Three dimensional phase-field simulation for non-isothermal binary alloy solidification: Comparison with LKT theory

Using the advanced algorithm combining parallel computing,adaptive mesh re-griding and multigrid methods,quantitative 3D phase-field simulations of non-isothermal solidification of binary alloy were carried out.The 3D phase-field simulation results were compared with the analytical LKT(Lipton,Kurz and Trivedi)theory.For comparison,the simulation and analytical results for 2D cases were also given.The 3D phase-field simulation results support the transport portion of the LKT theory.However,the tip radius and tip velocity predicted by the simulations are not in good agreement with the LKT theory over the whole range of undercooling.The stability parameter calculated from phase-field simulations varies significantly with the Peclet number,indicating that the stability criterion,which assumes that the stability parameter is constant,is invalid.

Comparative analysis of isothermal and non-isothermal solidification of binary alloys using phase-field model

Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field controlled equations. And the alternating direction implicit(ADI) algorithm for solving temperature field controlled equation was also employed to avoid the restriction of time step. Some characteristics of the Ni-Cu alloy were captured in the process of non-isothermal solidification, and the comparative analysis of the isothermal and the non-isothermal solidification was investigated. The simulation results indicate that the non-isothermal model is favorable to simulate the real solidification process of binary alloys, and when the thermal diffusivity decreases, the non-isothermal phase-field model is gradually consistent with the isothermal phase-field model.

Phase field simulation for non-isothermal solidification of multicomponent alloys coupled with thermodynamics database

In order to quantitively model the real solidification process of industrial multicomponent alloys, a non-isothermal phase field model was studied for multicomponent alloy fully coupled with thermodynamic and diffusion mobility database, which can accurately predict the phase equilibrium, solute diffusion coefficients, specific heat capacity and latent heat release in the whole system. The results show that these parameters are not constants and their values depend on local concentration and temperature. Quantitative simulation of solidification in multicomponent alloys is almost impossible without such parameters available. In this model, the interfacial region is assumed to be a mixture of solid and liquid with the same chemical potentials, but with different composition. The anti-trapping current is also considered in the model. And this model was successfully applied to industrial A1-Cu-Mg alloy for the free equiaxed dendrite solidification process.

Volume-averaged modeling of multiphase solidification with equiaxed crystal sedimentation in a steel ingot

Macrosegregation is a critical factor that limits the mechanical properties of materials.The impact of equiaxed crystal sedimentation on macrosegregation has been extensively studied,as it plays a significant role in determining the distribution of alloying elements and impurities within a material.To improve macrosegregation in steel connecting shafts,a multiphase solidification model that couples melt flow,heat transfer,microstructure evolution,and solute transport was established based on the volume-averaged Eulerian-Eulerian approach.In this model,the effects of liquid phase,equiaxed crystals,columnar dendrites,and columnar-to-equiaxed transition(CET)during solidification and evolution of microstructure can be considered simultaneously.The sedimentation of equiaxed crystals contributes to negative macrosegregation,where regions between columnar dendrites and equiaxed crystals undergo significant A-type positive macrosegregation due to the CET.Additionally,noticeable positive macrosegregation occurs in the area of final solidification in the ingot.The improvement in macrosegregation is beneficial for enhancing the mechanical properties of connecting shafts.To mitigate the thermal convection of molten steel resulting from excessive superheating,reducing the superheating during casting without employing external fields or altering the design of the ingot mold is indeed an effective approach to control macrosegregation.

Effect of Co on Solidification Characteristics and Microstructural Transformation of Non-equilibrium Solidified Cu-Ni Alloys

Non-equilibrium solidification structures of Cu55Ni45 and Cu55Ni43Co2 alloys were prepared by the molten glass purification cycle superheating method.The variation of the recalescence phenomenon with the degree of undercooling in the rapid solidification process was investigated using an infrared thermometer.The addition of the Co element affected the evolution of the recalescence phenomenon in Cu-Ni alloys.The images of the solid-liquid interface migration during the rapid solidification of supercooled melts were captured by using a high-speed camera.The solidification rate of Cu-Ni alloys,with the addition of Co elements,was explored.Finally,the grain refinement structure with low supercooling was characterised using electron backscatter diffraction(EBSD).The effect of Co on the microstructural evolution during nonequilibrium solidification of Cu-Ni alloys under conditions of small supercooling is investigated by comparing the microstructures of Cu55Ni45 and Cu55Ni43Co2 alloys.The experimental results show that the addition of a small amount of Co weakens the recalescence behaviour of the Cu55Ni45 alloy and significantly reduces the thermal strain in the rapid solidification phase.In the rapid solidification phase,the thermal strain is greatly reduced,and there is a significant increase in the characteristic undercooling degree.Furthermore,the addition of Co and the reduction of Cu not only result in a lower solidification rate of the alloy,but also contribute to the homogenisation of the grain size.

Advantages of rapid solidification over casting of Mg-0.4Zn-1Y alloy

The Mg-Y-Zn magnesium alloy system is commonly recognized for its remarkable combination of high strength and ductility,achieved even with minimal amounts of alloying elements.This exceptional performance is attributed to its unique microstructure,which includes Long-Period Stacking Ordered(LPSO)phases or the distinctive microstructure derived from the LPSO phase,referred to as the Mille-Feuille structure(MFS).This study systematically compares the traditional ingot metallurgy method with the rapid solidification technique,coupled with diverse heat treatments and extrusion processes.Microscopic analyses reveal variations in the presence of LPSO phases,Mille-Feuille structure,and grain size,leading to divergent mechanical and corrosion properties.The rapid solidification approach stands out,ensuring superior mechanical properties alongside a reasonable corrosion rate.

Solidification/Stabilization of Chromium in Red Mud-based Geopolymer

Up to 1.5wt%of Cr(Ⅲ)salts(CrCl_(3),and Cr_(2)O_(3))and Cr(Ⅵ)salts(Na_(2)CrO_(4),and CaCr_(2)O_(7))were incorporated into red mud-based geopolymers,respectively.The solidification/stabilization,compressive strength,and durability of the Cr-containing geopolymers were investigated.The experimental results indicate that the red mud-based geopolymer could effectively solidify/stabilize different types of Cr salts with solidification/stabilization rates of above 99.61%.Geopolymers are environmentally safe when the dosage of CaCr_(2)O_(7)is≤1.0wt%,or the dosage of CrCl_(3),Cr_(2)O_(3),and Na_(2)CrO_(4)is≤1.5wt%,respectively.The effects of Cr salts on the compressive strength varies with the type and content of Cr salts.The freeze-thaw cycle is more destructive to geopolymer properties than sulfate attack or acid rain erosion.The solidification/stabilization of Cr is mainly attributed to the following reasons:a)The chemical binding of Cr is related to the formation of Cr-containing hydrates(eg,magnesiochromite((Mg,Fe)(Cr,Al)_(2)O_(4)))and doping into N-A-S-H gel and C-A-S-H gel framework;b)The physical effect is related to the encapsulation by the hydration products(e g,N-A-S-H gel and C-A-S-H gel).This study provides a reference for the treatment of hazardous Cr-containing wastes by solid waste-based geopolymers.

Preparation of Laser Cladding Coating Undercooling Cu-based Alloy and Co on Non-equilibrium Solidification Structure

The effect of the gradient content of Co element on the solidification process of Cu-based alloy under deep under cooling conditions was explored.The non-equilibrium solidification structure of the under cooled alloy samples were analyzed.It is found that the rapidly solidified alloy has undergone twice grain refinement during the undercooling process.Characterization and significance of the maximum undercooling refinement structure of Cu60Ni35Co5 at T=253 K were analyzed.High-density defects were observed,such as dislocations,stacking faults networks,and twinning structures.The standard FCC diffraction pattern represents that it is still a single-phase structure.Based on the metallographic diagram,EBSD and TEM data analysis,it is illustrated that the occurrence of grain refinement under high undercooling is due to stress induced recrystallization.In addition,the laser cladding technology is used to coat Co-based alloy(Stellite12) coating on 304 stainless steel substrate;the microstructure of the coating cross-section was analyzed.It was found that the microstructure of the cross-section is presented as columnar crystals,planar crystals,and disordered growth direction,so that the coating has better hardness and wear resistance.By electrochemical corrosion of the substrate and coating,it can be seen that the Co and Cr elements present in the coating are more likely to form a dense passivation film,which improved the corrosion resistance of the coating.

Effect of solidification cooling rate on microstructure and tribology characteristics of Zn-4Si alloy

The main objective of this work was to modify the microstructure and enhance the tribological properties of a new Zn-4Si al-loy through a high solidification cooling rate(SCR).According to the results,by increasing the SCR from 2.0 to 59.5℃/s the average size of primary Si particles and that of the grains reduced from 76.1 and 3780μm to less than about 14.6 and 460μm,respectively.Augment-ing the SCR also enhanced the microstructural homogeneity,decreased the porosity content(by 50%),and increased the matrix hardness(by 36%).These microstructural changes enhanced the tribological behavior.For instance,under the applied pressure of 0.5 MPa,an in-crease in the SCR from 2.0 to 59.5℃/s decreased the wear rate and the average friction coefficient of the alloy by 57%and 23%,respect-ively.The wear mechanism was also changed from the severe delamination,adhesion,and abrasion in the slowly-cooled alloy to the mild tribolayer delamination/abrasion in the high-cooling-rate-solidified sample.

Irregular initial solidification by mold thermal monitoring in the continuous casting of steels:A review

Occasional irregular initial solidification phenomena,including stickers,deep oscillation marks,depressions,and surface cracks of strand shells in continuous casting molds,are important limitations for developing the high-efficiency continuous casting of steels.The application of mold thermal monitoring(MTM) systems,which use thermocouples to detect and respond to temperature variations in molds,has become an effective method to address irregular initial solidification phenomena.Such systems are widely applied in numerous steel companies for sticker breakout prediction.However,monitoring the surface defects of strands remains immature.Hence,indepth research is necessary to utilize the potential advantages and comprehensive monitoring of MTM systems.This paper summarizes what is included in the irregular initial solidification phenomena and systematically reviews the current state of research on these phenomena by the MTM systems.Furthermore,the influences of mold slag behavior on monitoring these phenomena are analyzed.Finally,the remaining problems of the formation mechanisms and investigations of irregular initial solidification phenomena are discussed,and future research directions are proposed.

Numerical simulation on directional solidification and heat treatment processes of turbine blades

Study on turbine blades is crucial due to their critical role in ensuring the efficient and reliable operation of aircraft engines.Nickel-based single crystal superalloys are extensively used in the hot manufacturing of turbine blades due to their exceptional high-temperature mechanical properties.The hot manufacturing of single crystal blades involves directional solidification and heat treatment.Experimental manufacturing of these blades is time-consuming,capital-intensive,and often insufficient to meet industrial demands.Numerical simulation techniques have gained widespread acceptance in blade manufacturing research due to their low energy consumption,high efficiency,and rapid turnaround time.This article introduces the modeling and simulation of hot manufacturing in single crystal blades.The discussion outlines the prevalent mathematical models employed in numerical simulations related to blade hot manufacturing.It encapsulates the advancements in research concerning macro to micro-level numerical simulation techniques for directional solidification and heat treatment processes.Furthermore,potential future trajectories for the numerical simulation of single crystal blade hot manufacturing are also discussed.

Oxidation behavior of ferrovanadium spinel particles in air:Isothermal kinetic and reaction mechanism

The oxidation behavior of ferrovanadium spinel(FeV_(2)O_(4)),synthesized via high-temperature solid-state reaction,was investigated using thermogravimetry,X-ray diffractometry,and X-ray photoelectron spectroscopy over the temperature range of 450–700℃.The results revealed that the oxidation process of FeV_(2)O_(4)can be divided into three stages with the second stage being responsible for maximum weight gain due to oxidation.Three classical methods were employed to analyze the reaction mechanisms and model functions for distinct oxidation stages.The random nucleation and subsequent growth(A_(3))kinetic model was found to be applicable to both initial and secondary stage.The third stage of oxidation was consistent with the three-dimensional diffusion,spherical symmetry(D_(3))kinetic mode.Both the model-function method and the model-free method were utilized to investigate the apparent activation energy of the oxidation reaction at each stage.It was found that the intermediates including Fe_(3)O_(4),VO_(2),V_(2)O_(3),and Fe_(2.5)V_(7.11)O_(16),played significant roles in the oxidation process prior to the final formation of FeVO_(4)and V_(2)O_(5)through oxidation of FeV_(2)O_(4).

Exploration of the coupled lattice Boltzmann model based on a multiphase field model:A study of the solid-liquid-gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann(PF-LBM)model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface,the interaction between dendrites and bubbles,and the effects of different temperatures,anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.%butanedinitrile alloy during the solidification process.The model adopts a multiphase field model to simulate the growth of dendrites,calculates the growth motions of dendrites based on the interfacial solute equilibrium;and adopts a lattice Boltzmann model(LBM)based on the Shan-Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase,which includes the interaction between solid-liquid-gas phases.The simulation results show that during the directional growth of columnar dendrites,bubbles first precipitate out slowly at the very bottom of the dendrites,and then rise up due to the different solid-liquid densities and pressure differences.The bubbles will interact with the dendrite in the process of flow migration,such as extrusion,overflow,fusion and disappearance.In the case of wide gaps in the dendrite channels,bubbles will fuse to form larger irregular bubbles,and in the case of dense channels,bubbles will deform due to the extrusion of dendrites.In the simulated region,as the dendrites converge and diverge,the bubbles precipitate out of the dendrites by compression and diffusion,which also causes physical phenomena such as fusion and spillage of the bubbles.These results reveal the physical mechanisms of bubble nucleation,growth and kinematic evolution during solidification and interaction with dendrite growth.

Lunar In Situ Large-Scale Construction:Quantitative Evaluation of Regolith Solidification Techniques

Lunar habitat construction is crucial for successful lunar exploration missions.Due to the limitations of transportation conditions,extensive global research has been conducted on lunar in situ material processing techniques in recent years.The aim of this paper is to provide a comprehensive review,precise classification,and quantitative evaluation of these approaches,focusing specifically on four main approaches:reaction solidification(RS),sintering/melting(SM),bonding solidification(BS),and confinement formation(CF).Eight key indicators have been identified for the construction of low-cost and highperformance systems to assess the feasibility of these methods:in situ material ratio,curing temperature,curing time,implementation conditions,compressive strength,tensile strength,curing dimensions,and environmental adaptability.The scoring thresholds are determined by comparing the construction requirements with the actual capabilities.Among the evaluated methods,regolith bagging has emerged as a promising option due to its high in situ material ratio,low time requirement,lack of hightemperature requirements,and minimal shortcomings,with only the compressive strength falling below the neutral score.The compressive strength still maintains a value of 2–3 MPa.The proposed construction scheme utilizing regolith bags offers numerous advantages,including rapid and large-scale construction,ensured tensile strength,and reduced reliance on equipment and energy.In this study,guidelines for evaluating regolith solidification techniques are provided,and directions for improvement are offered.The proposed lunar habitat design based on regolith bags is a practical reference for future research.

Phase field modeling of multiple dendrite growth of Al-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.

Microstructure evolution of isothermal holding treatment during melt solidification of Ti-6Al-4V alloy

Effect of isothermal holding treatment in the solidification process on the microstructure of Ti-6Al-4V alloy was studied by temperature controlled induced melting apparatus. The result shows that with isothermal holding treatment above the β transus temperature during solidification, the colony structure consisting of parallel lamellae was obtained. While the isothermal holding treatment was set at 960 °C, a unique bi-modal microstructure consisting of coarse primary α and fine secondary lamellar α was obtained. The primary lamellar α tended to break into several pieces, globularize and present equiaxed morphology. The formation mechanism of the equiaxed α can be explained with the atom immigration, high density dislocations, combined action with the interface tension of formed α phase during the isothermal holding treatment. After the isothermal holding, the retained β matrix transformed into fine lamellar α, thus, bi-modal microstructure was acquired. Compared with the lamellar structure, the grain boundary α presented discontinuously and cannot be distinguished from the primary α lamellae easily. The size of colonies α was greatly decreased. The microstructure tended to be much more homogeneous in the whole section of the samples.

Phase field modeling of dendritic coarsening during isothermal solidification

Dendritic coarsening in AI-2mol%Si alloy during isothermal solidification at 880K was investigated by phase field modeling. Three coarsening mechanisms operate in the alloy： （a） melting of small dendrite arms; （b） coalescence of dendrites near the tips leading to the entrapment of liquid droplets; （c） smoothing of dendrites. Dendrite melting is found to be dominant in the stage of dendritic growth, whereas coalescence of dendrites and smoothing of dendrites are dominant during isothermal holding. The simulated results provide a better understanding of dendrite coarsening during isothermal solidification.

Isothermal solidification behavior of typical Ni_3Al base superalloy IC6

Solidification sequence of a typical Ni 3Al base superalloy IC6 was studied by isothermal solidification method. The results show that the liquidus, solidus, melting point of the boride and secondary γ ′ precipitation temperature of the IC6 alloy are notably higher than those of conventional nickel base superalloys because of its higher Mo content. There is no eutectic γ ′ precipitation during the solidification of the alloy, but a kind of Mo rich δ Ni 0.76 Mo 1.24 primary phase precipitates together with γ phase by eutectic reaction L ′→ δ + γ + L ″ in the temperature range of 1 573～1 553 K, this δ Ni 0.76 Mo 1.24 phase has a primitive orthorhombic structure with a=0.917 8 nm, b=0.914 2 nm and c=0.882 8 nm. Moreover, Al element of the alloy segregates in dendritic areas during isothermal solidification process, which causes secondary γ ′ phase precipitate in the order of precedence from dendrites to interdendrites.

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.

Recent research progress on the phase-field model of microstructural evolution during metal solidification

Solidification structure is a key aspect for understanding the mechanical performance of metal alloys,wherein composition and casting parameters considerably influence solidification and determine the unique microstructure of the alloys.By following the principle of free energy minimization,the phase-field method eliminates the need for tracking the solid/liquid phase interface and has greatly accelerated the research and development efforts geared toward optimizing metal solidification microstructures.The recent progress in the application of phasefield simulation to investigate the effect of alloy composition and casting process parameters on the solidification structure of metals is summarized in this review.The effects of several typical elements and process parameters,including carbon,boron,silicon,cooling rate,pulling speed,scanning speed,anisotropy,and gravity,on the solidification structure are discussed.The present work also addresses the future prospects of phase-field simulation and aims to facilitate the widespread applications of phase-field approaches in the simulation of microstructures during solidification.