions. The die, the punch and the blank holder are modeled with Cnite element patches for forming simulation of each panel. Fig. 9 shows the tooling system for the analysis of the frame-frt-in. Draw-beads are expressed with curved lines and attached to the blank holder as shown in Fig. 2. An r-type adaptive mesh system is adopted for the precise description of the formed shape. Fig. 10 shows the e1ective plastic strain distribution and the thickness distribution in the frame-frt-in after forming simulation. The thickness distribution calculated has been compared with that in the real part for the frame-frt-in. Fig. 11 shows the quantitative comparison of the thickness variation along the designated line between the real product and the Cnite element simulation result. The Cgures show very close coincidence between the measured results and the calculated results. The comparison fully demonstrates that the result from Cnite element forming simulation of the front frame member is highly reliable and its result of the e1ective plastic strain distribution and the thickness distribution
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Fig. 11. Comparison of thickness distribution of the frame-frt-in: (a) measured section; (b) section A–A ; (c) section B–B ; (d) section C–C .
can be applied to the crash analysis as the initial condition for better description of the real crash behavior. Forming analyses of other panels were also carried out with the same procedures in order to obtain the e1ective plastic strain distribution and the thickness distribution as the forming histories that are to be considered as forming e1ects in the crash simulation. Distributions of the e1ective plastic strain and the thickness were mapped into new Cnite element mesh systems for the crash simulation. Fig. 12 shows the e1ective plastic strain distribution and the thickness distribution mapped from the simulation results for each part. 3. Crash analysis of the front side member A Cnite element model of the assembled front side member for the crash analysis is shown in Fig. 13. The total mesh system consists of 29842 four-node shell elements and 30788 nodal points. The welding points for assembling seven parts are 93 points that are also modeled in simulation. Finite element models of seven panels that compose the front side member are illustrated in Fig. 1 with the number of nodes and elements speciCed for each panel. The panels are obtained from the formed ones by trimming. Forming histories obtained from the forming analysis in the previous section are utilized as the initial condition of the crash analysis for accurate assessment of crashworthiness. The material speciCcation and the thickness for seven panels of the front side member are shown in Table 4. The dynamic behavior of materials is described with the Johnson–Cook constitutive
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Fig. 12. Distribution of the e1ective plastic strain and the thickness, respectively in parts of the front side member: (a) frame-frt-in; (b) frame-frt-out-A; (c) reinf-frt-frame-A; (d) reinf-frt-frame-C.
relation as shown in Eq. (1) which has Cve material constants: A; B; n; C and m [12,13]. M˙ m n [1 − T ∗ ]; M = [A + BM ] 1 + C ln M˙0
(1)
where T∗ =
T − Troom ; Tmelt − Troom
M˙0 = 1=s:
(2)
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Fig. 13. Finite element model of the front side member for crash analysis. Table 4 Materials with the initial thickness for each part of the front side member Part
Material
Thickness (mm)
Frame-frt-in Frame-frt-out-A Frame-frt-out-B Reinf-frt-frame-A Reinf-frt-frame-C Reinf-frt-frame-D Hook-tie-down
SPRC40 SPRC40 SPRC40 SAPH38 SPRC45 SPRC45 SPRC45
1.6 1.2 1.2 0.9 2.0 1.6 2.0
Table 5 Material constants in the Johnson–Cook constitutive relation for the dynamic material properties Material constant
SAPH38
SPRC40
SPRC45
A (MPa) B (MPa) n C m
295.5 550.39 0.576 0.039 0.43
294.1 667.5 0.622 0.06 0.375
345.1 703.2 0.6 0.046 0.33
The constants for three materials of the front side member are obtained from the static and dynamic tensile test with Instron 5500, Instron 8032, and a tension split Hopkinson bar apparatus [13]. The experimental results are tabulated in Table 5. Simulation conditions for the crash analysis of the front side member are explained in Fig. 14. One end of the front side member is Cxed and the other end is crashed by a moving rigid wall. The mass of the rigid wall is 200 kg and its initial velocity is 13:3 m=s.
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Fig. 14. Schematic diagram for crash analysis of the front side member.
Fig. 15. Deformed shapes of the front side member at 30 ms: (a) without forming histories; (b) with the thickness distribution; (c) with the e1ective plastic strain distribution; (d) with all forming histories.
Crash analysis of the front side member is carried out considering the forming histories obtained from the forming analysis. The crash analysis has been carried out for 30 ms. The analysis result is compared with the one without considering forming e1ects. The thickness distribution and the e1ective plastic strain distribution are considered separately or all together as the initial condition of the crash analysis of the front side member. Fig. 15 shows deformed shapes of the front side member in four di1erent cases of simulation: The Crst one is without considering the forming e1ect; the second one is with considering the thickness
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Fig. 16. Comparison of deformed shapes of the front side member: (a) without forming histories; (b) with all forming histories.
distribution; the third one is with considering the e1ective plastic strain distribution; and the fourth one is with considering all forming histories. The deformation proceeds from the struck end since the end region has several grooves to induce axial folding. After the front region is crushed with folding, the deformation proceeds to the rear region absorbing more kinetic energy. The results show that the Crst and second ones deform more than the third and forth ones and the third one with considering the e1ective plastic strain distribution is the strongest while the second one with considering the thickness distribution is the weakest. It is because the e1ective plastic strain distribution plays a role in crash as reinforcements with the increased Iow stress and the thickness distribution plays a role in crash as defects stemming from thinning due to stamping. When the e1ective plastic strain is considered as the forming history, the deformation proceeds less and slower than others. When the thickness is considered, deformation is concentrated on dimples in the grooved region and thus the energy is absorbed less than others. Fig. 16 demonstrates that the deformed shape with all forming histories considered is di1erent from the one of the designed front side member that did not consider any forming e1ect. The region with dimples undergoes severer deformation when the forming e1ect is not considered than when the forming histories are considered. The middle region undergoes more remarkable bending when the forming e1ect is not considered than the one with all forming histories considered. It is because the bending in the middle region is delayed when the e1ective plastic strain distribution is considered as the forming histories. These results show that the deformation mode is greatly changed when forming histories are considered in the crash analysis. The most inIuencing factor is the non-uniform distributions of the e1ective plastic strain and the thickness. The comparison fully demonstrates that the forming histories have to be considered in the crash analysis for accurate assessment of crashworthiness. The reaction forces normal to the wall are plotted with respect to the crushing distance in Fig. 17. The curves were obtained by Cltering the original curves from the crash analysis with
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H. Huh et al. / International Journal of Mechanical Sciences 45 (2003) 1645 – 1660 180 without forming effects with only thickness distribution with only strain distribution with all forming effects
Reaction force (kN)
150 120 90 60 30 0 0
50
100
150
200
250
300
Displacement (mm)
Fig. 17. Reaction force during the crash of the front side member.
Internal energy (kJ)
16 without forming effects with only thickness distribution with only strain distribution with all forming effects
12
8
4
0 0
50
100
150
200
250
300
Displacement (mm)
Fig. 18. Comparison of the energy absorption with respect to the displacement in the front side member during the crash for 30 ms.
the SAE600 Clter. The initial peak load is 138:3 kN when the forming e1ect is not considered and 155:6 kN when all forming histories are considered. The initial peak load increases by 13% when only the e1ective plastic strain is considered and decreases slightly when only the non-uniform thickness is considered compared to the one without the forming e1ect. The reaction force tends to increase more with deformation in the case of the analysis considering the e1ective plastic strain than without considering the e1ective plastic strain. The results explain that the strain hardening with the e1ective plastic strain from forming processes makes the maximum load increase and the non-uniform thickness distribution with the thinned region can be considered as the initial defect of the front side member. The absorbed energy during deformation is plotted in Fig. 18. The Cgure also demonstrates that energy absorption increases remarkably when the e1ective plastic strain is considered and decreases slightly when the non-uniform thickness distribution is considered. The energy absorption of the front side member has a larger value when all forming e1ects are considered than the one without forming
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e1ect. The di1erence is 5.3% at the crushing distance of 100 mm, 10.2% when the crushing distance is 200 mm, and 17.3% when the crushing distance is 250 mm. The most important phenomenon is that the energy absorption rate increases with deformation when the e1ective plastic strain is considered in the analysis, while the energy absorption rate decreases with deformation when the e1ective plastic strain is not considered. It is because the deformation is delayed with the sti1ened body when the e1ective plastic strain is considered. The Cgure shows that the displacement after 30 ms is 275:8 mm when the forming e1ect is not considered and 262:1 mm when all forming histories are considered. These results demonstrate that the strain hardening resulted from forming processes is dominant in calculation of the reaction force and energy absorption. It is noted from the results that the crash analysis of the front side member has to be carried out considering the forming e1ect, especially, the e1ective plastic strain, for accurate assessment of crashworthiness. 4. Conclusion Crash analysis of a front side member has been carried out in order to evaluate the crashworthiness accurately considering the forming history. The analysis investigated the di1erence of the crash mode, the reaction force and the energy absorption between the results with considering the forming history and without considering the forming e1ect. Forming analyses of parts of the front side member have been carried out to obtain the distribution of the thickness and the e1ective plastic strain as the forming history that were considered as the initial condition in the crash analysis. Forming analysis includes draw-bead formation and drawing analysis as the equivalent condition in the binder wrap process and the punch forming process. The crash analysis results considering the forming history were compared with that without the forming e1ect. The comparison explains that the e1ective plastic strain is dominant in the calculation of the crash mode, the reaction force and the energy absorption due to strain hardening. The analysis results fully demonstrated that the forming history should be considered for accurate assessment of crashworthiness at the design stage of auto-body members. References [1] Dutton T, Iregbu S, Sturt R, Kellicut A, Cowell B, Kavikondala K. The e1ect of forming on the crashworthiness of vehicles with hydroformed frame siderails. SAE paper 1999-01-3208, 1999. [2] Kellicut A, Cowell B, Kavikondala K, Dutton T, Iregbu S, Sturt R. Application of the results of forming simulation in crash models. Proceedings of NUMISHEET’99, BesanScon, France, 1999. p. 509 –14. [3] Lee S-H, Han C-S, Oh S-I, Wriggers P. Comparative crash simulations incorporating the results of sheet forming analyses. Engineering Computations 2001;18(5/6):744–58. [4] Kim KP, Huh H. Collapse analysis of an auto-body structure by a Cnite element limit method. Proceedings of the Sixth USNCCM, Dearborn, USA, 2003. p. 737– 42. [5] Kim KP, Huh H. Collapse analysis of auto-body structures considering the e1ect of fabrication. Key Engineering Materials 2003;233–236:737–42. [6] Mikami H, Suzuki H, Ishizawa M, Matsuoka Y. Crash simulation considered inIuence of stamping. Proceedings of HANPAM’99, Seoul, Korea, 1999. p. 187–200. [7] Huh H, Han SS. Numerical simulation of rectangular cup drawing process with draw-beads. Proceedings of NUMIFORM’95, Ithaca, USA, 1995. p. 723–8.
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[8] Cao J, Boyce MC. Drawbead penetration as a control element of material Iow. SAE paper 930517, Detroit, USA, 1993. [9] Choi TH, Huh H, Chun BK, Lee JH. Draw-bead simulation by an elasto-plastic Cnite element method with directional reduced integration. Journal of Materials Processing Technology 1997;63:666–71. [10] Meinders T, Geijselasers HJM, HuTetink J. Equivalent drawbead performance in deep drawing simulations. Proceedings of NUMISHEET’ 99, Besancon, France, 1999. p. 243–8. [11] Sunaga H, Kawa M, Makinouchi A. Drawbeads-simulation models and experimental veriCcation in sheet metal forming processes. Proceedings of NUMIFORM’98, Enschede, Netherlands, 1998. p. 917–23. [12] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the Seventh International Symposium on Ballistics, Hague, Netherlands, 1983. p. 541–7. [13] Kang WJ, Huh H. VeriCcation of tension split Hopkinson bar to identify the dynamic behavior of sheet metals. Experimental Mechanics 2002;42(1):8–17.