Fe-C合金枝晶生长的相场模拟

采用相场法模拟了Fe-C0.5mol%合金等温凝固中的枝晶生长过程,研究了各向异性模数、各向异性强度和过冷度对枝晶生长的影响.结果表明,在二维平面上,枝晶沿<100>方向生长时,形成四重对称的枝晶形貌;枝晶沿<110>方向生长时,形成六重对称的枝晶形貌.随着各向异性强度增加,枝晶生长速度增加,晶粒由类球状向枝晶转变.随着过冷度的增加,枝晶生长速度增大,溶质扩散层减小,枝晶变的粗大.     

强界面能各向异性下二元Ni-Cu合金枝晶生长过程的相场法模拟

基于Wheeler模型和Eggleston修正强界面能各向异性的方法,建立耦合溶质场和温度场的相场模型,模拟强界面能各向异性下Ni-Cu合金枝晶生长过程.结果表明:在强界面能各向异性作用下,界面方向枝晶生长不连续且枝晶出现棱角;由于枝晶尖端温度梯度和溶质梯度较大,枝晶生长迅速.当界面能各向异性强度低于临界值时,枝晶尖端生长速度随界面能各向异性强度的增加而增大;当界面能各向异性强度等于临界值时,枝晶尖端生长速度下降4.34％;当界面能各向异性强度大于临界值时,枝晶尖端生长速度随界面能各向异性强度的增加先增大到极大值后逐渐减小.当无量纲热过冷度较小时,晶体平衡形貌为类矩形;随着无量纲热过冷度的增加,晶体平衡形貌向枝晶转变,枝晶尖端生长速度先呈幂指数增加,然后呈线性增加,枝晶生长由扩散控制转变为动力学控制.     

硅材料界面形态演化过程的相场法研究

采用有限差分法求解高界面能各向异性的相场模型,对硅材料晶粒生长过程进行模拟,分析了界面能各向异性强度和过冷度对界面形态演化的影响。结果表明:在高界面能各向异性下,硅晶粒为典型小平面枝晶形态,模拟结果和实验结果吻合。随着界面能各向异性强度的增大,晶粒界面形态由类球状经光滑枝晶向小平面枝晶转变;随着过冷度的增加,晶粒界面形态由类矩形向小平面枝晶转变。Y轴正方向晶粒长度在界面能各向异性强度为0.15和0.1时相当,Y轴正方向晶粒尖端温度在界面能各向异性强度为0.15时略高于界面能各向异性强度为0.1时的值。     

Al-0.035Ni合金凝固过程微观组织的相场法数值模拟

采用相场法对Al-0.035Ni合金在凝固过程中的微观组织进行数值模拟。分别模拟时间步长、各向异性系数和过冷度下Al-0.035Ni合金的枝晶生长过程;分析了Al-0.035Ni合金中过冷度对溶质分布的影响。结果表明:随着时间步长的不断增大,晶粒生长由最初的近圆形向枝晶状形貌转变,沿晶轴方向的枝晶生长速率明显快于其他方向。当各向异性系数较小时晶体生长缓慢,晶核在各个方向上的生长速度并没有太大的差异;随着各向异性系数的增大,晶粒在主轴方向上的生长优势越发明显。合金等轴枝晶周围的热扩散层由于受过冷度的影响,其枝晶尖端具有不同的生长速率;当增大过冷度时,枝晶尖端的生长速率随之增大,尖端形核半径呈减小趋势。此外,过冷度对合金枝晶内的溶质偏析影响不容忽视,会在枝晶内形成明显的溶质梯度。     

纯Ni枝晶生长过程的相场法数值模拟

采用凝固过程相场模型,对纯Ni过冷熔体中的枝晶生长过程进行了计算模拟,研究了各向异性强度、过冷度、扰动等对枝晶生长的影响.结果表明:随着各向异性强度的增大,枝晶尖端生长速度加快,枝晶结构特征愈加明显;随着过冷度的增加,枝晶尖端稳定性遭到破坏,甚至出现分叉;扰动会促发侧向分枝的形成,但不影响枝晶尖端的稳态生长行为.     

Fe-C合金等温凝固过程的相场法模拟

基于KKS模型,采用耦合相场和溶质场的方法,对Fe-0．5mol％C合金凝固过程中的枝晶生长进行了模拟,并研究了过冷度、各向异性强度和扰动强度对枝晶生长形貌的影响。结果表明：随着过冷度的减小,枝晶主干细化,各向异性程度增大,晶粒生长速度减小,溶质扩散层厚度增加,枝晶的最高溶质浓度降低,溶质梯度减小;随着各向异性的增加,晶粒由海藻状转变为枝晶态,枝晶生长速度也随之增大;扰动强度引发了侧向分枝,侧枝间互相竞争生长,根部出现“颈缩”现象,但扰动强度的加入并不改变枝晶尖端的稳态行为。     

用相场法研究界面动力学各向异性对纯Ni枝晶生长的影响

基于耦合流场的Wheeler模型,对界面各向异性作用下纯镍枝晶生长过程进行模拟,研究了界面动力学各向异性对枝晶形貌及尖端生长行为的影响。结果表明:在仅有界面能各向异性(ε4)时,晶粒以枝晶方式沿<100>方向生长;在仅有界面动力学各向异性(εk)时,晶粒以枝晶方式沿<110>方向生长。界面同时存在ε4、εk时,随着εk的增加,晶粒优先生长方向由<100>过渡到<110>方向,[100]和[-100]方向尖端稳态速度减小,稳态温度升高。当ε4=εk=0.04时,随着凝固时间的推移,晶粒形貌由伞状经类正方形向发达枝晶形貌转变。     

HCP材料强界面能各向异性的相场模型

基于Karma模型和Eggleston修正强界面能各向异性的方法,建立HCP材料的强界面能各向异性相场模型。采用有限差分法对控制方程进行数值求解,模拟研究HCP材料的枝晶生长行为。结果表明：枝晶形貌呈现出明显的六重对称性,界面方向不连续,导致在主枝和侧枝的尖端出现棱角。当界面能的各向异性强度低于临界值（1/35）时,枝晶尖端稳态生长速度随着各向异性强度的增加而增加;当界面能各向异性强度值超过临界值时,尖端稳态生长速度降低0.89%;当进一步增加各向异性强度值时,尖端稳态速度增加且在各向异性强度值为0.04时达到极大值,随后减小。     

晶粒生长中高界面能各向异性的相场模拟

建立了一个能够模拟纯物质的计算有效的相场模型,该模型考虑了强动力学各向异性和高各向异性界面能。采用数值计算模拟了各种程度的各向异性（强动力学和高各向异性界面能）。在界面各向异性系数变化中,平衡晶体形貌从光滑过渡到出现角部,这之间有一临界值。小于临界值时,生长速度随界面能各向系数的增加单调增加;各向异性系数大于临界值时,随界面能各向系数的增加生长速度减小。在过冷度的变化过程中,生长速度从受热扩散控制转变到动力学控制,在热扩散控制时,生长速度随过冷度增加而增加,枝晶尖端半径随温度增加而减小;在动力学控制时生长速度和枝晶尖端半径随过冷度增加而增加,这与传统的微观可解理论认为R^2V=CONSTANT有所违背。     

相场参数对多元合金凝固过程影响的相场法模拟

利用由二元合金相场模型扩展获得的多元合金相场模型,以Fe-C-P合金为例,研究了各向异性系数和过冷度对合金凝固过程的影响.结果表明:随着各向异性系数的增大,二次枝晶越来越发达,枝晶尖端生长速度增大,且尖端速度波动的幅值增大;随着过冷度的增大,枝晶形貌更成熟,枝晶尖端的曲率半径减小,而枝晶尖端的生长速度呈线性增长趋势,溶质扩散层厚度减小,相应地溶质梯度增大.     

Phase-field modeling of dendritic growth of magnesium alloys with a parallel-adaptive mesh refinement algorithm

A two-dimensional phase field (PF) model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure.By applying a parallel-adaptive mesh refinement (Para-AMR) algorithm,the computational efficiency of the numerical model was greatly improved.Based on the PF model,a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy.The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient.A significant finding is acquired that with a large undercooling,the maximum solute concentration is located on both sides of the dendrite tip in the liquid,whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid.The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient,while the variation trend of the dendrite tip radius is the opposite.Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics,and the simulated results are consistent with the theoretical models proposed in the previously published works.     

来流对Al-Cu合金三维树枝晶生长的影响

建立了模拟二元合金树枝晶生长的三维元胞自动机模型,以Al-4%Cu(质量分数)为模型合金,模拟了合金过冷熔体中树枝晶的生长过程,研究了来流对枝晶生长的影响.结果表明,来流对合金过冷熔体中三维树枝晶生长影响显著,迎流侧枝晶尖端生长速度随来流速度的增大而增大,枝晶尖端半径随来流速度的增大而减小;随着来流速度的增大,枝晶尖端选择参数减小;在给定过冷度条件下,随界面能各向异性的增大,来流对枝晶尖端选择参数的影响增强;对于给定的合金(或界面能各向异性),来流对枝晶尖端选择参数的影响随着过冷度的增大而增强.     

Revealing the Diversity of Dendritic Morphology Evolution During Solidification of Magnesium Alloys using Synchrotron X-ray Imaging: A Review

In this paper, the diversity of complicated dendrite microstructure and its evolution behavior during solidification in different magnesium alloys under various processing conditions were illustrated using synchrotron X-ray imaging technique. A variety of dendritic morphologies and branching structures were revealed, i.e., sixfold plate-like symmetric structure in Mg-Al-based structure, 12-branch structure in Mg-Zn-based alloys and 18-branch structure in Mg-Sn- and Mg-Ca-based alloys as well as seaweed like hyper-branched structure in Mg-38wt%Zn alloy. In addition, a dendrite morphology and orientation transition with increasing addition of Zn content were also observed in Mg-Zn alloy, with dendrite growth pattern transform from anisotropy (low Zn addition) with sixfold symmetric snow-flake structure to relative isotropy (intermediate Zn addition) where seaweed morphology presented and then back to anisotropy (high Zn addition) when only 12 branches with preferred < $11\overline{2}1$ > orientations were observed. The phase-field model representing the typical dendritic morphologies and branching structures under various conditions was also depicted and discussed. Further, the two-dimensional (2D) real-time dendrite growth dynamics in different Mg-based alloys captured using synchrotron X-ray radiography for unveiling the originate of the α-Mg dendrite was reviewed. Following this, the four-dimensional (3D + time) synchrotron X-ray tomographic in situ observation of dendritic morphology evolution indicating the formation mechanism of the diverse dendritic morphology during Mg-Sn- and Mg-Zn-based alloys was also summarized. Finally, the future study on exploring the complicated dendritic morphologies and their origination during solidification of Mg-based alloys is prospected.     

Phase field method simulation of faceted dendrite growth with arbitrary symmetries

A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.     

铸造镁合金的枝晶生长模拟

根据hcp晶体学结构和优先生长方向,建立了铸造镁合金晶体生长的物理模型,提出了一种新的随机性模拟方法--虚拟生长中心计算模型.模型考虑了枝晶生长动力学、各向异性和二次枝晶臂粗化,采用枝晶形状函数揭示了一次枝晶和二次枝晶的生长演化过程.引入坐标变换技术可更快速准确计算任意晶向枝晶的生长捕获.耦合了微观溶质场计算,得到了更准确的枝晶生长形貌和溶质分布情况.对Mg-Al合金定向凝固和等轴晶生长的模拟验证了本模型的正确性.     

Numerical simulation of facet dendrite growth

Numerical simulation based on phase field method was performed to describe the solidification of silicon. The effect of anisotropy, undercooling and coupling parameter on dendrite growth shape was investigated. It is indicated that the entire facet dendrite shapes are obtained by using regularized phase field model. Steady state tip velocity of dendrite drives to a fixed value when γ≤0.13. With further increasing the anisotropy value, steady state tip velocity decreases and the size is smaller. With the increase in the undercooling and coupling parameter, crystal grows from facet to facet dendrite. In addition, with increasing coupling parameter, the facet part of facet dendrite decreases gradually, which is in good agreement with Wulfftheory.     

Quantitative multi-phase-field modeling of non-isothermal solidification in hexagonal multicomponent alloys

A quantitative multi-phase-field model for non-isothermal and polycrystalline solidification was developed and applied to dilute multicomponent alloys with hexagonal close-packed structures. The effects of Lewis coefficient and undercooling on dendrite growth were investigated systematically. Results show that large Lewis coefficients facilitate the release of the latent heat, which can accelerate the dendrite growth while suppress the dendrite tip radius. The greater the initial undercooling, the stronger the driving force for dendrite growth, the faster the growth rate of dendrites, the higher the solid fraction, and the more serious the solute microsegregation. The simulated dendrite growth dynamics are consistent with predictions from the phenomenological theory but significantly deviate from the classical JMAK theory which neglects the soft collision effect and mutual blocking among dendrites. Finally, taking the Mg-6Gd-2Zn (wt.%) alloy as an example, the simulated dendrite morphology shows good agreement with experimental results.

     

Co-Sn单相合金深过冷凝固时Co3Sn2 相生长形貌的演变机制

开展了(Co₆₀Sn₄₀)_100-xNb_x (x=0,0.4,0.6,0.8,at%)单相合金的深过冷凝固实验,研究了Co₃Sn₂相生长形貌的演变机制。结果表明,在小过冷度下,Co₃Sn₂相在x=0,0.4以海藻状的模式进行生长,随着添加的Nb含量增加至0.6at%,其生长形貌转变为树枝晶,并在x=0.8进一步转变为分形海藻晶,这主要是由于界面能各向异性和动力学各向异性的变化。随着过冷度的增加,(Co₆₀Sn₄₀)_99.4Nb_0.6合金中Co₃Sn₂相生长形貌在过冷度大于28 K时从树枝晶转变为分形海藻,当过冷度高于143 K时转变为密集海藻。少量的Nb添加在小过冷度和中间过冷度时能提高Co₃Sn₂相的生长速度,但是在大过冷度下会显著降低生长速度。Co₃Sn₂相生长速度随过冷度变化规律的转变对应其生长形貌从分形海藻向密集海藻的转变。