【作者】 于艳梅；

【导师】 杨根仓；

【作者基本信息】 西北工业大学 ， 材料加工工程， 2002， 博士

【摘要】 本文利用相场法微观组织数值模拟技术，对过冷纯物质和单相二元合金熔体中的枝晶生长过程进行了仿真，解决了这一先进模拟方法在建模和数值计算中遇到的若干关键问题，细致刻划了不同模拟条件下的枝晶生长方式，探讨了过冷熔体中的枝晶生长机制。具体的研究工作和主要结论如下： （1） 考虑界面各向异性和噪声，推导了纯物质和单相二元合金的相场模型，建立了相场模型参数与材料参数的关系。 （2） 基于均匀网格的有限差分法，编制了过冷熔体中枝晶生长的相场法数值模拟程序；提出了计算枝晶尖端速度、尖端半径、二次分支间距、固相率及溶质分配系数的计算方法，并在枝晶尖端半径的直接计算中首次考虑到拟合点数对结果的影响；开发了枝晶形貌、溶质及温度分布的计算机图像生成及动态显示技术。 （3） 研究了空间剖分步长△x、初始晶核半径r₀及界面厚度参数ε对模拟结果的影响，确定了这些关键参数的取值方法。结果表明，空间剖分步长应满足△x≤0.5ε；在保证初始晶核不被熔化的前提下，初始晶核半径可根据材料的毛细长度d₀在一个较大范围内选取；界面厚度参数的取值由无量纲过冷度△、各向异性系数γ、界面动力学系数β、热扩散率D_T综合决定，△、γ越大，获得可靠模拟结果所需要的界面厚度参数越小，而β和D_T则正好相反。 （4） 针对目前相场法可模拟尺度较小的现状，讨论了定温边界条件和Zero-Neumann温度边界条件对模拟结果的影响，并提出应依据不同的计算区域来确定其合适的温度边界条件。当计算区域限于固定尺寸时，Zero-Neumann温度边界条件导致一个逐渐衰减的枝晶生长速度，而定温边界条件导致一个逐渐加快的枝晶生长，前者与铸件中等轴晶生长行为一致，后者与其相反，此时应该选择Zero-Neumann温度边界条件。当计算区域随热扩散场不断增大而扩展时，Zero-Neumann温度边界条件和定温边界条件获得的尖端速度和尖端半径一致，此时两类温度边界条件都是合适的。 （5） 从节约计算量的角度选取毛细长度d₀和热扩散率D_T的取值，模拟了过冷纯物质熔体中的等轴晶生长，研究了噪声、过冷度、界面特性和其它热物性参数对枝晶尘长的影响。结果表明，引入噪声可引发侧向分支，但不改变枝晶尖端 于艳梅 西北卜业人学】：学博士学位论文的稳态行为：低过冷度下，等轴晶周围厚的热扩散层抑制了其侧向分支的生长，呈现无侧向分支的形貌，而在高过冷度下薄的热扩散层有利于侧向分支的生长，等轴晶呈现束状侧向分支的形貌；各向异性趋于增大枝晶尖端生长速度、减小尖端半径，而界面动力学系数（不考虑初始过冷度对界面动力学过冷度的影响）和热扩散率则反之；界面能趋于增大枝晶的横向尺寸并保持界面在扰动下的稳定。 （6）模拟了过冷纯镍和Ni30CU7。合金熔体中的自由枝晶生长，分别获得了它们在不同过冷度下的枝晶生长速度和溶质分配系数，模拟结果与实验结果及理论预测值一致，从而验证了本文的模拟结果。 门)分别在等温和非等温条件下模拟了过冷NiCll合金熔体中的自由枝晶生长，发现人为减小热扩散率可以获得具有完整侧向分支的枝晶。基于人为减小的热扩散率，模拟了不同过冷度下Ni3。C37。合金的枝晶生长方式，结果表明，过冷度对合金枝晶形貌的影响规律与纯物质大体相似。 （8）研究了过冷熔体中界面前沿的溶质分布规律。结果表明，溶质梯度项系数o影响固／液界面处溶质扩散层厚度和扩散层内的溶质分布，但对溶质分配系数k的影响甚弱；在忽略溶质梯度项和基于尖锐界面渐近联系相场模型参数和材料参数的条件下，模拟了＊乙。CU，。合金在不同过冷度下的生长行为，再现了溶质截留效应；同时发现一定厚度的弥散型运动界面上存在一个固、液两相间的化学势梯度，从而引起溶质截留效应，溶质梯度项和在薄界面条件下联系相场模型参数和材料参数并非是再现溶质截留现象的必要条件。 （9）在一定外界冷却速率下，模拟了过冷Ni七ll合金的枝晶生长过程中的再辉现象，获得了不同过冷度下熔体的再辉曲线，再辉曲线随过冷度的变化规律与实验结果定性一致。 （ 0）分别在等温和非等温条件下模拟了过冷 Ni－Cll合金熔体中枝晶的定向生长，分析了两种条件下获得的界面形态和平界面稳定性。结果表明，当过冷度大于20K，等温近似导致偏大的界面生长速度，同时还减小了绝对稳定性平界面的临界速度，故在等温模拟中随着过冷度的增大，其界面形貌呈现平一胞一平转变，并在较大过冷度下获得了绝对稳定的平界面，而在非等温模拟中只出现平一胞转变，高过冷度下的平界面趋于失稳，最终以胞晶方式生长。更多还原

【Abstract】 The dendrite growth in the undercooled melt of pure substance and binary single phase alloy is simulated by the phase-field method,some key problems in modeling and numerical computation of this kind of advanced microstructure simulation method are resolved,the dendrite growth behaviors under the different conditions are finely described,and the mechanism of the dendrite growth in the undercooled melt is discussed. The main research work and conclusions are as follows:(1) The phase-field models of pure substance and binary single phase alloy are derived in consideration of the interface anisotropy and noise,and the relations of the phase-field model parameters and the materials parameters are set up.(2) Based on the Finite Difference method with uniform grids,the phase-field simulation program of the dendrite growth into the undercooled melt are completed;the numerical methods to calculate the dendrite tip velocity,tip radius,secondary arm spacing,solid fraction,and solute partition coefficient are put forward,and the influence of the number of the fitting points on the simulation result is considered for the first time in the direct calculation of dendrite tip radius;the techniques of computer picture builder and dynamic display of dendrite morphology,solute and temperature distribution are developed.(3) The dependence of simulation results on the space step Ax,the initial nucleus radius r0,the interface width parameter ?is studied,and how to choose the values ofthese parameters is settled. The result indicated that for the space step, should be fulfilled;however,the value of initial nucleus radius may be chosen in a large range according to the capillary length d0 with the precondition that initial nucleus can’t be melted;the value of E is determined synthetically by the dimensionless undercooling A,anisotropy parametery,interface kinetic coefficient,thermal diffusivity DT,and the larger A or y,the less is ?that ensure the credible results,but for (1 or DT,it is just on the contrary to A or y.(4) Aiming at the status quo that the size of the phase-field simulation is relatively small,the influence of the constant temperature boundary condition and Zero-Neumann temperature boundary condition on the simulation results is discussed,and the idea that the correct temperature boundary condition should be adopted according to the different computation regions is presented. When the computationregion is limited to an unchanged size,the Zero-Neumann temperature boundary condition leads to a decaying dendrite growth velocity,whereas the constant temperature boundary condition leads to an increasing dendrite growth. The former is consistent with the real equiaxed dendrite growth in castings,but the latter is in contradiction with it. In this case,the Zero-Neumann condition is preferable to the constant temperature condition. When the computation region is enlarged continually with the computational time according to the increasing thermal diffusion scale,the Zero-Neumann and the constant temperature boundary conditions give the consistent results on tip velocities and tip radii. In this case,two types of temperature boundary conditions both are appropriate.(5) After the value of the capillary length do and thermal diffusivity DT is determined on the condition of decreasing computation quantity,the equiaxial crystal growth into the undercooled melt of pure substance is simulated,and the dependence of dendrite growth upon the noise,undercooling,interface characteristic and other thermal-physical parameters is investigated. The results indicated that the noise triggers the growth of side-branches,but doesn’t influence the steady state of the dendrite tip. In the low undercooled melt,the thick thermal diffusion layer surrounding the equiaxial crystal suppresses the growth of its side-branches,so the equiaxial crystal presents the morphology of no side-branches,whereas in the high undercooled melt,the thin thermal diffusion layer is advantageous to the growth of the side-branch,so the equiaxial cr更多还原