Bending Response of Lattice Structure Filled Tubes under Transverse Loading

Abstract

Thin-walled tubes are widely used as passive energy-absorbing structures in a variety of industries. These structures are typically filled with lightweight materials to improve their energy absorption capabilities. At this point, additive manufacturing technology offers a great chance researchers for the production of novel filler structures to increase the crashworthiness performance of thin-walled tubes. In the current work, additive manufacturable body-centered cubic (BCC) lattice structures are suggested as filling materials for thin-walled tubes, and the bending response of these structures is investigated under transverse loads via a finite element modeling approach. The aspect ratio and strut diameter are considered as design parameters, and three-point bending simulations are conducted to understand the transverse load bearing behaviors of the structures. Different loading offsets are also taken into account for three-point bending simulations. The numerical results revealed that the BCC lattice structures used as filler materials significantly increase the energy absorption performance of thin-walled tubes due to synergetic interactions. In particular, the simulation results revealed that the hybrid tubes can absorb up to 84% more energy than the empty tubes, while the crush force efficiency of these structures is up to 42% higher compared to the empty tubes. The present study also showed that the transverse crushing characteristics of tubes can be considerably improved by suitable selection of the design parameters. These primary outcomes reveal that the proposed lattice structures can be considered as a potential alternative to traditional filler materials for enhancing the bending response of thin-walled tubes under transverse loading.

Keywords

• Lattice structures
• Thin-Walled Tubes
• Energy Absorption Performance
• Finite Element Methods
• Transverse loading

References

1. [1] Meran AP, Baykasoglu C, Mugan A. Development of a design for a crash energy management system for use in a railway passenger car. Proc Inst Mech Eng Part F J Rail Rapid Transit 2016;230:206–19. https://doi.org/10.1177/0954409714533321.
2. [2] Bhutada S, Goel MD. Crashworthiness parameters and their improvement using tubes as an energy absorbing structure: an overview. Int J Crashworthiness 2021;0:1–32. https://doi.org/10.10 80/13588265.2021.1969845.
3. [3] Abramowicz W. Thin-walled structures as impact energy absorbers. Thin-Walled Struct 2003;41:91–107. https://doi.org/10.1016/S0263-8231(02)00082-4.
4. [4] Alghamdi AAA. Collapsible impact energy absorbers: An overview. Thin-Walled Struct 2001;39:189–213. https://doi.org/10.1016/S0263-8231(00)00048-3.
5. [5] Baroutaji A, Sajjia M, Olabi AG. On the crashworthiness performance of thin-walled energy absorbers: Recent advances and future developments. Thin-Walled Struct 2017;118:137–63. https://doi.org/10.1016/j.tws.2017.05.018.
6. [6] Mat F, Ismail KA, Yaacob S, Inayatullah O. Impact Response of Thin-Walled Tubes: A Prospective Review. Appl Mech Mater 2012;165:130–4. https://doi.org/10.4028/www.scientific.net/AMM.165.130.
7. [7] Olabi AG, Morris E, Hashmi MSJ. Metallic tube type energy absorbers: A synopsis. Thin-Walled Struct 2007;45:706–26. https://doi.org/10.1016/j.tws.2007.05.003.
8. [8] Yuen SCK, Nurick GN. The Energy-Absorbing Characteristics of Tubular Structures With Geometric and Material Modifications: An Overview. Appl Mech Rev 2008;61:020802. https://doi. org/10.1115/1.2885138.

9. [9] Karagiozova D, Alves M. Transition from progressive buckling to global bending of circular shells under axial impact - Part I: Experimental and numerical observations. Int J Solids Struct 2004;41:1565–80. https://doi.org/10.1016/j.ijsolstr.2003.10.005.
10. [10] Karagiozova D, Jones N. Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact. Thin-Walled Struct 2001;39:583–610. https://doi.org/10.1016/S0263-8231(01)00015-5.
11. [11] Baykasoglu C, Cetin MT. Energy absorption of circular aluminium tubes with functionally graded thickness under axial impact loading. Int J Crashworthiness 2015;20:95–106. https://doi.org/10. 1080/13588265.2014.982269.
12. [12] Emin M, Baykasoglu C, Tunay M. Quasi-static Axial Crushing Behavior of Thin-walled Circular Aluminum Tubes with Functionally Graded Thickness. Procedia Eng 2016;149:559–65. https://doi.org/10.1016/j.proeng.2016.06.705.
13. [13] Baykasoglu A, Baykasoglu C. Crashworthiness optimization of circular tubes with functionally-graded thickness. Eng Comput 2016;33:1560–85. https://doi.org/10.1108/EC-08-2015-0245.
14. [14] Qi C, Yang S. Crashworthiness and lightweight optimisation of thin-walled conical tubes subjectedto an oblique impact. Int J Crashworthiness 2014;19:334–51. https://doi.org/10.1080/1358826 5.2014.893788.
15. [15] Yang S, Qi C. Multiobjective optimization for empty and foam-filled square columns under oblique impact loading. Int J Impact Eng 2013;54:177–91. https://doi.org/10.1016/j.ijimpeng.2012.11.009.
16. [16] Baykasoğlu C, Baykasoğlu A, Tunay Çetin M. A comparative study on crashworthiness of thin-walled tubes with functionally graded thickness under oblique impact loadings. Int J Crashworthiness 2019;24:453–71. https://doi.org/10.1080/13588265.2018.1478775.
17. [17] Qiu N, Gao Y, Fang J, Sun G, Kim NH. Topological design of multi-cell hexagonal tubes under axial and lateral loading cases using a modified particle swarm algorithm. Appl Math Model 2018;53:567–83. https://doi.org/10.1016/j.apm.2017.08.017.
18. [18] Huang Z, Zhang X, Fu X. On the bending force response of thin-walled beams under transverse loading. Thin-Walled Struct 2020;154:106807. https://doi.org/10.1016/j.tws.2020.106807.
19. [19] Gao Q, Wang L, Wang Y, Guo F, Zhang Z. Optimization of foam-filled double ellipse tubes under multiple loading cases. Adv Eng Softw 2016;99:27–35. https://doi.org/10.1016/j. advengsoft.2016.05.001.
20. [20] Yu X, Qin Q, Zhang J, Wang M, Xiang C, Wang T. Low-velocity impact of density-graded foam-filled square columns. Int J Crashworthiness 2020;0:1–14. https://doi.org/10.1080/13588265.20 20.1807685.
21. [21] Altin M, Güler MA, Mert SK. The effect of percent foam fill ratio on the energy absorption capacity of axially compressed thin-walled multi-cell square and circular tubes. Int J Mech Sci 2017;131–132:368–79. https://doi.org/10.1016/j.ijmecsci.2017.07.003.
22. [22] Altin M, Acar E, Güler MA. Foam filling options for crashworthiness optimization of thin-walled multi-tubular circular columns. Thin-Walled Struct 2018;131:309–23. https://doi.org/10.1016/j. tws.2018.06.043.
23. [23] Gedikli H. Crashworthiness optimization of foam-filled tailor-welded tube using coupled finite element and smooth particle hydrodynamics method. Thin-Walled Struct 2013;67:34–48. https://doi.org/10.1016/j.tws.2013.01.020.
24. [24] Fang J, Sun G, Qiu N, Pang T, Li S, Li Q. On hierarchical honeycombs under out-of-plane crushing. Int J Solids Struct 2018;135:1–13. https://doi.org/10.1016/j.ijsolstr.2017.08.013.
25. [25] Zhu G, Li S, Sun G, Li G, Li Q. On design of graded honeycomb filler and tubal wall thickness for multiple load cases. Thin-Walled Struct 2016;109:377–89. https://doi.org/10.1016/j.tws.2016.09.017.
26. [26] Song HW, Wan ZM, Xie ZM, Du XW. Axial impact behavior and energy absorption efficiency of composite wrapped metal tubes. Int J Impact Eng 2000;24:385–401. https://doi.org/10.1016/S0734-743X(99)00165-7.
27. [27] Zhu G, Sun G, Liu Q, Li G, Li Q. On crushing characteristics of different configurations of metal-composites hybrid tubes. Compos Struct 2017;175:58–69. https://doi.org/10.1016/j. compstruct.2017.04.072.
28. [28] Meriç D, Gedikli H. Multi-objective optimization of energy absorbing behavior of foam-filled hybrid composite tubes. Compos Struct 2022;279:114771. https://doi.org/10.1016/j. compstruct.2021.114771.
29. [29] Sun G, Chen D, Zhu G, Li Q. Lightweight hybrid materials and structures for energy absorption: A state-of-the-art review and outlook. Thin-Walled Struct 2022;172:108760. https://doi. org/10.1016/j.tws.2021.108760.
30. [30] Mahmoud D, Elbestawi MA. Lattice structures and functionally graded materials applications in additive manufacturing of orthopedic implants: A review. J Manuf Mater Process 2017;1:1–19. https://doi.org/10.3390/jmmp1020013.
31. [31] Pan C, Han Y, Lu J. Design and optimization of lattice structures: A review. Appl Sci 2020;10:1–36. https://doi.org/10.3390/APP10186374.
32. [32] Maskery I, Aremu AO, Simonelli M, Tuck C, Wildman RD, Ashcroft IA, et al. Mechanical Properties of Ti-6Al-4V Selectively Laser Melted Parts with Body-Centred-Cubic Lattices of Varying cell size. Exp Mech 2015:1–12. https://doi.org/10.1007/s11340-015-0021-5.
33. [33] Gümrük R, Mines RAW. Compressive behaviour of stainless steel micro-lattice structures. Int J Mech Sci 2013;68:125–39. https://doi. org/10.1016/j.ijmecsci.2013.01.006.
34. [34] Turner AJ, Al Rifaie M, Mian A, Srinivasan R. Low-Velocity Impact Behavior of Sandwich Structures with Additively Manufactured Polymer Lattice Cores. J Mater Eng Perform 2018;27:2505–12. https://doi.org/10.1007/s11665-018-3322-x.
35. [35] Shen Y, Cantwell W, Mines R, Li Y. Low-velocity impact performance of lattice structure core based sandwich panels. J Compos Mater 2014;48:3153–67. https://doi.org/10.1177/0021998313507616.
36. [36] Mines RAW, Tsopanos S, Shen Y, Hasan R, McKown ST. Drop weight impact behaviour of sandwich panels with metallic micro lattice cores. Int J Impact Eng 2013;60:120–32. https://doi. org/10.1016/j.ijimpeng.2013.04.007.
37. [37] Gümrük R, Mines RAW, Karadeniz S. Static mechanical behaviours of stainless steel micro-lattice structures under different loading conditions. Mater Sci Eng A 2013;586:392–406. https://doi. org/10.1016/j.msea.2013.07.070.
38. [38] McKown S, Shen Y, Brookes WK, Sutcliffe CJ, Cantwell WJ, Langdon GS, et al. The quasi-static and blast loading response of lattice structures. Int J Impact Eng 2008;35:795–810. https://doi. org/10.1016/j.ijimpeng.2007.10.005.
39. [39] Smith M, Guan Z, Cantwell W. J. Finite element modelling of the compressive response of lattice structures manufactured using the selective laser melting technique. Int J Mech Sci 2013;67:28–41. https://doi.org/10.1016/j.ijmecsci.2012.12.004.
40. [40] Merkt S, Hinke C, Bültmann J, Brandt M, Xie YM. Mechanical response of TiAl6V4 lattice structures manufactured by selective laser melting in quasistatic and dynamic compression tests. J Laser Appl 2015;27:S17006. https://doi.org/10.2351/1.4898835.
41. [41] Cetin E, Baykasoğlu C. Energy absorption of thin-walled tubes enhanced by lattice structures. Int J Mech Sci 2019;158:471–84. https://doi.org/10.1016/j.ijmecsci.2019.04.049.
42. [42] Baykasoğlu A, Baykasoğlu C, Cetin E. Multi-objective crashworthiness optimization of lattice structure filled thin-walled tubes. Thin Walled Struct 2020;149. https://doi.org/10.1016/j. tws.2020.106630.
43. [43] Cetin E, Baykasoğlu C. Crashworthiness of graded lattice structure filled thin-walled tubes under multiple impact loadings. Thin-Walled Struct 2020;154. https://doi.org/10.1016/j.tws.2020.106849.
44. [44] Gao Q, Wang L, Wang Y, Wang C. Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading. Thin-Walled Struct 2016;100:105–12. https://doi.org/10.1016/j.tws.2015.11.020.
45. [45] Li G, Xu F, Sun G, Li Q. A comparative study on thin-walled structures with functionally graded thickness (FGT) and tapered tubes withstanding oblique impact loading. Int J Impact Eng 2015;77:68–83. https://doi.org/10.1016/j.ijimpeng.2014.11.003.
46. [46] Qiu N, Gao Y, Fang J, Feng Z, Sun G, Li Q. Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases. Finite Elem Anal Des 2015;104:89–101. https://doi. org/10.1016/j.finel.2015.06.004.
47. [47] Li P, Wang Z, Petrinic N, Siviour CR. Deformation behaviour of stainless steel microlattice structures by selective laser melting. Mater Sci Eng A 2014;614:116–21. https://doi.org/10.1016/j. msea.2014.07.015.
48. [48] Tripathy L, Lu WF. Evaluation of axially-crushed cellular truss structures for crashworthiness. Int J Crashworthiness 2017;8265:1-17. https://doi.org/10.1080/13588265.2017.1389630.
49. [49] Zhang X, Zhang H, Wang Z. Bending collapse of square tubes with variable thickness. Int J Mech Sci 2016;106:107–16. https://doi. org/10.1016/j.ijmecsci.2015.12.006.
50. [50] Karagiozova D, Nurick GN, Chung Kim Yuen S. Energy absorption of aluminium alloy circular and square tubes under an axial explosive load. Thin-Walled Struct 2005;43:956–82. https://doi. org/10.1016/j.tws.2004.11.002.
51. [51] Zhang Y, Liu T, Ren H, Maskery I, Ashcroft I. Dynamic compressive response of additively manufactured AlSi10Mg alloy hierarchical honeycomb structures. Compos Struct 2018;195:45–59. https://doi. org/10.1016/j.compstruct.2018.04.021.
52. [52] Zheng G, Wu S, Sun G, Li G, Li Q. Crushing analysis of foam-filled single and bitubal polygonal thin-walled tubes. Int J Mech Sci 2014;87:226–40. https://doi.org/10.1016/j.ijmecsci.2014.06.002.
53. [53] Bai Z, Sun K, Zhu F, Cao L, Hu J, Chou CC, et al. Crashworthiness optimal design of a new extruded octagonal multi-cell tube under dynamic axial impact. Int J Veh Saf 2018;10:40–57. https://doi. org/10.1504/IJVS.2018.093056.
54. [54] Hu D, Wang YY, Song B, Wang YY. Energy absorption characteristics of a foam-filled tri-tube under axial quasi-static loading: experiment and numerical simulation. Int J Crashworthiness 2018;23:417–32. https://doi.org/10.1080/1358826 5.2017.1331494.
55. [55] Azarakhsh S, Ghamarian A. Collapse behavior of thin-walled conical tube clamped at both ends subjected to axial and oblique loads. Thin-Walled Struct 2017;112:1–11. https://doi.org/10.1016/j. tws.2016.11.020.
56. [56] Zhu G, Sun G, Li G, Cheng A, Li Q. Modeling for CFRP structures subjected to quasi-static crushing. Compos Struct 2018;184:41–55. https://doi.org/10.1016/j.compstruct.2017.09.001.
57. [57] Huang Z, Zhang X. Three-point bending collapse of thin-walled rectangular beams. Int J Mech Sci 2018;144:461–79. https://doi. org/10.1016/j.ijmecsci.2018.06.001.
58. [58] Huang Z, Zhang X. Three-point bending of thin-walled rectangular section tubes with indentation mode. Thin-Walled Struct 2019;137:231–50. https://doi.org/10.1016/j.tws.2019.01.015.
59. [59] Santosa S, Banhart J, Wierzbicki T. Experimental and numerical analyses of bending of foam-filled sections. Acta Mech 2001;148:199–213. https://doi.org/10.1007/BF01183678.
60. [60] Zhang X, Zhang H. Static and dynamic bending collapse of thin-walled square beams with tube filler. Int J Impact Eng 2018;112:165–79. https://doi.org/10.1016/j.ijimpeng.2017.11.001.
61. [61] Zhang X, Zhang H, Leng K. Experimental and numerical investigation on bending collapse of embedded multi-cell tubes. Thin-Walled Struct 2018;127:728–40. https://doi.org/10.1016/j. tws.2018.03.011.