Three-dimensional adaptive phase field modeling of directional solidification of a binary alloy: 2D-3D transitions

International Journal of Heat and Mass Transfer

Volumn 53, Issue 9-10, 2010, Pages 2272-2283

  Tsai, Y L ^a   Chen, C C ^a   Lan, C W ^a,b  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b INDUSTRIAL TECHNOLOGY RESEARCH INSTITUTE   (Taiwan)

Author keywords

Adaptive; Directional solidification; Morphological instability; Phase field modeling; Three dimensional

Indexed keywords

3D TRANSITION; ADAPTIVE PHASE; ALLOY PROPERTIES; DIRECTIONAL SOLIDIFICATION; MORPHOLOGICAL INSTABILITY; MORPHOLOGICAL TRANSITIONS; PHASE-FIELD MODELING; SIMULATED RESULTS; THREE-DIMENSIONAL (3D);

BINARY ALLOYS; CRYSTALLIZATION; SOLID SOLUTIONS; SOLIDIFICATION;

THREE DIMENSIONAL;

EID: 76749114786     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2009.11.040     Document Type: Article

References (25)

1. Rutter J.W., and Chalmers B. A prismatic substructure formed during solidification of metals. Can. J. Phys. B 31 (1953) 15-39
2. Bower T.F., Brody H.D., and Flemings M.C. Trans. TMS-AIME 236 (1966) 624-634
3. Kurz W., and Fisher D.J. Acta Materialia 29 (1981) 11-20
4. Hunt J.D., and Lu S.-Z. Numerical modeling of cellular/dendritic array growth spacing and structure predictions. Mater. Trans. A 27 (1996) 611-623
5. Ungar L.H., and Brown R.A. Cellular interface morphologies in directional solidification IV the formation of deep cells. Phys. Rev. B 31 (1985) 5931-5940
6. Boettinger W.J., Warren J.A., Beckermann C., and Karma A. Phase-field simulation of solidification. Annu. Rev. Mater. Res. 32 (2002) 163-194
7. Boettinger W.J., Coriell S.R., Greer A.L., Karma A., Kurz W., Rappaz M., and Trivedi R. Solidification microstructures: recent developments, future directions. Acta Mater. 48 (2000) 43-70
8. Warren J.A., and Langer J.S. Prediction of dendritic spacings in a directional-solidification experiment. Phys. Rev. E 47 (1993) 2702-2712
9. Wheeler A.A., Boettinger W.J., and McFadden G.B. Phase-field model for isothermal phase transitions in binary alloys. Phys. Rev. A 45 (1992) 7424-7439
10. Provatas N., Goldenfeld N., and Dantzig J. Efficient computation of dendritic microstructures using adaptive mesh refinement. Phys. Rev. Lett. 80 (1998) 3308-3311
11. Ahmad N.A., Wheeler A.A., Boettinger W.J., and McFadden G.B. Solute trapping and solute drag in a phase-field model of rapid solidfication. Phys. Rev. E 58 (1998) 3436-3450
12. Karma A., and Rappel W.J. Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys. Rev. E 53 (1996) 3017-3020
13. Chen C.C., Tsai Y.L., and Lan C.W. Adaptive phase field simulation of dendritic crystal growth in a forced flow 2D vs. 3D morphologies. Int. J. Heat Mass Transfer 52 (2009) 1158-1166
14. Chen C.C., and Lan C.W. Efficient adaptive three-dimensional phase-field simulation of dendritic crystal growth from various supercoolings using rescaling. J. Crystal Growth 311 (2009) 702-706
15. Karma A. Phase-field formulation for quantitative modeling of alloy solidification. Phys. Rev. Lett. 87 (2001) 115701
16. Lan C.W., Shih C.J., and Lee M.H. Quantitative phase field simulation of deep cells in directional solidification of an alloy. Acta Materialia 53 (2005) 2285-2294
17. Lan C.W., Shih C.J., and Hsu W.T. Long-time scale morphological dynamics near the onset of instability during directional solidification of an alloy. J. Cryst. Growth 264 (2004) 379-384
18. Lan C.W., and Shih C.J. Phase field simulation of non-isothermal free dendritic growth of a binary alloy in a forced flow. J. Cryst. Growth 264 (2004) 472-482
19. Echebarria B., Folch R., Karma A., and Plapp M. Quantitative phase-field model of alloy solidification. Phys. Rev. E 70 (2004) 061604
20. R. Trivedi, Shan Liu, B. Echebarria, A. Karma, Microstructural scaling relationships in cellular patterns, in: Proceeding of the Annual Meeting of the Minerals, Metals & Materials Society, 2005.
21. Meca E., and Plapp M. Phase-field study of the cellular bifurcation in dilute binary alloys. Metal. Mater. Trans. A 38A (2007) 1407-1416
22. Plapp M., and Dejmek M. Stability of hexagonal solidification patterns. Europhys. Lett. 65 2 (2004) 276-282
23. Lan C.W., Liu C.C., and Hsu C.M. An adaptive finite volume method for incompressible heat flow problems in solidification. J. Comput. Phys. 178 (2002) 464-497
24. Lan C.W., Lee M.H., Chuang M.H., and Shih C.J. Phase field modeling of convective and morphological instability during directional solidification of an alloy. J. Cryst. Growth 295 (2006) 202-208
25. Bergeon N., Trivedi R., Billia B., Echebarria B., Karma A., Liu S., Weiss C., and Mangelinck N. Necessity of investigating microstructure formation during directional solidification of transparent alloys in 3D. Adv. Space Res. 36 (2005) 80-85