Modeling solid-state sintering with externally applied pressure: a geometric force approach

Shaohua Chen; Yaopengxiao Xu; Yang Jiao; Shaohua Chen; Yaopengxiao Xu; Yang Jiao

doi:10.3934/matersci.2017.1.75

AIMS Materials Science

2017, Volume 4, Issue 1: 75-88. doi: 10.3934/matersci.2017.1.75

Previous Article Next Article

Research article

Modeling solid-state sintering with externally applied pressure: a geometric force approach

Materials Science and Engineering, Arizona State University, Tempe, AZ 85287

Received: 18 November 2016 Accepted: 21 December 2016 Published: 29 December 2016

Solid-state sintering is one of the most widely used material processing technologies in modern manufacturing. The preponderance of previous computer simulations focused on free sintering (without externally applied pressures), in which the morphology evolution and densification in the system are driven by surface energy reduction. In this work, we develop an efficient algorithm to simulate solid-state sintering with hot pressing by explicitly considering interfacial diffusion as well as rigid body movement under external pressure. Particle movements including both translations and rotations are taken into account in the model, which are directed by the associated local stress state in the sintering system. A novel “geometric force” is also introduced to stochastically model geometrically necessary plastic deformations of the sintering particles to accommodate the initial fast densification due to the applied pressure. Subsequent evolution of the overall morphology and inter-particle connections are mainly controlled by interfacial energy minimization, while coarsening is considered in the later sintering stages. The utility of our method is illustrated by sintering 2D compacts of polydisperse circular particles and equal-sized elliptical particles. Significant coarsening occurs in the polydisperse particle system, while no significant grain growth is observed in the equal-sized ellipse system.
- hot pressing sintering,
- rigid-body motion,
- plastic flow,
- interfacial diffusion,
- geometric force
Citation: Shaohua Chen, Yaopengxiao Xu, Yang Jiao. Modeling solid-state sintering with externally applied pressure: a geometric force approach[J]. AIMS Materials Science, 2017, 4(1): 75-88. doi: 10.3934/matersci.2017.1.75

Related Papers:

Abstract

Solid-state sintering is one of the most widely used material processing technologies in modern manufacturing. The preponderance of previous computer simulations focused on free sintering (without externally applied pressures), in which the morphology evolution and densification in the system are driven by surface energy reduction. In this work, we develop an efficient algorithm to simulate solid-state sintering with hot pressing by explicitly considering interfacial diffusion as well as rigid body movement under external pressure. Particle movements including both translations and rotations are taken into account in the model, which are directed by the associated local stress state in the sintering system. A novel “geometric force” is also introduced to stochastically model geometrically necessary plastic deformations of the sintering particles to accommodate the initial fast densification due to the applied pressure. Subsequent evolution of the overall morphology and inter-particle connections are mainly controlled by interfacial energy minimization, while coarsening is considered in the later sintering stages. The utility of our method is illustrated by sintering 2D compacts of polydisperse circular particles and equal-sized elliptical particles. Significant coarsening occurs in the polydisperse particle system, while no significant grain growth is observed in the equal-sized ellipse system.

References

[1]	German RM (1996) Sintering Theory and Practice, New Work: Wiley.
[2]	Olevsky EA, Tikare V, Garino T (2006) Multi-Scale Study of Sintering: A Review. J Am Ceram Soc 89: 1914–1922. doi: 10.1111/j.1551-2916.2006.01054.x
[3]	Kuczynski GC (1949) Self-diffusion in sintering of metallic particles. AIME TRANS 185: 169–178.
[4]	Chawla N, Deng X (2005) Microstructure and mechanical behavior of porous sintered steels. Mater Sci Eng A 390: 98–112. doi: 10.1016/j.msea.2004.08.046
[5]	Coble RL (1961) Sintering Crystalline Solids. I. Intermediate and Final State Diffusion Models. J Appl Phys 32: 787–792.
[6]	Olevsky EA (1998) Theory of sintering: from discrete to continuum. Mater Sci Eng R Rep 23: 41–100. doi: 10.1016/S0927-796X(98)00009-6
[7]	James P (1972) Fundamental Aspects of the Consolidation of Powders. Part II. Powder Met Int 4: 193–198.
[8]	Coble RL, Ellis JS (1963) Hot-Pressing Alumina—Mechanisms of Material Transport. J Am Ceram Soc 46: 438–441. doi: 10.1111/j.1151-2916.1963.tb11771.x
[9]	Coble RL (1970) Diffusion Models for Hot Pressing with Surface Energy and Pressure Effects as Driving Forces. J Appl Phys 41: 4798–4807. doi: 10.1063/1.1658543
[10]	Wilson T, Shewmon P (1966) The role of interfacial diffusion in the sintering of copper. AIME MET SOC TRANS 236: 48–58.
[11]	Wilkinson DS, Ashby MF (1975) Pressure sintering by power law creep. Acta Metall 23: 1277–1285. doi: 10.1016/0001-6160(75)90136-4
[12]	Kang SJ (2004) Sintering: densification, grain growth and microstructure, Butterworth-Heinemann.
[13]	Oliver J, Oller S, Cante JC (1996) A plasticity model for simulation of industrial powder compaction processes. Int J Solids Struct 33: 3161–3178. doi: 10.1016/0020-7683(95)00249-9
[14]	Gethin DT, Tran VD, Lewis RW, et al. (1994) Investigation of powder compaction processes. Int J Powder Metall 30: 385–398.
[15]	Chtourou H, Guillot M, Gakwaya A (2002) Modeling of the metal powder compaction process using the cap model. Part I. Experimental material characterization and validation. Int J Solids Struct 39: 1059–1075.
[16]	Ransing RS, Gethin DT, Khoei AR, et al. (2000) Powder compaction modelling via the discrete and finite element method. Mater Design 21: 263–269. doi: 10.1016/S0261-3069(99)00081-3
[17]	Martin CL, Bouvard D, Shima S (2003) Study of particle rearrangement during powder compaction by the Discrete Element Method. J Mech Phys Solids 51: 667–693. doi: 10.1016/S0022-5096(02)00101-1
[18]	Chtourou H, Gakwaya A, Guillot M (2002) Modeling of the metal powder compaction process using the cap model. Part II: Numerical implementation and practical applications. Int J Solids Struct 39: 1077–1096.
[19]	Aydin I, Briscoe BJ, Ozkan N (1997) Modeling of Powder Compaction: A Review. MRS Bull 22: 45–51.
[20]	Ozkan N (1994) Compaction and sintering of ceramic powders [PhD thesis]. London: Imperial College London.
[21]	Chen S, Xu Y, Jiao Y (2016) Modeling morphology evolution and densification during solid-state sintering via kinetic Monte Carlo simulation. Model Simul Mater Sci Eng 24: 85003. doi: 10.1088/0965-0393/24/8/085003
[22]	Aydin I, Briscoe BJ, Ozkan N (1997) Modeling of Powder Compaction: A Review. MRS Bull 22: 45–51.
[23]	Janssen H (1895) Versuche über getreidedruck in silozellen. Zeitschr d Vereines deutscher Ingenieure 39: 1045–1049.
[24]	Walker D (1966) An approximate theory for pressures and arching in hoppers. Chem Eng Sci 21: 975–997. doi: 10.1016/0009-2509(66)85095-9
[25]	Kadiri MS, Michrafy A, Dodds JA (2005) Pharmaceutical powders compaction: Experimental and numerical analysis of the density distribution. Powder Technol 157: 176–182. doi: 10.1016/j.powtec.2005.05.025
[26]	Michrafy A, Kadiri MS, Dodds JA (2003) Wall Friction and its Effects on the Density Distribution in the Compaction of Pharmaceutical Excipients. Chem Eng Res Des 81: 946–952.
[27]	Shang C, Sinka IC, Pan J (2011) Constitutive Model Calibration for Powder Compaction Using Instrumented Die Testing. Exp Mech 52: 903–916.
[28]	Hew P (1997) Geometric Moments, Central Moments and Statistics.
[29]	Mukundan R, Ramakrishnan KR (1998) Moment functions in image analysis theory and applications, London: World scientific.
[30]	Teh CH, Chin RT (1988) On image analysis by the methods of moments. IEEE Trans Pattern Anal Mach Intell 10: 496–513. doi: 10.1109/34.3913
[31]	Honarvar B, Paramesran R, Lim CL (2014) Image reconstruction from a complete set of geometric and complex moments. Signal Process 98: 224–232. doi: 10.1016/j.sigpro.2013.11.037
[32]	Teague MR (1980) Image analysis via the general theory of moments. J Opt Soc Am 70: 920–930. doi: 10.1364/JOSA.70.000920
[33]	Swinkels FB, Wilkinson DS, Arzt E, et al. (1983) Mechanisms of hot-isostatic pressing. Acta Metall 31: 1829–1840. doi: 10.1016/0001-6160(83)90129-3
[34]	Brewin PR, Coube O, Doremus P, et al. (2007) Modelling of Powder Die Compaction, New York: Springer Science & Business Media.
[35]	Walker DM (1966) An approximate theory for pressures and arching in hoppers. Chem Eng Sci 21: 975–997. doi: 10.1016/0009-2509(66)85095-9
[36]	Nedderman RM (2005) Statics and Kinematics of Granular Materials, London: Cambridge University Press.
[37]	Ramqvist L (1966) Theories of Hot Pressing. Powder Metall 9: 1–25. doi: 10.1179/pom.1966.9.17.001
[38]	Atkinson HV, Davies S (2000) Fundamental aspects of hot isostatic pressing: An overview. Metall Mater Trans A 31: 2981–3000. doi: 10.1007/s11661-000-0078-2
[39]	Zhang Y, Xia C, Ni M (2012) Simulation of sintering kinetics and microstructure evolution of composite solid oxide fuel cells electrodes. Int J Hydrog Energy 37: 3392–3402. doi: 10.1016/j.ijhydene.2011.11.020
[40]	Tikare V, Braginsky M, Olevsky EA (2003) Numerical Simulation of Solid-State Sintering: I, Sintering of Three Particles. J Am Ceram Soc 86: 49–53. doi: 10.1111/j.1151-2916.2003.tb03276.x
[41]	Wakai F, Shinoda Y, Akatsu T (2004) Methods to calculate sintering stress of porous materials in equilibrium. Acta Mater 52: 5621–5631. doi: 10.1016/j.actamat.2004.08.021
[42]	Metropolis N, Rosenbluth AW, Rosenbluth MN, et al. (1953) Equation of State Calculations by Fast Computing Machines. J Chem Phys 21: 1087–1092. doi: 10.1063/1.1699114
[43]	Jiao Y, Stillinger FH, Torquato S (2011) Nonuniversality of density and disorder in jammed sphere packings. J Appl Phys 109: 013508.

Reader Comments

Your name:*

Email:*
© 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)