Interdendritic microsegregation development of high-strength low-alloy steels during continuous casting process

A 1-D model based on DICTRA software was used to simulate Mn microsegregation in high-strength low-alloy steels during continuous casting. The experimentally determined (using a cumulative profiling method) segregation results were in good agreement with the modelling results. Steels undergoing solidification via a peritectic reaction had a larger segregation range than non-peritectic steels ascribed to trapping of the alloying atoms in liquid by austenite acting as a diffusion barrier. Subsequent, post-solidification cooling through the single phase austenite field decreased the microsegregation level, although the last γ→α phase transformation did affect the segregation profile in the solute-depleted dendrite centre. Simulation indicates that segregation levels could be reduced by decreasing either secondary dendrite arm spacing or adopting faster cooling rates through solidification.     

Segregation and eutectic formation in solidification of Fe-1C-1 5-Cr steel

Abstract

The microstructure and solute segregation have been investigated in a continuously cast bloom and laboratory cast ingot of Fe–1C–1.5Cr (wt-%) steel. Eutectic carbide formation was observed only in the centreline region in the continuously cast bloom. In both specimens, the maximum chromium level detected was 3% in the columnar and 5% in the equiaxed region, while the minimum remained at 1.2% in both regions. The corresponding segregation ratios (C _max/C _min) were 2.5 and 5, in agreement with many previous studies. By numerical modelling of microsegregation it has been shown that the equilibrium partition coefficient of chromium k _Cr, which changes with carbon content, has a significant effect on chromium distribution during solidification. The carbon distribution may be taken to be in equilibrium during solidification, while that of chromium develops a concentration gradient in the solid. Numerical predictions of segregation behaviour, assuming local equilibrium at the liquid/solid interface, backdiffusion in the solid and complete mixing in the residual liquid, are consistent with experimental results in the columnar and equiaxed regions. The conclusion that eutectic carbide observed in the centreline region must have resulted from macrosegregation is supported by an estimate of the composition of the enriched liquid.     

Computer prediction of microsegregation in peritectic alloy systems

Abstract

A numerical model for the prediction of solidification and the accompanying microsegregation in peritectic alloys is described. Several finite difference schemes have been tested, based on one-dimensional computational cells for microsegregation calculations. The method selected as the most efficient is that of a fixed computational grid with both solid/solid and solid/liquid boundaries able to move freely between the nodal planes, using a Lagrangian interpolation procedure due to Crank in order to determine solute gradients at the interfaces. The solution method is essentially explicit, although the composition and position of the solid/solid interface have to be floated in an implicit manner to obtain consistent, unique, solutions in multicomponent alloys. Microsegregation and non­equilibrium solidus temperatures have been computed for a number of alloy steel systems using the proposed model and satisfactory agreement obtained with experimental results.     

Coupled problem of heat transfer,hydrodynamics, and solidification in a melt

A mathematical model is constructed which describes thermal and hydrodynamic phenomena accompanying the solidification process in a melt. The equations of hydrodynamics take into account viscoelasticity and compressibility of liquid metal. An example of calculations pertaining to solidification of an ingot is given.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 6, pp. 1109–1118, December, 1981.     

Effect of cooling rate on solidification of electron beam melted silicon ingots

Solidification rate has a significant influence on purification of silicon due to segregation of impurities at a liquid–solid interface of a solidifying silicon ingot. A mathematical model is developed to evaluate time-dependent position of the liquid–solid interface and solidification rate of electron beam melted ingots. A series of solidification experiments with different cooling rates are conducted to measure position of a line which separates directionally grown columnar crystals visible in cross-sections of the solidified ingots. Results show that not the whole ingot solidifies directionally when the reduction rate of the beam current is larger than 1.67 mA/s. The position of the dividing line depends on cooling rate and the experimental trend is consistent with that resulted from theoretical simulations. Modeling shows that the solidification rate changes fast when the beam current reduces linearly that is detrimental for segregation of impurities. It also predicts that an exponential reduction of the beam current leads to a uniform solidification rate which is beneficial to segregation of impurities, though not all exponential current reductions lead to this kind of solidification behavior.     

Modelling of non-equilibrium solidification in ternary alloys: comparison of 1D, 2D,and 3D cellular automaton–finite difference simulations

Abstract

A cellular automaton–finite difference (CAFD) computer model is presented that describes the solidification of multicomponent multiphase alloys at the microscopic level. The objective of the model is to enable the prediction of microsegregation patterns and the appearance of non-equilibrium constituents during non-equilibrium freezing. To support the development of the model, coupling with a thermodynamic software package, ThermoCalc, has been achieved to obtain accurate thermodynamic data for multicomponent alloys. The CAFD model has been used to generate evolving dendritic structures in two and three dimensions. A simple one-dimensional (1D) CAFD plate model, which assumes that adjacent dendrite arms are plates, has also been developed. Recently, experimental results of a study carried out on a directionally solidified Al–3.95Cu–0.8 Mg alloy (cooling rate of 0.378 K s^-1) have been reported. In the present investigation, a comparison between 1D, 2D, and 3D simulations of microsegregation and these experimental results is made, with respect to the amounts of non-equilibrium constituents and solute profiles in the primary -Al phase, for the same alloy and solidification conditions.     

Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys

Abstract

A pure macroscopic two-dimensional numerical model has been developed, capable of capturing the effects of dendritic arm coarsening on the transport phenomena occurring during a binary alloy solidification process. The general continuum conservation equations are aptly modified to take into account shrinkage induced fluid flow. Simultaneously, the effective permeability of the mushy zone is numerically modelled according to the microscopic coarsening kinetics. Moreover, a new nodal latent heat updating algorithm is proposed that takes into account dendritic arm coarsening considerations. The numerical results are first tested against experimental results reported in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation is predicted, compared with that dictated by shrinkage induced fluid flow alone. Physical insights are also developed regarding the effects of various parameters on the overall macrosegregation.     

Effects of Pulsed Magnetic Field on Microsegregation of Solute Elements in a Ni-Based Single Crystal Superalloy

The effects of a pulsed magnetic field(PMF) on the microsegregation of solute elements during directional solidification of a Ni-based single crystal superalloy were experimentally investigated,and the results show that the PMF significantly affects the microsegregation of Al,Ti,Co,Mo and W elements in the alloy.However,the distribution behavior differs for both positive and negative segregation elements.With the PMF,the microsegregation of negative segregation elements,Co and W,was restrained effectively,while that of positive segregation elements,Al,Tiand Mo,was aggravated.A segregation model was established to reveal the distribution mechanism of the elements with PMF.It is considered that,under the action of PMF,the jumping of solute atoms from the liquid phase to solid phase is hindered,but the jumping of solute atoms from the solid phase into liquid phase is promoted during solidification.As a result,the effective distribution coefficient of the solute atoms is reduced,which leads to the reduction of microsegregation of negative segregation elements and aggravation of microsegregation of positive segregation elements.     

Numerical Simulation of Transport Phenomena in Solidification of Multicomponent Ingot Using a Continuum Model

A continuum model proposed for dendrite solidification of multicomponent alloys, with any partial solid back diffusion, was used to numerically simulate the macroscopic solidification transport phenomena and macrosegregations in an upwards directionally solidified plain carbon steel ingot. The computational results of each macroscopic field of the physical variables involved in the solidification process at a middle solidification stage were presented.     

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.     

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.     

Preferred growth orientation and microsegregation behaviors of eutectic in a nickel-based single-crystal superalloy

A nickel-based single-crystal superalloy was employed to investigate the preferred growth orientation behavior of the (γ + γ′) eutectic and the effect of these orientations on the segregation behavior. A novel solidification model for the eutectic island was proposed. At the beginning of the eutectic island’s crystallization, the core directly formed from the liquid by the eutectic reaction, and then preferably grew along [100] direction. The crystallization of the eutectic along [110] always lagged behind that in [100] direction. The eutectic growth in [100] direction terminated on impinging the edge of the dendrites or another eutectic island. The end of the eutectic island’s solidification terminates due to the encroachment of the eutectic liquid/solid interface at the dendrites or another eutectic island in [110] direction. The distribution of the alloying elements depended on the crystalline axis. The degree of the alloying elements’ segregation was lower along [100] than [110] direction with increasing distance from the eutectic island’s center.     

Equi-axed growth and related segregations in cast metallic alloys

Full-scale trials of DC ingots and laboratory scale directional solidification experiments have been performed to study the effect of grain structure on macro-segregation in industrial cast products. An Al alloy sheet ingot was cast with constant casting conditions (speed, superheat, cooling rate) except for the grain refiner: the first half of the ingot was non-inoculated, while the second half was inoculated. The results indicate that the extent and intensity of the centreline segregation is modified via the grain-refinement treatment: the finer the grains are, the more intense is the macro-segregation.Numerical simulations of directional solidification of binary Al–Cu alloys have been carried out with the help of a 2D finite volume software which takes account of the movement of the liquid with respect to the solid in the mushy zone. It is possible to account for the segregation pattern of the directionally solidified ingots that exhibit columnar or coarse equi-axed grain structures. Contrarily, the intense segregation of the fine-grained ingots is not yet understood.     

Equi-axed growth and related segregations in cast metallic alloys

Full-scale trials of DC ingots and laboratory scale directional solidification experiments have been performed to study the effect of grain structure on macro-segregation in industrial cast products. An Al alloy sheet ingot was cast with constant casting conditions (speed, superheat, cooling rate) except for the grain refiner: the first half of the ingot was non-inoculated, while the second half was inoculated. The results indicate that the extent and intensity of the centreline segregation is modified via the grain-refinement treatment: the finer the grains are, the more intense is the macro-segregation.

Numerical simulations of directional solidification of binary Al-Cu alloys have been carried out with the help of a 2D finite volume software which takes account of the movement of the liquid with respect to the solid in the mushy zone. It is possible to account for the segregation pattern of the directionally solidified ingots that exhibit columnar or coarse equi-axed grain structures. Contrarily, the intense segregation of the fine-grained ingots is not yet understood.     

Two‐phase thermo‐mechanical and macrosegregation modelling of binary alloys solidification with emphasis on the secondary cooling stage of steel slab continuous casting processes

As an approach towards a better modelling of solidification problems, we introduce a thermo‐mechanical and macrosegregation model that considers a solidifying alloy as a binary mixture made of a liquid and a solid phase. Macroscopic conservation laws for mass, momentum and solute are obtained by spatial averaging of the respective microscopic conservation equations. Assuming local thermal equilibrium, a single equation for the conservation of the mixture energy is then written. A single equation can be obtained for the solute as well by invoking a proper microsegregation rule. The numerical implementation in a two‐dimensional finite element code is then detailed. Lastly, some examples of simulations of academic tests as well as industrial applications for continuous casting of steel slabs are discussed. They particularly enlighten the ability of the formulation to describe the formation of central macrosegregation during the secondary cooling of slab continuous casting processes. Copyright © 2006 John Wiley & Sons, Ltd.     

Kinetic aspects of the solidification of aluminium-zinc alloys

A method for determination of the kinetics of linear and volumetric dendritic growth on the basis of a model of dendritic solidification process referred to one mole of alloy has been presented. The model parameters have been derived using Krupkowski's equation of dendritic solidification for the case of Al-40 wt% Zn alloy solidified at a definite rate. The constructed kinetics curves have been analysed using the Johnson—Mehl relation and compared with that of Chalmers. The results of calculation concerning the maximum microsegregation have made it possible to define the linear and volumetric dendritic growth rates. The relationships between these rates and the experimental cooling rate of ingot have been discussed.     

Transport Properties and Transport Phenomena in Casting Nickel Superalloys

Nickel superalloys that are used in the high-temperature regions of gas-turbine engines are cast by directional solidification (DS). In the DS processes, the castings are cooled from below, and three zones exist during solidification: (1) an all-solid zone at the bottom, (2) a “mushy zone” that is comprised of solid and liquid material, and (3) an overlying all-liquid zone. Computer simulations can be useful in predicting the complex transport phenomena that occur during solidification, but realistic simulations require accurate values of the transport properties. In addition to transport properties, the thermodynamic equilibria between the solid and liquid during solidification must also be known with reasonable accuracy. The importance of using reasonably accurate estimations of the transport properties is illustrated by two-dimensional simulations of the convection during solidification and the coincidental macrosegregation in the DS castings of multicomponent Ni-base alloys. In these simulations, we examine the sensitivity of the calculated results to measured partition ratios, thermal expansion coefficients, and viscosities that are estimated by regression analyses and correlations of existing property data.     

等轴晶移动对宏观偏析影响的数值模拟

建立了自由等轴晶移动对宏观偏析影响的数学模型,对铸锭凝固过程中的对流和溶质分布进行了数值模拟.在模型中按照临界固相分数将糊状区分为紧密树枝晶和自由等轴晶两个不同的区域.对带冒口铸钢锭的宏观偏析进行了数值模拟,并同实验结果进行了比较.与假设糊状区内固相静止的模型相比,考虑等轴晶移动的模型得到的溶质分布结果与实验结果更接近.在凝固过程中,等轴晶随液体流动并在铸锭的底部中心聚集,在凝固后的铸锭中形成锥形的负偏析.还发现,在铸锭的中心靠上的区域形成正偏析,在铸锭的外部区域形成负偏析.