Skip to main content
SpringerLink
Log in

Constrained crystal growth during solidification of particles and splats in uniform droplet sprays

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Uniform droplet spraying (UDS) is a novel process used to produce ideally narrow (mono-size) distributions of molten metal droplets for various applications. The crystallite size is a primary determinant of mechanical properties in solidified alloy deposits and thus in need of predictive modeling. This project reports on employing UDS as a paradigm for solidification modeling of mono-size solid droplets in an oil bath, as well as planar and globular splats on a cooling substrate, for magnesium alloys AZ91D and Mg97ZnY2. The model combines a nucleation and dendrite fragmentation description from solidification theory, with a framework for constrained growth of crystalline domains confined by adjacent developing ones. The latter is based on differential attributes of the dynamic temperature field during solidification, derived from semi-analytical expressions for the simple droplet and splat geometries above. The modeling results are validated against measured domain size distributions on section micrographs, and found to be within a − 10% to + 14% estimation error range. Further improvement of the model via numerical thermal descriptions for off-line material design and optimization in additive manufacturing is discussed, along with its use as real-time structural observer for closed-loop control based on temperature measurements in UDS-based processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Hall E (1951) The deformation and ageing of mild steel: III discussion of results. Proc Phys Soc Sect B 64:747

    Article  Google Scholar 

  2. Petch N (1953) The cleavage strength of polycrystals. J Iron Steel Inst 174:25–28

    Google Scholar 

  3. DeGarmo EP, Black JT, Kohser RA, Klamecki BE (1997) Materials and process in manufacturing. Prentice Hall, Upper Saddle River

    Google Scholar 

  4. Lavernia EJ, Srivatsan TS (2010) The rapid solidification processing of materials: science, principles, technology, advances, and applications. J Mater Sci 45:287

    Article  Google Scholar 

  5. Steen PH, Karcher C (1997) Fluid mechanics of spin casting of metals. Annu Rev Fluid Mech 29:373–397

    Article  Google Scholar 

  6. Pekguleryuz M, Kaplan H, Neelameggham R, Hryn J, Nyberg E, Powell B, Cole G, Nie J (2002) Magnesium technology 2002, Part I: Primary production, environmental issues, high-temperature alloys. JOM 54:18–21

    Article  Google Scholar 

  7. Chun J-H, Passow CH (1993) Production of charged uniformly sized metal droplets, in, Google Patents

  8. Ranganathan R (2007) Liquid medium droplet deposition of copper, Doctor of Philosophy Dissertation, Northeastern University, Boston, MA

  9. Fortner W (1999) Construction of uniform droplet spray apparatus for mono-sized brass powder production. In: MS Thesis, Northeastern University

  10. Tuffile C (2001) Rapid epitaxial growth in mono-size droplet deposition of Sn and Sn-Pb alloys, Doctor of Philosophy Dissertation, Northeastern University, Boston, MA

  11. Passow CH, Chun J-H, Ando T (1993) Spray deposition of a Sn-40 Wt Pct Pb alloy with uniform droplets. Metall Trans A 24:1187–1193

    Article  Google Scholar 

  12. Pillai SK (2008) Processing of iron-based glass-forming alloys by the uniform-droplet spray process. In: Northeastern University

  13. Abesi Y (1999) Uniform droplet spraying of aluminium alloys, Master of Science Thesis. Northeastern University, Boston, MA

  14. Rayleigh L (1878) On the instability of jets. Proc Lond Math Soc 1:4–13

    Article  MathSciNet  Google Scholar 

  15. Ando T, Tuffile C, DiVenuti A, Chun J-H (1997) Calorimetric enthalpy measurement of traveling uniform droplets. J Mater Synth Process(USA) 5:31–37

    Google Scholar 

  16. Chen C-A, Acquaviva P, Chun J-H, Ando T (1996) Effects of droplet thermal state on deposit microstructure in spray forming. Scr Mater 34:689–696

    Article  Google Scholar 

  17. Tuffile C, Ando T, Chun J-H (1998) Characterization of the in-flight solidification of Sn-Pb uniform droplets, Solidification 1998, Indianapolis, IN, 359–371

  18. Acquaviva P, Chen C-A, Chun J-H, Ando T (1997) Thermal modeling of deposit solidification in uniform droplet spray forming. J Manuf Sci Eng 119:332–340

    Article  Google Scholar 

  19. Lipton J, Kurz W, Trivedi R (1987) Rapid dendrite growth in undercooled alloys. Acta Metall 35:957–964

    Article  Google Scholar 

  20. Aziz MJ, Kaplan T (1988) Continuous growth-model for interface motion during alloy solidification. Acta Metall 36:2335–2347

    Article  Google Scholar 

  21. Boettinger WJ, Coriell SR, Trivedi R (1988) Application of dendritic growth theory to the interpretation of rapid solidification microstructure. In: The Fourth Conference on Rapid Solidification Processing: Principles and Technology, University of California Santa Barbara, pp 13–25

  22. DiVenuti AG, Ando T (1998) A free dendritic growth model accommodating curved phase boundaries and high Peclet number conditions. Metall Mater Trans A 29:3047–3056

    Article  Google Scholar 

  23. Galenko P, Phanikumar G, Funke O, Chernova L, Reutzel S, Kolbe M, Herlach D (2007) Dendritic solidification and fragmentation in undercooled Ni–Zr alloys. Mater Sci Eng A 449:649–653

    Article  Google Scholar 

  24. Karma A (1998) Model of grain refinement in solidification of undercooled melts. Int J Non-Equilib Process(UK) 11:201–233

    Google Scholar 

  25. Tuffile CD, Ando T (2000) Epitaxial crystal growth in Sn and Sn-Pb alloys processed by mono-size droplet deposition. J Mater Process Manu 8:232–244

    Article  Google Scholar 

  26. Lu H, Ando T (2002) Modeling and characterization of the solidification of mono-size copper droplets. In: The Proceedings of the JSME Materials and Processing Conference, The Japan Society of Mechanical Engineers, pp 337–342

  27. Roy S, Ando T (2010) Nucleation kinetics and microstructure evolution of traveling ASTM F75 droplets. Adv Eng Mater 12:912–919

    Article  Google Scholar 

  28. Bialiauskaya V (2007) The nucleation kinetics of travelling Fe-17at% B droplets produced by the uniform-droplet spray process, Doctor of Philosophy Dissertation, Northeastern University, Boston, MA

  29. Zhang D (2007) Modeling and characterization of the solidification of mono-sized Mg-Al droplets produced by the uniform droplet spray process, in: MIE department, Northeastern University, Boston

  30. Fukuda H (2009) Droplet-based processing of magnesium alloys for the production of high-performance bulk materials. In: Northeastern University

  31. Carter GF (1979) Principles of physical and chemical metallurgy. American Society for Metals

  32. An J, Li RG, Chen CM, Xu Y, Chen X, Guo ZX, Liu YB (2007) Comparative studies on wear behaviour between as cast AZ91 and Mg97Zn1Y2 magnesium alloys. Mater Sci Tech-Lond 23:1208–1214

    Article  Google Scholar 

  33. Kawamura Y, Hayashi K, Inoue A, Masumoto T (2001) Rapidly solidified powder metallurgy Mg(97)Zn(1)Y(2) alloys with excellent tensile yield strength above 600 MPa. Mater Trans 42:1172–1176

    Article  Google Scholar 

  34. Matsumoto R, Otsu M, Yamasaki M, Mayama T, Utsunomiya H, Kawamura Y (2012) Application of mixture rule to finite element analysis for forging of cast Mg-Zn-Y alloys with long period stacking ordered structure. Mat Sci Eng A-Struct 548:75–82

    Article  Google Scholar 

  35. Villars P (1995) Handbook of ternary alloy phase diagram. The Material Information Society

  36. Wang BS, Liu YB, An J, Li RG, Su ZG, Su GH, Lu Y, Cao ZY (2008) Morphologies of microstructure in Mg97Zn1Y2 ribbon upon ageing at different temperatures. Mater Trans 49:1768–1774

    Article  Google Scholar 

  37. Yaghmazadeh M (2017) Evolution of core-shell structures in Al-Bi and Al-Sn alloy droplets. In: Northeastern University

  38. Gonzalez R, Woods R, Eddins S (2009) Digital image processing using Matlab” Gatesmark Publishing. In: LLC

  39. Boettinger W (1988) Application of dendritic growth theory to the interpretation of rapid solidification microstructure, Rapid Solidification Processing: Principles and Technology 13

  40. Petrovic S, Robinson T, Judd RL (2004) Marangoni heat transfer in subcooled nucleate pool boiling. Int J Heat Mass Transf 47:5115–5128

    Article  Google Scholar 

  41. Porter D, Esterling K (1992) Phase transformations, metals and alloys, 2nd edn. Chapman & Hall, London

    Book  Google Scholar 

  42. Lu H, Ando T (2002) 513 Modeling and characterization of the solidification of mono-size copper droplets. In: The Proceedings of the JSME Materials and Processing Conference (M&P) 10.1, The Japan Society of Mechanical Engineers, pp 337–342

  43. Langer JS (1980) Instabilities and pattern formation in crystal growth. Rev Mod Phys 52:1

    Article  Google Scholar 

  44. Connors K (1990) Introduction to chemical kinetics, Chemical Kinetics: the study of reactioon rates in solution

  45. Carslaw H, Jaeger J (1959) Conduction of heat in solids. Oxford Science Publications, Oxford

    MATH  Google Scholar 

  46. Wang P, Sun H, Wong PY, Fukuda H, Ando T (2012) Modeling of droplet-based processing for the production of high-performance particulate materials using the level set method. Numer Heat Transfer Part A Appl 61:401–416

    Article  Google Scholar 

  47. Yin FL, Zhu S, Liu J, Liang YY (2012) Numerical simulation of molten metal droplet impinging in uniform droplet spray rapid prototyping. Mater Sci Forum 704-705:680–684

    Article  Google Scholar 

  48. Qi LH, Chao YP, Luo J, Zhou JM, Hou XH, Li HJ (2012) A novel selection method of scanning step for fabricating metal components based on micro-droplet deposition manufacture. Int J Mach Tool Manu 56:50–58

    Article  Google Scholar 

  49. Du J, Wang X, Bai H, Zhao GX, Zhang YB (2017) Numerical analysis of fused-coating metal additive manufacturing. Int J Therm Sci 114:342–351

    Article  Google Scholar 

  50. Murr LE, Johnson WL (2017) 3D metal droplet printing development and advanced materials additive manufacturing. J Mater Res Technol 6:77–89

    Article  Google Scholar 

Download references

Funding

Y. Liao appreciates the financial support by startup funding from the Department of Mechanical Engineering at the University of Nevada, Reno.

Author information

Authors and Affiliations

  1. Department of Materials Science, Montanuniversität Leoben, 8700, Leoben, Austria

    Yiannos Ioannou

  2. Fukuda Metal Foil & Powder Co. Ltd, Kyoto, 607-8305, Japan

    Hiroki Fukuda

  3. Department of Mechanical and Manufacturing Engineering, University of Cyprus, CY-1678, Nicosia, Cyprus

    Claus Rebholz

  4. Department of Mechanical Engineering, University of Nevada Reno, Reno, NV, 89557, USA

    Yiliang Liao

  5. Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, 02115, USA

    Teiichi Ando

  6. College of Engineering & Computer Science, Vin University, Hanoi, Vietnam

    Charalabos C. Doumanidis

Authors
  1. Yiannos Ioannou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroki Fukuda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Claus Rebholz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yiliang Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Teiichi Ando
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Charalabos C. Doumanidis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiliang Liao.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ioannou, Y., Fukuda, H., Rebholz, C. et al. Constrained crystal growth during solidification of particles and splats in uniform droplet sprays. Int J Adv Manuf Technol 107, 1205–1221 (2020). https://doi.org/10.1007/s00170-020-05107-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-020-05107-1

Keywords

Search

Navigation