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Mechanical and energy absorption properties of functionally graded lattice structures based on minimal curved surfaces

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Abstract

Compared with uniform structures, functionally graded lattice structures can control mechanical properties through varying structures and their volume fraction. In this study, a three-period minimal curved surface method was used to generate functional lattice structure with linear or quadratic function (LF or QF) gradient strategy in the forming direction, and the samples were fabricated by selective laser melting (SLM) using the Ti-6Al-4V metal powder. The mechanical properties, deformation behaviors, and energy absorption performance of graded lattice structures, LF, and QF I-Wrapped Package (IW-P) lattice structures were systematically investigated through experiment and finite element analysis (FEA). Based on the experimental and numerical simulation results, the LF lattice structure shows higher elastic modules and yield strength during small strain period. And the merits of performance increased layer-by-layer under large strain. Additionally, the simulation results based on Johnson-Cook and failure model show that this model can reflect structural compression deformation behavior and mechanical performance prediction. Furthermore, the elastic modulus of LF lattice structure is higher than uniform lattice structures by nearly 61.52% under the same lattice volume fraction. Compared to other lattice structures, the LF or QF lattice structures have better support performance under small strain and stronger energy absorption capacity under large strain with the same volume fraction, respectively, which shows superior potential to be applied to manufacture protective devices or vibration damping devices.

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Abbreviations

t* :

Matrix phase region

L :

Length of a lattice unit

a :

TPMS function periodicities

ρ ∗ :

the volume fraction

n, m, A, B, C :

The model contants based on the flow stress data gained from mechanical tests.

D 1, D 2, D 3, D 4, D 5 :

Johnson-Cook model constants

σ S :

Equivalent stress

ε e :

Equivalent plastic strain

ε p :

Equivalent plastic strain rate

ε 0 :

Reference equivalent plastic strain rate

T :

Temperature during manufacturing

ε f :

Fracture strain

σ * :

Stress triaxiality

W :

Energy absorption per lattice unit volume

σ :

Stress

ε :

Strain

ε d :

Maximum strain at the onset of the densification stage

LF:

Linear function

QF:

Quadratic function

SLM:

Selective laser melting

IW-P:

I-Wrapped Package

FEA:

Finite element analysis

FGS:

Function graded structures

TPMS:

Triply periodic minimal surfaces

AM:

Additive Manufacturing

IW-P FGS:

I-Wrapped Package Function graded structure

LF IW-P:

Linear Function I-Wrapped Package

QF IW-P:

Quadratic Function I-Wrapped Package

References

  1. Liu Z, Zhang Y, Zhang M, Tan G, Zhu Y, Zhang Z, Ritchie RO (2019) Adaptive structural reorientation: developing extraordinary mechanical properties by constrained flexibility in natural materials. Acta Biomater 86:96–108

    Article  Google Scholar 

  2. Ren L, Li B, Song Z, Liu Q, Ren L, Zhou X (2019) 3D printing of structural gradient soft actuators by variation of bioinspired architectures. J Mater Sci 54:6542–6551

    Article  Google Scholar 

  3. Chen G, Luo H, Zhang Z, Fan X (2020) Flexural deformation and fracture behaviors of the sandwich turtle rib bones with hierarchical woven fibers. Colloid Interface Sci Commun 34:100230

    Article  Google Scholar 

  4. Ott J, Lazalde M, Gu GX (2020) Algorithmic-driven design of shark denticle bioinspired structures for superior aerodynamic properties. Bioinspiration Biomimetics 15:026001

    Article  Google Scholar 

  5. Mannan S, Paul Knox J, Basu S (2017) Correlations between axial stiffness and microstructure of a species of bamboo. R Soc Open Sci 4:160412

    Article  MathSciNet  Google Scholar 

  6. Zhang S, Guo J, Ma X, Peng X, Qiu Z, Ying J, Wang J (2017) Smart PDMS sponge with switchable pH-responsive wetting surface for oil/water separation. New J Chem 41:8940–8946

    Article  Google Scholar 

  7. Frey M, Biffi G, Adobes-Vidal M, Zirkelbach M, Wang Y, Tu K, Hirt AM, Masania K, Burgert I, Keplinger T et al (2019) Adv Sci 6:1802190

    Article  Google Scholar 

  8. Luo W, Liu H, Wang C, Qin Y, Liu Q, Wang J (2019) Bioprinting of human musculoskeletal interface. Adv Eng Mater 21:1900019

    Article  Google Scholar 

  9. Chen D, Liu Q, Han Z, Zhang J, Song H, Wang K, Song Z, Wen S, Zhou Y, Yan C, Shi Y (2020) 4D printing strain self-sensing and temperature self-sensing integrated sensor-actuator with bioinspired gradient gaps. Adv Sci 7:2000584

    Article  Google Scholar 

  10. Jin Y, Kong HY, Zhou XY, Li GY, Du JK (2020) Design and characterization of sheet-based gyroid porous structures with bioinspired functional gradients. Materials 13:31

    Article  Google Scholar 

  11. Singhal P, Small W, Cosgriff-Hernandez E, Maitland DJ, Wilson TS (2014) Low density biodegradable shape memory polyurethane foams for embolic biomedical applications. Acta Biomater 10:67–76

    Article  Google Scholar 

  12. Lee J, Chang JY (2016) Preparation of a compressible and hierarchically porous polyimide sponge via the sol-gel process of an aliphatic tetracarboxylic dianhydride and an aromatic triamine. Chem Commun (Camb) 52:10419–10422

    Article  Google Scholar 

  13. Si Y, Yu J, Tang X, Ge J, Ding B (2014) Ultralight nanofibre-assembled cellular aerogels with superelasticity and multifunctionality. Nat Commun 5:5802

    Article  Google Scholar 

  14. Bencherif SA, Warren Sands R, Ali OA, Li WA, Lewin SA, Braschler TM, Shih TY, Verbeke CS, Bhatta D, Dranoff G, Mooney DJ (2015) Injectable cryogel-based whole-cell cancer vaccines. Nat Commun 6:7556

    Article  Google Scholar 

  15. Duan G, Koehn-Serrano M, Greiner A (2017) Highly efficient reusable sponge-type catalyst carriers based on short electrospun fibers. Macromol Rapid Commun 38:1600511

    Article  Google Scholar 

  16. Jiang S, Agarwal S, Greiner A (2017) Low-density open cellular sponges as functional materials. Angew Chem Int Ed Eng 56:15520–15538

    Article  Google Scholar 

  17. Das S, Sutradhar A (2020) Multi-physics topology optimization of functionally graded controllable porous structures: application to heat dissipating problems. Mater Des 193:108775

    Article  Google Scholar 

  18. Kaur I, Singh P, Flow and thermal transport characteristics of triply-periodic minimal surface (TPMS)-based gyroid and Schwarz-P cellular materials, Numerical Heat Transfer Part a-Applications, 79 (2021).

  19. Liang Y, Zhou W, Liu Y, Li Z, Yang Y, Xi H, Wu Z (2021) Energy absorption and deformation behavior of 3D printed triply periodic minimal surface stainless steel cellular structures under compression. Steel Res Int 92:2000411

    Article  Google Scholar 

  20. Plocher J, Panesar A (2020) Effect of density and unit cell size grading on the stiffness and energy absorption of short fibre-reinforced functionally graded lattice structures. Addit Manuf 33:101171

    Google Scholar 

  21. Xiao LJ, Xu X, Song WD, Hu ML (2020) A multi-cell hybrid approach to elevate the energy absorption of micro-lattice materials. Materials 13:4083

    Article  Google Scholar 

  22. Bharti I, Gupta N, Gupta KM (2013) Novel applications of functionally graded nano, optoelectronic and thermoelectric materials. Int J Mater Mech Manuf 1:221–224

    Google Scholar 

  23. Ataee A, Li Y, Brandt M, Wen C (2018) Ultrahigh-strength titanium gyroid scaffolds manufactured by selective laser melting (SLM) for bone implant applications. Acta Mater 158:354–368

    Article  Google Scholar 

  24. Xu W, Lu X, Hayat MD, Tian J, Huang C, Chen M, Qu X, Wen C (2019) Fabrication and properties of newly developed Ti35Zr28Nb scaffolds fabricated by powder metallurgy for bone-tissue engineering. J Mater Res Technol 8:3696–3704

    Article  Google Scholar 

  25. Xu W, Tian J, Liu Z, Lu X, Hayat MD, Yan Y, Li Z, Qu X, Wen C (2019) Novel porous Ti35Zr28Nb scaffolds fabricated by powder metallurgy with excellent osteointegration ability for bone-tissue engineering applications. Mater Sci Eng C Mater Biol Appl 105:110015

    Article  Google Scholar 

  26. Vijayavenkataraman S, Kuan LY, Lu WF (2020) 3D-printed ceramic triply periodic minimal surface structures for design of functionally graded bone implants. Mater Des 191:108602

    Article  Google Scholar 

  27. Xiao R, Feng X, Fan R, Chen S, Song J, Gao L, Lu Y (2020) 3D printing of titanium-coated gradient composite lattices for lightweight mandibular prosthesis. Compos Part B 193:108057

    Article  Google Scholar 

  28. Jun Z, Xing A, Jianxin D, Jinghai W (2004) Thermal shock behaviors of functionally graded ceramic tool materials. J Eur Ceram Soc 24:847–854

    Article  Google Scholar 

  29. Konyashin I, Zaitsev AA, Sidorenko D, Levashov EA, Konischev SN, Sorokin M, Hlawatschek S, Ries B, Mazilkin AA, Lauterbach S, Kleebe HJ (2017) On the mechanism of obtaining functionally graded hardmetals. Mater Lett 186:142–145

    Article  Google Scholar 

  30. Nejad MZ, Alamzadeh N, Hadi A (2018) Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition. Compos Part B 154:410–422

    Article  Google Scholar 

  31. Saleh B, Jiang J, Fathi R, Al-hababi T, Xu Q, Wang L, Song D, Ma A (2020) 30 Years of functionally graded materials: an overview of manufacturing methods, Applications and Future Challenges. Compos Part B 201:108376

    Article  Google Scholar 

  32. Al-Ketan O, Lee DW, Rowshan R, Abu Al-Rub RK (2020) Functionally graded and multi-morphology sheet TPMS lattices: design, manufacturing, and mechanical properties. J Mech Behav Biomed Mater 102:103520

    Article  Google Scholar 

  33. Bai L, Gong C, Chen X, Sun Y, Xin L, Pu H, Peng Y, Luo J (2020) Mechanical properties and energy absorption capabilities of functionally graded lattice structures: experiments and simulations. Int J Mech Sci 182:105735

    Article  Google Scholar 

  34. Mirzaali MJ, de la Nava AH, Gunashekar D, Nouri-Goushki M, Veeger RPE, Grossman Q, Angeloni L, Ghatkesar MK, Fratila-Apachitei LE, Ruffoni D, Doubrovski EL, Zadpoor AA (2020) Mechanics of bioinspired functionally graded soft-hard composites made by multi-material 3D printing. Compos Struct 237:111867

    Article  Google Scholar 

  35. Li D, Liao W, Dai N, Dong G, Tang Y, Xie YM (2018) Optimal design and modeling of gyroid-based functionally graded cellular structures for additive manufacturing. Comput Aided Des 104:87–99

    Article  Google Scholar 

  36. López de Lacalle LN, Fernández A, Olvera D, Lamikiz A, Olvera D, Rodríguez C, Elias A (2011) Monitoring deep twist drilling for a rapid manufacturing of light high-strength parts. Mech Syst Signal Process 25:2745–2752

    Article  Google Scholar 

  37. Calleja-Ochoa A, Gonzalez-Barrio H, Lopez de Lacalle N, Martinez S, Albizuri J, Lamikiz A (2021) A new approach in the design of microstructured ultralight components to achieve maximum functional performance. Materials (Basel) 14:1588

    Article  Google Scholar 

  38. Massarwi F, Machchhar J, Antolin P, Elber G (2018) Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition. Comput Aided Des 102:148–159

    Article  MathSciNet  Google Scholar 

  39. Liu F, Mao Z, Zhang P, Zhang DZ, Jiang J, Ma Z (2018) Functionally graded porous scaffolds in multiple patterns: new design method, physical and mechanical properties. Mater Des 160:849–860

    Article  Google Scholar 

  40. Ma Z, Zhang DZ, Liu F, Jiang J, Zhao M, Zhang T (2020) Lattice structures of Cu-Cr-Zr copper alloy by selective laser melting: microstructures, mechanical properties and energy absorption. Mater Des 187:108406

    Article  Google Scholar 

  41. Zhou H, Zhao M, Ma Z, Zhang DZ, Fu G (2020) Sheet and network based functionally graded lattice structures manufactured by selective laser melting: design, mechanical properties, and simulation. Int J Mech Sci 175:105480

    Article  Google Scholar 

  42. Yang L, Yan C, Cao W, Liu Z, Song B, Wen S, Zhang C, Shi Y, Yang S (2019) Compression–compression fatigue behaviour of gyroid-type triply periodic minimal surface porous structures fabricated by selective laser melting. Acta Mater 181:49–66

    Article  Google Scholar 

  43. Jia H, Lei H, Wang P, Meng J, Li C, Zhou H, Zhang X, Fang D (2020) An experimental and numerical investigation of compressive response of designed Schwarz Primitive triply periodic minimal surface with non-uniform shell thickness. Extreme Mech Lett 37:100671

    Article  Google Scholar 

  44. de Aquino DA, Maskery I, Longhitano GA, Jardini AL, del Conte EG (2020) Investigation of load direction on the compressive strength of additively manufactured triply periodic minimal surface scaffolds. Int J Adv Manuf Technol 109:771–779

    Article  Google Scholar 

  45. Maskery I, Ashcroft IA (2020) The deformation and elastic anisotropy of a new gyroid-based honeycomb made by laser sintering. Addit Manuf 36:101548

    Google Scholar 

  46. Liu F, Ran Q, Zhao M, Zhang T, Zhang DZ, Su Z (2020) Additively manufactured continuous cell-size gradient porous scaffolds: pore characteristics, mechanical properties and biological responses in vitro. Materials (Basel) 13:2589

    Article  Google Scholar 

  47. Zhao M, Zhang DZ, Liu F, Li Z, Ma Z, Ren Z (2020) Mechanical and energy absorption characteristics of additively manufactured functionally graded sheet lattice structures with minimal surfaces. Int J Mech Sci 167:105262

    Article  Google Scholar 

  48. Zhang X, Wang J, Liu T (2021) 3D printing of polycaprolactone-based composites with diversely tunable mechanical gradients via multi-material fused deposition modeling. Compos Commun 23:100600

    Article  Google Scholar 

  49. Wang Y, Xia J, Luo Z, Yan H, Sun J, Lu E (2020) Self-supporting topology optimization method for selective laser melting(star). Addit Manuf 36:101506

    Google Scholar 

  50. Yu G, Li Z, Li S, Zhang Q, Hua Y, Liu H, Zhao X, Dhaidhai DT, Li W, Wang X (2020) The select of internal architecture for porous Ti alloy scaffold: a compromise between mechanical properties and permeability. Mater Des 192:108754

    Article  Google Scholar 

  51. Baroutaji A, Arjunan A, Stanford M, Robinson J, Olabi AG (2021) Deformation and energy absorption of additively manufactured functionally graded thickness thin-walled circular tubes under lateral crushing. Eng Struct 226:111324

    Article  Google Scholar 

  52. Erdem M, Gok K, Gokce B, Gok A (2017) Numerical analysis of temperature, screwing moment and thrust force using finite element method in bone screwing process. J Mech Med Biol 17:1750016

    Article  Google Scholar 

  53. Gök A, Demirci HI, Gök K (2014) Determination of experimental, analytical, and numerical values of tool deflection at ball end milling of inclined surfaces. Proc Institut Mech Eng Part E: JProcess Mechanical Engineering 230:111–119

    Article  Google Scholar 

  54. Gök A (2017) 2D numeric simulation of serrated-chip formation in orthogonal cutting of AISI316H stainless steel. Mater Tehnol 51:953–956

    Article  Google Scholar 

  55. Upadhyay BD, Sonigra SS, Daxini SD (2021) Numerical analysis perspective in structural shape optimization: a review post 2000. Adv Eng Softw 155:102992

    Article  Google Scholar 

  56. Zhou H, Zhao M, Ma Z, Zhang DZ, Fu G (2020) Sheet and network based functionally graded lattice structures manufactured by selective laser melting: design, mechanical properties, and simulation. Int J Mech Sci 175:105480

    Article  Google Scholar 

  57. Sobolev AV, Radchenko MV (2016) Use of Johnson–Cook plasticity model for numerical simulations of the SNF shipping cask drop tests. Nucl EnergyTechnol 2:272–276

    Google Scholar 

  58. Zhao M, Zhang DZ, Liu F, Li Z, Ma Z, Ren Z (2020) Mechanical and energy absorption characteristics of additively manufactured functionally graded sheet lattice structures with minimal surfaces. Int J Mech Sci 167:105262

    Article  Google Scholar 

  59. Liang Y, Zhou W, Liu Y, Li Z, Yang Y, Xi H, Wu Z (2020) Energy absorption and deformation behavior of 3D printed triply periodic minimal surface stainless steel cellular structures under compression. Steel Research International 92:2000411

    Article  Google Scholar 

  60. Yang L, Ferrucci M, Mertens R, Dewulf W, Yan C, Shi Y, Yang S (2020) 2-An investigation into the effect of gradients on the manufacturing fidelity of triply periodic minimal surface structures with graded density fabricated by selective laser melting. J Mater Process Technol 275:116367

    Article  Google Scholar 

  61. Calignano F, Lorusso M, Pakkanen J, Trevisan F, Ambrosio EP, Manfredi D, Fino P (2016) Investigation of accuracy and dimensional limits of part produced in aluminum alloy by selective laser melting. Int J Adv Manuf Technol 88:451–458

    Article  Google Scholar 

  62. Qiu C, Yue S, Adkins NJE, Ward M, Hassanin H, Lee PD, Withers PJ, Attallah MM (2015) Influence of processing conditions on strut structure and compressive properties of cellular lattice structures fabricated by selective laser melting. Mater Sci Eng A 628:188–197

    Article  Google Scholar 

  63. Guo X, Zheng X, Yang Y, Yang X, Yi Y (2019) Mechanical behavior of TPMS-based scaffolds: a comparison between minimal surfaces and their lattice structures. Sn Appl Sci 1:1145

    Article  Google Scholar 

  64. Wang Z, Wang X, Gao T, Shi C (2020) Mechanical behavior and deformation mechanism of triply periodic minimal surface sheet under compressive loading. Mech Adv Mater Struct 196:109100

    Google Scholar 

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Funding

This work was supported by the Key projects of Chongqing Natural Science Foundation (cstc2020jcyj-zdxmX0021), and the National High Technology Research and Development Program of China (863Program:2015AA042501).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400044, China

    Xiangyu Ma, David Z. Zhang, Miao Zhao & Fangqiong Luo

  2. Chongqing Key Laboratory of Metal Additive Manufacturing (3D Printing), Chongqing University, Chongqing, 400044, China

    Xiangyu Ma, David Z. Zhang, Miao Zhao & Fangqiong Luo

  3. College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter, EX4 4QF, UK

    David Z. Zhang & Hailun Zhou

  4. Mechanical and Electrical Engineering College, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Junjie Jiang

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  1. Xiangyu Ma
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  2. David Z. Zhang
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  3. Miao Zhao
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  4. Junjie Jiang
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Contributions

Xiangyu Ma and David Z. Zhang designed the work, performed the research, and analyzed the data. Xiangyu Ma, David Z. Zhang, Miao Zhao, Junjie Jiang, Fangqiong Luo, and Hailun Zhou discussed the results and wrote the manuscript. All authors contributed to drafting and revising the manuscript.

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Correspondence to David Z. Zhang.

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Ma, X., Zhang, D.Z., Zhao, M. et al. Mechanical and energy absorption properties of functionally graded lattice structures based on minimal curved surfaces. Int J Adv Manuf Technol 118, 995–1008 (2022). https://doi.org/10.1007/s00170-021-07768-y

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