相场方法模拟合金无序—有序相转变和晶粒长大
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摘要
相场法作为材料微观组织演变的一种模拟方法已经被越来越广泛的应用到各种常见的微组织演化的模拟当中。它通过场变量简单明了地表征出任何一种复杂组织的几何形貌、可以在相同的物理和数学模型下模拟诸如:形核、长大和粗化等不同的现象。因此它是计算机模拟各种微组织演化的首选方法,例如模拟凝固以及枝晶形成、Ostwald熟化、失稳分解、有序-无序相转变、马氏体相变、晶粒长大等等。为此,本论文探讨了宏观和微观相场法在晶粒长大和合金沉淀相析出两种微观组织演化中的具体应用。
首先,应用宏观相场方法采用多序参量唯象晶粒长大相场模型,对单相多晶材料中最基本的显微组织演化过程之一晶粒长大进行二维模拟,初步验证了相场方法的有效性,结果表明模型符合经典长大规律,晶粒尺寸分布是时间相关的,并可以由Weibull函数很好的描述。在此基础上探讨了势阱参数λ和能量梯度系数K_i的大小对晶粒长大和晶粒尺寸分布的影响,得到结论:λ值越大越会抑制晶粒生长,随着K_i的增大,晶粒生长加速,并且所形成的晶界也越厚。其次,应用微观相场法在原子层面上对合金有序-无序相转变进行仿真,以Al_3Li合金作为具体研究对象,对其δ′相析出过程进行简单研究,探讨了δ′相沉淀机制、得出其粗化行为随有序相长大而发生。
Phase-field method, as a method of simulating material microstructure evolution, has been applied to all common microstructure evolution simulation. It can simply characterize the geometric shape of any complex organization also can simulate different microstructure evolution such as: nucleation growth and coarsening in the same physical and mathematical model. So phase-field method has been the preferred method for computer simulating material microstructure evolution, just like solidification and dendrite growth, Ostwald pirening, Spinodal decomposition, order-disorder phase transformation, Martensitic transformation, grain growth and so on. In this thesis, we study Macro-phase field and Micro-phase field in the field of grain growth and alloy precipitation precipitates microstructure evolution.
First, the normal grain growth under the condition of single phase was simulated in 2D by means of the macro-phase field method. The effectiveness of the phase-field method was proved. The results show that the phase-field model accords with the classic model of growth, and grain size distribution which can well described by Weibull function is time-dependent. On this basis, we study grain size and grain size distribution which are affected by the value of the potential well parametersγand the energy gradient coefficient K_i. Conclusion: first, theγ-value greater inhibit grain growth, with the increase of K_i, grain growth accelerated, and by theformation of grain boundaries and the more thick. Second, the atomic-scale computer simulation of order-disorder phase transformation is conducted under the micro-phase field model. We choose Al_3Li alloy as a specificstudy and researchδ′precipitation precipitates. We discuss the mechanism ofδ′precipitation and find the coarsening behavior ofδ′is taken place as the same time as the growth of order-phase.
首先,应用宏观相场方法采用多序参量唯象晶粒长大相场模型,对单相多晶材料中最基本的显微组织演化过程之一晶粒长大进行二维模拟,初步验证了相场方法的有效性,结果表明模型符合经典长大规律,晶粒尺寸分布是时间相关的,并可以由Weibull函数很好的描述。在此基础上探讨了势阱参数λ和能量梯度系数K_i的大小对晶粒长大和晶粒尺寸分布的影响,得到结论:λ值越大越会抑制晶粒生长,随着K_i的增大,晶粒生长加速,并且所形成的晶界也越厚。其次,应用微观相场法在原子层面上对合金有序-无序相转变进行仿真,以Al_3Li合金作为具体研究对象,对其δ′相析出过程进行简单研究,探讨了δ′相沉淀机制、得出其粗化行为随有序相长大而发生。
Phase-field method, as a method of simulating material microstructure evolution, has been applied to all common microstructure evolution simulation. It can simply characterize the geometric shape of any complex organization also can simulate different microstructure evolution such as: nucleation growth and coarsening in the same physical and mathematical model. So phase-field method has been the preferred method for computer simulating material microstructure evolution, just like solidification and dendrite growth, Ostwald pirening, Spinodal decomposition, order-disorder phase transformation, Martensitic transformation, grain growth and so on. In this thesis, we study Macro-phase field and Micro-phase field in the field of grain growth and alloy precipitation precipitates microstructure evolution.
First, the normal grain growth under the condition of single phase was simulated in 2D by means of the macro-phase field method. The effectiveness of the phase-field method was proved. The results show that the phase-field model accords with the classic model of growth, and grain size distribution which can well described by Weibull function is time-dependent. On this basis, we study grain size and grain size distribution which are affected by the value of the potential well parametersγand the energy gradient coefficient K_i. Conclusion: first, theγ-value greater inhibit grain growth, with the increase of K_i, grain growth accelerated, and by theformation of grain boundaries and the more thick. Second, the atomic-scale computer simulation of order-disorder phase transformation is conducted under the micro-phase field model. We choose Al_3Li alloy as a specificstudy and researchδ′precipitation precipitates. We discuss the mechanism ofδ′precipitation and find the coarsening behavior ofδ′is taken place as the same time as the growth of order-phase.
引文
[1]P.Haasen,Phase Transformation in Materials,Materials Science and Technology-A Comprehensive Treatment,Ser.eds.:R.W.Cahn,P.Haasen,VCH,Weinheim,1991,vol 5,324.
[2]D.Raabe,Computational Materials Science:The Simulation of Materials,Microstructural and Properties,Wiley-VCH,1998,6.
[3]Y.Wang and L.Q.Chen,Methods in Materials Research,John Wiley & Sons.Inc.2000,2a.3,1
[4]Nasr M.G.The Emerging Role of Multiscale Modeling in Nano-and Micro-mechanics of Materials,J.Comp.Meth.Engr.Science,CMES,2002,3(2),147.
[5]Hobenberg,H.W.Theory of dynamic critical phenomena,Rev.Mod.Phys,1977,49,435.
[6]Elder,K.Langevin simulations of nonequilibrium phenomena,Comp.Phys,1993,7,27
[7]Wang,Y.Modeling of dynamical evolution of micr/mesoscopic morphlogical paterns in coherent phase transformations,Computer simulation in materials science,eds:H.O.Kirchner,Kluwer Academic Publishers,1996,325.
[8]Chen,L.Q.Computer Simulation of coupled grain growth in two-phase systems,J.Am.Ceram.Soc.1996,79,1163.
[9]Cahn,J.W.On spinodal decomposition,Acta Metall,1961,9,795.
[10]J.D.Gunton,Phase transformations and critical phenomena,eds:C.Domb,Academic press,1983,vol.8,267.
[11]Y.Wang and L.Q.Chen,Methods in Materials Research,John Wiley & Sons.Inc.,2000,2a.3,
[12]C.Shen Development of computational tools for microstructural engineering of Ni-based superalloys by means of the phase field method,Materials Design Approaches and Experiences,2001
[13]Y.H.Wen Microstructure.elolution during the α_2 to α_2+O transformation in Ti-Al-Nb alloys,Acta Mater,2000,48,4125
[14]Andrei Kazaryan Mordeling of micro structural evolution in solids,the dissertation for Ph.D,2001,47.
[15]Y.U.Wang Nanoscale phase field microelaticity theory of dislocations:model and 3D simulation,Acta Mater,2001,49,1847.
[16]荆涛.凝固过程数值模拟[M].北京:电子工业出版社,2002.5.
[17]武利民.涂料技术基础[M].北京:化学工业出版社,1999.63-65.
[18]于艳梅,杨根仓.过冷熔体中枝晶生长的相场法数值模拟.物理学报,2001.50:2423-2428
[19]Khachaturyan A.G.Microscopic theory of diffusion in crystalline solid solutions and the time evolution of the diffuse scattering of x-ray and thermal neutrons,Soviet Phys.Solid State,1968,9,2040.
[20]Chen,L.Q.On formation of virtual ordered phase along a phase decomposition path,Phys.Rev.B,1991,44,4681.
[21]Mebed A M,Koyama T,Miyazaki T.Spinodal decomposition existence of the β Ti-Cr binary alloy computer simulation of the real alloy system and experimental investigations[J].Comptutational Materials Science,1999,14(1-4):318-322.
[22]罗伯 D[德],项金钟,吴兴惠.计算材料学[M].北京:化学工业出版社,2002.
[23]Koyama T,Miyazaki T,Mebed M.Computer Simulations of Decomposition in Real Alloy Systems Based on the Modified Khachatuyran Diffusion Equation[J].Metallurgical and Materials Transactions,1995,A26(10):2617-2623.
[24]Rubin G,Khachaturyan A G Three-Dimensional model of precipitation of ordered intermetallics[J].Acta.Materialia,1999,47(7):1995-2002.
[25]Poduri R,Chen L Q.Computer simulation of morphological evolution and coarsening of δ'(Al_3Li)precipitates in Al-Li alloys[J].Acta.Materialia,1998,46(11):3915-3928.
[26]赵宇宏.合金沉淀过程原子尺度计算机模拟[D].西安:西北工业大学博士论文,2003.
[27]李晓玲.δ′相沉淀过程原子层面计算机研究[D].西安:西北工业大学博士论文.2002.
[28]Wen Y H,Wang Y,Chen L Q.Influence of an applied strain field on microstructural evolution during the α_2→O phase transformation in Ti-Al-Nb system [J].Acta.materialia,2001,49(1):13-20.
[29]Chen Qing,Ma Ning,Wu Kaisheng,et al.Quantitative phase field modeling of diffusion-controlled precipitate growth and dissolutionin Ti-Al-V[J].ScdptaMaterialia,2004,50(4):471-476.
[30]Miyazaki T,Koyama T,Kozakal T.Computer simulation of the phase transformation in real alloy systems based on the phase field method[J].Materials Science and Engineering,2001,A312(1-2):38-49.
[31]Poduri R,Chen L Q.Computer-simulation of atomic ordenng and compositional clustering in the pseudobinary Ni_3Al-Ni_3V system[J].Acta.Materialia,1998,46(5):1719-1729.
[32]Fan D,Chen L Q.Solute segregation and antiphase boundary motion in a B2 single phase Acta Mater,1999,47:3695-3703.
[33]Fan D,Chen L Q,Chen S P.Effect of grain boundary width on grain growth in a diffuseinterface field model.Materials Science and Engineering,1997,A238:78-84.
[34]Calm J W,Hilliard J E.Free energy of a nonuniform system.I.Interfacial free energy.Journal of Chemical Physics,1958,28(2):258-267.
[35]D.N.Fan,Computer simulation of micro structural evolution in multiphase materials using a diffuse-interface field model,the dissertation for Ph.D,1996,112.
[36]Khachaturyan A G.Theory of structural transformations in solids.New York:Wiley,1983:139
[37]Chen L Q,Khachaturyan A G.Formation of virtual ordered states along a phase-decomposition path.Phys.Rev.B,1991;44:4681-4684
[38]Chen L Q,Khachaturyan A G.Kinetics of virtual phase formation during precipitation of ordered intermetallics.Phys.Rev.B,1992;46:5899-5905
[39]Chen L Q,Khachaturyan A G.Dynamics of simultaneous ordering and phase separation and effect of long-range Coulomb interactions.Phys.Rev.Lett.,1993;70:1477-1480
[40]Chen L O.Thermodynamics and kinetics of order-disorder processes derived from the cluster-activation method and microscopic diffusion theory.Phys.Rev.B,1994;49:3791-3799
[41]Chen L Q,Wang Y Z.The continuum field approach to modeling microstructural evolution.JOM.,1996,12:13-18
[42]Chen L Q,Khachaturyan A G.Computer simulation of structural transformations during precipitation of an ordered intermetallic phase.Acta metall,mater.,1991;39:2533-2551
[43]Chen L Q,Khachaturyan A G.Computer simulation of decomposition reactions accompanied by a congruent ordering of the second kind.Scripta Metall,1991;25:61-66
[44]Poduri R,Chen L Q.Non-classical Nucleation Theory of Ordered Intermetallic Precipitates-Application to the Al-LiAlloy.Acta mater.,1996;44:4253-4259
[45]Poduri R,Chen L Q.Computer simulation of the kinetics of order-disorder and phase separation duringprecipitation of δ'(Al3Li)in Al-Li alloys.Acta mater.,1997;45:245-255
[46]Poduri R,Chen L Q.Computer simulation of morphological evolution and coarsening of δ'(Al3Li)precipitates in Al-Li alloys.Acta mater.,1998;46:3915-3928
[47]Poduri R,Chen L Q.Computer-simulation of atomic ordering and compositional clustering in the pseudobinary.Ni3Al-Ni3V system.Acta mater.,1998;46:1719-1729
[48]Chen L Q,Simmons J A.Microscopic master equation approach to diffusional transformations in inhomogeneous systems-single site approximation and direct exchange mechanism.Acta mater.,1994;42:2943-2954
[49]Wang Y Z,Chen L Q,Khachaturyan A G.Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap.Acta metall,mater.,1993;41:279-296
[50]Wang Y Z,Chen L Q,Khachaturyan A G.Shape evolution of a precipitate during strain-induced coarsening A computer simulation.Scripta Metall.,1991;25:1387-1392
[511 Chen L Q,Wang Y Z,Khachaturyan A G.Transformation-induced elastic strain effect on the precipitation kinetics of ordered intermetallics.Phil.Mag.Lett.,1991;64:241-251
[52]Chen L Q.A computer simulation technique for spinodal decomposition and ordering in ternary systems.Seripta Metall.,1993;29:683-688
[53]Chen L Q.Computer simulation of spinodal decomposition in ternary systems.Acta metall,mater.,1994;42:3503,3513
[54]Oono Y,Puri S.Computationally efficient modeling of ordering of quenched phases.Phys Rev Lett,1987;58:836-839
[55]Holms B L,Einegard W C.Grain growth in zone-refined Tin.Acta Metall,1959,7:411-414.
[56]王超.不同初始组织的晶粒长大仿真与理论研究:博士学位论文.北京:北京科技大学,2003.
[57]秦湘阁.不同算法和参数的晶粒长大Potts模型研究:博士学位论文.北京:北京科技大学,2003.
[58]Hillert M.On the theory of normal and abnormal grain growth.Acta Metall,1965,13(3):227-238.
[59]毛卫民,赵新兵.金属的再结晶与晶粒长大.北京:冶金工业出版社,1994
[60]Fayad W,Thompson C V,Frost H J.Steady-state grain size distributions resulting from grain growth in two dimensions,Script Mater,1999,40(10):1199-1204.
[2]D.Raabe,Computational Materials Science:The Simulation of Materials,Microstructural and Properties,Wiley-VCH,1998,6.
[3]Y.Wang and L.Q.Chen,Methods in Materials Research,John Wiley & Sons.Inc.2000,2a.3,1
[4]Nasr M.G.The Emerging Role of Multiscale Modeling in Nano-and Micro-mechanics of Materials,J.Comp.Meth.Engr.Science,CMES,2002,3(2),147.
[5]Hobenberg,H.W.Theory of dynamic critical phenomena,Rev.Mod.Phys,1977,49,435.
[6]Elder,K.Langevin simulations of nonequilibrium phenomena,Comp.Phys,1993,7,27
[7]Wang,Y.Modeling of dynamical evolution of micr/mesoscopic morphlogical paterns in coherent phase transformations,Computer simulation in materials science,eds:H.O.Kirchner,Kluwer Academic Publishers,1996,325.
[8]Chen,L.Q.Computer Simulation of coupled grain growth in two-phase systems,J.Am.Ceram.Soc.1996,79,1163.
[9]Cahn,J.W.On spinodal decomposition,Acta Metall,1961,9,795.
[10]J.D.Gunton,Phase transformations and critical phenomena,eds:C.Domb,Academic press,1983,vol.8,267.
[11]Y.Wang and L.Q.Chen,Methods in Materials Research,John Wiley & Sons.Inc.,2000,2a.3,
[12]C.Shen Development of computational tools for microstructural engineering of Ni-based superalloys by means of the phase field method,Materials Design Approaches and Experiences,2001
[13]Y.H.Wen Microstructure.elolution during the α_2 to α_2+O transformation in Ti-Al-Nb alloys,Acta Mater,2000,48,4125
[14]Andrei Kazaryan Mordeling of micro structural evolution in solids,the dissertation for Ph.D,2001,47.
[15]Y.U.Wang Nanoscale phase field microelaticity theory of dislocations:model and 3D simulation,Acta Mater,2001,49,1847.
[16]荆涛.凝固过程数值模拟[M].北京:电子工业出版社,2002.5.
[17]武利民.涂料技术基础[M].北京:化学工业出版社,1999.63-65.
[18]于艳梅,杨根仓.过冷熔体中枝晶生长的相场法数值模拟.物理学报,2001.50:2423-2428
[19]Khachaturyan A.G.Microscopic theory of diffusion in crystalline solid solutions and the time evolution of the diffuse scattering of x-ray and thermal neutrons,Soviet Phys.Solid State,1968,9,2040.
[20]Chen,L.Q.On formation of virtual ordered phase along a phase decomposition path,Phys.Rev.B,1991,44,4681.
[21]Mebed A M,Koyama T,Miyazaki T.Spinodal decomposition existence of the β Ti-Cr binary alloy computer simulation of the real alloy system and experimental investigations[J].Comptutational Materials Science,1999,14(1-4):318-322.
[22]罗伯 D[德],项金钟,吴兴惠.计算材料学[M].北京:化学工业出版社,2002.
[23]Koyama T,Miyazaki T,Mebed M.Computer Simulations of Decomposition in Real Alloy Systems Based on the Modified Khachatuyran Diffusion Equation[J].Metallurgical and Materials Transactions,1995,A26(10):2617-2623.
[24]Rubin G,Khachaturyan A G Three-Dimensional model of precipitation of ordered intermetallics[J].Acta.Materialia,1999,47(7):1995-2002.
[25]Poduri R,Chen L Q.Computer simulation of morphological evolution and coarsening of δ'(Al_3Li)precipitates in Al-Li alloys[J].Acta.Materialia,1998,46(11):3915-3928.
[26]赵宇宏.合金沉淀过程原子尺度计算机模拟[D].西安:西北工业大学博士论文,2003.
[27]李晓玲.δ′相沉淀过程原子层面计算机研究[D].西安:西北工业大学博士论文.2002.
[28]Wen Y H,Wang Y,Chen L Q.Influence of an applied strain field on microstructural evolution during the α_2→O phase transformation in Ti-Al-Nb system [J].Acta.materialia,2001,49(1):13-20.
[29]Chen Qing,Ma Ning,Wu Kaisheng,et al.Quantitative phase field modeling of diffusion-controlled precipitate growth and dissolutionin Ti-Al-V[J].ScdptaMaterialia,2004,50(4):471-476.
[30]Miyazaki T,Koyama T,Kozakal T.Computer simulation of the phase transformation in real alloy systems based on the phase field method[J].Materials Science and Engineering,2001,A312(1-2):38-49.
[31]Poduri R,Chen L Q.Computer-simulation of atomic ordenng and compositional clustering in the pseudobinary Ni_3Al-Ni_3V system[J].Acta.Materialia,1998,46(5):1719-1729.
[32]Fan D,Chen L Q.Solute segregation and antiphase boundary motion in a B2 single phase Acta Mater,1999,47:3695-3703.
[33]Fan D,Chen L Q,Chen S P.Effect of grain boundary width on grain growth in a diffuseinterface field model.Materials Science and Engineering,1997,A238:78-84.
[34]Calm J W,Hilliard J E.Free energy of a nonuniform system.I.Interfacial free energy.Journal of Chemical Physics,1958,28(2):258-267.
[35]D.N.Fan,Computer simulation of micro structural evolution in multiphase materials using a diffuse-interface field model,the dissertation for Ph.D,1996,112.
[36]Khachaturyan A G.Theory of structural transformations in solids.New York:Wiley,1983:139
[37]Chen L Q,Khachaturyan A G.Formation of virtual ordered states along a phase-decomposition path.Phys.Rev.B,1991;44:4681-4684
[38]Chen L Q,Khachaturyan A G.Kinetics of virtual phase formation during precipitation of ordered intermetallics.Phys.Rev.B,1992;46:5899-5905
[39]Chen L Q,Khachaturyan A G.Dynamics of simultaneous ordering and phase separation and effect of long-range Coulomb interactions.Phys.Rev.Lett.,1993;70:1477-1480
[40]Chen L O.Thermodynamics and kinetics of order-disorder processes derived from the cluster-activation method and microscopic diffusion theory.Phys.Rev.B,1994;49:3791-3799
[41]Chen L Q,Wang Y Z.The continuum field approach to modeling microstructural evolution.JOM.,1996,12:13-18
[42]Chen L Q,Khachaturyan A G.Computer simulation of structural transformations during precipitation of an ordered intermetallic phase.Acta metall,mater.,1991;39:2533-2551
[43]Chen L Q,Khachaturyan A G.Computer simulation of decomposition reactions accompanied by a congruent ordering of the second kind.Scripta Metall,1991;25:61-66
[44]Poduri R,Chen L Q.Non-classical Nucleation Theory of Ordered Intermetallic Precipitates-Application to the Al-LiAlloy.Acta mater.,1996;44:4253-4259
[45]Poduri R,Chen L Q.Computer simulation of the kinetics of order-disorder and phase separation duringprecipitation of δ'(Al3Li)in Al-Li alloys.Acta mater.,1997;45:245-255
[46]Poduri R,Chen L Q.Computer simulation of morphological evolution and coarsening of δ'(Al3Li)precipitates in Al-Li alloys.Acta mater.,1998;46:3915-3928
[47]Poduri R,Chen L Q.Computer-simulation of atomic ordering and compositional clustering in the pseudobinary.Ni3Al-Ni3V system.Acta mater.,1998;46:1719-1729
[48]Chen L Q,Simmons J A.Microscopic master equation approach to diffusional transformations in inhomogeneous systems-single site approximation and direct exchange mechanism.Acta mater.,1994;42:2943-2954
[49]Wang Y Z,Chen L Q,Khachaturyan A G.Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap.Acta metall,mater.,1993;41:279-296
[50]Wang Y Z,Chen L Q,Khachaturyan A G.Shape evolution of a precipitate during strain-induced coarsening A computer simulation.Scripta Metall.,1991;25:1387-1392
[511 Chen L Q,Wang Y Z,Khachaturyan A G.Transformation-induced elastic strain effect on the precipitation kinetics of ordered intermetallics.Phil.Mag.Lett.,1991;64:241-251
[52]Chen L Q.A computer simulation technique for spinodal decomposition and ordering in ternary systems.Seripta Metall.,1993;29:683-688
[53]Chen L Q.Computer simulation of spinodal decomposition in ternary systems.Acta metall,mater.,1994;42:3503,3513
[54]Oono Y,Puri S.Computationally efficient modeling of ordering of quenched phases.Phys Rev Lett,1987;58:836-839
[55]Holms B L,Einegard W C.Grain growth in zone-refined Tin.Acta Metall,1959,7:411-414.
[56]王超.不同初始组织的晶粒长大仿真与理论研究:博士学位论文.北京:北京科技大学,2003.
[57]秦湘阁.不同算法和参数的晶粒长大Potts模型研究:博士学位论文.北京:北京科技大学,2003.
[58]Hillert M.On the theory of normal and abnormal grain growth.Acta Metall,1965,13(3):227-238.
[59]毛卫民,赵新兵.金属的再结晶与晶粒长大.北京:冶金工业出版社,1994
[60]Fayad W,Thompson C V,Frost H J.Steady-state grain size distributions resulting from grain growth in two dimensions,Script Mater,1999,40(10):1199-1204.