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Analytical modeling of deposited filaments for high viscosity material-based piston-driven direct ink writing

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Abstract

High viscosity material-based piston-driven direct ink writing (HVMPD-DIW) has developed as one of the most popular additive manufacturing (AM) techniques and many efforts have been made in analytical modeling of deposited filaments (DF) for this process. However, previous works failed to realize a full quantitative analytical modeling of the DF in HVMPD-DIW as they ignored the changes in cross-sectional shape and lacked prediction of height. Herein, an improved analytical model is proposed for DF in HVMPD-DIW considering both the changes in cross-sectional shape and height prediction. This study could predict flow rate, deposition statuses, and width and height of DF. To fulfill this objective, first, an analytical model of flow rate is described to predict the flow rate of DF in time domain. Secondly, three deposition statuses are summarized and analytical dividing lines are derived to determine deposition statuses based on the dimensionless nozzle velocity and the dimensionless height. Thirdly, width and height of DF are predicted based on the determined deposition statuses. Finally, Nivea Crème is selected as the high viscosity material reference and flow rate, and filaments deposition experiments are conducted to validate the proposed model experimentally. The effectiveness and prediction accuracy of the proposed model are validated as the relative errors between analytical and experimental results are less than 4.31% and 3.90% for flow rate and cross-sectional dimensions (width and height), respectively. The current work demonstrates an effective and accurate approach for analytical prediction of flow rate, deposition statuses, and width and height of DF in HVMPD-DIW.

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Abbreviations

\(\tau\) :

Shear stress

\(\dot{\gamma }\) :

Shear rate

\({\tau }_{0}\) :

Yield stress

K :

Consistency index

n :

Flow index

A p :

Cross-sectional area of piston

D p :

Piston diameter

v p :

Piston velocity

Q :

Flow rate

L 0 :

Initial fill length

t :

Time since the piston stated moving

B :

Bulk modulus

P :

Pressure in syringe

ρ :

Density

L n :

Length of nozzle

A n :

Inner cross-sectional area of nozzle

d n :

Inner diameter of nozzle

Q u :

Steady-state flow rate under a unit pressure

τ w :

Shear stress at nozzle wall

v e :

Average velocity of extruded filament

\(\alpha\) :

Die-swelling factor

h :

Distance between nozzle bottom and substrate

v n :

Nozzle velocity

h d :

Height of deposited filament

w d :

Width of deposited filament

\({\theta }_{C}\) :

Static contact angle

V * :

Dimensionless nozzle velocity, = \({v}_{n}/{v}_{e}\)

H * :

Dimensionless height, = \(h/\alpha {d}_{n}\)

D n :

Outer diameter of nozzle

β :

Ratio of \({D}_{n}\) to\({d}_{n}\), = \({D}_{n}/{d}_{n}\)

\(\gamma\) :

\(\left({\theta }_{C}-\frac{\mathrm{sin}2{\theta }_{C}}{2}\right){\left(\frac{1}{1-\mathrm{cos}{\theta }_{C}}\right)}^{2}\)

d f :

Diameter of deposited filament under freeform-deposition

\(\lambda\) :

\(\left(\theta_C-2\sin\;2\theta_C\right)/\pi\)  

References

  1. Frazier WE (2014) Metal additive manufacturing: a review. J Mater Eng Perform 23(6):1917–1928. https://doi.org/10.1007/s11665-014-0958-z

    Article  Google Scholar 

  2. Bikas H, Stavropoulos P, Chryssolouris G (2016) Additive manufacturing methods and modelling approaches: a critical review. Int J Adv Manuf Technol 83(1):389–405. https://doi.org/10.1007/s00170-015-7576-2

    Article  Google Scholar 

  3. Niu X, Singh S, Garg A, Singh H, Panda B, Peng X et al (2019) Review of materials used in laser-aided additive manufacturing processes to produce metallic products. Front Mech Eng 14(3):282–298. https://doi.org/10.1007/s11465-019-0526-1

    Article  Google Scholar 

  4. Jiménez A, Bidare P, Hassanin H, Tarlochan F, Dimov S, Essa K (2021) Powder-based laser hybrid additive manufacturing of metals: a review. Int J Adv Manuf Technol 114(1):63–96. https://doi.org/10.1007/s00170-021-06855-4

    Article  Google Scholar 

  5. Rasaki SA, Xiong D, Xiong S, Su F, Idrees M, Chen Z (2021) Photopolymerization-based additive manufacturing of ceramics: a systematic review. J Adv Ceram 10(3):442–471. https://doi.org/10.1007/s40145-021-0468-z

    Article  Google Scholar 

  6. Indurkar A, Pandit A, Jain R, Dandekar P (2021) Plant-based biomaterials in tissue engineering. Bioprinting 21:e00127. https://doi.org/10.1016/j.bprint.2020.e00127

    Article  Google Scholar 

  7. Kalkal A, Kumar S, Kumar P, Pradhan R, Willander M, Packirisamy G et al (2021) Recent advances in 3D printing technologies for wearable (bio)sensors. Addit Manuf 46:102088. https://doi.org/10.1016/j.addma.2021.102088

    Article  Google Scholar 

  8. Kumar P, Rajak DK, Abubakar M, Ali SGM, Hussain M (2021) 3D printing technology for biomedical practice: a review. J Mater Eng Perform. https://doi.org/10.1007/s11665-021-05792-3

    Article  Google Scholar 

  9. Shahzad A, Lazoglu I (2021) Direct ink writing (DIW) of structural and functional ceramics: recent achievements and future challenges. Compos B Eng 225:109249. https://doi.org/10.1016/j.compositesb.2021.109249

    Article  Google Scholar 

  10. Armstrong CD, Yue L, Deng Y, Qi HJ (2022) Enabling direct ink write edible 3D printing of food purees with cellulose nanocrystals. J Food Eng 330:111086. https://doi.org/10.1016/j.jfoodeng.2022.111086

    Article  Google Scholar 

  11. Lewis JA (2006) Direct ink writing of 3D functional materials. Adv Funct Mater 16(17):2193–2204. https://doi.org/10.1002/adfm.200600434

    Article  Google Scholar 

  12. Saadi MASR, Maguire A, Pottackal NT, Thakur MSH, Ikram MM, Hart AJ et al (2022) Direct ink writing: a 3D printing technology for diverse materials. Adv Mater 34(28):2108855. https://doi.org/10.1002/adma.202108855

    Article  Google Scholar 

  13. Tu Y, Hassan A, Arrieta-Escobar JA, Khaleeq uz Zaman U, Xue F, Ali S et al (2022) Predictive modeling of extruded filament in the air for bioink in direct ink writing using numerical simulation. Procedia CIRP 112:394–9. https://doi.org/10.1016/j.procir.2022.09.026

    Article  Google Scholar 

  14. Jessop ZM, Al-Sabah A, Gao N, Kyle S, Thomas B, Badiei N et al (2019) Printability of pulp derived crystal, fibril and blend nanocellulose-alginate bioinks for extrusion 3D bioprinting. Biofabrication 11(4):045006. https://doi.org/10.1088/1758-5090/ab0631

    Article  Google Scholar 

  15. Chen XB, Jun K (2004) Modeling of positive-displacement fluid dispensing processes. IEEE Trans Electron Packag Manuf 27(3):157–163. https://doi.org/10.1109/TEPM.2004.843083

    Article  Google Scholar 

  16. Wang F, Mao P, He H (2016) Dispensing of high concentration Ag nano-particles ink for ultra-low resistivity paper-based writing electronics. Sci Rep 6(1):21398. https://doi.org/10.1038/srep21398

    Article  Google Scholar 

  17. Smith PT, Basu A, Saha A, Nelson A (2018) Chemical modification and printability of shear-thinning hydrogel inks for direct-write 3D printing. Polymer 152:42–50. https://doi.org/10.1016/j.polymer.2018.01.070

    Article  Google Scholar 

  18. Tu R, Sodano HA (2021) Additive manufacturing of high-performance vinyl ester resin via direct ink writing with UV-thermal dual curing. Addit Manuf 46:102180. https://doi.org/10.1016/j.addma.2021.102180

    Article  Google Scholar 

  19. Hinton Thomas J, Jallerat Q, Palchesko Rachelle N, Park Joon H, Grodzicki Martin S, Shue H-J et al (2015) Three-dimensional printing of complex biological structures by freeform reversible embedding of suspended hydrogels. Sci Adv 1(9):e1500758. https://doi.org/10.1126/sciadv.1500758

    Article  Google Scholar 

  20. Zhu F, Cheng L, Yin J, Wu ZL, Qian J, Fu J et al (2016) 3D printing of ultratough polyion complex hydrogels. ACS Appl Mater Interfaces 8(45):31304–31310. https://doi.org/10.1021/acsami.6b09881

    Article  Google Scholar 

  21. Franchin G, Wahl L, Colombo P (2017) Direct ink writing of ceramic matrix composite structures. J Am Ceram Soc 100(10):4397–4401. https://doi.org/10.1111/jace.15045

    Article  Google Scholar 

  22. Xu C, An C, Li Q, Xu S, Wang S, Guo H et al (2018) Preparation and performance of pentaerythrite tetranitrate-based composites by direct ink writing. Propell Explos Pyrotech 43(11):1149–1156. https://doi.org/10.1002/prep.201800069

    Article  Google Scholar 

  23. Yang L, Zeng X, Ditta A, Feng B, Su L, Zhang Y (2020) Preliminary 3D printing of large inclined-shaped alumina ceramic parts by direct ink writing. J Adv Ceram 9(3):312–319. https://doi.org/10.1007/s40145-020-0369-6

    Article  Google Scholar 

  24. Wu X, Tu T, Dai Y, Tang P, Zhang Y, Deng Z et al (2021) Direct ink writing of highly conductive MXene frames for tunable electromagnetic interference shielding and electromagnetic wave-induced thermochromism. Nano-Micro Lett 13(1):148. https://doi.org/10.1007/s40820-021-00665-9

    Article  Google Scholar 

  25. Sun L, Parker ST, Syoji D, Wang X, Lewis JA, Kaplan DL (2012) Direct-write assembly of 3D silk/hydroxyapatite scaffolds for bone co-cultures. Adv Healthc Mater 1(6):729–735. https://doi.org/10.1002/adhm.201200057

    Article  Google Scholar 

  26. Kim M, Choi J-W (2021) Rubber ink formulations with high solid content for direct-ink write process. Addit Manuf 44:102023. https://doi.org/10.1016/j.addma.2021.102023

    Article  Google Scholar 

  27. Sun K, Wei T-S, Ahn BY, Seo JY, Dillon SJ, Lewis JA (2013) 3D printing of interdigitated Li-ion microbattery architectures. Adv Mater 25(33):4539–4543. https://doi.org/10.1002/adma.201301036

    Article  Google Scholar 

  28. Wehner M, Truby RL, Fitzgerald DJ, Mosadegh B, Whitesides GM, Lewis JA et al (2016) An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature 536(7617):451–455. https://doi.org/10.1038/nature19100

    Article  Google Scholar 

  29. Frutiger A, Muth JT, Vogt DM, Mengüç Y, Campo A, Valentine AD et al (2015) Capacitive soft strain sensors via multicore–shell fiber printing. Adv Mater 27(15):2440–2446. https://doi.org/10.1002/adma.201500072

    Article  Google Scholar 

  30. Oleff A, Küster B, Stonis M, Overmeyer L (2021) Process monitoring for material extrusion additive manufacturing: a state-of-the-art review. Progr Addit Manuf 6(4):705–730. https://doi.org/10.1007/s40964-021-00192-4

    Article  Google Scholar 

  31. Ravi P, Chepelev LL, Stichweh GV, Jones BS, Rybicki FJ (2022) Medical 3D printing dimensional accuracy for multi-pathological anatomical models 3D printed using material extrusion. J Digit Imaging 35(3):613–622. https://doi.org/10.1007/s10278-022-00614-x

    Article  Google Scholar 

  32. Yang J, Tao JL, Franck C (2021) Smart digital image correlation patterns via 3D printing. Exp Mech 61(7):1181–91. https://doi.org/10.1007/s11340-021-00720-x

    Article  Google Scholar 

  33. Tu Y, Hassan A, Arrieta-Escobar JA, Zaman UKU, Siadat A, Yang G (2022) Modeling and evaluation of freeform extruded filament based on numerical simulation method for direct ink writing. Int J Adv Manuf Technol 120(5):3821–9. https://doi.org/10.1007/s00170-022-08999-3

    Article  Google Scholar 

  34. Pierre A, Weger D, Perrot A, Lowke D (2018) Penetration of cement pastes into sand packings during 3D printing: analytical and experimental study. Mater Struct 51(1):22. https://doi.org/10.1617/s11527-018-1148-5

    Article  Google Scholar 

  35. Vlasea M, Toyserkani E (2013) Experimental characterization and numerical modeling of a micro-syringe deposition system for dispensing sacrificial photopolymers on particulate ceramic substrates. J Mater Process Technol 213(11):1970–1977. https://doi.org/10.1016/j.jmatprotec.2013.05.011

    Article  Google Scholar 

  36. Lee JM, Yeong WY (2015) A preliminary model of time-pressure dispensing system for bioprinting based on printing and material parameters. Virtual Phys Prototyp 10(1):3–8. https://doi.org/10.1080/17452759.2014.979557

    Article  Google Scholar 

  37. Suntornnond R, Tan EYS, An J, Chua CK (2016) A Mathematical model on the resolution of extrusion bioprinting for the development of new bioinks. Materials (Basel) 9(9):756. https://doi.org/10.3390/ma9090756

    Article  Google Scholar 

  38. Haghbin N, Bone D, Young K (2021) Controlled extrusion-based 3D printing of micro-channels with the geometric modelling of deposited roads. J Manuf Process 67:406–417. https://doi.org/10.1016/j.jmapro.2021.04.067

    Article  Google Scholar 

  39. Athanasiadis M, Pak A, Afanasenkau D, Minev IR (2019) Direct writing of elastic fibers with optical, electrical, and microfluidic functionality. Adv Mater Technol 4(7):1800659. https://doi.org/10.1002/admt.201800659

    Article  Google Scholar 

  40. Percoco G, Arleo L, Stano G, Bottiglione F (2021) Analytical model to predict the extrusion force as a function of the layer height, in extrusion based 3D printing. Addit Manuf 38:101791. https://doi.org/10.1016/j.addma.2020.101791

    Article  Google Scholar 

  41. Chen XB, Shoenau G, Zhang WJ (2000) Modeling of time-pressure fluid dispensing processes. IEEE Trans Electron Packag Manuf 23(4):300–305. https://doi.org/10.1109/6104.895075

    Article  Google Scholar 

  42. del-Mazo-Barbara L, Ginebra M-P (2021) Rheological characterisation of ceramic inks for 3D direct ink writing: a review. J Eur Ceram Soc. https://doi.org/10.1016/j.jeurceramsoc.2021.08.031

  43. Plachy R, Hellmich C, Arthofer F, Robin S, Holzner A, Scheiner S (2021) Hydrostatic compression tests, capillary rheometry tests, and extrusion tests performed on unvulcanized rubber confirm importance of compressibility for die swell — arguments from dimensional analysis. Polym Test 101:107289. https://doi.org/10.1016/j.polymertesting.2021.107289

    Article  Google Scholar 

  44. Valipour Motlagh N, Taghipour-Gorjikolaie M (2018) Fuzzy based models for estimating static contact angle and sliding angle of liquid drops. Prog Org Coat 119:183–193. https://doi.org/10.1016/j.porgcoat.2018.02.029

    Article  Google Scholar 

  45. Yuk H, Zhao X (2018) A new 3D printing strategy by harnessing deformation, instability, and fracture of viscoelastic inks. Adv Mater 30(6):1704028. https://doi.org/10.1002/adma.201704028

    Article  Google Scholar 

  46. Paxton N, Smolan W, Böck T, Melchels F, Groll J, Jungst T (2017) Proposal to assess printability of bioinks for extrusion-based bioprinting and evaluation of rheological properties governing bioprintability. Biofabrication 9(4):044107. https://doi.org/10.1088/1758-5090/aa8dd8

    Article  Google Scholar 

  47. Tu Y, Arrieta-Escobar JA, Hassan A, Zaman UKu, Siadat A, Yang G (2021) Optimizing process parameters of direct ink writing for dimensional accuracy of printed layers. 3D Print Addit Manuf. https://doi.org/10.1089/3dp.2021.0208

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Funding

This work has been supported by the China Scholarship Council (No. 201906020135).

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Authors and Affiliations

  1. School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing, 100191, People’s Republic of China

    Yongqiang Tu & Gongliu Yang

  2. LCFC, Arts Et Métiers ParisTech, F-57000, Metz, France

    Yongqiang Tu & Ali Siadat

  3. Additive Manufacturing Institute, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Yongqiang Tu

  4. ERPI, Université de Lorraine, F-54000, Nancy, France

    Alaa Hassan

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Contributions

YT: methodology, analytical modeling, test, and writing—original draft. AH: writing—review and editing. AS: supervision. GY: supervision.

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Correspondence to Yongqiang Tu.

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Tu, Y., Hassan, A., Siadat, A. et al. Analytical modeling of deposited filaments for high viscosity material-based piston-driven direct ink writing. Int J Adv Manuf Technol 123, 3387–3398 (2022). https://doi.org/10.1007/s00170-022-10511-w

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