Revisiting dynamics and models of microsegregation during polycrystalline solidification of binary alloy

Microsegregation formed during solidification is of great importance to material properties.The conventional Lever rule and Scheil equation are widely used to predict solute segregation.However,these models always fail to predict the exact solute concentration at a high solid fraction because of theoretical assumptions.Here,the dynamics of microsegregation during polycrystalline solidification of refined Al-Cu alloy is studied via two-and three-dimensional quantitative phase-field simulations.Simulations with different grain refinement level,cooling rate,and solid diffusion coefficient demonstrate that solute segregation at the end of solidification (i.e.when the solid fraction is close to unit) is not strongly correlated to the grain morphology and back diffusion.These independences are in accordance with the Scheil equation which only relates to the solid fraction,but the model predicts a much higher liquid concentration than simulations.Accordingly,based on the quantitative phase-field simulations,a new analytical microsegregation model is derived.Unlike the Scheil equation or the Lever rule that respectively overestimates or underestimates the liquid concentration,the present model predicts the liquid concentration in a pretty good agreement with phase-field simulations,particularly at the late solidification stage.     

A Modified Cellular Automaton Model for the Quantitative Prediction of Equiaxed and Columnar Dendritic Growth

Since the characteristic of dendrite is an important factor determining the performance of castings, a twodimensional cellular automaton model with decentered square algorithm is developed for quantitatively predicting the dendritic growth during solidification process. The growth kinetics of solid/liquid interface are determined by the local equilibrium composition and local actual liquid composition, and the calculation of the solid fraction increment is based on these two compositions to avoid the solution of growth velocity. In order to validate the developed model, quantitative simulations of steady-state dendritic features over a range of undercooling was performed and the results exhibited good agreement with the predictions of LGK（Liptone Glicksman-Kurz） model. Meanwhile, it is demonstrated that the proposed model can be applied to simulate multiple equiaxed dendritic growth, as well as columnar dendritic growth with or without equiaxed grain formation in directional solidification of AleC u alloys. It has been shown that the model is able to simulate the growth process of multi-dendrites with various preferential orientations and can reproduce a wide range of complex dendritic growth phenomena such as nucleation, coarsening of dendrite arms, side branching in dendritic morphologies, competitive growth as well as the interaction among surrounding dendrites.     

Oxide bifilms in aluminium alloy castings – a review

Abstract

Aluminium alloy castings are most widely used in automobile industry because of their light weight, better castability and improved properties. The liquid aluminium surface easily oxidises during melting, transferring and pouring operation which may entrain oxide films into the casting. Research work has shown that the entrainment of this surface film and formation of bifilms in castings appear to be the source of most of the casting defects leading to a significant reduction in the mechanical properties of aluminium alloy castings. In this paper, the phenomenon of formation of oxide bifilms in aluminium alloy castings, effect of these bifilms on casting properties and their assessment techniques are discussed. For enhancing the quality of casting, research should focus towards development of process techniques for healing of bifilms in liquid metal during solidification.     

铝(镁)合金消失模铸造近净成形技术研究进展

阐述了铝(镁)合金消失模铸造技术的研究现状,着重介绍了铝(镁)合金消失模铸造在金属液充型、振动凝固、压力凝固以及消失模壳型铸造等技术方面的最新研究进展。研究表明,铝(镁)合金在消失模铸造过程中,需重点解决针孔、缩松等缺陷,提高液态合金的充型能力和铸件的力学性能;通过采用振动凝固和压力凝固的手段,可以提高金属液充型能力、细化组织、提高组织致密性,明显提高铸件力学性能。真空低压消失模壳型铸造技术,可以解决普通消失模铸造易于出现的孔洞和夹杂等缺陷以及浇不足和浇注温度高等问题,是一种生产复杂薄壁高质量铝、镁合金精密铸件的新方法。     

Modelling of the thermo-physical and physical properties for solidification of Ni-based superalloys

The thermo-physical and physical properties of the liquid and solid phases are critical components in the modelling of casting simulations. Such properties include the fraction solid transformed, enthalpy release, thermal conductivity, volume and density all as a function of temperature. Due to the difficulty in experimentally determining such properties at solidification temperatures, little information exists for multi-component alloys. As part of the development of a new computer programme for modelling of materials properties (JMatPro), extensive work has been carried out on the development of sound, physically based models for these properties. Wide ranging results will presented for Ni-based alloys, which will include more detailed information concerning the phases formed during solidification and their composition and the density change of the liquid that intrinsically occurs during solidification due to its change in composition.     

差压铸造薄壁铝硅合金铸件的位置效应

采用差压铸造工艺,研究垂直缝隙式浇注系统浇注的铝合金硅铸件不同位置的组织和力学性能变化.采用石英砂型、SiC砂型和冷铁,浇口处铸件的晶粒最细小,致密度高、力学性能最好;铸件冷端的组织和性能次之;位于两者之间的铸件的组织和性能最差.分析表明对于具有垂直缝隙式浇注系统,差压铸造凝固压力对金属的凝固作用具有位置效应,浇口处液态金属温度高,凝固时间长,凝固压力对浇口处金属的凝固作用显著;铸件冷端金属凝固时间短,凝固压力对该处金属的凝固作用不显著,铸型的冷却速度对铸件组织和性能的影响起显著作用.浇口处与冷端之间的金属液体的凝固受压力和冷却速度的影响小,铸件的晶粒尺寸最大、密度最小、性能最低.冷却速度提高,铸件的任意位置的组织和性能都相应得到提高.     

Continuum model for predicting macrosegregation in dendritic alloys

“Macrosegregation” represents a class of defects in cast products of serious concern to both alloy producers and users. Many types of macrosegregation result from thermosolutal convection in the solid plus liquid and all-liquid regions of a solidifying alloy, and this has spurred modeling and simulations, which treat the solid plus liquid region (i.e., the mushy zone) as a porous medium of variable porosity and permeability. Simulations include scenarios in which the convection is strong enough to make channels in the mushy zone region, and these channels lead to localized segregates known as “freckles”. Using Pb-10 wt.% Sn as a model alloy, we simulated vertical solidification with various solidification rates. By sufficiently increasing the cooling rate at the bottom surface, convection can be suppressed enough to prevent the formation of freckles. The simulation is an example of relating microstructural metrics to a macroscopic property of the porous medium used in continuum theory. In this case, the property is the permeability, which is governed by two microstructural metrics: the volume fraction of liquid and a characteristic length in the dendritic microstructure. Permeability data, relevant to columnar dendritic solidification, are reviewed, and recommendations for future work on determining the permeability in terms of microstructural metrics are given.     

Computer model of unidirectional solidification of single crystals of high temperature alloys

Abstract

I t has been common practice to use mould withdrawal unidirectional solidification to produce single crystal castings. To grow single crystals successfully, it is important to control several solidification parameters, such as the morphology of the solidification front (solid/liquid interface), thermal gradient, and growth rate during solidification. It is the aim of this study to develop a solidification model that can predict such solidification parameters for various design and operating conditions. The solidification phenomena in the process modelled are basically controlled by two heat transfer mechanisms: conduction and radiation. A set of heat transfer equations and boundary conditions were employed to describe mathematically the heat transfer phenomena. Then the finite difference method was used numerically to solve these equations for specified boundary conditions to obtain the temperature distribution and temperature variation in the casting. The solidification parameters can subsequently be deduced from these temperature data. Several thin plate castings were tested using the model developed. The following design and operating conditions were evaluated: susceptor temperature (power input), withdrawal speed, changes of cross-sectional area in the casting, and geometrical arrangement of the casting tree.

MST/1422     

The description of morphologically stable regimes for steady state solidification based on the maximum entropy production rate postulate

The maximum entropy production rate (MEPR) in the solid–liquid zone is developed and tested as a possible postulate for predicting the stable morphology for the special case of steady state directional solidification (DS). The principle of MEPR states that, if there are sufficient degrees of freedom within a system, it will adopt a stable state at which the entropy generation (production) rate is maximized. Where feasible, the system will also try and adopt a steady state. The MEPR postulate determines the most probable state and therefore allows pathway selections to occur in an open thermodynamic system. In the context of steady state solidification, pathway selections are reflected in the corresponding morphological selections made by the system in the solid–liquid (mushy) zone in order to cope with the required entropy production. Steady state solidification is feasible at both close to, and far from equilibrium conditions. Based on MEPR, a model is proposed for examining the stability of various morphologies that have been experimentally observed during steady state directional solidification. This model employs a control volume approach for entropy balance, including the entropy generation term (S _gen), which depends on the diffuse zone and average temperature of the solid–liquid region within the control volume. In this manner, the model takes a different approach from the successful kinetic models that have been able to predict key features of stable morphological patterns. Unstable planar interfaces, faceted cellular arrays, cell–dendrite transitions, half cells both faceted and smooth, and other transitions such as the absolute stability transition at high solid/liquid velocities are examined with the model. Uncommon solidification morphological features such as non-crystallographic dendrites and discontinuous cell-tip splitting are also examined with the model. The preferred morphological change-direction for the emergence of the stable morphological feature is inferred with the MEPR postulate in a manner analogous to the free energy minimization principle(s) when used for predicting phase stability and metastable phase formation. Aspects of mixed-mode order transformation characteristics are also discussed for non-equilibrium solidification containing a diffuse interface, in contrast to classifying solidification as purely a first order transformation. The MEPR model predictions are shown to follow the experimental transitions observed to date in several historical studies.     

On preventing HAZ cracking in laser welded DS Rene 80 superalloy

Abstract

The heat affected zone (HAZ) cracking behaviour in a laser beam directionally solidified (DS) Rene 80 nickel based superalloy subjected to preweld heat treatments was studied. The HAZ cracks in the alloy are grain boundary liquation cracks caused by liquation reaction of both non-equilibrium secondary solidification product, MC carbides and equilibrium solid state reaction product, γ′ precipitates. In contrast to theoretical prediction based a preweld heat treatment that reduced grain boundary liquid film thickness did not result in a lower HAZ cracking, which can be related to concomitant reduction in the ability of the base alloy to relax welding stress. In addition, formation of intergranular M₅B₃ boride particles in preweld alloy appeared to have aided cracking susceptibility by lowering grain boundary liquation temperature and widening the brittle temperature range in the HAZ during cooling. Based on the analysis of the results, application of a new preweld heat treatment that prevents the formation of the intergranular borides and induces moderate base alloy hardness resulted in a nearly crack free HAZ in laser welded DS Rene 80 superalloy.     

Pb-Sn合金侧向凝固过程A偏析的数值模拟

基于二元系凝固过程热溶质的传输行为,建立了描述A偏析形成及演化的数学模型,给出了固相分数与温度场及浓度场的耦合关系.先用已有的实验结果验证了模型的正确性,然后模拟计算了Pb-Sn合金侧向凝固过程A偏析的形成及演化过程,并研究了浮力数对A偏析形成位置及偏析程度的影响.结果表明,在糊状区中双扩散对流引起的密度变化,导致局部流动,形成偏析通道;为了维持偏析通道中局部液体的流动,枝晶间的液体通过糊状区从液相区得到补充.在相同的凝固条件下,浮力数越小,A偏析的形成时间愈迟,偏析的程度也越小.     

低合金高强焊丝退火工艺研究

研究了一种铁基合金焊丝从铸态到焊丝最终成型的制备过程。分析了焊丝制备工艺以及制备过程中合金的组织和性能。采用各种不同温度对材料进行热处理,寻求最佳的处理方案,以降低材料的硬度,并初步探求材料在不同温度参数下去应力软化处理的效果。合金钢丝经1020℃×15min去应力软化处理（空冷）后,硬度由29．8HRC降至21．1HRC,满足了后续拉拔工艺的要求。     

Volume change during the solidification of SG iron: comparison between experimental results and simulation

In order to understand the shrinkage behaviour of spheroidal graphite (SG) iron during solidification, a volume change kinetic model was set up to simulate the volume change during the eutectic solidification, which was presented in an earlier paper. Furthermore in the present work experiments were carried out for comparison with theoretical prediction. The microstructure of the mushy zone during the solidification of SG cast iron was obtained by the quenching method and analysed by normal metallography and image analysis. The results show that the mushy zone exists in front of the interface between the liquid and the solid. The study by quantitative stereology shows that the graphite fraction in the mushy zone has the same trend as that of the theoretical prediction and the silicon content in cast iron strongly influences graphitization during the solidification. A heat-transfer model to stimulate the heat transfer of the experimental apparatus was developed. A modified Rappaz’s model was used to simulate the eutectic growth under fully equilibrium conditions. The theoretical prediction has been compared with the experimental results, and found to be in good agreement with each other. This revised version was published online in November 2006 with corrections to the Cover Date.     

Positive segregation as a function of buoyancy force during steel ingot solidification

Abstract

We analyze theoretically and experimentally solute redistribution in the dendritic solidification process and positive segregation during solidification of steel ingots. Positive segregation is mainly caused by liquid flow in the mushy zone. Changes in the liquid steel velocity are caused by the temperature gradient and by the increase in the solid fraction during solidification. The effects of buoyancy and of the change in the solid fraction on segregation intensity are analyzed. The relationships between the density change, liquid fraction and the steel composition are considered. Such elements as W, Ni, Mo and Cr decrease the effect of the density variations, i.e. they show smaller tendency to segregate. Based on the modeling and experimental results, coefficients are provided controlling the effects of chemical composition, secondary dendrite arm spacing and the solid fraction.     

Mold-filling characteristics and solidification behavior of magnesium alloy in vacuum suction casting process

A novel semi-solid processing technique, called new vacuum suction casting (NVSC), is used to manufacture high-quality components of AZ91D Mg alloy directly from a liquid metal. The resulting apparent morphologies and microstructures of castings are characterized in detail and linked to the corresponding mold-filling behavior and subsequent solidification behavior. It is revealed that the semi-solid metal (SSM) with higher viscosity can be caused to fill the mold with “solid-front fill”, as compared with the liquid metal “spraying” in the conventional vacuum suction casting (CVSC) process. The smooth filling achieved in the NVSC process diminishes some disadvantages inherent for the CVSC sheets, and generates castings with better surface finish and structures with high integrity. The microstructure of the CVSC sheet consists of the fine and homogeneous supersaturated α-Mg solid solution due to the extremely high cooling rate. In the NVSC microstructure, the “preexisting” primary solid particles, with the morphology of near-globules or rosettes, disperse in the homogeneous matrix consisting of fine near-equiaxed secondary α-Mg grains and fine precipitates of β-Mg₁₇Al₁₂ intermetallics. In addition, owing to rapid solidification, the volume fraction of the β phase in the sheets obtained by both the processes is much lower than that in the as-cast ingot.     

On the formation of the stircast structure

The conditions of solidification in a stirred bulk liquid are investigated to explain the non-dendritic microstructure of stircast alloys. A model of stirred solidification is presented, which allows a comparison of the solidification behaviour of metal alloys and organic analogues. This shows that nucleation and growth of solid in e bulk liquid is facilitated under the influence of stirring, provided the Prandtl-number is greater than unity. It is shown further that the solute gradient ahead of the solid-liquid interface of floating particles in a bulk liquid is reduced by the fluid flow. Combined with the thermal properties, and in analogy with the constitutional supercooling criterion, A is shown that solid growth in metals is likely to be cellular in an early stage of the solidification, In contrast, in stirred organic analogues, the solidification is dendritic in the early stage.     

Computational Modeling of Columnar to Equiaxed Transition in Alloy Solidification

The columnar to equiaxed transition (CET) provides a challenging simulation goal for computational models of alloy solidification, in addition to being an important technological feature of many casting processes. CET thus provides an industrially relevant test‐case for those developing numerical models across a range of scales. Whether or not CET occurs depends on numerous experimental parameters such as cooling rate, speed of columnar growth, thermal gradient in the liquid, and level of grain refiner in the alloy. Information on columnar and equiaxed grain structure, and the transition between the two, is very useful for foundry engineers, at the macroscopic scale of the casting. The detailed microstructure within each grain is determined by typically dendritic growth and local transport of solute and heat. This paper presents a review of recent progress on modeling CET at multiple length scales. It is evident that, whilst micro‐models can provide simulations of physical phenomena, such as the evolution of dendrite morphology, at scales 10^?3 to 10^?5 m, finite computational resources preclude this resolution over the length scale of castings which is in the 10^?2–10⁰ m range. Instead, reasonably accurate models of CET formation in castings can be achieved by meso‐scale modeling featuring 10^?3–10^?2 m phenomena. Such meso‐scale models make use of analytical expressions to simulate dendrite growth in undercooled melts. Recent progress in modeling of CET, at both macro/meso‐ and micro‐scales is reviewed, and computational challenges yet to be met are summarized.     

Vibrational Coupling and Kapitza Resistance at a Solid–Liquid Interface

The rapid development and application of nanotechnologies have promoted an increasing interest in research on heat transfer across the solid/liquid interface. In this study, molecular dynamics simulations are carried out to elucidate the effect of vibrational coupling between the solid and the liquid phases on the Kapitza thermal resistance. This is accomplished by altering the atomic mass and interatomic interaction strength in the solid phase (thus, the vibrational properties), while keeping the solid–liquid interfacial interaction unchanged. In this way, the Kapitza resistance can be altered with a constant work of adhesion between the solid and the liquid phases. The simulation results show that the overlap degree between the vibrational density of states profiles of the interfacial liquid layer and the outermost solid layer, which measures the degree of interfacial vibrational coupling, increases with larger atomic mass and weaker inter-atomic interaction in the solid phase. An inverse relation exists between the Kapitza resistance and the overlap degree of the vibrational density of states profiles. It means that the Kapitza resistance decreases with better interfacial vibrational coupling. The simulations show that the Kapitza resistance is not only affected by the interfacial bonding strength but also the vibrational coupling between the solid and the liquid atoms. The interfaces with better thermal transport efficiency should be the ones with stronger interfacial interaction and preferable vibrational coupling between solid and liquid phases.     

复杂镍基单晶铸件显微孔洞的形成机理EI北大核心CSCD

采用高分辨透射X射线三维成像技术研究高速凝固法(high rate solidification,HRS)制备的3种成分复杂单晶铸件叶身和缘板部位的铸态显微孔洞分布情况。结果表明:凝固温度范围和枝晶排列曲折程度对孔洞的影响很大。铸件叶身部位,不同成分单晶的枝晶排列方式相同。其中,一代单晶的凝固温度范围最大,其孔洞体积分数也最大。二代单晶和三代单晶的凝固范围差异不大,孔洞体积分数主要受共晶体积分数的影响。随着单晶代次的增加,合金中难熔元素的含量将会增加,继而引起叶身部位共晶体积分数的增加。因此,合金最后凝固阶段枝晶间的空隙尺寸增加,液相压降降低,导致形成孔洞的体积分数减小。相比于叶身部位,缘板部位的孔洞主要由枝晶曲折程度决定。一代单晶缘板部位的枝晶曲折程度变化不明显,其孔洞体积分数与叶身部位的孔洞体积分数差异不大。二代单晶和三代单晶缘板部位的枝晶曲折程度逐渐增加,其孔洞体积分数增加。     

A lattice Boltzmann model for solidification of water droplet on cold flat plate

Since the solidification of water droplet is the initial and essential process in the whole process of frosting, a model is developed by the lattice Boltzmann method (LBM) that applies the velocity and temperature distribution functions to investigate the solidification process of water droplet on cold flat plate. The thermal transport and liquid–solid phase transition in the present model are both based on the pseudo-potential model combined with the enthalpy formation. By this LB model, the solidification process is simulated in form of temperature and solid phase variations in water droplet on cold flat plate, and the shape of solid phase in freezing can also be predicted. In addition, we apply the present LB model to preliminarily study the frost formation process. Numerical results agree well with our experimental data.