Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Journal of Materials Science
Published in: Journal of Materials Science 8/2018

04-12-2017 | Interface Behavior

Implementation of a phase field model for simulating evolution of two powder particles representing microstructural changes during sintering

Authors: Sudipta Biswas, Daniel Schwen, Vikas Tomar

Published in: Journal of Materials Science | Issue 8/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this work, we present a multiphysics phase field model for capturing microstructural evolution during solid-state sintering processes. The model incorporates modifications of phase field equations to include rigid-body motion, elastic deformation, and heat conduction. The model correctly predicts consolidation of powder particles during sintering because of two competing mechanisms—neck formation and grain growth. The simulations show that the material undergoes three distinctive stages during the sintering process—stage I where neck or grain boundary between two particles is formed, stage II in which neck length stabilizes and growth or shrinkage of individual particles initiates, and finally stage III with rapid grain growth leading to disappearance of one of the grains. The driving forces corresponding to different mechanisms are found to be dependent on the radius of the particles, curvature at the neck location, surface energy, and grain boundary energy. In addition, variation in temperature is found to significantly influence the microstructure evolution by affecting the diffusivity and grain boundary mobility of the sintered material. The model is also used to compare sintering simulation results in 2D and 3D. It is observed that due to higher curvature in 3D, model predicts faster microstructural evolution in 3D when compared to 2D simulations under identical boundary conditions.
previous article Differentiating between intergranular and transgranular fracture in polycrystalline aggregates
next article Si nanospring films for compliant interfaces

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Langer J, Hoffmann MJ, Guillon O (2009) Direct comparison between hot pressing and electric field-assisted sintering of submicron alumina. Acta Mater 57(18):5454–5465CrossRef
2.
Stanciu LA, Kodash VY, Groza JR (2001) Effects of heating rate on densification and grain growth during field-assisted sintering of α-Al2O3 and MoSi2 powders. Metall Mater Trans A 32(10):2633–2638CrossRef
3.
Chaim R et al (2008) Sintering and densification of nanocrystalline ceramic oxide powders: a review. Adv Appl Ceram 107(3):159–169CrossRef
4.
Dahl P et al (2007) Densification and properties of zirconia prepared by three different sintering techniques. Ceram Int 33(8):1603–1610CrossRef
5.
Guyot P et al (2014) Hot pressing and spark plasma sintering of alumina: discussion about an analytical modelling used for sintering mechanism determination. Scripta Mater 84–85:35–38CrossRef
6.
Groza JR, Cirtis JD, Krämer M (2000) Field assisted sintering of nanocrystalline titanium nitride. J Am Ceram Soc 83(5):1281–1283CrossRef
7.
Groza JR (2000) Sintering activation by electrical field. Mater Sci Eng 287:8CrossRef
8.
Muccillo R, Muccillo ENS (2013) An experimental setup for shrinkage evaluation during electric field-assisted flash sintering: application to yttria-stabilized zirconia. J Eur Ceram Soc 33(3):515–520CrossRef
9.
Grigoryev E (2011) High voltage electric discharge consolidation of tungsten carbide - cobalt powder. In: Cuppoletti J (ed) Nanocomposites with unique properties and applications in medicine and industry. InTech
10.
Groza JR, Garcia M, Schneider JA (2001) Surface effect in field assisted sintering. J Mater Res 16(01):286–292CrossRef
11.
Vanmeensel K et al (2005) Modelling of the temperature distribution during field assisted sintering. Acta Mater 53(16):4379–4388CrossRef
12.
Tiwari D, Basu B, Biswas K (2009) Simulation of thermal and electric field evolution during spark plasma sintering. Ceram Int 35(2):699–708CrossRef
13.
Maizza G et al (2007) Relation between microstructure, properties and spark plasma sintering (SPS) parameters of pure ultrafine WC powder. Sci Technol Adv Mater 8(7–8):644–654CrossRef
14.
Kraft T, Riedel H (2004) Numerical simulation of solid state sintering; model and application. J Eur Ceram Soc 24(2):345–361CrossRef
15.
Olevsky E, Froyen L (2006) Constitutive modeling of spark-plasma sintering of conductive materials. Scripta Mater 55(12):1175–1178CrossRef
16.
Braginsky M, Tikare V, Olevsky E (2005) Numerical simulation of solid state sintering. Int J Solids Struct 42(2):621–636CrossRef
17.
Tikare V, Braginsky M, Olevsky EA (2003) Numerical simulation of solid-state sintering: I, sintering of three particles. J Am Ceram Soc 86(1):49–53CrossRef
18.
Tikare V et al (2010) Numerical simulation of microstructural evolution during sintering at the mesoscale in a 3D powder compact. Comput Mater Sci 48(2):317–325CrossRef
19.
Bjørk R et al (2015) Modeling the microstructural evolution during constrained sintering. J Am Ceram Soc 98(11):3490–3495CrossRef
20.
Boettinger WJ et al (2002) Phase-field simulation of solidification. Annu Rev Mater Res 32(1):163–194CrossRef
21.
Loginova I, Amberg G, Agren J (2001) Phase-field simulations of non-isothermal binary alloy solidification. Acta Mater 49(4):573–581CrossRef
22.
23.
Uehara T, Tsujino T (2005) Phase field simulation of stress evolution during solidification. J Cryst Growth 275(1–2):e219–e224CrossRef
24.
Grafe U et al (2000) Simulations of the initial transient during directional solidification of multicomponent alloys using the phase field method. Modell Simul Mater Sci Eng 8(6):871–879CrossRef
25.
Hu S, Henager CH Jr (2009) Phase-field modeling of void lattice formation under irradiation. J Nucl Mater 394(2–3):155–159CrossRef
26.
Hu SY, Henager CH Jr (2010) Phase-field simulation of void migration in a temperature gradient. Acta Mater 58(9):3230–3237CrossRef
27.
Li Y et al (2011) Phase-field modeling of void evolution and swelling in materials under irradiation. Sci China Phys Mech Astron 54(5):856–865CrossRef
28.
Millett PC et al (2011) Phase-field simulation of irradiated metals: part I: void kinetics. Comput Mater Sci 50(3):949–959CrossRef
29.
Millett PC et al (2009) Void nucleation and growth in irradiated polycrystalline metals: a phase-field model. Modell Simul Mater Sci Eng 17(6):064003CrossRef
30.
Millett PC, Tonks M (2011) Application of phase-field modeling to irradiation effects in materials. Curr Opin Solid State Mater Sci 15(3):125–133CrossRef
31.
Ahmed K et al (2014) Phase field simulation of grain growth in porous uranium dioxide. J Nucl Mater 446(1–3):90–99CrossRef
32.
Anderson MP et al (1984) Computer simulation of grain growth—I. Kinetics. Acta Metall 32(5):783–791CrossRef
33.
Kazaryan A et al (2000) Generalized phase-field model for computer simulation of grain growth in anisotropic systems. Phys Rev B 61(21):14275–14278CrossRef
34.
Tikare V, Holm EA (1998) Simulation of grain growth and pore migration in a thermal gradient. J Am Ceram Soc 81(3):480–484CrossRef
35.
Wang YU (2006) Computer modeling and simulation of solid-state sintering: a phase field approach. Acta Mater 54(4):953–961CrossRef
36.
Deng J (2012) A phase field model of sintering with direction-dependent diffusion. Mater Trans 53(2):385–389CrossRef
37.
Ahmed K et al (2013) Phase field modeling of the effect of porosity on grain growth kinetics in polycrystalline ceramics. Modell Simul Mater Sci Eng 21(6):065005CrossRef
38.
Chanthapan S et al (2012) Sintering of tungsten powder with and without tungsten carbide additive by field assisted sintering technology. Int J Refract Metal Hard Mater 31:114–120CrossRef
39.
Biswas S et al (2016) A study of the evolution of microstructure and consolidation kinetics during sintering using a phase field modeling based approach. Extreme Mech Lett 7:78–89CrossRef
40.
41.
Gaston D et al (2009) MOOSE: A parallel computational framework for coupled systems of nonlinear equations. Nucl Eng Des 239(10):1768–1778CrossRef
42.
Tonks M, Gaston D, Millett P, Andrš D, Talbot P (2012) An object-oriented finite element framework for multiphysics phase field simulations. Comput Mater Sci 51(1):20–29CrossRef
43.
Novascone SR et al (2015) Evaluation of coupling approaches for thermomechanical simulations. Nucl Eng Des 295:910–921CrossRef
44.
Tonks MR et al (2016) Development of a multiscale thermal conductivity model for fission gas in UO2. J Nucl Mater 469:89–98CrossRef
45.
Moelans N, Blanpain B, Wollants P (2008) An introduction to phase-field modeling of microstructure evolution. Calphad 32(2):268–294CrossRef
46.
Verma D et al (2016) Relating interface evolution to interface mechanics based on interface properties. JOM 69(1):30–38CrossRef
47.
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):254–259CrossRef
48.
Zhang R-J et al (2014) Thermodynamic consistent phase field model for sintering process with multiphase powders. Trans Nonferrous Met Soc China 24(3):783–789CrossRef
49.
Permann CJ et al (2016) Order parameter re-mapping algorithm for 3D phase field model of grain growth using FEM. Comput Mater Sci 115:18–25CrossRef
50.
Khachaturyan A-G (1983) Theory of structural transformations in solids. Wiley, Hoboken
51.
Hu SY, Chen LQ (2001) A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater 49(11):1879–1890CrossRef
52.
Yongsheng L et al (2014) Effects of temperature gradient and elastic strain on spinodal decomposition and microstructure evolution of binary alloys. Modell Simul Mater Sci Eng 22(3):035009CrossRef
53.
Tonks M et al (2010) Analysis of the elastic strain energy driving force for grain boundary migration using phase field simulation. Scripta Mater 63(11):1049–1052CrossRef
54.
Zhang L et al (2013) A quantitative comparison between and elements for solving the Cahn–Hilliard equation. J Comput Phys 236:74–80CrossRef
55.
Grujicic M, Zhao H, Krasko GL (1997) Atomistic simulation of Sigma 3 (111) grain boundary fracture in tungsten containing various impurities. Int J Refract Metal Hard Mater 15(5–6):341–355CrossRef
56.
Lassner E, Schubert W-D (1999) Tungsten: properties, chemistry, technology of the element, alloys, and chemical compounds. Springer, New YorkCrossRef
57.
Johnson RA (1982) Point-defect calculations for tungsten. Phys. Rev. B 27(4):2014–2018CrossRef
58.
Lee JS, Minkwitz C, Herzig C (1997) Grain boundary self-diffusion in polycrystalline tungsten at low temperatures. Phys Stat Sol 202:931–940CrossRef
59.
Kumar V (2011) Simulations and modeling of unequal sized particles sintering. In: Department of metallurgical engineering. The University of Utah
60.
Schwen D et al (2017) Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT. Comput Mater Sci 132:36–45CrossRef
61.
Millett PC et al (2012) Phase-field simulation of intergranular bubble growth and percolation in bicrystals. J Nucl Mater 425(1–3):130–135CrossRef
62.
Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140CrossRef
63.
Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys 28(2):258–267CrossRef
64.
Gao Z et al (2012) Kinetics of densification and grain growth of pure tungsten during spark plasma sintering. Metall Mater Trans B 43(6):1608–1614CrossRef
Metadata
Title
Implementation of a phase field model for simulating evolution of two powder particles representing microstructural changes during sintering
Authors
Sudipta Biswas
Daniel Schwen
Vikas Tomar
Publication date
04-12-2017
Publisher
Springer US
Published in
Journal of Materials Science / Issue 8/2018
Print ISSN: 0022-2461
Electronic ISSN: 1573-4803
DOI
https://doi.org/10.1007/s10853-017-1846-3

Other articles of this Issue 8/2018

Journal of Materials Science 8/2018 Go to the issue

Ceramics

The effect of the TiC particle size on the preferred oxidation temperature for self-healing of oxide ceramic matrix materials

Interface Behavior

Shock compression of Cu x Zr100−x metallic glasses from molecular dynamics simulations

Interface Behavior

Atomistic modeling of Mg/Nb interfaces: shear strength and interaction with lattice glide dislocations

Interface Behavior

Anisotropy effect on strain-induced instability during growth of heteroepitaxial films

Interface Behavior

Mesoscale models of interface mechanics in crystalline solids: a review

Interface Behavior

Cell responses to physical forces, and how they inform the design of tissue-engineered constructs for bone repair: a review

Premium Partners

    Image Credits