Effect of partition coefficient on microsegregation during solidification of aluminium alloys

In the modeling of microsegregation, the partition coefficient is usually calculated using data from the equilibrium phase diagrams. The aim of this study was to experimentally and theoretically analyze the partition coefficient in binary aluminum--copper alloys. The sam- ples were analyzed by differential thermal analysis （DTA）, which were melted and quenched from different temperatures during solidifica- tion. The mass fraction and composition of phases were measured by image processing and scanning electron microscopy （SEM） equipped with an energy-dispersive X-ray spectroscopy （EDS） unit. These data were used to calculate as the experimental partition coefficients with four different methods. The experimental and equilibrium partition coefficients were used to model the concentration profile in the primary phase. The modeling results show that the profiles calculated by the experimental partition coefficients are more consistent with the experi- mental profiles, compared to those calculated using the equilibrium partition coefficients.

Microsegregation and Rayleigh number variation during the solidification of superalloy Inconel 718

The microstructure and composition of the residual liquid at different temperatures were investigated by scanning electron microscopy （SEM） and energy dispersive X-ray spectrometer （EDX） associated with the Thermo-calc software calculation of the equilibrium phase diagrams of Inconel 718 and segregated liquid. The liquid density difference and Rayleigh number variation during solidification were estimated as well. It is found that the heavy segregation of Nb in liquid prompts the precipitation of δ and Laves phase directly from liquid and the resultant quenched liquid microstructure consists of pro-eutectic γ＋eutectic,or complete eutectic according to the content of Nb from low to high. The liquid density increases with decreasing temperature during the solidification of Inconel 718 and the liquid density difference is positive. The largest relative Rayleigh number occurs at 1320°C when the liquid fraction is about 40vol%.

Numerical simulation of microstructure evolution and microsegregation of U-Nb alloy during solidification process

In this work, a cellular automaton model has been developed to simulate the microstructure evolution of U-Nb alloy during the solidification process. The preferential growth orientation, solute redistribution in both liquid and solid, solid/liquid interface solute conservation, interface curvature and the growth anisotropy were considered in the model. The model was applied to simulate the dendrite growth and Nb microsegregation behavior of U-5.5 Nb alloy during solidification, and the predicted results showed a reasonable agreement with the experimental results. The effects of cooling rates on the solidification microstructure and composition distribution of U-5.5 Nb were investigated by using the developed model. The results show that with the increase of the cooling rate, the average grain size decreases and the Nb microsegregation increases.

Phase field simulation of the columnar dendritic growth and microsegregation in a binary alloy

This paper applies a phase field model for polycrystalline solidification in binary alloys to simulate the formation and growth of the columnar dendritic array under the isothermal and constant cooling conditions. The solidification process and microsegregation in the mushy zone are analysed in detail. It is shown that under the isothermal condition solidification will stop after the formation of the mushy zone, but dendritic coarsening will progress continuously, which results in the decrease of the total interface area. Under the constant cooling condition the mushy zone will solidify and coarsen simultaneously. For the constant cooling solidification, microsegregation predicted by a modified Brody- Flemings model is compared with the simulation results. It is found that the Fourier number which characterizes microsegregation is different for regions with different microstructures. Dendritic coarsening and the larger area of interface should account for the enhanced Fourier number in the region with well developed second dendritic arms.

Effect of melting rate on microsegregation and primary MC carbides in M2 high-speed steel during electroslag remelting

Large-size primary MC carbides can significantly reduce the performance of M2 high-speed steel.To better control the morphology and size of primary MC carbides,the effect of melting rate on microsegregation and primary MC carbides of M2 steel during electroslag remelting was investigated.When the melting rate is decreased from 2 kg·min^(-1) to 0.8 kg·min^(-1),the columnar dendrites are gradually coarsened,and the extent of segregation of Mo and V is alleviated,while the segregation of Cr becomes severe.At 2 kg·min^(-1),the number of primary MC carbides per unit area with the sizes in the range of 2 μm to 6 μm accounts for about 75% of all MC carbides,while the carbides are mainly concentrated on the size larger than 8 μm at 0.8 kg·min^(-1).Thermodynamic calculations based on the Clyne-Kurz (simplified to C-K) model shows that MC carbide can be precipitated in the final solidification stage and a smaller secondary dendrite arm spacing caused by higher melting rate (2 kg·min^(-1) in this experiment) facilitates the refinement of primary MC carbides.

SOLIDIFICATION AND MICROSEGREGATION BEHAVIORS OF NICKEL-BASE SINGLE CRYSTAL SUPERALLOY SOLIDIFIED AT MEDIUM COOLING RATE

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Microsegregation and Improved Methods of Squeeze Casting 2024 Aluminium Alloy

The squeeze casting of a 2024 Al alloy was carried out to investigate the effect on microsegregation in the alloy of the application of pressure followed by diffusion annealing. The experimental results indicate that an optimum applied pressure followed by an optimum diffusion annealing process can markedly reduce the degree of microsegregation and improve the mechanical properties to a degree that can approach the level of forged 2024 Al alloy.

Numerical Simulation of Morphology and Microsegregation Evolution during Solidification of Al-Si Alloy

A stochastic model coupled with transient calculations for the distributions of temperature, solute and velocity during the solidification of binary alloy is presented. The model can directly describe the evolution of both morphology and segregation during dendritic crystal growth. The model takes into account the curvature and growth anisotropy of dendritic crystals. Finite difference method is used to explicitly track the sharp solid liquid (S/L) interface on a fixed Cartesian grid. Two-dimensional mesoscopic calculations are performed to simulate the evolution of columnar and equiaxed dendritic morphologies of an AI-7 wt pct Si alloy. The effects of heat transfer coefficient on the evolution of both the dendrite morphology and segregation patterns during the solidification of binary alloys are analyzed. This model is applied to the solidification of small casting. Columnar-to-equiaxed transition is analyzed in detail. The effects of heat transfer coefficient on final casting structures are also studi

Modeling solidification structure evolution and microsegregation under pressure condition

Solidification microstructure and microsegregation were simulated under a constant pressure condition using the cellular automaton method. First, a single dendrite evolution was simulated and compared under pressure condition and under normal condition, respectively. The solidification microstructure and microsegregation were then simulated. Through simulation, it may be concluded that if the growth direction of the dendrite is parallel to the pressure direction, dendrite growth will be hindered. On the other hand, pressure has no influence on the dendrite evolution. However, when two dendrites grow in close contact, solute enrichment occurs in the dendrites, which hinders the growth of the dendrites. In addition, the solute is preferentially enriched along the pressure direction.

Particle size dependence of the microsegregation and microstructure in the atomized Ni-based superalloy powders:Theoretical and experimental study

The microstructure and microsegregation of atomized powder,which depend on their sizes,are of great importance to the mechanical properties of the consolidated bulk materials.Therefore,it is necessary to reveal the relationship between particle size and powder attributes.The effects of particle size on the so-lidification characterization of the atomized Ni-based superalloy powders were studied via finite element simulation.Based on the simulations,a model was developed to predict the microsegregation and mi-crostructure of atomized powders with different sizes and study the influence of thermal history on the powder attributes during the atomization processes.The radiation heat transfer and temperature gradi-ent within the rapid solidification alloy powders were taken into account in this model.For validating the accuracy of the model,the predictions of the present model were compared with the microsegregation and microstructure of the specific size powder close to the screen mesh size.The results showed that mi-crostructure depended primarily on the temperature gradient within the powder,while the solidification rate had a more significant effect on the microsegregation.The model predicted microstructure features in agreement with the experiment,and for microsegregation,the deviations of prediction for most ele-ments were less than 10%.This work provides a new model to precisely predict the microsegregation and microstructure of the atomized alloy powders and sets a foundation to control the powder features for various engineering applications.

Effect of nitrogen on microstructure and microsegregation of martensitic stainless steel 4Cr13 produced by electroslag remelting

Two ingots of 4Cr13 martensitic stainless steel with different nitrogen contents,0.023 and 0.121 mass%,were produced by vacuum induction furnace and electroslag remelting.The microstructure and the microsegregation of the electroslag remelting ingot were analyzed by optical microscopy,scanning electron microscopy and electron microprobe analysis.Thermo-Calc software was used to calculate the nitrogen solubility changes during solidification of high nitrogen martensitic stainless steel and the equilibrium and non-equilibrium phase diagrams of 4Cr13 steel with different nitrogen contents.The solubility of nitrogen in 4Cr13 steel reached the lowest value of 0.118%before the start of the peritectic reaction.The microstructure of 4Cr13 steel was martensite,retained austenite and primary carbide M_(7)C_(3).Higher nitrogen content increased the content of retained austenite in martensitic stainless steel,inhibited the precipitation of primary carbides and refined the dendrites.Higher nitrogen content could effectively inhibit the microsegregation of C element in martensitic stainless steel;however,it had little effect on Cr,V,Nb and Ti.The peritectic reaction was first carried out in high nitrogen steel during solidification,which advanced the transformation of austenite and inhibited the microsegregation of C element.

Simulation of the Dendrite Morphology and Microsegregation in Solidification of Al–Cu–Mg Aluminum Alloys

Since most typical alloys in industrial applications are multicomponent with three or more components, and various CA models proposed in the past mainly focus on the binary alloys, a two-dimensional modified cellular automaton model allowing for the quantitatively predicting dendrite growth of multicomponent alloys in the low P6clet number regime is presented. The elimination of the mesh-induced anisotropy is achieved by adopting a modified virtual front tracking method. A new efficient method based on the lever rule is applied to calculate the solid fraction increment of the interfacial cells. The thermodynamic data such as liquidus temperature, the partition coefficients, and the slope of liquidus surface, needed for determining the dynamics of dendrite growth, are obtained by coupling with PanEngine. This model is applied to simulate the dendrite morphology and microsegregation of A1-Cu-Mg temary alloy both for single and multi- dendrites growth. The simulated results demonstrate that the difference of the concentration distribution profiles ahead of the dendrite tip for each alloying element mainly results from the different partition coefficients and solute diffusion coefficients. Comparison with the prediction of analytical model is carded out and it reveals the correctness of the model. Consequently, the difference in interdendritic microsegregation behavior of different components is analyzed.

Effect of cooling rate on microstructure,microsegregation and mechanical properties of cast Ni-based superalloy K417G

The effects of different solidification rates after pouring on the microstructures,microsegregation and mechanical properties of cast superalloy K417 G were investigated.Scheil-model was applied to calculate the temperature range of solidification.The casting mould with different casting runners was designed to obtain three different cooling rates.The microstructures were observed and the microsegregation was investigated.Also,high temperature tensile test was performed at 900℃ and stress rupture test was performed at 950℃ with the stress of 235 MPa.The results showed that the secondary dendrite arm spacing,microsegregation,the size and volume fraction of γ＇phase and the size of γ/γ＇eutectic increased with decreasing cooling rate,but the volume fraction of γ/γ＇ eutectic decreased.In the cooling rate range of 1.42℃s^-1–0.849 s^-1,the cast micro-porosities and carbides varied little,while the volume fraction and size of phase and γ/γ＇ eutectic played a decisive role on mechanical properties.The specimen with the slowest cooling rate of 0.84℃ s^-1 showed the best comprehensive mechanical properties.

Quantitative effects of phase transition on solute partition coefficient,inclusion precipitation, and microsegregation for high-sulfur steel solidification

Segregation and inclusion precipitation are the common behaviours of steel solidification, which are resulted from the redistribution and diffusion of the solute elements at the solid-liquid interface. The effect of the phase transition of high-sulfur free-cutting steel is quantified in the present work for the solute partition coefficient(ki), inclusion precipitation, and microsegregation by establishing a coupling model of microsegregation and inclusion precipitation, wherein the quantified dependencies of ki in terms of temperature, phase and carbon(C) content were applied. Results showed that the solidification temperature range and phase transition of high-sulfur steel that under different solidification paths and C contents were quite different, leading to differences in ki and eventually in microsegregation. kC,kP, and kS were mainly affected by phase composition and kSi was primarily by temperature, while kMn depended on both phase composition and temperature during solidification. Increasing the C content within the interval 0.07-0.48 wt%, the ‘proportion of the δ phase maintained temperature region during solidification’(Pδ), kave Pand kave S(kiave, the average value of the ki across the whole stages of solidification)decreased monotonically, whereas kave Cincreased linearly. The peritectic reaction impacted on the phase composition and ki, leading to the change in microsegregation. Such effect of the peritectic reaction was more significant at the last stage of solidification. When the Pδ was between 75% and 100%(corresponding to 0.07-0.16 wt% C), the solidification path resulted in a greater effect on the microsegregation of solutes C, P, and S because of the peritectic reaction. The microsegregation of solutes Mn and S were comprehensively influenced by kMn, kS and Mn S precipitation as well. The studies would help reveal the solute redistribution at the solid-liquid interface, and improve the segregation of high-sulfur steel by controlling the solidification and precipitation in practice.

Effect of titanium and rare earth microalloying on microsegregation,eutectic carbides of M2 high speed steel during ESR process

The effects of RE and Ti microalloying during electroslag remelting(ESR)process on the microsegregation and morphology of eutectic M2C carbides in M2 high speed steel were investigated.The results show that the addition of 0.2 wt%RE can alleviate the segregation of C,W,Mo,V and Cr,while the morphology of eutectic M2C carbides hardly changes.The microalloying with the addition of 0.5 wt%Ti has the lowest degree of microsegregation due to the improvement of primary dendrites by the effective heterogeneous nucleating agent of(Ti,V)(C,N)particles.The addition of Ti makes the mo rphology of M2C carbides change from rod-like or maze-like shape into a coarse feathery shape,exhibiting anisotropic facet growth characteristics.For the microalloying of 0.2 wt%RE and 0.5 wt%Ti,the segregation of the main metal alloying elements is slightly more severe than that of the addition of only RE or Ti.Under the combined action of RE and Ti,the feathery eutectic M2C becomes thinner and shorter and tends to be isolated or distributed in a discontinuous network.

Microstructure, Microsegregation, and Mechanical Properties of Directional Solidified Mg–3.0Nd–1.5Gd Alloy

The microstructure, microsegregation, and mechanical properties of directional solidified Mg–3.0Nd–1.5Gd ternary alloys were experimentally studied. Experimental results showed that the solidification microstructure was composed of dendrite primary a（Mg） phase and interdendritic a（Mg） · Mg12（Nd, Gd） eutectic and Mg5 Gd phase. The primary dendrite arm spacing k1 and secondary dendrite arm spacing k2 were found to be depended on the cooling rate R in the form k1= 8.0415 9 10-6R-0.279 and k2= 6.8883 9 10-6R-0.205, respectively, under the constant temperature gradient of40 K/mm and in the region of cooling rates from 0.4 to 4 K/s. The concentration profiles of Nd and Gd elements calculated by Scheil model were found to be deviated from the ones measured by EPMA to varying degrees, due to ignorance of the back diffusion of the solutes Nd and Gd within a（Mg） matrix. And microsegregation of Gd depended more on the growth rate, compared with Nd microsegregation. The directionally solidified experimental alloy exhibited higher strength than the non-directionally solidified alloy, and the tensile strength of the directionally solidified experimental alloy was improved,while the corresponding elongation decreased with the increase of growth rate.

Microstructure and microsegregation of directionally solidified Ti–45Al–8Nb alloy with different solidification rates

Microstructure and microsegregation of directionally solidified Ti-45Al-8Nb alloy were investigated by scanning electron microscopy（SEM）,transmission electron microscopy（TEM） and electron probe microanalyzer（EPMA）.For the alloy solidified at the solidification rates（v） ranging from 10 to 400 μm·s^（-1）,the microstructure of the mushy zone exhibits a cellular-dendritic structure at lower growth rate（v=10-50 μm·s^（-1）） and a typical dendritic morphology at higher growth rate（v = 100-400 μm·s^（-1））.The relationship between primary dendrite arm spacing（λ_1）and v is λ_1=1.08×10~3v^（-0.35）.Al and Nb elements segregate at interdendritic zone and in the dendritic core,respectively.In solid of mushy zone,a relatively flat concentration profile is observed for the typical dendrite structure,and Nb enriches in B2 phase induced by β→α＋βtransformation.The content of B2 phase is hardly affected by v.The extent of microsegregation in steady-state zone decreases at a lower growth rate because holding the samples at higher temperature after solidification for a long time can homogenize the solid effectively.

Effect of Nb Content on Solidification Characteristics and Microsegregation in Cast Ti-48Al-xNb Alloys

Microstructural evolution in nonequihbrium solidification of Ti-48Al-xNb alloys with Nb contents ranging from2 to 8 at%has been studied by containerless electromagnetic levitation.Levitated drops of controlled undercooling were quenched onto chill copper substrates and subjected to phase and microstructure analysis.With increasing Nb content,the solidification path changes gradually from hyperperitectic solidification to hypoperitectic solidification and both solidification segregation（S-segregation） and β-solidification gradually increase.A transition from typical hypoperitectic solidification to a sole solidification of the β phase beyond a critical undercooling is revealed for the Ti-48Al-8Nb hypoperitectic alloy.For the Ti-48Al-2Nb alloy,the morphologies of the primary β dendrites are not observed.With increasing undercooling,the coarsening of the lamellar colonies occurs,which can be attributed to the transition of the primary β dendritic morphology.Furthermore,the solute concentration profiles for the final solidification microstructure are obtained to examine the segregation behaviors of alloying elements.With increasing Nb content,the undercooling eliminating S-segregation gradually increases.

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.

Reduction in Microsegregation in Al-Cu Alloy by Alternating Magnetic Field

The microsegregation behavior of the Al-4.5 wt%Cu alloy solidified at different cooling rates under the alternating magnetic field(AMF) was investigated.The experimental results showed that the amount of non-equilibrium eutectics in the interdendritic region decreased upon applying the AMF at the same cooling rate.The change in microsegregation could be explained quantificationally by the modifications of dendritic coarsening,solid-state back diffusion and convection in the AMF.The enhanced diffusivity in the solid owing to the AMF was beneficial for the improvement in microsegregation compared to the cases without an AMF.In contrast,the enhanced dendritic coarsening and forced convection in the AMF were found to aggravate the microsegregation level.Considering the contributions of the changes in above factors,an increase in solid diffusivity was found to be primarily responsible for the reduced microsegregation in the AMF.In addition,the microsegregation in the AMF was modeled using the analytical model developed by Voller.The calculated and experimental results were in reasonable agreement.