Skip to main content
SpringerLink
Log in

Modeling and Simulation of Sintering Process Across Scales

  • Review article
  • Published:
Archives of Computational Methods in Engineering Aims and scope Submit manuscript

Abstract

Sintering, as a thermal process at elevated temperature below the melting point, is widely used to bond contacting particles into engineering products such as ceramics, metals, polymers, and cemented carbides. Modelling and simulation as important complement to experiments are essential for understanding the sintering mechanisms and for the optimization and design of sintering process. We share in this article a state-to-the-art review on the major methods and models for the simulation of sintering process at various length scales. It starts with molecular dynamics simulations deciphering atomistic diffusion process, and then moves to microstructure-level approaches such as discrete element method, Monte–Carlo method, and phase-field models, which can reveal subtle mechanisms like grain coalescence, grain rotation, densification, grain coarsening, etc. Phenomenological/empirical models on the macroscopic scales for estimating densification, porosity and average grain size are also summarized. The features, merits, drawbacks, and applicability of these models and simulation technologies are expounded. In particular, the latest progress on the modelling and simulation of selective and direct-metal laser sintering based additive manufacturing is also reviewed. Finally, a summary and concluding remarks on the challenges and opportunities are given for the modelling and simulations of sintering process.

Graphical Abstract

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
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39
Fig. 40
Fig. 41
Fig. 42
Fig. 43
Fig. 44

Similar content being viewed by others

References

  1. German RM (1996) Sintering theory and practice. Wiley, New York

    Google Scholar 

  2. Walker RF (1995) Mechanism of material transport during sintering. J Am Ceram Soc 38(6):187–197

    Article  Google Scholar 

  3. Bordia R, Olevsky E (2009) Advances in sintering science and technology. J Am Ceram Soc 92(7):1383

    Article  Google Scholar 

  4. Kang SJL, Bordia R, Bouvard D, Olevsky E (2012) Advances in sintering research. J Am Ceram Soc 95(8):2357

    Article  Google Scholar 

  5. Bordia RK, Kang SJL, Olevsky EA (2017) Current understanding and future research directions at the onset of the next century of sintering science and technology. J Am Ceram Soc 100(6):2314–2352

    Article  Google Scholar 

  6. Raether F, Seifert G, Ziebold H (2019) Simulation of Sintering across Scales. Adv Theory Simul 2(7):1–19

    Article  Google Scholar 

  7. Olakanmi EO, Cochrane RF, Dalgarno KW (2015) A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: processing, microstructure, and properties. Prog Mater Sci 74:401–477

    Article  Google Scholar 

  8. Sing SL, Yeong WY, Wiria FE, Tay BY, Zhao Z, Zhao L, Tian Z, Yang S (2017) Direct selective laser sintering and melting of ceramics: a review. Rapid Prototyping J 23(3):611–623

    Article  Google Scholar 

  9. Stuijts AL (1973) Synthesis of materials from powders by sintering. Annu Rev Mater Sci 3(1):363–395

    Article  Google Scholar 

  10. Yu M, Grasso S, Mckinnon R, Saunders T, Reece MJ (2017) Review of flash sintering: materials, mechanisms and modelling. Adv Appl Ceram 116(1):24–60

    Article  Google Scholar 

  11. Thümmler F, Thomma W (1967) The sintering process. Metall Rev 12(1):69–108

    Google Scholar 

  12. Singh S, Sharma VS, Sachdeva A (2016) Progress in selective laser sintering using metallic powders: a review. Mater Sci Technol 32(8):760–772

    Google Scholar 

  13. Rojek J, Nosewicz S, Maździarz M, Kowalczyk P, Wawrzyk K, Lumelskyj D (2017) Modeling of a sintering process at various scales. Procedia Eng 177:263–270

    Article  Google Scholar 

  14. Ding L, Davidchack RL, Pan J (2009) A molecular dynamics study of sintering between nanoparticles. Comput Mater Sci 45(2):247–256

    Article  Google Scholar 

  15. Liu ZJ, Cheng Q, Li K, Wang YZ, Zhang J (2020) The interaction of nanoparticulate Fe\(_2\)O\(_3\) in the sintering process: a molecular dynamics simulation. Powder Technol 367:97–104

    Article  Google Scholar 

  16. Zhang Y, Wu L, Guo X, Jung YG, Zhang J (2016) Molecular dynamics simulation of electrical resistivity in sintering process of nanoparticle silver inks. Comput Mater Sci 125:105–109

    Article  Google Scholar 

  17. Liu J, Wang M, Liu P, Sun R, Yang Y, Zou G (2021) Molecular dynamics study of sintering of Al nanoparticles with/without organic coatings. Comput Mater Sci 190(January):110265

    Article  Google Scholar 

  18. Goudeli E, Pratsinis SE (2016) Crystallinity dynamics of gold nanoparticles during sintering or coalescence. AIChE J 62(2):589–598

    Article  Google Scholar 

  19. Zhang Z, Fu G, Wan B, Su Y, Jiang M (2021) Research on sintering process and thermal conductivity of hybrid nanosilver solder paste based on molecular dynamics simulation. Microelectron Reliab 126:114203

    Article  Google Scholar 

  20. Sementa L, Barcaro G, Monti S, Carravetta V (2018) Molecular dynamics simulations of melting and sintering of Si nanoparticles: a comparison of different force fields and computational models. Phys Chem Chem Phys 20(3):1707–1715

    Article  Google Scholar 

  21. Raut JS, Bhagat RB, Fichthorn KA (1998) Sintering of aluminum nanoparticles: a molecular dynamics study. Nanostruct Mater 10(5):837–851

    Article  Google Scholar 

  22. Meng L, Zhang Y, Yang X, Zhang J (2019) Atomistic modeling of resistivity evolution of copper nanoparticle in intense pulsed light sintering process. Phys B 554:31–34

    Article  Google Scholar 

  23. Koparde VN, Cummings PT (2005) Molecular dynamics simulation of titanium dioxide nanoparticle sintering. J Phys Chem B 109(51):24280–24287

    Article  Google Scholar 

  24. Koparde VN, Cummings PT (2008) Phase transformations during sintering of titania nanoparticles. ACS Nano 2(8):1620–1624

    Article  Google Scholar 

  25. Koparde VN, Cummings PT (2008) Sintering of titanium dioxide nanoparticles: a comparison between molecular dynamics and phenomenological modeling. J Nanopart Res 10(7):1169–1182

    Article  Google Scholar 

  26. Zhang Y, Deng Y, Zeng Q, Wen D, Zhao H, Gao M, Dai X, Wu A (2020) Sintering reaction and microstructure of MAl (M = Ni, Fe, and Mg) nanoparticles through molecular dynamics simulation. Chin Phys B 29(11):116601

    Article  Google Scholar 

  27. Seong Y, Kim Y, German R, Kim S, Kim SG, Kim SJ, Kim HJ, Park SJ (2016) Dominant mechanisms of the sintering of copper nano-powders depending on the crystal misalignment. Comput Mater Sci 123:164–175

    Article  Google Scholar 

  28. Samsonov VM, Alymov MI, Talyzin IV, Vasilyev SA (2019) Size dependence of the melting temperature and mechanisms of the coalescence/sintering on the nanoscale. J Phys 1352(1)

  29. Yousefi M, Khoie MM (2015) Molecular dynamics simulation of Ni/Cu-Ni nanoparticles sintering under various crystallographic, thermodynamic and multi-nanoparticles conditions. Eur Phys J D 69(3)

  30. Cao J, Li L, Zhang C (2021) The coalescence of Cu nanoparticles with different interfacial lattice structures: a molecular dynamics study. Mod Phys Lett B 35(9):1–12

    Article  Google Scholar 

  31. Zhan L, Zhu X, Qin X, Wu M, Li X (2021) Sintering mechanism of copper nanoparticle sphere-plate of crystal misalignment: a study by molecular dynamics simulations. J Market Res 12:668–678

    Google Scholar 

  32. Mao Q, Luo KH (2015) Molecular dynamics simulation of sintering dynamics of many TiO\(_2\) nanoparticles. J Stat Phys 160(6):1696–1708

    Article  MATH  Google Scholar 

  33. He H, Rong Y, Zhang L (2019) Molecular dynamics studies on the sintering and mechanical behaviors of graphene nanoplatelet reinforced aluminum matrix composites. Modell Simul Mater Sci Eng 27(6)

  34. Alarifi HA, Atis M, Özdoǧan C, Hu A, Yavuz M, Zhou Y (2013) Molecular dynamics simulation of sintering and surface premelting of silver nanoparticles. Mater Trans 54(6):884–889

    Article  Google Scholar 

  35. Zhou X, Cao J, Feng H, Cao Y, Fan Y, Chen J (2013) ME molecular dynamics simulation of the sintering process of the porous ITO material. Adv Mater Res 602–604:1744–1748

    Google Scholar 

  36. Peng P, Chen JC, Ruan J (2013) Preparation of ITO target by molecular dynamics simulation with normal pressure sintering method. Adv Mater Res 634–638:1771–1775

    Article  Google Scholar 

  37. Suzuki A, Nakamura K, Sato R, Okushi K, Tsuboi H, Hatakeyama N, Endou A, Takaba H, Kubo M, Williams MC, Miyamoto A (2009) Multi-scale theoretical study of support effect on sintering dynamics of Pt. Surf Sci 603(20):3049–3056

    Article  Google Scholar 

  38. Nguyen NH, Henning R, Wen JZ (2011) Molecular dynamics simulation of iron nanoparticle sintering during flame synthesis. J Nanopart Res 13(2):803–815

    Article  Google Scholar 

  39. Malti A, Kardani A, Montazeri A (2021) An insight into the temperature-dependent sintering mechanisms of metal nanoparticles through MD-based microstructural analysis. Powder Technol 386:30–39

    Article  Google Scholar 

  40. Zhang L, Li Q, Tian S, Hong G (2019) Molecular dynamics simulation of the Cu/Au nanoparticle alloying process. J Nanomater, 2019

  41. Tian S, Dai X, Li M, Zhang L, Chen J (2020) Influence of initial distance and heating rate on the aggregation of Cu and Au nanoparticles: A MD study. Mod Phys Lett B 34(supp01):1–12

    Article  Google Scholar 

  42. Henz BJ, Hawa T, Zachariah M (2009) Molecular dynamics simulation of the kinetic sintering of Ni and Al nanoparticles. Mol Simul 35(10–11):804–811

    Article  Google Scholar 

  43. Liang M, Xiong Z, Hu Y, Liu Y, Shen T, Sun S, Zhu Y (2020) Surface evolution of Janus Cu-Ag nanoparticles: influence of atom arrangements and interface structures. Funct Mater Lett 13(7):4–7

    Article  Google Scholar 

  44. Yang C, Jing X, Miao H, Xu J, Lin P, Li P, Liang C, Wu Y, Yuan J (2021) The physical properties and effects of sintering conditions on rSOFC fuel electrodes evaluated by molecular dynamics simulation. Energy 216

  45. Nakao K, Kohno H, Ishimoto T, Koyama M (2013) Molecular dynamics study for sintering characteristics of solid oxide fuel cell anode. ECS Trans 50(30):1–9

    Article  Google Scholar 

  46. Nakao K, Kohno H, Ishimoto T, Koyama M (2013) Moleular dynamics study for sintering property analysis of Ni-YSZ cermet. ECS Trans 57(1):1407–1413

    Article  Google Scholar 

  47. Xu J, Sakanoi R, Higuchi Y, Ozawa N, Sato K, Hashida T, Kubo M (2013) Molecular dynamics simulation of Ni nanoparticles sintering process in Ni/YSZ multi-nanoparticle system. J Phys Chem C 117(19):9663–9672

    Article  Google Scholar 

  48. Fu P, Yan M, Zeng M, Wang Q (2017) Sintering process simulation of a solid oxide fuel cell anode and its predicted thermophysical properties q. Appl Therm Eng 125:209–219

    Article  Google Scholar 

  49. Zhu Y, Li N, Li W, Niu L, Li Z (2022) Atomistic study on the sintering process and the strengthening mechanism of Al-graphene system. Materials 15(7):2644

    Article  Google Scholar 

  50. Mahmood AA, Elektorowicz M (2016) A review of discrete element method research on particulate systems. IOP Conf Ser 136(1):012034

    Google Scholar 

  51. Harthong B, Jérier JF, Dorémus P, Imbault D, Donzé FV (2009) Modeling of high-density compaction of granular materials by the Discrete Element Method. Int J Solids Struct 46(18–19):3357–3364

    Article  MATH  Google Scholar 

  52. Oñate E, Owen R (2011) Particle-based methods: fundamentals and applications. Springer, Dordrecht

    Book  MATH  Google Scholar 

  53. Kloss C, Goniva C (2011) LIGGGHTS - Open source discrete element simulations of granular materials based on lammps. Suppl Proc 2:781–788

    Article  Google Scholar 

  54. Paredes-Goyes B, Jauffres D, Missiaen JM, Martin CL (2021) Grain growth in sintering: A discrete element model on large packings. Acta Mater 218:117182

    Article  Google Scholar 

  55. Ericson C (2005) Real-time collision detection. Elsevier, San Francisco

    Google Scholar 

  56. Ogarko V, Luding S (2012) A fast multilevel algorithm for contact detection of arbitrarily polydisperse objects. Comput Phys Commun 183(4):931–936

    Article  Google Scholar 

  57. Kruggel-Emden H, Simsek E, Rickelt S, Wirtz S, Scherer V (2007) Review and extension of normal force models for the Discrete Element Method. Powder Technol 171(3):157–173

    Article  Google Scholar 

  58. Martin C, Bouvard D, Shima S (2003) Study of particle rearrangement during powder compaction by the Discrete Element Method. J Mech Phys Solids 51(4):667–693

    Article  MATH  Google Scholar 

  59. Jiang M, Yu H-S, Leroueil S (2007) A simple and efficient approach to capturing bonding effect in naturally microstructured sands by discrete element method. Int J Numer Methods Eng 69(6):1158–1193

    Article  MATH  Google Scholar 

  60. Parhami F, McMeeking RM (1998) A network model for initial stage sintering. Mech Mater 27(2):111–124

    Article  Google Scholar 

  61. Bouvard D, McMeeking RM (2005) Deformation of interparticle necks by diffusion-controlled creep. J Am Ceram Soc 79(3):666–672

    Article  Google Scholar 

  62. Pan J, Le H, Kucherenko S, Yeomans JA (1998) A model for the sintering of spherical particles of different sizes by solid state diffusion. Acta Mater 46(13):4671–4690

    Article  Google Scholar 

  63. Martin CL, Schneider LC, Olmos L, Bouvard D (2006) Discrete element modeling of metallic powder sintering. Scr Mater 55(5):425–428

    Article  Google Scholar 

  64. Rasp T, Jamin C, Wonisch A, Kraft T, Guillon O (2012) Shape distortion and delamination during constrained sintering of ceramic stripes: discrete element simulations and experiments. J Am Ceram Soc 95(2):586–592

    Article  Google Scholar 

  65. Wonisch A, Guillon O, Kraft T, Moseler M, Riedel H, Rödel J (2007) Stress-induced anisotropy of sintering alumina: discrete element modelling and experiments. Acta Mater 55(15):5187–5199

    Article  Google Scholar 

  66. Luding S, Manetsberger K, Müllers J (2005) A discrete model for long time sintering. J Mech Phys Solids 53(2):455–491

    Article  MATH  Google Scholar 

  67. Martin S, Guessasma M, Léchelle J, Fortin J, Saleh K, Adenot F (2014) Simulation of sintering using a non smooth discrete element method. Application to the study of rearrangement. Comput Mater Sci 84:31–39

    Article  Google Scholar 

  68. Nosewicz S, Rojek J, Chmielewski M (2020) Discrete element framework for determination of sintering and postsintering residual stresses of particle reinforced composites. Materials 13(18):4015

    Article  Google Scholar 

  69. Martin CL, Yan Z, Jauffres D, Bouvard D, Bordia RK (2016) Sintered ceramics with controlled microstructures: numerical investigations with the Discrete Element Method. J Ceram Soc Jpn 124(4):340–345

    Article  Google Scholar 

  70. Beloglazov II, Boikov AV, Petrov PA (2020) Discrete element simulation of powder sintering for spherical particles. Key Eng Mater 854:164–171

    Article  Google Scholar 

  71. Besler R, da Silva MR, Dosta M, Heinrich S, Janssen R (2016) Discrete element simulation of metal ceramic composite materials with varying metal content. J Eur Ceram Soc 36(9):2245–2253

    Article  Google Scholar 

  72. Nosewicz S, Rojek J, Pietrzak K, Chmielewski M (2013) Viscoelastic discrete element model of powder sintering. Powder Technol 246:157–168

    Article  Google Scholar 

  73. Lichtner A, Roussel D, Röhrens D, Jauffres D, Villanova J, Martin CL, Bordia RK (2018) Anisotropic sintering behavior of freeze-cast ceramics by optical dilatometry and discrete-element simulations. Acta Mater 155:343–349

    Article  Google Scholar 

  74. Yan Z, Martin CL, Guillon O, Bouvard D, Lee CS (2014) Microstructure evolution during the co-sintering of Ni/BaTiO\(_3\) multilayer ceramic capacitors modeled by discrete element simulations. J Eur Ceram Soc 34(13):3167–3179

    Article  Google Scholar 

  75. Teixeira MHP, Skorych V, Janssen R, González SYG, De Noni A, Rodrigues Neto JB, Hotza D, Dosta M (2021) High heating rate sintering and microstructural evolution assessment using the discrete element method. Open Ceram 8:100182

    Article  Google Scholar 

  76. Iacobellis V, Radhi A, Behdinan K (2019) Discrete element model for ZrB\(_2\)-SiC ceramic composite sintering. Compos Struct 229(September):111373

    Article  Google Scholar 

  77. Mashhadi M, Khaksari H, Safi S (2015) Pressureless sintering behavior and mechanical properties of ZrB\(_2\)-SiC composites: effect of SiC content and particle size. J Market Res 4(4):416–422

    Google Scholar 

  78. Shaheen MY, Thornton AR, Luding S, Weinhart T (2021) The influence of material and process parameters on powder spreading in additive manufacturing. Powder Technol 383:564–583

    Article  Google Scholar 

  79. Haeri S (2017) Optimisation of blade type spreaders for powder bed preparation in additive manufacturing using DEM simulations. Powder Technol 321:94–104

    Article  Google Scholar 

  80. Nan W, Ghadiri M (2019) Numerical simulation of powder flow during spreading in additive manufacturing. Powder Technol 342:801–807

    Article  Google Scholar 

  81. Chen H, Wei Q, Zhang Y, Chen F, Shi Y, Yan W (2019) Powder-spreading mechanisms in powder-bed-based additive manufacturing: experiments and computational modeling. Acta Mater 179:158–171

    Article  Google Scholar 

  82. Ma Y, Evans TM, Philips N, Cunningham N (2020) Numerical simulation of the effect of fine fraction on the flowability of powders in additive manufacturing. Powder Technol 360:608–621

    Article  Google Scholar 

  83. Wang L, Li EL, Shen H, Zou RP, Yu AB, Zhou ZY (2020) Adhesion effects on spreading of metal powders in selective laser melting. Powder Technol 363:602–610

    Article  Google Scholar 

  84. Zhao Y, Koizumi Y, Aoyagi K, Yamanaka K, Chiba A (2017) Characterization of powder bed generation in electron beam additive manufacturing by discrete element method (DEM). Mater Today 4(11):11437–11440

    Google Scholar 

  85. Markl M, Körner C (2018) Powder layer deposition algorithm for additive manufacturing simulations. Powder Technol 330:125–136

    Article  Google Scholar 

  86. Xin H, Sun WC (2018) J. Fish. Discrete element simulations of powder-bed sintering-based additive manufacturing. Int J Mech Sci 149:373–392

    Article  Google Scholar 

  87. Ganeriwala R, Zohdi TI (2016) A coupled discrete element-finite difference model of selective laser sintering. Granular Matter 18(2)

  88. Steuben JC, Iliopoulos AP, Michopoulos JG (2016) Discrete element modeling of particle-based additive manufacturing processes. Comput Methods Appl Mech Eng 305:537–561

    Article  MathSciNet  MATH  Google Scholar 

  89. Lee WH, Zhang Y, Zhang J (2017) Discrete element modeling of powder flow and laser heating in direct metal laser sintering process. Powder Technol 315:300–308

    Article  Google Scholar 

  90. Xin L, Boutaous M, Xin S, Siginer DA (2017) Numerical modeling of the heating phase of the selective laser sintering process. Int J Therm Sci 120:50–62

    Article  Google Scholar 

  91. Steuben JC, Iliopoulos AP, Michopoulos JG (2016) On multiphysics discrete element modeling of powder-based additive manufacturing processes. In: International design engineering technical conferences and computers and information in engineering conference, pp V01AT02A032

  92. Xin L, Boutaous M, Xin S, Siginer DA (2017) Multiphysical modeling of the heating phase in the polymer powder bed fusion process. Addit Manuf 18:121–135

    Google Scholar 

  93. Anderson MP, Srolovitz DJ, Grest GS, Sahni PS (1984) Computer simulation of grain growth - I. Kinetics. Acta Metall 32(5):783–791

    Article  Google Scholar 

  94. Tikare V, Braginsky M, Olevsky EA (2003) Numerical simulation of solid-state sintering: I, sintering of three particles. J Am Ceram Soc 86(1):49–53

    Article  MATH  Google Scholar 

  95. Bordère S, Bernard D (2008) Full resolution of the Monte Carlo time scale demonstrated through the modelling of two-amorphous-particles sintering. Comput Mater Sci 43(4):1074–1080

    Article  Google Scholar 

  96. Bordère S (2006) The impact of fluctuations on the sintering kinetics of two particles demonstrated through Monte Carlo simulation. Scr Mater 55(10):879–882

    Article  Google Scholar 

  97. Bordèred S, Gendron D, Heintz JM, Bernard D (2005) Monte Carlo prediction of non-newtonian viscous sintering: experimental validation for the two-glass-cylinder system. J Am Ceram Soc 88(8):2071–2078

    Article  Google Scholar 

  98. Bordère S, Gendron D, Bernard D (2006) Improvement in the accuracy of calculated interface morphologies within Monte Carlo simulations of sintering processes. Scr Mater 55(3):267–270

    Article  Google Scholar 

  99. Rao Madhavrao L, Rajagopalan R (1989) Monte Carlo simulations for sintering of particle aggregates. J Mater Res 4(5):1251–1256

    Article  Google Scholar 

  100. Akhtar MK, Lipscomb GG, Pratsinis SE (1994) Monte Carlo simulation of particle coagulation and sintering. Aerosol Sci Technol 21(1):83–93

    Article  Google Scholar 

  101. Zeng P, Tikare V (1998) Potts model simulation of grain size distributions during final stage sintering. Materials Research Society Symposium - Proceedings 529:77–83

    Article  Google Scholar 

  102. Morhac M, Morhacova E (2000) Monte Carlo simulation algorithms of grain growth in polycrystalline materials. Cryst Res Technol 35(1):117–128

    Article  Google Scholar 

  103. Braginsky M, Tikare V, Olevsky E (2005) Numerical simulation of solid state sintering. Int J Solids Struct 42(2):621–636

    Article  MATH  Google Scholar 

  104. Neizvestny I, Shwartz NL, Yanovitskaya Z, Zverev A (2007) Monte Carlo simulation of porous layers sintering. Key Eng Mater 352:5–8

    Article  Google Scholar 

  105. Kim HS, Park JW (2009) Computational study on the microstructural evolution and the change of electrical resistivity of sintered materials. J Electron Mater 38(3):475–481

    Article  Google Scholar 

  106. Raether F, Seifert G (2018) Modeling inherently homogeneous sintering processes. Adv Theory Simul 1(5):1–8

    Article  Google Scholar 

  107. Luque A, Aldazabal J, Martín-Meizoso A, Martínez-Esnaola JM, Sevillano JG, Farr R (2005) Simulation of the microstructural evolution during liquid phase sintering using a geometrical Monte Carlo model. Modell Simul Mater Sci Eng 13(7):1057–1070

    Article  MATH  Google Scholar 

  108. Liu PL (2006) The relation between the distribution of dihedral angles and the wetting angle during liquid phase sintering. Comput Mater Sci 36(4):468–473

    Article  Google Scholar 

  109. Mori K, Matsubara H, Noguchi N (2004) Micro-macro simulation of sintering process by coupling Monte Carlo and finite element methods. Int J Mech Sci 46(6):841–854

    Article  MATH  Google Scholar 

  110. Wang X, Atkinson A (2018) Combining densification and coarsening in a Cellular Automata-Monte-Carlo simulation of sintering: methodology and calibration. Comput Mater Sci 143:338–349

    Article  Google Scholar 

  111. Hara S, Shikata K, Shikazono N, Izumi S, Sakai S (2013) Monte Carlo study on the constraint effect of YSZ phase on Ni sintering in Ni-YSZ composite system. ECS Trans 57(1):2857–2863

    Article  Google Scholar 

  112. Guo JY, Xu CX, Hu AM, Oakes KD, Sheng FY, Shi ZL, Dai J, Jin ZL (2012) Sintering dynamics and thermal stability of novel configurations of Ag clusters. J Phys Chem Solids 73(11):1350–1357

    Article  Google Scholar 

  113. Qiu F, Egerton TA, Cooper IL (2008) Monte Carlo simulation of nano-particle sintering. Powder Technol 182(1):42–50

    Article  Google Scholar 

  114. Hao S, Huang C, Zou B, Wang J, Liu H, Zhu H (2011) Three dimensional simulation of microstructure evolution for ceramic tool materials. Comput Mater Sci 50(12):3334–3341

    Article  Google Scholar 

  115. Cheng H, Huang C, Liu H, Zou B (2009) Monte Carlo simulation of microstructure evolution in nano-composite ceramic tool materials. Comput Mater Sci 47(2):326–331

    Article  Google Scholar 

  116. Zhao YH, Zhang Y, Zhang DH (2008) Monte-Carlo simulation for the grain growth of Si\(_3\)Nb\(_4\) during sintering process. Key Eng Mater 368–372:1673–1676

    Article  Google Scholar 

  117. Suzuki H, Matsubara H (1999) Microstructural design of grain boundaries in alumina based ceramics. Key Eng Mater 161–163:453–456

    Google Scholar 

  118. Keum YT, Jeon JH, Auh KH (2002) Computer simulation of ceramic sintering processes. J Ceram Process Res 3(3):195–200

    Google Scholar 

  119. Matsubara H (1999) Computer simulations for the design of microstructural developments in ceramics. Comput Mater Sci 14(1–4):125–128

    Article  Google Scholar 

  120. Gu T, Gu M, Du H, Zhao B (2017) Simulation of microstructure evolution and prediction of mechanical properties of material of alumina ceramic cutting tools. In: 2017 IEEE international conference on mechatronics and automation, ICMA 2017, pp 270–274

  121. Weiner M, Zienert T, Schmidtchen M, Hubálková J, Aneziris CG, Prahl U (2022) A new approach for sintering simulation of irregularly shaped powder particles Part II: statistical powder modeling. Adv Eng Mater 24(8):2200443

    Article  Google Scholar 

  122. Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140

    Article  Google Scholar 

  123. Chen LQ, Zhao Y (2021) From classical thermodynamics to phase-field method. Prog Mater Sci 124:100868

    Article  Google Scholar 

  124. Qin RS, Bhadeshia HK (2010) Phase field method. Mater. Sci Technol 26(7):803–811

    Google Scholar 

  125. van de Walle A, Nataraj C, Liu Z-K (2018) The thermodynamic database database. Calphad 61:173–178

    Article  Google Scholar 

  126. Andersson JO, Helander T, Hoglund LH, Shi PF, Sundman B (2002) THERMO-CALC & DICTRA, computational tools for materials science. Calphad 26(2):273–312

    Article  Google Scholar 

  127. Chen LQ, Yang W (1994) Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: the grain-growth kinetics. Phys Rev B 50(21):15752–15756

    Article  Google Scholar 

  128. Chen L-Q (1995) A novel computer simulation technique for modeling grain growth. Scr Metall Mater 32(1):115–120

    Article  Google Scholar 

  129. Folch R, Plapp M (2003) Towards a quantitative phase-field model of two-phase solidification. Phys Rev E 68:010602

    Article  MATH  Google Scholar 

  130. Wang YU (2006) Computer modeling and simulation of solid-state sintering: a phase field approach. Acta Mater 54(4):953–961

    Article  Google Scholar 

  131. Biswas S, Schwen D, Singh J, Tomar V (2016)A study of the evolution of microstructure and consolidation kinetics during sintering using a phase field modeling based approach, vol 7

  132. Kumar V, Fang ZZ, Fife PC (2010) Phase field simulations of grain growth during sintering of two unequal-sized particles. Mater Sci Eng, A 528(1):254–259

    Article  Google Scholar 

  133. Biswas S, Schwen D, Tomar V (2018) Implementation of a phase field model for simulating evolution of two powder particles representing microstructural changes during sintering. J Mater Sci 53(8):5799–5825

    Article  Google Scholar 

  134. Chockalingam K, Kouznetsova VG, van der Sluis O, Geers MG (2016) 2D Phase field modeling of sintering of silver nanoparticles. Comput Methods Appl Mech Eng 312:492–508

    Article  MathSciNet  MATH  Google Scholar 

  135. Deng J (2012) A phase field model of sintering with direction-dependent diffusion. Mater Trans 53(2):385–389

    Article  Google Scholar 

  136. Asp K, Ågren J (2006) Phase-field simulation of sintering and related phenomena-a vacancy diffusion approach. Acta Mater 54(5):1241–1248

    Article  Google Scholar 

  137. Kazaryan A, Wang Y, Patton BR (1999) Generalized phase field approach for computer simulation of sintering: incorporation of rigid-body motion. Scr Mater 41(5):487–492

    Article  Google Scholar 

  138. Dzepina B, Balint D, Dini D (2019) A phase field model of pressure-assisted sintering. J Eur Ceram Soc 39(2–3):173–182

    Article  Google Scholar 

  139. Vuppuluri A, Vedantam S (2019) Simulation of grain growth under simultaneous grain boundary migration and grain rotation using multi-order parameter phase-field model. J Mater Sci 54:506–514

    Article  Google Scholar 

  140. Shinagawa K (2014) Simulation of grain growth and sintering process by combined phase-field/discrete-element method. Acta Mater 66:360–369

    Article  Google Scholar 

  141. Zhao Z, Zhang X, Zhang H, Tang H, Liang Y (2022) Numerical investigation into pressure-assisted sintering using fully coupled mechano-diffusional phase-field model. Int J Solids Struct 234–235:111253

    Article  Google Scholar 

  142. Shulin T, Xiaomin Z, Zhipeng Z, Zhouzhi W (2020) Driving force evolution in solid-state sintering with coupling multiphysical fields. Ceram Int 46(8):11584–11592

    Article  Google Scholar 

  143. Villanueva W, Grönhagen K, Amberg G, Ågren J (2009) Multicomponent and multiphase simulation of liquid-phase sintering. Comput Mater Sci 47(2):512–520

    Article  Google Scholar 

  144. Malik Tahir A, Malik A, Amberg G (2016) Modeling of the primary rearrangement stage of liquid phase sintering. Modell Simul Mater Sci Eng 24(7):075009

    Article  Google Scholar 

  145. Ravash H, Vanherpe L, Vleugels J, Moelans N (2017) Three-dimensional phase-field study of grain coarsening and grain shape accommodation in the final stage of liquid-phase sintering. J Eur Ceram Soc 37(5):2265–2275

    Article  Google Scholar 

  146. Yang Q, Kirshtein A, Ji Y, Liu C, Shen J, Chen LQ (2018) A thermodynamically consistent phase-field model for viscous sintering. J Am Ceram Soc 102(2):674–685

    Article  Google Scholar 

  147. Zhang RJ, Chen ZW, Fang W, Qu XH (2014) Thermodynamic consistent phase field model for sintering process with multiphase powders. Trans Nonferr Met Soc China (English Edition) 24(3):783–789

    Article  Google Scholar 

  148. Liu L, Gao F, Li B, Hu G (2011) Phase-field simulation of process in sintering ceramics. Adv Mater Res 154–155:1674–1679

    Article  Google Scholar 

  149. Wei C, Li S (2012) Microstructure evolution in sintering of alumina-zirconia ceramics simulated by a modified phase field method. Mater Sci Forum 715–716:788–793

    Article  Google Scholar 

  150. Yabansu YC, Rehn V, Hötzer J, Nestler B, Kalidindi SR (2019) Application of Gaussian process autoregressive models for capturing the time evolution of microstructure statistics from phase-field simulations for sintering of polycrystalline ceramics. Modell Simul Mater Sci Eng 27(8):084006

    Article  Google Scholar 

  151. Zhang X, Liao Y (2018) A phase-field model for solid-state selective laser sintering of metallic materials. Powder Technol 339:677–685

    Article  Google Scholar 

  152. Zhang Z, Yao X, Ge P (2020) Phase-field-model-based analysis of the effects of powder particle on porosities and densities in selective laser sintering additive manufacturing. Int J Mech Sci 166:105230

    Article  Google Scholar 

  153. Satpathy BB, Nandy J, Sahoo S (2018) Investigation of consolidation kinetics and microstructure evolution of Al alloys in direct metal laser sintering using phase field simulation. IOP Conf Ser 338:012045

    Article  Google Scholar 

  154. Vikrant KSN, Rheinheimer W, García RE (2020) Electrochemical drag effect on grain boundary motion in ionic ceramics.NPJ Comput Mater, 6:165

  155. Plapp M (2011) Unified derivation of phase-field models for alloy solidification from a grand-potential functional. Phys Rev E 84:031601

    Article  Google Scholar 

  156. Choudhury A, Nestler B (2012) Grand-potential formulation for multicomponent phase transformations combined with thin-interface asymptotics of the double-obstacle potential. Phys Rev E 85:021602

    Article  Google Scholar 

  157. Hötzer J, Jainta M, Steinmetz P, Nestler B, Dennstedt A, Genau A, Bauer M, Köstler H, Rüde U (2015) Large scale phase-field simulations of directional ternary eutectic solidification. Acta Mater 93:194–204

    Article  Google Scholar 

  158. Hötzer J, Seiz M, Kellner M, Rheinheimer W, Nestler B (2019) Phase-field simulation of solid state sintering. Acta Mater 164:184–195

    Article  Google Scholar 

  159. Greenquist I, Tonks MR, Aagesen LK (2020) Zhang Y (2019) Development of a microstructural grand potential-based sintering model. Comput Mater Sci 172:109288

    Article  Google Scholar 

  160. Kubendran Amos PG, Nestler B (2020) Grand-potential based phase-field model for systems with interstitial sites. Sci Rep 10(1):22423

    Article  Google Scholar 

  161. Greenquist I, Tonks M, Cooper M, Andersson D, Zhang Y (2020) Grand potential sintering simulations of doped UO2 accident-tolerant fuel concepts. J Nucl Mater 532:152052

    Article  Google Scholar 

  162. Yang Y, Oyedeji TD, Kühn P, Xu BX (2020) Investigation on temperature-gradient-driven effects in unconventional sintering via non-isothermal phase-field simulation. Scr Mater 186:152–157

    Article  Google Scholar 

  163. Yang Y, Ragnvaldsen O, Bai Y, Yi M, X B, Xu (2019) 3D non-isothermal phase-field simulation of microstructure evolution during selective laser sintering.NPJ Comput Mater, 5:81

  164. Penrose O, Fife PC (1990) Thermodynamically consistent models of phase-field type for the kinetic of phase transitions. Physica D 43(1):44–62

    Article  MathSciNet  MATH  Google Scholar 

  165. Warren JA, Boettinger WJ (1995) Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method. Acta Metall Mater 43(2):689–703

    Article  Google Scholar 

  166. Yang Y, Kühn P, Yi M, Egger H, Xu BX (2020) Non-isothermal phase-field modeling of heat-melt-microstructure-coupled processes during powder bed fusion. JOM 72(4):1719–1733

    Article  Google Scholar 

  167. Yang Y, Yi M, Xu B (2020) Non-isothermal phase-field simulation of microstructure in powder-based additive manufacturing. J Central South Univ 51(11):3019–3031

    Google Scholar 

  168. Wang X, Liu Y, Li L, Yenusah CO, Xiao Y, Chen L (2021) Multi-scale phase-field modeling of layer-by-layer powder compact densification during solid-state direct metal laser sintering. Mater Des 203:109615

    Article  Google Scholar 

  169. Yi M, Chang K, Liang C, Zhou L, Yang Y, Yi X, Xu B (2021) Computational study of evolution and fatigue dispersity of microstructures by additive manufacturing. Chin J Theor Appl Mech 53(12):3265–3275

    Google Scholar 

  170. Schottky G (1965) A theory of thermal diffusion based on the lattice dynamics of a linear chain. Phys Status Solidi B 8(1):357–368

    Article  Google Scholar 

  171. Zhang L, Tonks MR, Millett PC, Zhang Y, Chockalingam K, Biner B (2012) Phase-field modeling of temperature gradient driven pore migration coupling with thermal conduction. Comput Mater Sci 56:161–165

    Article  Google Scholar 

  172. Palmour III H, Hare TM (1987) Rate controlled sintering revisited, pp 17–34

  173. Kingery WD, Berg M (1955) Study of the initial stages of sintering solids by viscous flow, evaporation-condensation, and self-diffusion. J Appl Phys 26(10):1205–1212

    Article  Google Scholar 

  174. Johnson DL, Cutler IB (1963) Diffusion sintering: I, initial stage sintering models and their application to shrinkage of powder compacts. J Am Ceram Soc 46(11):541–545

    Article  Google Scholar 

  175. Kim BN, Suzuki TS, Morita K, Yoshida H, Sakka Y, Matsubara H (2016) Densification kinetics during isothermal sintering of 8YSZ. J Eur Ceram Soc 36(5):1269–1275

    Article  Google Scholar 

  176. Wang J, Raj R (1990) Estimate of the activation energies for boundary diffusion from rate-controlled sintering of pure alumina, and alumina doped with Zirconia or Titania. J Am Ceram Soc 73(5):1172–1175

    Article  Google Scholar 

  177. Coble RL (1961) Sintering crystalline solids. II. experimental test of diffusion models in powder compacts. J Appl Phys, 32(5):793–799

  178. Coble RL (1961) Sintering crystalline solids. I. Intermediate and final state diffusion models. J Appl Phys, 32(5):787–792

  179. Kang SJL, Jung YI (2004) Sintering kinetics at final stage sintering: Model calculation and map construction. Acta Mater 52(15):4573–4578

    Article  Google Scholar 

  180. Zhao J, Harmer MP (1992) Effect of pore distribution on microstructure development: III, model experiments. J Am Ceram Soc 75(4):830–843

    Article  Google Scholar 

  181. Wu H, Liu W, Lin L, Li Y, Tian Z, Nie G, An D, Li H, Wang C, Xie Z, Wu S (2020) Sintering kinetics involving densification and grain growth of 3D printed Ce-ZrO\(_2\)/Al\(_2\)O\(_3\). Mater Chem Phys 239:1–6

    Article  Google Scholar 

  182. Senda T, Bradt RC (1990) Grain growth in sintered ZNO and ZNO-bi\(_2\)o\(_3\) ceramics. J Am Ceram Soc 73(1):106–114

    Article  Google Scholar 

  183. Speight M (1968) Growth kinetics of grain-boundary precipitates. Acta Metall 16(1):133–135

    Article  Google Scholar 

  184. Ardell A (1972) On the coarsening of grain boundary precipitates. Acta Metall 20(4):601–609

    Article  MathSciNet  Google Scholar 

  185. Xiao SQ, Gong MF (2021) Microstructure evolution and sintering kinetics of Ti(C,N)-based cermet. J Phys, 1777(1)

  186. Olevsky EA (1998) Theory of sintering: From discrete to continuum. Mater Sci Eng R Rep 23(2):41–100

    Article  Google Scholar 

  187. Riedel H, Zipse H, Svoboda J (1994) Equilibrium pore surfaces, sintering stresses and constitutive equations for the intermediate and late stages of sintering-II. Diffusional densification and creep. Acta Metall Mater, 42(2):445–452

  188. Green R (1972) A plasticity theory for porous solids. Int J Mech Sci 14(4):215–224

    Article  MATH  Google Scholar 

  189. Shima S, Oyane M (1976) Plasticity theory for porous metals. Int J Mech Sci 18(6):285–291

    Article  Google Scholar 

  190. Riedel H, Kozák V, Svoboda J (1994) Densification and creep in the final stage of sintering. Acta Metall Mater 42(9):3093–3103

    Article  Google Scholar 

  191. Jagota A, Mikeska KR, Bordia RK (1990) Isotropic constitutive model for sintering particle packings. J Am Ceram Soc 73(8):2266–2273

    Article  Google Scholar 

  192. Petersson A, Ågren J (2007) Modelling WC-Co sintering shrinkage-Effect of carbide grain size and cobalt content. Mater Sci Eng, A 452–453:37–45

    Article  Google Scholar 

  193. Kim HG, Gillia O, Bouvard D (2003) A phenomenological constitutive model for the sintering of alumina powder. J Eur Ceram Soc 23(10):1675–1685

    Article  Google Scholar 

  194. Baranov VG, Devyatko YN, Tenishev AV, Khomyakov OV (2015) Phenomenological model of sintering of oxide nuclear fuel with doping admixtures. Phys At Nucl 78(12):1345–1352

    Article  Google Scholar 

  195. Bordia RK, Scherer GW (1988) On constrained sintering-I. Constitutive model for a sintering body. Acta Metall, 36(9):2393–2397

  196. Bordia RK, Scherer GW (1988) On constrained sintering-I. Constitutive model for a sintering body.Acta Metallurgica, 36(9):2393–2397

  197. Bordia RK, Zuo R, Guillon O, Salamone SM, Rödel J (2006) Anisotropic constitutive laws for sintering bodies. Acta Mater 54(1):111–118

    Article  Google Scholar 

  198. Riedel H, Blug B (2002) A comprehensive model for solid state sintering and its application to silicon carbide. Multiscale Deform Fract Mater Struct 84:49–70

    Article  Google Scholar 

  199. Stark S, Neumeister P (2018) A continuum model for sintering processes incorporating elasticity effects. Mech Mater 122:26–41

    Article  Google Scholar 

  200. Zuo R, Rödel J (2004) Temperature dependence of constitutive behaviour for solid-state sintering of alumina. Acta Mater 52(10):3059–3067

    Article  Google Scholar 

  201. Aulbach E, Zuo R, Rödel J (2004) Laser-assisted high-resolution loading dilatometer and applications. Exp Mech 44:71–75

    Article  Google Scholar 

  202. Gillia O, Josserond C, Bouvard D (2001) Viscosity of wc-co compacts during sintering. Acta Mater 49(8):1413–1420

    Article  Google Scholar 

  203. Fang C, Wu W, Lin YJ, Chen YH, Doanh T (2016) On sintering of tiny glass beads in oscillating diametric compressions.Granular Matter 18(4)

  204. Kuz’mov AV, Shtern MB (2005) Mechanics of sintering materials with bimodal pore distribution. I. Effective characteristics of biporous materials and equations for the evolution of pores of different radii. Powder Metall Met Ceram, 44(9-10):429–434

  205. Olevsky E, Skorohod V, Petzow G (1997) Densification by sintering incorporating phase transformations. Scr Mater 37(5):635–643

    Article  Google Scholar 

  206. Hawa T, Zachariah MR (2007) Molecular dynamics simulation and continuum modeling of straight-chain aggregate sintering: development of a phenomenological scaling law. Phys Rev B 76(5):1–9

    Article  Google Scholar 

  207. Zachariah MR, Carrier MJ (1999) Molecular dynamics computation of gas-phase nanoparticle sintering: a comparison with phenomenological models. J Aerosol Sci 30(9):1139–1151

    Article  Google Scholar 

  208. Li F, Pan J, Guillon O, Cocks A (2010) Predicting sintering deformation of ceramic film constrained by rigid substrate using anisotropic constitutive law. Acta Mater 58(18):5980–5988

    Article  Google Scholar 

  209. Wakai F, Shinoda Y (2009) Anisotropic sintering stress for sintering of particles arranged in orthotropic symmetry. Acta Mater 57(13):3955–3964

    Article  Google Scholar 

  210. Guillon O, Aulbach E, Rödel J, Bordia RK (2007) Constrained sintering of alumina thin films: comparison between experiment and modeling. J Am Ceram Soc 90(6):1733–1737

    Article  Google Scholar 

  211. Mokrane A, Boutaous M, Xin S (2018) Process of selective laser sintering of polymer powders: modeling, simulation, and validation. C R Mécanique 346(11):1087–1103

    Article  Google Scholar 

  212. Shen F, Yuan S, Chua CK, Zhou K (2018) Development of process efficiency maps for selective laser sintering of polymeric composite powders: modeling and experimental testing. J Mater Process Technol 254:52–59

    Article  Google Scholar 

  213. Brighenti R, Cosma MP, Marsavina L, Spagnoli A, Terzano M (2021) Laser-based additively manufactured polymers: a review on processes and mechanical models. J Mater Sci 56(2):961–998

    Article  Google Scholar 

  214. Papazoglou EL, Karkalos NE, Karmiris-Obratański P, Markopoulos AP (2022) On the modeling and simulation of SLM and SLS for metal and polymer powders: a review. Arch Comput Methods Eng 29(2):941–973

    Article  Google Scholar 

  215. Hornsby PR, Maxwell AS (1992) Mechanism of sintering between polypropylene beads. J Mater Sci 27(9):2525–2533

    Article  Google Scholar 

  216. Frenkel J (1945) Viscous flow of crystalline bodies under the action of surface tension. J. Phys. (USS R) 9(5):385

    Google Scholar 

  217. Scherer GW (1977) Sintering of low-density glasses: I, theory. J Am Ceram Soc 60(5–6):236–239

    Article  Google Scholar 

  218. Pokluda O, Bellehumeur CT, Vlachopoulos J (1997) Modification of Frenkel’s model for sintering. AIChE J 43(12):3253–3256

    Article  Google Scholar 

  219. Bellehumeur CT, Kontopoulou M, Vlachopoulos J (1998) The role of viscoelasticity in polymer sintering. Rheol Acta 37(3):270–278

    Article  Google Scholar 

  220. Balemans C, Hulsen M, Anderson P (2017) Sintering of two viscoelastic particles: a computational approach. Appl Sci 7(5):516

    Article  Google Scholar 

  221. Andena L, Rink M, Polastri F (2004) Simulation of PTFE sintering: Thermal stresses and deformation behavior. Polym Eng Sci 44(7):1368–1378

    Article  Google Scholar 

  222. Peyre P, Rouchausse Y, Defauchy D, Régnier G (2015) Experimental and numerical analysis of the selective laser sintering (SLS) of PA12 and PEKK semi-crystalline polymers. J Mater Process Technol 225:326–336

    Article  Google Scholar 

  223. Childs TH, Tontowi AE (2001) Selective laser sintering of a crystalline and a glass-filled crystalline polymer: experiments and simulations. Proc Inst Mech Eng B 215(11):1481–1495

    Article  Google Scholar 

  224. Tian X, Peng G, Yan M, He S, Yao R (2018) Process prediction of selective laser sintering based on heat transfer analysis for polyamide composite powders. Int J Heat Mass Transf 120:379–386

    Article  Google Scholar 

  225. Hossain M, Steinmann P (2015) Continuum physics of materials with time-dependent properties. Adv Appl Mech 48:141–259

    Article  Google Scholar 

  226. Hossain M, Possart G, Steinmann P (2009) A small-strain model to simulate the curing of thermosets. Comput Mech 43(6):769–779

    Article  MATH  Google Scholar 

  227. Park S, Shou W, Makatura L, Matusik W, Fu KK (2022) 3D printing of polymer composites: materials, processes, and applications. Matter 5(1):43–76

    Article  Google Scholar 

  228. Hossain M, Possart G, Steinmann P (2010) A finite strain framework for the simulation of polymer curing. Part II. Viscoelasticity and shrinkage. Comput Mech, 46(3):363–375

  229. Hossain M, Possart G, Steinmann P (2009) A finite strain framework for the simulation of polymer curing. Part I: elasticity. Comput Mech 44(5):621–630

    MathSciNet  MATH  Google Scholar 

  230. Maeshima T, Kim Y, Zohdi TI (2021) Particle-scale numerical modeling of thermo-mechanical phenomena for additive manufacturing using the material point method. Comput Particle Mech 8(3):613–623

    Article  Google Scholar 

  231. Shigaki I, Narazaki H (1999) A machine-learning approach for a sintering process using a neural network. Product Plan Control 10(8):727–734

    Article  Google Scholar 

  232. Abreu MG, Pallone EM, Ferreira JA, Campos JV, Sousa RV (2021) Evaluation of machine learning based models to predict the bulk density in the flash sintering process. Mater Today Commun 27:1–5

    Google Scholar 

  233. Mallick A, Dhara S, Rath S (2021) Application of machine learning algorithms for prediction of sinter machine productivity. Mach Learn Appl 6:100186

    Google Scholar 

  234. Tang J, Geng X, Li D, Shi Y, Tong J, Xiao H, Peng F (2021) Machine learning-based microstructure prediction during laser sintering of alumina. Sci Rep 11(1):10724

    Article  Google Scholar 

  235. Kim DH, Zohdi TI (2022) Tool path optimization of selective laser sintering processes using deep learning. Comput Mech 69(1):383–401

    Article  MathSciNet  MATH  Google Scholar 

  236. Renaux M, Méresse D, Pellé J, Thuault A, Morin C, Nivot C, Courtois C (2021) Mechanical modelling of microwave sintering and experimental validation on an alumina powder. J Eur Ceram Soc 41(13):6617–6625

    Article  Google Scholar 

  237. Katz JD (1992) Microwave sintering of ceramics. Annu Rev Mater Sci 22(1):153–170

    Article  Google Scholar 

  238. Guillon O, Gonzalez-Julian J, Dargatz B, Kessel T, Schierning G, Räthel J, Herrmann M (2014) Field-assisted sintering technology/spark plasma sintering: Mechanisms, materials, and technology developments. Adv Eng Mater 16(7):830–849

    Article  Google Scholar 

  239. Biesuz M, Sglavo VM (2019) Flash sintering of ceramics. J Eur Ceram Soc 39(2–3):115–143

    Article  Google Scholar 

  240. Serrazina R, Vilarinho PM, Senos AM, Pereira L, Reaney IM, Dean JS (2020) Modelling the particle contact influence on the Joule heating and temperature distribution during FLASH sintering. J Eur Ceram Soc 40(4):1205–1211

    Article  Google Scholar 

  241. Semenov AS, Trapp J, Nöthe M, Eberhardt O, Kieback B, Wallmersperger T (2021) Thermo-electro-mechanical modeling of spark plasma sintering processes accounting for grain boundary diffusion and surface diffusion. Comput Mech 67(5):1395–1407

    Article  MathSciNet  MATH  Google Scholar 

  242. Guillon O, Elsässer C, Gutfleisch O, Janek J, Korte-Kerzel S, Raabe D, Volkert CA (2018) Manipulation of matter by electric and magnetic fields: toward novel synthesis and processing routes of inorganic materials. Mater Today 21(5):527–536

    Article  Google Scholar 

  243. Hu Y (2021) Recent progress in field-assisted additive manufacturing: materials, methodologies, and applications. Mater Horiz 8(3):885–911

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support from 15th Thousand Youth Talents Program of China, National Science and Technology Major Project (J2019-IV-0014-0082), Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-I-0419G01), and a project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. Xu would acknowledge the funding of German Science Foundation in the framework of SFB TRR270 and SFB TRR361 (Project Number 405553726 and 492661287). This work is partially supported by High Performance Computing Platform of Nanjing University of Aeronautics and Astronautics.

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control for Aerospace Structures & Institute for Frontier Science & Key Lab for Intelligent Nano Materials and Devices of Ministry of Education & College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, 210016, China

    Min Yi, Wenxuan Wang, Ming Xue & Qihua Gong

  2. MIIT Key Lab of Aerospace Information Materials and Physics & College of Physics, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, 211106, China

    Qihua Gong

  3. Institute of Materials Science, Technische Universität Darmstadt, 64287, Darmstadt, Germany

    Bai-Xiang Xu

Authors
  1. Min Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenxuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ming Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qihua Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bai-Xiang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MY:Conceptualization, Resources, Supervision, Project administration, Funding acquisition, Writing—original draft & review & editing. WW: Conceptualization, Investigation, Data curation, Writing—original draft. MX: Conceptualization, Investigation, Data curation, Writing—original draft. QG: Conceptualization, Resources, Supervision, Project administration, Writing—original draft & review & editing. B-XX: Conceptualization, Project administration, Funding acquisition, Writing—review.

Corresponding authors

Correspondence to Min Yi or Qihua Gong.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yi, M., Wang, W., Xue, M. et al. Modeling and Simulation of Sintering Process Across Scales. Arch Computat Methods Eng 30, 3325–3358 (2023). https://doi.org/10.1007/s11831-023-09905-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11831-023-09905-0

Search

Navigation