Phase field modeling of dendrite growth

Single dendrite and multi-dendrite growth for A1-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites dur-ing solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms.When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.     

In situ and real-time 3-D microtomography investigation of dendritic solidification in an Al–10 wt.% Cu alloy

The microstructural evolution of an Al–10 wt.% Cu alloy was investigated during solidification at constant cooling rate by in situ synchrotron X-ray microtomography with a resolution of 2.8 μm. Solidification of this alloy leads to a coarse dendritic microstructure which was fully characterized in terms of variation with temperature of the solid fraction, the specific surface area of the solid–liquid interface and the local curvatures of the solid phase. By analysing the evolution with solid fraction of individual dendrites, at least two coarsening mechanisms were clearly identified in addition to solidification growth. The first mechanism involves remelting of small secondary dendrite arms to the benefit of bigger adjacent arms. The second is the coalescence of adjacent secondary arms, with progressive filling of the inter-arm spacing and coalescence at the tips. Although this mechanism preferentially occurs at high solid fractions, these results show that the evolution of the dendritic microstructure during solidification is complex and involves the occurrence of various mechanisms operating concurrently. In situ X-ray tomography thus allows revisiting the various models which have been proposed to account for dendrite coarsening during solidification.     

Phase field modeling of multiple dendrite growth of AI-Si binary alloy under isothermal solidification

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.     

MC碳化物准快速凝固形态与生长机制研究

本文对ＴｉＡｌ合金激光表面合金化表面改性层中ＴｉＣ生长形态的生长过程及机理进行了研究。发现在冷却速度为１０＾２℃／ｓ量级的准快速凝固上。     

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.     

MC碳化物非平衡凝固液/固界面结构及生长机制

在冷却速度为10^2-10^5K/s的激光快速凝固条件下，对Jackson因子约为5－7的TiC型MC碳化物典型小面晶体液／固界面结构、生长形态及生长机制进行了系统的实验研究和理论分析。结果表明，尽管MC碳化物的生长形态随着凝固冷却速度的变化而发生显著变化，但其液／固界面始终保持原子尺度上光滑，其微观生长机制始终为台阶侧向生长，在10^2-10^5K/s凝固冷却速度条件下，MC碳化物生长机制并未发生由侧向生长机制向连续生长机制的转化。     

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.

     

定向凝固Ti-46Al-8Nb合金的微观组织演变与微观偏析(英文)

在3～70μm/s的生长速度范围内对Ti-46Al-8Nb(摩尔分数,%)合金进行定向凝固实验,研究其微观组织演变和微观偏析形式。在该生长速度范围内,固-液界面表现为规则的枝晶生长,一次枝晶间距随着生长速度的加快而逐渐减小。在定向凝固过程中观察到典型的L+β→α包晶反应,最终得到具有α2/γ层片和B2相的微观组织。在各个晶粒中,层片与β相枝晶初始生长方向呈0°或45°。包晶反应导致严重的成分偏析,在凝固过程中,铝富集在枝晶间,铌富集在枝晶心部。随着α相的形核和生长,铌的偏析程度逐渐增大,从而促进B2相的析出,而富集在枝晶间的铝在包晶反应发生后逐渐变得均匀、一致。     

Unveiling the Growth Mechanism of Faceted Primary Al2Cu with Complex Morphologies During Solidification

The growth characteristic of primary faceted Al₂Cu intermetallic compounds (IMCs) during solidification was observed directly by synchrotron radiography. The formation and transition mechanisms of Al₂Cu IMCs with diverse morphologies were elucidated by first-principle calculations combined with electron backscatter diffraction analysis. The Al₂Cu crystals preferred to grow along the [001] direction and were bounded by {110} planes with the lowest surface energy. The faceted Al₂Cu rod-like clusters consisted of multiple crystals with complete rod, hollowness and partial sides, which was attributed to the increase in strain energy and solute redistribution during solidification. The faceted Al₂Cu with branches was characteristic with the perpendicular relationship between the main branches and side steps and partial coalescence at the junction, which was ascribed to the continuous propagation and growth of newly formed crystals along the diagonal direction.     

Comparison of dendrite and dispersive structure in rapidly solidified Cu–Co immiscible alloy with different heat flow modes

Rapid solidification of Cu–Co immiscible alloy was investigated by glass-fluxing, spray casting and melt-spinning techniques. Both the transition from dendrite to dispersive structure and corresponding scale evolution were revealed and further elucidated in terms of the heat flow mode, nucleation and growth processes under different solidification conditions. With the increase of undercooling, columnar dendrite is replaced by dispersive structure due to the immiscible effect. In contrast, equiaxed dendrite forms in spray cast alloy due to multiple nucleation events and becomes thinner for the case of higher cooling rate. Ascribed to the enhanced non-equilibrium effect and insufficient period for collision and coagulation processes between separated droplets, fine globular dispersion appears upon the diameter of spray casting reaching 4 mm. As for the melt-spun ribbon with the highest cooling rate, a single-phase solid solution microstructure with refined grain of cellular morphology can be obtained, which is attributed to the suppression of liquid phase separation by instant solidification.     

In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy

High-brilliance synchrotron X-radiation microscopy and further image processing allowed in situ observations of local solute-enrichment during fragmentation of dendrite arms under normal non-forced-convection conditions during directional solidification of an Al–20 wt.% Cu alloy. An open dendritic network is exposed to solute-rich liquid which arrives from the solidification front. At grain boundaries such openness is even more pronounced, leaving higher-order branches highly exposed to the incoming solute-rich liquid stream. It was found that streaming of solute-enriched liquid at the tip of high-order branches promotes growth by local undercooling. Further solute advection and local solute rejection due to the local growth causes solute pile-up at the roots of the branches. This solute pile-up alters the local compositional balance at the solid–liquid interface at the root, causing the root to remelt, which in turn results in further branch detachment.     

TiAl合金激光表面合金层中TiC凝固生长形态及机制

利用碳对TiAl金属间化合物合金进行激光表面合金化 ,制得了以TiC (MC碳化物 )为增强相的复合材料涂层 ,研究了MC碳化物的凝固生长形态及生长机制。结果表明 :在激光扫描速度为 6 .0mm/s的凝固条件下 ,MC碳化物呈现微观上具有“小片链状”生长特征的树枝状生长形态 ;当激光扫描速度增加至 16 .4mm/s时 ,其生长形态又转化为具有“三维网络”生长特征的发达树枝晶 ;TiC与Al3 Ti共晶的动力学生长过程及MC碳化物所固有的侧向生长机制是影响MC碳化物凝固生长形态选择的重要因素     

In situ observation of Si faceted dendrite growth from low-degree-of-undercooling melts

We directly observed the transition of crystal growth behavior of Si in a low undercooling region. We succeeded in observing the initiation of faceted dendrite growth from a portion of parallel twins with increasing degrees of undercooling. The critical undercooling for growing a faceted dendrite was experimentally determined to be ΔT = 10 K. We also confirmed that parallel twins associated with faceted dendrite growth were formed between grain boundaries and not at grain boundaries during melt growth. The parallel-twin formation was explained in terms of a model of twin formation on the {1 1 1} facet plane at the growth interface.     

Origin of intragranular crystallographic misorientations in hot-dip Al–Zn–Si coatings

The origin of intragranular variations of the crystallographic orientation in hot-dip Al–Zn–Si coatings is discussed based on new experimental results and modelling. The solidification microstructure in as-received 55Al–43.4Zn–1.6Si (in wt.%) coatings deposited on steel plates in an industrial production line was analyzed by electron backscattered diffraction, glow-discharge optical emission spectroscopy and atomic force microscopy (AFM). The results were compared with those obtained in coatings re-solidified under different cooling and mechanical loading conditions. Continuous variations of the crystallographic orientation as large as 35° were observed within individual grains of Al–Zn–Si, consistent with previous studies. However, the mechanisms previously proposed for the origin of intragranular crystallographic misorientations had to be revisited. The new experimental data acquired during this study indicate that the solidification shrinkage accumulating in the area of the grain envelope is the driving force for the formation of intragranular misorientations. The solidification shrinkage leads to the development of tensile stresses in the oxide film covering the coating while it solidifies. Estimations based on AFM profiles and phase field simulations of the dendritic structure indicate that the stresses applied on the dendrite network are sufficient to deform plastically the dendrite arms during solidification.     

镍基合金焊接熔池凝固组织模拟

对原有元胞自动机中网格的捕获规则进行修正,完善了"对角线模拟角度"法则,并用其成功地模拟了镍基合金熔池凝固过程枝晶生长以及晶界偏析情况.结果表明,在焊接熔池凝固过程中,不同取向的晶粒之间存在着激烈的竞争生长.结晶取向与温度梯度最大的方向相一致的晶粒生长速度快,将其它取向的晶粒淘汰,在竞争中能够持续生长.同时,在枝晶与枝晶、枝晶臂与枝晶臂之间的残余液相中,存在溶质堆积现象,在凝固过程结束后,形成了严重的晶界偏析.     

超高温度梯度下凝固速率对一种镍基单晶高温合金定向凝固组织的影响

采用区域熔炼液态金属冷却超高温度梯度定向凝固法(ZMLMC),研究凝固速率对一种镍基高温合金微观组织的影响。结果显示:在温度梯度基本不变的条件下,随着凝固速率的提高,枝晶结构逐渐细化,一次枝晶间距λ1与二次枝晶间距λ2减小,且λ1和λ2分别与V-1/4和V-1/2呈线性关系;γ’相尺寸随凝固速率的提高而减小,形貌逐渐趋向于立方状,而在同一速率下,枝晶干的γ’相形状相对较规则,接近立方形,枝晶间的γ’相则趋于无规,其尺寸也较枝晶干区域更为粗大;γ/γ’共晶尺寸随凝固速率的提高而减小,分布趋于弥散,但总的体积分数变化不大。     

In Situ Observation of Growth Behavior and Morphology of Delta-Ferrite as Function of Solidification rate in an AISI304 Stainless Steel

It was presented the in situ observation of growth behavior and morphology of delta-ferrite as a function of solidification rate in an AISI304 stainless steel. The specimens have been solidified and observed using confocal scanning laser microscopy (CSLM). The δ-phase always appears like cells on the sample surface when critical supercooling occurs, during which the L→δ transformation starts. The solid-liquid (S-L) interface is found to be finger shaped and has no faceted shape. γ phase appears among δ grains due to partitioning of Ni into the melt during solidification, when solidification rate is higher. The mergence of observed δ cells is possible for the steel sample cooled at 7.5℃/min. The formation of dendrites can be observed on the free surface of the steel sample cooled at 150℃/min. The size of solidified delta grains decreases from 120 to 20-80μm, and the volume fraction of solidified austenite increases with increase in solidification rate from 7.5 to 150℃/min. The relation between the tip radius of δ cell and its growth rate is deduced, and the results agree with the experimental values.     

凝固理论进展与快速凝固

本文综述了凝固理论的某些新进展，对高生长速率下的凝固热力学与形核、生长动力学，特别是非平衡溶质分配系数，形核孕育期与相选择，化学成分及熔体热历史对形核机制的影响，平界面的绝对稳定性，快速的枝晶／胞晶生长以及样品体积内快凝过程的发展等问题给出了定量的表述，文中还指出了对快凝过程进行分析和设计的工作步骤。     

Uncertainty quantification in modelling equiaxed alloy solidification

Numerical simulations can provide insight into physical phenomena during alloy solidification processes that cannot be observed experimentally. These model predictions depend on the material, process and numerical parameters which contain inherit uncertainties due to their origin in experimental measurements or model assumptions. As a step towards understanding the effect of uncertain inputs on solidification process modelling, uncertainty quantification and sensitivity analysis are performed on a transient model of transport phenomena during the solidification of grain refined Al-4.5 wt.% Cu in a rectangular cavity. The effect of microstructural model parameters, thermal boundary conditions and material property input uncertainties are examined for their effect on macrosegregation levels and solidification time. Predictions of the macrosegregation level are most sensitive to the dendrite arm spacing of the rigid mushy zone.     

Phase-field simulation of dendritic growth for binary alloys with complicate solution models

1 INTRODUCTION The formation of complex microstructures during solidification of metals and alloys have fas- cinated researchers in materials science and related areas for so many years , especially the formation of dendritic structures . In many commercial al- loys , microstructural features that determine the mechanical integrity of a cast ingot ,such as solute segregation, grain size and porosity , all depend critically on the morphologies and velocities of in- dividual or arrays of gr…