镁基合金自由枝晶生长的相场模拟研究

利用定量相场模型, 以Mg-0.5 wt.%Al合金为例模拟了基面((0001)面)内镁基合金的等温自由枝晶生长过程. 通过研究该合金体系数值模拟的收敛性, 获得了最优化值耦合参数λ = 5.5及网格宽度Δx/W₀ = 0.4, 并在该参数下系统研究了各向异性强度和过饱和度对枝晶尖端生长速度、尖端曲率半径、Péclet数及稳定性常数σ^* 的影响. 结果表明, 由微观可解性理论得到的稳定性系数σ^* 与ε₆ 拟合值σ^*≅ ε₆ ^1.81905, 更接近理想值σ ^* (ε₆) ≅ε₆ ^1.75. 此外, 当过饱和度Ω < 0.6时, 稳定性系数σ ^* 不随ε₆ 的变化而变化, 而当Ω > 0.6时, 稳定性系数σ ^* 随着ε₆ 的增加而减小. 这反映了枝晶的生长由扩散控制向动力学控制的转变. 随着过饱和度的增加, 枝晶形貌由雪花状枝晶向圆状枝晶转变.     

相场法模拟多元合金过冷熔体中的枝晶生长

在二元合金相场模型研究的基础上,进行扩展获得了多元合金相场模型.以Al-Si-Mg三元合金为例,采用该相场模型实现了逼真地模拟多元合金凝固过程的等轴枝晶生长,得到了二次或更高次晶臂生长等复杂的枝晶形貌.随着第三组元Mg含量的减少,枝晶的二次枝晶越发达,枝晶中溶质的偏析越严重,枝晶尖端的生长速率和半径越大,与丁二腈-丙酮体系中枝晶尖端生长速率、半径随溶质浓度变化关系的理论计算和实验结果相符合.另外,枝晶初生晶臂中心的溶质浓度最低,在被二次晶臂包围的界面区域的溶质浓度最高;固液界面区域具有较大的浓度梯度,其中枝晶尖端前沿的梯度最大.关键词：相场法多元合金凝固过程枝晶生长     

过冷熔体中枝晶生长的相场模拟

本文利用相场方法对过冷镍熔体中枝晶生长过程进行了模拟,发现在过冷度低于 200 K时,生长速度与过冷度之间近似呈幂函数关系,当过冷度高于 200 K时,生长速度与过冷度之间基本呈线性关系。伴随着速度/过冷度之间关系的变化,枝晶尖端半径/过冷度的关系则呈现先减小后增加的趋势,并在 200 K时达到最小。本文还将模拟结果与实验值和经典LKT理论进行了比较,对上述关系转变的物理机制进行了分析。     

过冷熔体中枝晶生长的相场法数值模拟

利用相场法模拟了过冷纯金属熔体中的枝晶生长过程,研究了各向导性、界面动力学、热扩散和界面能对枝晶生长的影响.结果表明,热噪声可以促发侧向分支的形成,但不影响枝晶尖端的稳态行为;随着各向异性的增加,枝晶尖端生长速度增加,尖端半径减小;当界面动力学系数减小及在界面动力学系数小于1的条件下热扩散系数减小时,枝晶尖端生长速度随之减小,而尖端半径相应增大;界面能趋于增大枝晶尺度并保持界面在扰动下的稳定,界面能越大,形成侧向分支的趋势越小关键词：过冷枝晶生长相场法数值模拟     

三维枝晶生长的相场法数值模拟研究

基于薄界面限制、耦合界面能各向异性的相场模型,采用动态计算区域的加速算法,对纯物质的三维枝晶生长进行了定量模拟,真实再现了枝晶的生长过程.对枝晶尖端进行了剖切分析,表明主枝截面上各向异性没有主枝方向各向异性明显;对枝晶尖端生长速度、尖端半径、Peclet数及临界稳定性参数σ^*进行模拟计算,并与同条件下报道值进行了对比分析,两者符合良好,并得到了与结晶理论相一致的枝晶生长规律,证实了相场方法模拟三维空间枝晶生长可行有效.关键词：相场方法枝晶生长微观组织三维数值模拟     

强迫对流影响二元合金非等温凝固枝晶生长的相场法模拟

在二元合金相场模型的研究基础上,建立了耦合溶质场、温度场和流场的相场模型,采用Simple算法求解质量和动量守恒方程,用交替隐式有限差分法求解温度控制方程,模拟了流场作用下二元合金等温和非等温凝固过程中枝晶的生长过程,研究了流场对枝晶生长形貌、溶质场和温度场分布情况的影响,将流场作用下二元合金等温和非等温凝固枝晶生长过程进行比较,分析了由于凝固潜热的释放对流场作用下凝固枝晶生长的影响．关键词：相场法对流非等温凝固枝晶生长     

热扰动对过冷熔体中二次枝晶生长影响的相场法模拟

用相场法模拟了过冷纯物质二次枝晶的生长过程,并定量地研究了过冷度、各向异性、热扰动振幅等参数对二次枝晶的影响. 通过加入热扰动,相场法能更真实地模拟过冷熔体中二次枝晶的生长,计算得到的二次枝晶间距和幅值与由Wentzel_Kramers_Brillouin方法得到的结果符合较好. 模拟结果表明,过冷度和各向异性对二次枝晶有较大影响. 当过冷度增大时,二次枝晶间距随之减小;当各向异性增大时,二次枝晶间距随之增大,但二次枝晶幅值则随之减小. 热扰动振幅主要影响二次枝晶幅值,而对二次枝晶间距影响较弱.关键词：相场法热扰动枝晶生长二次枝晶     

相场法模拟NiCu合金非等温凝固枝晶生长

利用相场模型与溶质场、温度场进行耦合计算,以Ni-40.83%Cu合金为例模拟了二元合金枝晶生长过程.系统研究相场模型中相场和温度场耦合强度对枝晶形貌和浓度分布的影响.模拟结果表明:随着耦合强度的增加,相场受温度场的影响加大,界面前沿变得不稳,扰动被放大,主枝上出现了二次枝晶.同时,枝晶尖端的生长速率增大,而枝晶尖端的曲率半径减小,枝晶前沿的溶质富集现象也更严重;另外,计算结果与Ivantsov理论符合较好.关键词：相场法NiCu合金枝晶生长Ivantsov理论     

相场方法模拟铝合金三维枝晶生长

以相场模型为基础,采用宏微观耦合方法和界面捕获液态方法对铝合金枝晶生长进行模拟计算.为解决试样全场微观计算的困难,采取宏微观耦合的计算方法,试样整体计算温度场,而微观组织计算只在一个确定的宏观单元内进行,宏观微观计算交替耦合进行.在不改变相场模型的条件下,提出界面捕获液态计算方法.赋值计算单元界面标志,只对界面处的单元求解相场变量,当枝晶生长时,捕获液态单元为界面从而推进界面,并对捕获到的单元校正相场变量.通过界面捕获液态方法加速相场模型的计算,实现了铝合金试件局部三维单晶粒和多晶粒的模拟.对模拟结果与实关键词：相场方法液态捕获微观组织枝晶     

自由枝晶生长相场模型的自适应有限元法模拟

采用自适应有限元方法求解了相场模型的控制方程,利用自适应有限元法在求解效率和精度上的优势,模拟了计算域较大,界面层厚度较薄的情况下镍过冷熔体中单个完整等轴晶的演化过程,使相场模型模拟结果更接近于真实物理模型,并探讨了二次枝晶臂的演化机理.模拟结果表明,二次枝晶臂的演化主要由热扩散控制,并受随机扰动影响,在四个象限内呈现出不对称生长.同时,受枝晶臂生长时排出的潜热积聚作用,同一侧的枝晶臂对新的二次枝晶臂的产生有促进作用.此外,二次枝晶臂出现合并、缩颈熔断、轴向熔化和径向熔化等四种粗化方式.关键词：自由枝晶生长相场自适应有限元法     

A phase-field model for simulating various spherulite morphologies of semi-crystalline polymers

A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.     

Effect of solidification temperature range on the dendritic growth mode

Electromagnetic levitation technique was used to undercool bulk samples of Co-20% Cu and Co-60% Cu alloys and high undercoolings up to 303 and 110 K were achieved,respectively.The dendritic growth velocities were measured as a function of undercooling.The dendrite growth velocity of the Co-20% Cu alloy was much higher than that of the Co-60% Cu alloy.The experimental data were analyzed on the basis of the LKT/BCT dendritic growth model by taking into account non-equilibrium interface kinetics.It has been re...     

Phase-field lattice-Boltzmann investigation of dendritic evolution under different flow modes

ABSTRACT

Numerical modelling offers an effective method to investigate the effect of convection on dendritic growth; however, the current numerical approach to modelling convection behaviour is simplified, e.g. only simulating a shear flow by setting a constant inlet velocity and a zero-velocity-gradient outlet boundary condition. In this work, based on a phase-field lattice-Boltzmann approach, the effect of various flow modes on dendritic growth is investigated by introducing an external force term to induce flow. Numerical tests (2-D and 3-D) validate that the results according to the force-induced flow agree well with those by the velocity-imposed flow. Intricate convection effects under complex boundary conditions are discussed in detail. Furthermore, this force-induced flow mode allows additional freedom by eliminating the restriction on the initial position of the nuclei, which provides new ways to the microstructure modelling under complex convection.     

Influence of isothermal approximation on the phase-field simulation of directional growth in undercooled melt

By using the phase-field approach,we have simulated the directional growth of alloys in undercooled moten states under the isothermal and nonisothermal conditions.The influences of the isothermal approximation on simulation results are discussed.We found that for undercooling greater than 25K,the isothermal approximation overestimates the interface growth velocity and reduces a critical velocity for an absolute stable planar interface,thus in this simulation,the uinterface morphology shows the plane-cell-plane transition with increasing initial undercooling of the mele,and the planar interface obtained under a large undercooling is absolutely stable.Whereas in the nonisothermal simulation,only plane-cell transition occures in the same range of the initial undercoolings of the melt,and the planar interface tends to be destabilized and evolve into cells.     

A generalised model of hydrogen diffusion in metals with multiple trap types

Continuum modelling of hydrogen diffusion in metals, which accounts for both trapping and an imposed force field, is revisited. A generalised model of hydrogen diffusion and trapping is developed as a continuous interpretation of the discrete random-walk theory. A system of nonlinear equations describing the phenomenon of diffusion with multiple types of traps is derived without the assumption of a local equilibrium among hydrogen populations in dissimilar positions. Lattice-trap interchange kinetics can degenerate into local equilibrium as a limit case. Moreover, certain terms in general equations may be negligible in specific situations. By removing these terms, known particularised models of hydrogen diffusion and trapping are recovered. Determining the terms, which are disregarded in reduced models, enables a straightforward assessment of the applicability of these models. The advantages and limitations of particularised models applied to hydrogen embrittlement analyses are discussed.     

A simple model for lamellar peritectic coupled growth with peritectic reaction

The lamellar peritectic coupled growth in Fe-Ni peritectic system was investigated using the equilibrium Boettinger-Jackson-Hunt model. It was found that the slope of the undercooling vs. lamellar spacing is very near zero around the minimum overheating, and the coupled growth can exist under this condition even if the slope of the undercooling vs. lamellar spacing curve is slightly smaller than zero. In addition, the peritectic reaction can never reach completion during the peritectic coupled growth. So the equilibrium peritectic coupled growth was modified by considering the incompletion of the peritectic reaction. It was shown that when the fractions of the peritectic reaction reach 60%–80% completion, the calculated undercooling vs. lamellar spacing curves agree well with the experimental observations in the directionally solidified Fe-Ni alloys. Supported by the National Natural Science Foundation of China (Grant Nos. 50395102 and 50271020) and the Program for New Century Excellent Talents in University (Grant No. 05-0530)     

Unified phase-field model for epitaxial growth of multi-scale three-dimensional islands on insulating surfaces

In this paper we present a unified phase-field model for non-equilibrium growths of various three-dimensional metal islands on insulating surfaces. We introduce a phase-field variable to distinguish the island from the non-island regions and substrate and a density variable to describe local density of deposited adatoms. Two partial differential equations with appropriate boundary conditions, as the governing equations, are used to describe the evolution of the three-dimensional metal islands and the diffusion of adatoms. We solve the equations by using an adaptive mesh refinement method so that we can simulate the non-equilibrium growth of three-dimensional metal islands from tens of nanometers to several micrometers. We investigate the dependence of simulated results on the model parameters and experimental conditions. Equilibrium shape of such islands can be obtained through sufficient post-deposition relaxation. Experimental trends of island size and shape on various scales are obtained with reasonable parameters. This method should be a good approach to non-equilibrium growths of multi-scale three-dimensional metal islands.     

Phase-field simulation of dendritic growth in a binary alloy with thermodynamics data

This paper simulates the dendrite growth process during non-isothermal solidification in the Al-Cu binary alloy by using the phase-field model. The heat transfer equation is solved simultaneously. The thermodynamic and kinetic parameters are directly obtained from existing database by using the Calculation of Phase Diagram （CALPHAD） method. The effects of the latent heat and undercooling on the dendrite growth, solute and temperature profile during the solidification of binary alloy are investigated. The results indicate that the dendrite growing morphologies could be simulated realistically by linking the phase-field method to CALPHAD. The secondary arms of solidification dendritic are better developed with the increase of undercooling. Correspondingly, the tip speed and the solute segregation in solid-liquid interface increase, but the tip radius decreases.