近年来发展起来的PFM模型根据"溶质捕捉"和"溶质牵引"两种机制对金属及合金快速凝固过程进行数学描述及模拟, 较好地反映了金属凝固的物理本质. 介绍了PFM模型发展过程、研究现状及理论模型, 并对发展前景进行了展望.
参考文献
[1] | 周尧和;胡壮麒.凝固技术[M].北京:机械工业出版社,1998:10. |
[2] | Fife P C.Models for phase separation and their mathematics[J].Electronic Journal of Differential Equations,2000(48):1-26. |
[3] | Caginalp G;Xie W .Phase-field and sharp-interface alloy models[J].Physical Review E,1993,48:1897-1909. |
[4] | Caginalp G .Phase field models and sharp interface limits: some differences in subtle situations[J].Rocky Mountain Journal of Mathematics,1991,21(02):603-616. |
[5] | Fabbri M;Voller V R .The phase-field in the sharpinterface limit: a comparison between model parameters[J].Journal of Computational Physics,1997,130:256. |
[6] | Kessler D A;Koplik J;Levine H .Pattern selection in fingered growth phenomena[J].Advances in Physics,1988,37:255-339. |
[7] | Langer J S .Instabilities and pattern formation in crystal growth[J].Reviews of Modern Physics,1980,52:1-28. |
[8] | Taylor J E;Cahn J W .Link anisotropic sharp and diffuse surface motion laws via gradient flows[J].Journal of Statistical Physics,1992,77:183-197. |
[9] | Vladimrova N;Malagoli A;Mauri R .Diffusion driven phase separation of deeply quenched mixtures[J].Physical Review E,1998,58(06):7691-7699. |
[10] | Charach C;Zaltzman B .Interfacial kinetics effect in planar solidification problems without initial undercooling[J].Mathematical Methods in the Applied Sciences,1994,4:331-354. |
[11] | Collet P .Thermodynamic limit of the ginzburg-landau equation[J].Nonlinearity,1994,7:1175-1190. |
[12] | Levermore C D;Oliver M .The complex Ginzburg-Landau equation as a model problem[J].Lectures in Applied Mathematics,1996,31:141-189. |
[13] | Wheeler A A;Bottinger W J;McFadden G B .Phase-field model for isothermal phase transitions in binary alloys[J].Physical Review A,1992,45(10):7424-7439. |
[14] | Wheeler A A;McFadden G B;Bottinger W J .Phase-field model for solidification of a eutectic alloy[J].Proceedings of the Royal Society of London,1996,A452:495-525. |
[15] | Bates P;Fife P .Spectral comparison principles for the Cahn-Hilliard and phase field equations,and time scales for coarsening[J].Physica D-Nonlinear Phenomena,1990,43:335-348. |
[16] | Warren J A;Boettinger W J;Caginalp G .A phase-field model of dendritic growth in a binary alloy[J].Acta Metallurgica et Materialia,1995,A43:689-698. |
[17] | Steinbach I.;Nestler B.;Seesselberg M.;Prieler R.;Schmitz GJ.;Rezende JLL.;Pezzolla F. .A PHASE FIELD CONCEPT FOR MULTIPHASE SYSTEMS[J].Physica, D. Nonlinear phenomena,1996(3):135-147. |
[18] | Conti M. .Thermal and chemical diffusion in the rapid solidification of binary alloys[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,2000(1):642-650. |
[19] | Conti M. .Interface dynamics, instabilities, and solute bands in rapid directional solidification[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,1998(2 Pt.b):2071-2078. |
[20] | Losert W;Stillman D A;Cummins H Z et al.Selection of doublet cellular patterns in directional solidification through spatially periodic perturbations[J].Physical Review E,1998,58(06):7492-7506. |
[21] | Ahmad NA.;Boettinger WJ.;McFadden GB.;Wheeler AA. .Solute trapping and solute drag in a phase-field model of rapid solidification[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,1998(3 Pt.b):3436-3450. |
[22] | Kim SG.;Suzuki T.;Kim WT. .Phase-field model for binary alloys[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,1999(6 Pt.b):7186-7197. |
[23] | Conti M .Planar isothermal solidification from an undercooled melt: unsteady solute segregation studied with the phase-field model[J].Physical Review E,1997,55:701-707. |
[24] | Caginalp G .An analysis of a phase field model of a free boundary[J].Archive For Rational Mechanics and Analysis,1986,92:205-245. |
[25] | Caginalp G .Stefan and Hele-Shaw type models as asymptotic limits of phase field equations[J].Physical Review A,1989,39:887-896. |
[26] | Caginalp G;Chen X .Convergence of the phase field model to its sharp interface limits[J].European Journal of Applied Mathematics,1998,9:417-445. |
[27] | Caginalp G;Jones J .A derivation and analysis of phase field models of thermal alloys[J].Annals of Physics,1995,237:66-107. |
[28] | Caginalp G;Fife P C .Phase-field methods for interfacial boundaries[J].Physical Review B,1986,33(11):7792-7795. |
[29] | Wang S L;Sekerka R F;Wheeler A A et al.Thermodynamically-consistent phase-field models for solidification[J].Physica D-Nonlinear Phenomena,1993,69:189-200. |
[30] | Fried E;Gutin M E .Continuum theory of thermally induced phase transitions based on an order parameter[J].Physica D-Nonlinear Phenomena,1993,68:326-343. |
[31] | Conti M .Solute trapping in directional solidification at high speed: a 1-D study with a phase-field model[J].Physical Review E,1997,56:3717-3720. |
[32] | Charach C;Keizman Y .Solute trapping effects in planar isothermal solidification of dilute binary alloys[J].PHYSICAL REVIEW E,1997,54:588-599. |
[33] | Weeler A A;Bottinger W J;Mcfadden .Phase-field model of solute trapping during solidification[J].Physical Review E,1993,47(03):1893-1909. |
[34] | Kaplan T;Aziz M J;Gray L J .Application of Onsager's reciprocity relations to interface motion during phase transformations[J].Journal of Chemical Physics,1989,90:1133-1140. |
[35] | Aziz M J;Bottinger W J .On the transition from short-range diffusion-limited to collision-limited growth in alloy solidification[J].Acta Metallurgica Et Materialia,1994,42(02):527-537. |
[36] | Collins J B;Levine H .Diffuse interface model of diffusion-limited crystal growth[J].Physical Review B,1985,31:6119-6122. |
[37] | Bechhoefer J;Lowen H;Tuckerman L S .Dynamical mechanism for the formation of metastable phases[J].Physical Review Letters,1991,67:1266-1269. |
[38] | Ryo Kobayshi .Modeling and numerical simulation of dendritic crystal growth[J].Physica D-Nonlinear Phenomena,1993,63:410-423. |
[39] | Wang S L;Sekerka R F .Computation of the dendritic operating state at large supercoolings by the phase field model[J].Physical Review E,1996,53(04):3760-3776. |
[40] | Karma A;Rappel W J .Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics[J].Physical Review E,1996,53:3017. |
[41] | Wang S L;Sekerka R F .Algorithms for phase field computation of the dentritic operating state at large supercoolings[J].Journal of Computational Physics,1996,127:110-117. |
[42] | Wheeler A A;Murray B T;Schaefer R J .Computation of dendrites using a phase field model[J].Physica D-Nonlinear Phenomena,1993,66:243-262. |
[43] | Karma A .Phase-field model of eutectic growth[J].Physical Review E,1994,49(03):2245-2250. |
[44] | Elder K R;Drolet F;Kosterlitz J M et al.Directional solidification in two and three dimensions[J].Physical Review Letters,1994,72:677. |
[45] | K. R. Elder;J. D. Gunton;Martin Grant .Nonisothermal eutectic crystallization[J].Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics,1996(6):6476-6484. |
[46] | Drolet F.;Grant M.;Kosterlitz JM.;Elder KR. .Phase-field modeling of eutectic growth[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,2000(6 Pt.b):6705-6720. |
[47] | Mcffadden G B;Wheeler A A;Braun R J et al.Phase-field models for anistropic interface[J].Physical Review E,1993,48(03):2016-2024. |
[48] | Beckermann C;Diepers H J;Steinbach I et al.Modeling melt convection in phase-field simulations of solidification[J].Journal of Computational Physics,1999,154:468-496. |
[49] | H.-J. DIEPERS;C. BECKERMANN;I. STEINBACH .SIMULATION OF CONVECTION AND RIPENING IN A BINARY ALLOY MUSH USING THE PHASE-FIELD METHOD[J].Acta materialia,1999(13):3663-3678. |
[50] | Tong X;Beckermann C;Karma A .Velocity and shape selections of dendritic crystals in a forced flow[J].Physical Review E,2000,61:R49-R52. |
[51] | Voller V R;Beckermann C .Approximate models of microsegregation with coarsening[J].Metallurgical and Materials Transactions A:Physical Metallurgy and Materials Science,1999,30:3016-3019. |
[52] | Conti M .Solidification of binary alloys: thermal effects studied with the phase-field model[J].Physical Review E,1997,55:765-771. |
[53] | Bates P W;Fife P C .Dynamics of nucleation for the Cahn-Hilliard equation[J].SIAM Journal of Applied Mathematics,1993,53:990-1008. |
[54] | Langer J S .Theory of spinodal decomposition in alloys[J].Annals of Physics,1971,65:53-86. |
[55] | Cahn J W .Phase separation by spinodal decomposition in isotropic systems[J].Journal of Chemical Physics,1965,42:93-99. |
[56] | Koga T;Kawasaki K .Spinodal decomposition in binary fluids: Effects of hydrodynamic interactions[J].Physical Review A,1991,44:R817. |
[57] | Grant C P .Spinodal decomposition for the Cahn-Hilliard equation[J].Communications in Partial Differential Equations,1993,18:453-490. |
[58] | Eyre D J .Systems of Cahn-Hilliard equations[J].SIAM Journal of Applied Mathematics,1993,53:1686-1712. |
[59] | Pego R L .Front migration in the nonlinear Cahn-Hilliard equation[J].Proceedings of the Royal Society of London,1989,A422:261-278. |
[60] | Brush L N;Sekerka R F .A numerical study of two-dimensional growth forms in the presence of anisotropic growth kinetics[J].Journal of Crystal Growth,1989,96:419-441. |
[61] | Norio Akaiwa;D. I. Meiron .Two-dimensional late-stage coarsening for nucleation and growth at high-area fractions[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,1996(1):R13-R16. |
[62] | Meakin P .Formation of fractal clusters and networks by irreversible diffusion-limited aggregation[J].Physical Review Letters,1983,51:1119-1124. |
[63] | AlSunaidi A.;Gonzalez AE.;Blaisten-Barojas E.;Lach-hab M. .Cluster-cluster aggregation in binary mixtures[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,2000(1):550-556. |
[64] | Bogoyavlenskiy VA.;Chernova NA. .Diffusion-limited aggregation: A revised mean-field approach[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,2000(5 Pt.b):5422-5428. |
[65] | Gade D M;Joy M P .Self-organized criticality in dynamics without branch[J].Physical Review E,1998,57(05):5019-5022. |
上一张
下一张
上一张
下一张
计量
- 下载量()
- 访问量()
文章评分
- 您的评分:
-
10%
-
20%
-
30%
-
40%
-
50%