Comptes Rendus
no. 11
Computational methods in welding and additive manufacturing/Simulation numérique des procédés de soudage et de fabrication additive
A two-dimensional simulation of grain structure growth within the substrate and the fusion zone during direct metal deposition
Jingwei Zhang1  ; Wei Li1  ; Lei Yan1  ; Frank Liou1
1 Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO, 65401, USA
Comptes Rendus. Mécanique, Volume 346 (2018) no. 11, pp. 1072-1086.

In this paper, a predictive multi-scale model based on a cellular automaton (CA)-finite element (FE) method has been developed to simulate thermal history and microstructure evolution during metal solidification for the Direct Metal Deposition (DMD) process. The macroscopic FE calculation that is validated by thermocouple experiment is developed to simulate the transient temperature field and cooling rate of single layer and multiple layers. In order to integrate the different scales, a CA–FE coupled model is developed to combine with thermal history and simulate grain growth. In the mesoscopic CA model, heterogeneous nucleation sites, grain growth orientation and rate, epitaxial growth, re-melting of pre-existing grains, metal addition, grain competitive growth, and columnar to equiaxed phenomena are simulated. The CA model is able to show the entrapment of neighboring cells and the relationship between undercooling and the grain growth rate. The model predicts the grain size, and the morphological evolution during the solidification phase of the deposition process. The developed “decentered polygon” growth algorithm is appropriate for the non-uniform temperature field. Finally, the single and multiple-layer DMD experiment is conducted to validate the characteristics of grain features in the simulation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2018.08.003
Mots clés : Finite element, Cellular automata, Grain morphology, Direct metal deposition, Decentered polygon algorithm
Jingwei Zhang 1 ; Wei Li 1 ; Lei Yan 1 ; Frank Liou 1

1 Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO, 65401, USA 
@article{CRMECA_2018__346_11_1072_0,
     author = {Jingwei Zhang and Wei Li and Lei Yan and Frank Liou},
     title = {A two-dimensional simulation of grain structure growth within the substrate and the fusion zone during direct metal deposition},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {1072--1086},
     publisher = {Elsevier},
     volume = {346},
     number = {11},
     year = {2018},
     doi = {10.1016/j.crme.2018.08.003},
     language = {en},
}
TY  - JOUR
AU  - Jingwei Zhang
AU  - Wei Li
AU  - Lei Yan
AU  - Frank Liou
TI  - A two-dimensional simulation of grain structure growth within the substrate and the fusion zone during direct metal deposition
JO  - Comptes Rendus. Mécanique
PY  - 2018
SP  - 1072
EP  - 1086
VL  - 346
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crme.2018.08.003
LA  - en
ID  - CRMECA_2018__346_11_1072_0
ER  - 
%0 Journal Article
%A Jingwei Zhang
%A Wei Li
%A Lei Yan
%A Frank Liou
%T A two-dimensional simulation of grain structure growth within the substrate and the fusion zone during direct metal deposition
%J Comptes Rendus. Mécanique
%D 2018
%P 1072-1086
%V 346
%N 11
%I Elsevier
%R 10.1016/j.crme.2018.08.003
%G en
%F CRMECA_2018__346_11_1072_0
Jingwei Zhang; Wei Li; Lei Yan; Frank Liou. A two-dimensional simulation of grain structure growth within the substrate and the fusion zone during direct metal deposition. Comptes Rendus. Mécanique, Volume 346 (2018) no. 11, pp. 1072-1086. doi : 10.1016/j.crme.2018.08.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.08.003/

[1] M. Rappaz Modelling of microstructure formation in solidification processes, Int. Mater. Rev., Volume 34 (1989) no. 3, pp. 93-124

[2] M.P. Anderson; D.J. Srolovitz; G.S. Grest; P.S. Sahni Computer simulation of grain growth, I: kinetics, Acta Metall., Volume 32 ( May 1984 ) no. 5, pp. 783-791

[3] D.J. Srolovitz; M.P. Anderson; P.S. Sahni; G.S. Grest Computer simulation of grain growth, II: grain size distribution, topology, and local dynamics, Acta Metall., Volume 32 (1984) no. 5, pp. 793-802

[4] Y. Saito; M. Enomoto Monte Carlo simulation of grain growth, ISIJ Int., Volume 32 (1992) no. 3, pp. 267-274

[5] L.-Q. Chen Phase-Field Models for Microstructure Evolution, 2002

[6] C.E. Krill; L.-Q. Chen Computer simulation of 3-D grain growth using a phase-field model, Acta Mater., Volume 50 (2002) no. 12, pp. 3059-3075

[7] B. Böttger; J. Eiken; I. Steinbach Phase field simulation of equiaxed solidification in technical alloys, Acta Mater., Volume 54 (2006) no. 10, pp. 2697-2704

[8] N. Moelans; B. Blanpain; P. Wollants An introduction to phase-field modeling of microstructure evolution, Calphad, Volume 32 ( Jun. 2008 ) no. 2, pp. 268-294

[9] S. Sahoo; K. Chou Phase-field simulation of microstructure evolution of Ti–6Al–4V in electron beam additive manufacturing process, Addit. Manuf., Volume 9 (2016), pp. 14-24

[10] J. Nandy; H. Sarangi; S. Sahoo Microstructure evolution of Al–Si–10Mg in direct metal laser sintering using phase-field modeling, Adv. Manuf., Volume 6 (2018) no. 1, pp. 107-117

[11] M. Rappaz; C.-A. Gandin Probabilistic modelling of microstructure formation in solidification processes, Acta Metall. Mater., Volume 41 (1993) no. 2, pp. 345-360

[12] C.-A. Gandin; M. Rappaz A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes, Acta Metall. Mater., Volume 42 (1994) no. 7, pp. 2233-2246

[13] C.-A. Gandin; J.-L. Desbiolles; M. Rappaz; P. Thevoz A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures, Metall. Mater. Trans. A, Volume 30 (1999) no. 12, pp. 3153-3165

[14] A. Choudhury; K. Reuther; E. Wesner; A. August; B. Nestler; M. Rettenmayr Comparison of phase-field and cellular automaton models for dendritic solidification in Al–Cu alloy, Comput. Mater. Sci., Volume 55 (2012), pp. 263-268

[15] X. Doré Modelling of microsegregation in ternary alloys: application to the solidification of Al–Mg–Si, Acta Mater., Volume 48 (2000) no. 15, pp. 3951-3962

[16] D.J. Jarvis; S.G.R. Brown; J.A. Spittle Modelling of non-equilibrium solidification in ternary alloys: comparison of 1D, 2D, and 3D cellular automaton-finite difference simulations, Mater. Sci. Technol., Volume 16 (2000) no. 11–12, pp. 1420-1424 (2000)

[17] M. Grujicic; G. Cao; R.S. Figliola Computer simulations of the evolution of solidification microstructure in the LENSTM rapid fabrication process, Appl. Surf. Sci., Volume 183 (2001), pp. 43-57

[18] S.M. Kelly; S.L. Kampe Microstructural evolution in laser-deposited multilayer Ti–6Al–4V builds, part I: microstructural characterization, Metall. Mater. Trans. A, Volume 35 (2004) no. 6, pp. 1869-1879

[19] S.M. Kelly; S.L. Kampe Microstructural evolution in laser-deposited multilayer Ti–6Al–4V builds, part II: thermal modeling, Metall. Mater. Trans. A, Volume 35 (2004) no. 6, pp. 1869-1879

[20] W. Tan; Y.C. Shin Multi-scale modeling of solidification and microstructure development in laser keyhole welding process for austenitic stainless steel, Comput. Mater. Sci., Volume 98 ( Feb. 2015 ), pp. 446-458

[21] S. Chen; G. Guillemot; C.-A. Gandin 3D coupled cellular automaton (CA)-finite element (FE) modeling for solidification grain structures in gas tungsten arc welding (GTAW), ISIJ Int., Volume 54 (2014) no. 2, pp. 401-407

[22] S. Chen; G. Guillemot; C.-A. Gandin Three-dimensional cellular automaton-finite element modeling of solidification grain structures for arc-welding processes, Acta Mater., Volume 115 (2016), pp. 448-467

[23] A. Zinoviev; O. Zinovieva; V. Ploshikhin; V. Romanova; R. Balokhonov Evolution of grain structure during laser additive manufacturing. Simulation by a cellular automata method, Mater. Des., Volume 106 (2016), pp. 321-329

[24] G. Lütjering Influence of processing on microstructure and mechanical properties of (α+β) titanium alloys, Mater. Sci. Eng. A, Volume 243 (1998) no. 1–2, pp. 32-45

[25] J.N. Reddy; D.K. Gartling The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC Press, Taylor & Francis Group, Boca Raton, FL, USA, 2010

[26] L.C.A.R.L. Phillips Laser Beam Propagation Through Random Media, vol. PM152, SPIE Press Book Monograph, 2005

[27] M. Alimardani; E. Toyserkani; J.P. Huissoon A 3{D} dynamic numerical approach for temperature and thermal stress distributions in multilayer laser solid freeform fabrication process, Opt. Lasers Eng., Volume 45 (2007) no. 12, pp. 1115-1130

[28] C. Lampa; A.F.H. Kaplan; J. Powell; C. Magnusson An analytical thermodynamic model of laser welding, J. Phys. D, Appl. Phys., Volume 30 (1997) no. 9, p. 1293

[29] H. Liu; T. Sparks Modeling and verification of temperature distribution and residual stress in laser aided metal deposition process, 4th Intelligent Systems Center, Volume 1 (2012), pp. 1-7

[30] W. Oldfield A quantitative approach to casting solidification: freezing of cast iron, Trans. Amer. Soc. Met., Volume 59 (1966), p. 945

[31] W. Kurz; D.J. Fisher Appendix 7 and 8, Fundamentals of Solidification, Trans. Tech. Publication, 1992, pp. 226-246

[32] W. Kurz; D.J. Fisher Appendix 9, Fundamentals of Solidification, Trans. Tech. Publication, 1992, pp. 247-260

[33] R. Chen; Q. Xu; B. Liu A modified cellular automaton model for the quantitative prediction of equiaxed and columnar dendritic growth, J. Mater. Sci. Technol., Volume 30 (2014) no. 12, pp. 1311-1320

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Recent advances in the metallurgy of aluminium alloys. Part I: Solidification and casting

Philippe Jarry; Michel Rappaz

C. R. Phys (2018)

Modeling of solidification: Grain structures and segregations in metallic alloys

Charles-André Gandin

C. R. Phys (2010)

Control of melt convection by a travelling magnetic field during the directional solidification of Al–Ni alloys

Kader Zaïdat; Nathalie Mangelinck-Noël; René Moreau

C. R. Méca (2007)