Study on Dynamic Mechanics of Node-Enhanced Graded Lattice Structure and Application Optimization in Automobile Energy Absorbing Box
Abstract
:1. Introduction
2. Materials and Methods
2.1. Structure Design and Material
2.2. Finite Element Model
2.2.1. Drop Hammer Impact Test
2.2.2. Split Hopkinson Pressure Bar (SHPB) Test
3. Dynamic Simulation Results and Discussion
3.1. Drop Hammer Impact
3.2. Split Hopkinson Pressure Bar (SHPB)
4. Optimization of an Automotive Energy Absorption Box Application Based on a Graded Lattice Structure
4.1. Parameter for Design of an Automotive Energy Absorption Box
4.2. Multi-Objective Optimization Design Based on a Genetic Algorithm
4.2.1. Design of Experiment (DOE) Method
4.2.2. The Response Surface Method and Sensitivity Analysis
4.3. Optimization Result and Discussion
5. Conclusions
- (1)
- Under the impact load of a falling hammer, lattice structures with different impact energies will generate different compression deformations, and lattice structures designed with different gradient strategies will have different effects. When the impact is not enough to achieve structural densification, the gradient lattice structure RGNBCC-Z shows excellent energy absorption and impact resistance at low-speed impact. When the impact energy is large enough to achieve densification of the structure, the advantage of the rod diameter graded lattice structure RGNBCC-Z will no longer exist. In terms of peak impact force, the HGNBCC-Z is significantly smaller than the other structure, demonstrating good buffering performance under high-speed impact.
- (2)
- Under high strain rate load impact, the load-bearing performance of a node-enhanced lattice structure (NBCC) is significantly enhanced compared to a BCC. The load-bearing capacity and energy absorption effect of the highly graded lattice structure HGNBCC-Z are greater than the NBCC. The RGNBCC-Z shows a wave like upward trend due to the presence of weak layers.
- (3)
- Based on the graded lattice structure, the automotive energy absorption box was optimized. A multi-objective optimization algorithm was used to optimize the model. The optimization result shows that the maximum peak impact force was reduced by 45.6% and the specific energy absorption increased by 30.4%. The effect of the optimization was obvious, and it is of great practical significance to conduct structure optimization of automotive energy absorption boxes.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Silva, D.F.M.; Silva, C.M.A.; Braganca, I.M.F.; Nielsen, C.V.; Alves, L.M.; Martins, P.A.F. On the Performance of Thin-Walled Crash Boxes Joined by Forming. Materials 2018, 11, 1118. [Google Scholar] [CrossRef] [PubMed]
- Abdullah, N.A.Z.; Sani, M.S.M.; Salwani, M.S.; Husain, N.A. A review on crashworthiness studies of crash box structure. Thin-Walled Struct. 2020, 153, 106795. [Google Scholar] [CrossRef]
- Tan, H.L.; He, Z.C.; Li, E.; Cheng, A.G.; Chen, T.; Tan, X.W.; Li, Q.Q.; Xu, B. Crashworthiness design and multi-objective optimization of a novel auxetic hierarchical honeycomb crash box. Struct. Multidiscip. Optim. 2021, 64, 2009–2024. [Google Scholar] [CrossRef]
- Hussein, R.D.; Ruan, D.; Lu, G.; Guillow, S.; Yoon, J.W. Crushing response of square aluminium tubes filled with polyurethane foam and aluminium honeycomb. Thin-Walled Struct. 2017, 110, 140–154. [Google Scholar] [CrossRef]
- Zhu, G.; Sun, G.; Yu, H.; Li, S.; Li, Q. Energy absorption of metal, composite and metal/composite hybrid structures under oblique crushing loading. Int. J. Mech. Sci. 2018, 135, 458–483. [Google Scholar] [CrossRef]
- Wang, G.F.; Zhang, Y.L.; Zheng, Z.J.; Chen, H.B.; Yu, J.L. Crashworthiness design and impact tests of aluminum foam-filled crash boxes. Thin-Walled Struct. 2022, 180, 109937. [Google Scholar] [CrossRef]
- Feng, Q.; Tang, Q.; Liu, Z.; Liu, Y.; Setchi, R. An investigation of the mechanical properties of metallic lattice structures fabricated using selective laser melting. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2018, 232, 1719–1730. [Google Scholar] [CrossRef]
- Dong, G.; Tang, Y.; Li, D.; Zhao, Y.F. Design and optimization of solid lattice hybrid structures fabricated by additive manufacturing. Addit. Manuf. 2020, 33, 101116. [Google Scholar] [CrossRef]
- Liu, F.; Wang, L.; Jin, D.; Liu, X.; Lu, P. Equivalent Beam Model for Spatial Repetitive Lattice Structures with Hysteretic Nonlinear Joints. Int. J. Mech. Sci. 2021, 200, 106449. [Google Scholar] [CrossRef]
- Yin, H.F.; Zhang, W.Z.; Zhu, L.C.; Meng, F.B.; Liu, J.E.; Wen, G.L. Review on lattice structures for energy absorption properties. Compos. Struct. 2023, 304, 116397. [Google Scholar] [CrossRef]
- Pan, C.; Han, Y.F.; Lu, J.P. Design and Optimization of Lattice Structures: A Review. Appl. Sci. 2020, 10, 6374. [Google Scholar] [CrossRef]
- Al-Saedi, D.S.J.; Masood, S.H.; Faizan-Ur-Rab, M.; Alomarah, A.; Ponnusamy, P. Mechanical properties and energy absorption capability of functionally graded F2BCC lattice fabricated by SLM. Mater. Des. 2018, 144, 32–44. [Google Scholar] [CrossRef]
- Bai, L.; Gong, C.; Chen, X.; Zheng, J.; Xin, L.; Xiong, Y.; Wu, X.; Hu, M.; Li, K.; Sun, Y. Quasi-Static compressive responses and fatigue behavior of Ti-6Al-4 V graded lattice structures fabricated by laser powder bed fusion. Mater. Des. 2021, 210, 110110. [Google Scholar] [CrossRef]
- Wu, B.; Sun, F.; Wang, L.; Chen, M.; Lu, Y.; Jiang, D. Characterization of mechanical equivalent properties for node enhanced graded lattice structure. Model. Simul. Mater. Sci. Eng. 2023, 31, 065016. [Google Scholar] [CrossRef]
- Cetin, E.; Baykasoğlu, C. Energy absorption of thin-walled tubes enhanced by lattice structures. Int. J. Mech. Sci. 2019, 157, 471–484. [Google Scholar] [CrossRef]
- Zhou, G.; Yan, P.; Wang, Q.; Dai, S.; Li, X.; Hao, Y.; Wang, Y. Design optimization of a novel NPR crash box based on multi-objective genetic algorithm. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 2022, 236, 3309–3325. [Google Scholar] [CrossRef]
- Wang, C.; Li, Y.; Zhao, W.; Zou, S.; Zhou, G.; Wang, Y. Structure design and multi-objective optimization of a novel crash box based on biomimetic structure. Int. J. Mech. Sci. 2018, 138, 489–501. [Google Scholar] [CrossRef]
- Wang, C.; Lu, G.; Zhao, W.; Wang, Y. Modeling and multi-objective optimization of a bionic crash box with folding deformation. Struct. Multidiscip. Optim. 2020, 61, 283–299. [Google Scholar] [CrossRef]
- Mohammadiha, O.; Beheshti, H.; Aboutalebi, F.H. Multi-objective optimisation of functionally graded honeycomb filled crash box under oblique impact loading. Int. J. Crashworthiness 2015, 20, 44–59. [Google Scholar] [CrossRef]
- Kechagias, S.; Oosterbeek, R.N.; Munford, M.J.; Ghouse, S.; Jeffers, J.R.T. Controlling the mechanical behaviour of stochastic lattice structures: The key role of nodal connectivity. Addit. Manuf. 2022, 54, 102730. [Google Scholar] [CrossRef]
- Geng, X.; Ma, L.; Liu, C.; Zhao, C.; Yue, Z. A FEM study on mechanical behavior of cellular lattice materials based on combined elements. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 2017, 712, 188–198. [Google Scholar] [CrossRef]
- Xiao, L.; Song, W.; Xu, X. Experimental study on the collapse behavior of graded Ti-6Al-4V micro-lattice structures printed by selective laser melting under high-speed impact. Thin-Walled Struct. 2020, 155, 106970. [Google Scholar] [CrossRef]
- Maconachie, T.; Leary, M.; Lozanovski, B.; Zhang, X.Z.; Qian, M.; Faruque, O.; Brandt, M. SLM lattice structures: Properties, performance, applications and challenges. Mater. Des. 2019, 183, 108137. [Google Scholar] [CrossRef]
- Yu, G.; Li, X.; Dai, L.; Xiao, L.; Song, W. Compressive properties of imperfect Ti-6Al-4V lattice structure fabricated by electron beam powder bed fusion under static and dynamic loadings. Addit. Manuf. 2022, 49, 102497. [Google Scholar] [CrossRef]
- Muiruri, A.; Maringa, M.; du Preez, W. High Strain Rate Properties of Various Forms of Ti6Al4V(ELI) Produced by Direct Metal Laser Sintering. Appl. Sci. 2021, 11, 8005. [Google Scholar] [CrossRef]
- Wang, B.; Xiao, X.; Astakhov, V.P.; Lin, Z. The effects of stress triaxiality and strain rate on the fracture strain of Ti6Al4V. Eng. Fract. Mech. 2019, 219, 106627. [Google Scholar] [CrossRef]
- Deng, Y.L.; Sun, J.J.; Ni, X.Y.; Xiong, D.S. Multilayers of poly(ethyleneimine)/poly(acrylic acid) coatings on Ti6Al4V acting as lubricated polymer-bearing interface. J. Biomed. Mater. Res. Part B 2020, 108, 2141–2152. [Google Scholar] [CrossRef]
- Drumond, T.P.; Greco, M.; Cimini, C.A., Jr. Numerical analysis of an UAS impact in a reinforced wing fixed leading edge. J. Braz. Soc. Mech. Sci. Eng. 2021, 43, 532. [Google Scholar] [CrossRef]
- Wu, H.P.; Li, X.F.; Mei, Q.F.; Chen, J.; Wu, G.H. Flow behavior of diffusion bonding interface of Ti6Al4V alloy over a wide range of strain rates. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 2019, 761, 138067. [Google Scholar] [CrossRef]
- Wang, C.; Suo, T.; Li, Y.; Xue, P.; Tang, Z.A. New Experimental and Numerical Framework for Determining of Revised J-C Failure Parameters. Materials 2018, 8, 396. [Google Scholar] [CrossRef]
- Biswas, N.; Ding, J.L. Numerical study of the deformation and fracture behavior of porous Ti6Al4V alloy under static and dynamic loading. Int. J. Impact Eng. 2015, 82, 89–102. [Google Scholar] [CrossRef]
- Yang, L.; Yan, C.; Han, C.; Chen, P.; Yang, S.; Shi, Y. Mechanical response of a triply periodic minimal surface cellular structures manufactured by selective laser melting. Int. J. Mech. Sci. 2018, 148, 149–157. [Google Scholar] [CrossRef]
- Zhou, H.L.; Zhao, M.; Ma, Z.B.; Zhang, D.Z.; Fu, G. Sheet and network based functionally graded lattice structures manufactured by selective laser melting: Design, mechanical properties, and simulation. Int. J. Mech. Sci. 2020, 175, 105480. [Google Scholar] [CrossRef]
- Belardi, V.G.; Fanelli, P.; Trupiano, S.; Vivio, F. Multiscale analysis and mechanical characterization of open-cell foams by simplified FE modeling. Eur. J. Mech. A Solids 2021, 89, 104291. [Google Scholar] [CrossRef]
- Fan, W.; Xie, R.H.; Davidson, M.; Yin, H.F.; Lai, K.Y.; Wu, Q.L. Crashworthiness and energy absorption of UHPFRC-steel composite sandwich structures under impact loading. Compos. Struct. 2023, 311, 116813. [Google Scholar] [CrossRef]
- Prabhu, S.; Qiu, T. Modeling of sand particle crushing in split Hopkinson pressure bar tests using the discrete element method. Int. J. Impact Eng. 2021, 156, 103974. [Google Scholar] [CrossRef]
- Wang, X.; Qin, R.X.; Chen, B.Z. Laser-based additively manufactured bio-inspired crashworthy structure: Energy absorption and collapse behavior under static and dynamic loadings. Mater. Des. 2021, 211, 110128. [Google Scholar] [CrossRef]
- Li, M.; Hao, H.; Cui, J.; Hao, Y.F. Numerical investigation of the failure mechanism of cubic concrete specimens in SHPB tests. Def. Technol. 2022, 18, 1–11. [Google Scholar] [CrossRef]
- Xie, C.; Wang, D.; Zong, L.; Wang, S.; Kong, D. Multi-objective crashworthiness optimization of energy-absorbing box with gradient lattice structure. Appl. Math. Model. 2023, 121, 304–320. [Google Scholar] [CrossRef]
- Song, S.Y.; Zhou, H.P.; Jia, Z.C.; Xu, L.Y.; Zhang, C.; Shi, M.H.; Hu, G.M. Effects of cutting parameters on the ultimate shear stress and specific cutting energy of sisal leaves. Biosyst. Eng. 2022, 218, 189–199. [Google Scholar] [CrossRef]
- Wei, W.H.; Li, Y.L.; Li, Y.T.; Xu, Y.Q.; Yang, C.Y. Research on Tool Wear Factors for Milling Wood-plastic Composites Based on Response Surface Methodology. BioResources 2021, 16, 151–162. [Google Scholar] [CrossRef]
A (MPa) | B (MPa) | C | n | D1 | D2 | D3 | D4 |
---|---|---|---|---|---|---|---|
1567 | 952 | 0.01 | 0.4 | −0.09 | 0.25 | −0.5 | 0.014 |
Lattice Type | Impact Velocity (m/s) | Impact Energy (J) | (mm) | PCF (kN) | EA (J) | MCF (kN/m) |
---|---|---|---|---|---|---|
BCC | 7.5 | 337.5 | 6.43 | 36.66 | 214.13 | 33.30 |
NBCC | 5.87 | 42.13 | 205.16 | 34.95 | ||
HGNBCC-Z | 5.85 | 41.34 | 210.56 | 35.99 | ||
RGNBCC-Z | 8.65 | 33.12 | 262.14 | 30.31 | ||
BCC | 19.5 | 2281.5 | 24.40 | 118.51 | 1650.2 | 67.63 |
NBCC | 22.84 | 109.69 | 1776.9 | 77.80 | ||
HGNBCC-Z | 22.82 | 104.88 | 1793.1 | 78.56 | ||
RGNBCC-Z | 22.92 | 119.36 | 1746.6 | 76.20 |
Density (kg/m3) | Elastic Modulus (GPa) | Poisson’s Ratio | A (MPa) | B (MPa) | C | n | |
---|---|---|---|---|---|---|---|
Value | 2670 | 25.8 | 0.3 | 135 | 306 | 0.0069 | 0.619 |
Parameters | Description | Initial Value | Range |
---|---|---|---|
D1 (mm) | Small rod diameter | 2 | 1–2 |
D2 (mm) | Large rod diameter | 2 | 2–3 |
M | Gradient change factor | / | 1–2 |
T (mm) | Box wall thickness | 2.2 | 2–2.4 |
Number | D1 (mm) | D2 (mm) | M (mm) | T (mm) | PCF (kN) | SEA (J/kg) |
---|---|---|---|---|---|---|
1 | 1.2 | 2.8 | 2 | 2.2 | 209,547 | 9213.314 |
2 | 1.5 | 2.42 | 1.06 | 2.184 | 298,457 | 8306.277 |
3 | 1.66 | 2.7 | 1.66 | 2.168 | 300,812 | 7776.364 |
4 | 1.58 | 2.94 | 1.54 | 2.152 | 312,349 | 7435.381 |
5 | 1.1 | 2.18 | 1.26 | 2.312 | 227,235 | 10260.39 |
6 | 1.94 | 2.62 | 1.22 | 2.344 | 417,333 | 6747.729 |
7 | 1.54 | 2.74 | 1.7 | 2.328 | 295,735 | 7878.949 |
8 | 1.9 | 2.26 | 1.58 | 2.2 | 387,136 | 7849.654 |
9 | 1.3 | 2.78 | 1.3 | 2.28 | 281,996 | 8071.654 |
10 | 1.22 | 2.22 | 1.98 | 2.392 | 233,254 | 10281.51 |
11 | 1.38 | 2.1 | 1.02 | 2.024 | 257,876 | 9861.545 |
12 | 1.18 | 2.9 | 1.46 | 2.216 | 255,562 | 8417.838 |
13 | 1.46 | 2.86 | 1.34 | 2.12 | 304,793 | 7729.13 |
14 | 1.7 | 2.38 | 1.86 | 2.04 | 285,008 | 8601.383 |
15 | 1.34 | 2.98 | 1.18 | 2.36 | 316,811 | 7218.179 |
16 | 1.82 | 2.34 | 1.74 | 2.136 | 313,861 | 8097.555 |
17 | 1.78 | 2.3 | 1.42 | 2.376 | 326,460 | 7877.582 |
18 | 1.62 | 2.54 | 1.9 | 2.056 | 285,672 | 8507.53 |
19 | 1.14 | 2.06 | 1.38 | 2.088 | 212,082 | 11180.59 |
20 | 1.06 | 2.66 | 1.94 | 2.104 | 205,468 | 10284.46 |
21 | 1.42 | 2.58 | 1.62 | 2.296 | 276,855 | 8549.234 |
22 | 1.86 | 2.82 | 1.1 | 2.008 | 367,005 | 6754.973 |
23 | 1.98 | 2.46 | 1.78 | 2.232 | 405,089 | 7270.836 |
24 | 1.26 | 2.14 | 1.14 | 2.264 | 251,850 | 9801.693 |
25 | 1.74 | 2.02 | 1.5 | 2.248 | 330,662 | 8850.027 |
Parameters | Initial Value | Optimization Value | Rounding Value |
---|---|---|---|
D1/mm | 2 | 1.0398 | 1.04 |
D2/mm | 2 | 2.6516 | 2.65 |
M/mm | / | 1.8642 | 1.86 |
T/mm | 2.2 | 2.0126 | 2.01 |
Object Variable | Initial Value | Optimization Value | Simulation Value |
---|---|---|---|
PCF (kN) | 361.71 | 184.65 | 179.08 |
SEA (J/kg) | 8329 | 10,728 | 10,396 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Wu, B.; Chen, Q.; Liu, F.; Chen, M.; Lu, Y.; Jiang, D.; Yi, Y. Study on Dynamic Mechanics of Node-Enhanced Graded Lattice Structure and Application Optimization in Automobile Energy Absorbing Box. Materials 2023, 16, 6893. https://doi.org/10.3390/ma16216893
Wu B, Chen Q, Liu F, Chen M, Lu Y, Jiang D, Yi Y. Study on Dynamic Mechanics of Node-Enhanced Graded Lattice Structure and Application Optimization in Automobile Energy Absorbing Box. Materials. 2023; 16(21):6893. https://doi.org/10.3390/ma16216893
Chicago/Turabian StyleWu, Bin, Qiulong Chen, Fuyuan Liu, Min Chen, Yi Lu, Di Jiang, and Yang Yi. 2023. "Study on Dynamic Mechanics of Node-Enhanced Graded Lattice Structure and Application Optimization in Automobile Energy Absorbing Box" Materials 16, no. 21: 6893. https://doi.org/10.3390/ma16216893