Comparison of Cellular Automaton and Phase Field Models to Simulate Dendrite Growth in Hexagonal Crystals

A cellular automaton (CA)-finite element (FE) model and a phase field (PF)-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals.In the CA-FE model,the conservation equations of mass and energy were solved in order to calculate the temperature field,solute concentration,and the dendritic growth morphology.CA-FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing (SDAS) vs cooling rate.In the PF model,a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials.Another PF variable was considered to determine the evolution of solute concentration.Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz (LGK),showing quantitatively good agreement in the tip growth velocity at a given melt undercooling.Application to magnesium alloy AZ91 (approximated with the binary Mg-8.9 wt% Al) illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites growth.     

Effects of high magnetic fields on solidification microstructure of Al–Si alloys

The effects of high magnetic fields on the solidification microstructure of Al–Si alloys were investigated. Al–7.2 wt%Si and Al–11.8 wt%Si alloys were solidified in various high magnetic fields at different cooling rates. The secondary dendrite arm spacing (SDAS) of the primary Al dendrites and the lamellar spacing (LS) of the eutectics were measured. It was found that the application of a high magnetic field could decrease the SDAS of the primary Al dendrites in Al–7.2 wt%Si alloys and the LS of the eutectics in Al–11.8 wt%Si alloys. The effects of the high magnetic field on the SDAS decreased with increasing cooling rate. The decrease in the SDAS and LS can be attributed to the decrease of the solute diffusivity in the liquid ahead of the solid/liquid interface during the growth of the dendrite and eutectic. This decrease is caused by the high magnetic field which can damp the convection and avoid its contributions to the diffusion.     

Effect of cooling rates on the dendritic morphology transition of Mg–6Gd alloy by in situ X-ray radiography

The effect of cooling rate on the transition of dendrite morphology of a Mg-6 Gd(wt%) alloy was semiquantitatively analyzed under a constant temperature gradient by using synchrotron X-ray radiographic technique. Results show that equiaxed dendrites, including exotic 'butterfly-shaped' dendrite morphology, dominate at high cooling rate(1 K/s). When the cooling rate decreases in the range of 0.5–1 K/s, the equiaxed-to-columnar transition takes place, and solute segregates at the center of two long dendrite arms(LDA) of the 'butterfly-shaped' dendrite. When the cooling rate is lower than 0.3 K/s, directional solidification occurs and the columnar dendritic growth direction gradually rotates from the crystalline axis to the thermal gradient direction with an increase in cooling rate. Meanwhile, interface moves faster but the dendrite arm spacing decreases. Floating, collision and rotation of dendrites under convection were also studied in this work.     

Phase-field simulation for the evolution of solid/liquid interface front in directional solidification process

In this study, the phase field method was used to study the multi-controlling factors of dendrite growth in directional solidification. The effects of temperature gradient, propelling velocity, thermal disturbance and growth orientation angle on the growth morphology of the dendritic growth in the solid/liquid interface were discussed. It is found that the redistribution of solute leads to multilevel cavity and multilevel fusion to form multistage solute segregation, and the increase of temperature gradient and propelling velocity can accelerate the dendrite growth of directional solidification, and also make the second dendrites more developed, which reduces the primary distance and the solute segregation. When the temperature gradient is large, the solid-liquid interface will move forward in a flat interface mode, and the thermal disturbance does not affect the steady state behavior of the directionally solidified dendrite tip. It only promotes the generation and growth of the second dendrites and forms the asymmetric dendrite. Meanwhile, it is found that the inclined dendrite is at a disadvantage in the competitive growth compared to the normal dendrite, and generally it will disappear. When the inclination angle is large, the initial primary dendrite may be eliminated by its secondary or third dendrite.     

Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation – Part I: Model description

Part I of this two-part investigation presents a volume-averaging multiphase solidification model that accounts for mixed columnar-equiaxed solidification, non-dendritic and dendritic crystal growth, nucleation of equiaxed grains, columnar primary dendrite tip tracking, melt flow, sedimentation of equiaxed crystals, and their influence on macrostructure and macrosegregation. Five distinct thermodynamic phases (phase regions) are defined: solid dendrites in equiaxed grains, the interdendritic melt between equiaxed dendrites, solid dendrites in columnar trunks, the interdendritic melt between trunk dendrites, and the extradendritic melt. These five phase regions are quantified by their volume fractions and characterized by their solute concentrations. The five phase regions are grouped into three hydrodynamic phases: equiaxed grains consisting of solid dendrites and interdendritic melt, columnar trunks consisting of solid dendrites and interdendritic melt, and extradendritic melt. The extradendritic melt is separated from the interdendritic melt with a grain envelope, whose profile connects the primary, secondary or tertiary dendrite tips to form a ‘natural’ enclosure of the equiaxed grains or columnar trunks. The envelope is further simplified as a volume-equivalent sphere for equiaxed grains, or as volume-equivalent cylinder for columnar trunks by use of morphological shape factors. Expansion of the envelopes during solidification is determined by dendrite growth kinetics, using the Kurz–Giovanola–Trivedi model for growth of columnar primary dendrite tips and the Lipton–Glicksman–Kurz model for growth of columnar secondary dendrite tips (radial growth of the columnar trunk) and equiaxed primary dendrite tips. The solidification of the interdendritic melt is driven by the supersaturation of the interdendritic melt and governed by the diffusion in the interdendritic melt region. Illustrative process simulations and model verifications are presented in Part II.     

冷却过程对AZ61镁合金凝固组织的影响

将AZ61镁合金液态凝固过程分为高温熔体和凝固两个阶段,研究各阶段冷却速率对铸态组织的影响,不同冷速下铸态合金枝晶间距的变化及其对显微硬度的影响。结果表明:在高温熔体阶段随着冷却速率从0.65℃/s增加到15.9℃/s,枝晶组织不断细化且尺寸更均匀,一次枝晶间距从230μm逐渐减小到80μm,二次枝晶间距从12.8μm逐渐减小到9.2μm;凝固阶段在7.8℃/s至23.0℃/s不同冷却速率下,一次枝晶间距从105μm逐渐减小到73μm,二次枝晶间距从10.6μm逐渐减小到8.8μm。两个阶段显微硬度值随冷却速率增大都呈增高趋势。相对于凝固阶段,高温熔体阶段的冷却速率变化对铸态凝固组织的影响更显著。     

高温合金定向凝固过程中枝晶生长与溶质对流数值模拟

目的 针对高温合金叶片在定向凝固过程中容易出现雀斑缺陷,从而导致叶片报废的问题,对定向凝固枝晶生长与溶质对流进行模拟研究,以揭示雀斑缺陷的形成规律。方法 针对CM247LC合金定向凝固过程,采用相场模型模拟凝固过程枝晶生长,采用格子Boltzmann模型模拟溶质浓度差引起的自然对流。采用基于双重网格的GPU并行算法对相场-格子Boltzmann模型进行数值求解。研究在不同晶体取向角度与取向差条件下的枝晶形貌、对流速度及溶质羽流的演变规律。结果 当晶体取向角度不同时,在枝晶生长过程中,液相区域的平均对流速度均表现为周期性变化。当晶体取向角度较大时,随着晶体取向角度的变大,一次枝晶臂间距变大。当枝晶间存在晶体取向差时,溶质羽流倾向于在发散型晶界附近发起;随着晶体取向差的增大,溶质羽流发起时间提前。溶质羽流的形成阻碍了枝晶尖端及附近枝晶侧臂的生长。结论 晶体取向角度对溶质羽流形成的影响较小,较大的晶体取向差对溶质羽流的形成有促进作用。     

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     

强磁场下Cu-50%Ag合金定向凝固过程中的组织及固液界面形貌演变

目的 研究强磁场下Cu-50%(质量分数)Ag合金定向凝固过程中的组织演变、固液界面形貌变化及溶质迁移行为,分析强磁场对金属凝固过程的作用机制,为强磁场下的金属材料制备提供理论借鉴和指导。方法 在不同的凝固速率与磁场条件下进行定向凝固和淬火实验,对合金的定向凝固组织、糊状区与固液界面形貌以及溶质分布行为进行考察。结果 强磁场破坏了凝固组织的定向生长,使凝固组织转变为枝晶与等轴晶共存的形貌;强磁场诱发了熔体对流,减少了糊状区中溶质的含量;强磁场改变了固液界面处的溶质分布和固液界面形貌,破坏了固液界面的稳定性。结论 强磁场通过洛伦兹力和热电磁力的共同作用,诱发了糊状区内液相的纵向环流,改变了固液界面及糊状区中的组织形貌与元素分布。     

Modelling the Solidification Microstructure Formation of Cobalt Dendritic Alloys

In the present work a mathematical model has been developed to explain the microstructure characteristics obtained during the solidification process of dendritic cobalt alloys, under ordinary low cooling rate conditions. The model, taking into account physical aspects such as undercooling, cooling rate, solute diffusion, interfacial energy, and dendrite tip morphology, allowed results to explain the experimental microstructure changes observed when the processing conditions were varied. The mathematical model involved micro and macroscopic phenomena occurring during the solidification process of metallic alloys. The solutions of the governing equations were obtained applying a non-coupled scheme, which enables the possibility to simulate the solidification of complex geometry castings.     

Dendrite coarsening during solidification of hypo- and hyper-eutectic Al-Cu alloys

Dendrite coarsening during cooling at a constant rate was compared at various stages of solidification with that during isothermal holding for Al-Cu alloys of hypo- and hypereutectic compositions. For each specimen, the undercooling for the initial dendrite formation and the time elapsed after it were measured directly. The dendrite arm spacing was shown to be determined solely by the latter, and the dendrite structure was therefore coarsening-controlled from the early stage of solidification. The rate of coarsening in terms of the dendrite arm spacing during solidification at a constant cooling rate was same as that during isothermal holding in all the alloys tested. Numerical values of the fractional rate of solidification were evaluated for the hypo-eutectic compositions and the results show that the rate of dendrite coarsening does not depend on the fractional rate of solidification. Aluminium dendrites show structural coarsening with progressive solidification in the same way as during isothermal holding. CuAl₂ dendrites show curved boundaries after isothermal holding whereas those cooled at a constant rate are faceted.     

Computer simulation of solidification and microsegregation in presence of particles

A computer simulation was used to study the influence of particles on microsegregation during solidification. Particles in the melt can affect the solidification microstructure by changing the cooling curves, acting as barriers to solute diffusion, reducing the metal volume, affecting the coarsening process, etc. The computer simulation model used in the present work calculates the effect of particles of different thermal properties on the cooling curves and the consequent changes to microsegregation and dendrite arm spacing. The microsegregation calculations are valid for cases where the interparticle spacing is much smaller than the dendrite arm spacing. By using the simulation, it was possible to study various contributing factors in isolation as well as in combination so that the relative significance of each factor could be evaluated. It was observed that the reduction of liquid volume by the presence of the particles was the largest contributing factor to the influence of particles on the solidification microstructure. Thus, the changes in matrix microstructure of cast metal matrix composites depend more on the volume fraction of the reinforcing particles than on the properties of the particles themselves. Irrespective of the thermal properties of the particles, the dendrite arm spacing and microsegregation in the composite matrix was seen to be less than in the unreinforced alloy solidified under the same external conditions.

MST/3405     

Formation and Evolution of Non-dendritic Microstructures of Semi-solid Alloys Prepared by Shearing/Cooling Roll Process

The shearing/cooling roll （SCR） process was adopted to prepare semi-solid A2017 alloy. The formation and evolution of non-dendritic microstructures in semi-solid A2017 alloy were studied. It is shown that the microstructures of semi-solid billets transform from coarse dendrites into fine equiaxed grains as the pouring temperature of molten alloy decreases o.r roll-shoe cavity height is reduced. From the inlet to the exit of roll-shoe cavity, microstructure of semi-solid slurry near the shoe surface is in the order of coarse dendrites, degenerated dendrites or equiaxed grains, but fine equiaxed grains are near the roll surface. Microstructural evolution of semi-solid slurry prepared by SCR process is that the molten alloy nucleates and grows into dendrite firstly on the roll and shoe＇s surface. Under the shearing and stirring given by the rotating roll, the dendrites crush off and disperse into the melt. Under the shearing and stirring on semi-solid slurry with high volume fraction of solid, the dendrite arms fracture and form equiaxed grain microstructures.     

Effect of transverse static magnetic field on radial microstructure of hypereutectic aluminum alloy during directional solidification

The effect of different scales thermoelectric magnetic convection(TEMC)on the radial solidification microstructure of hypereutectic Al alloy has been investigated under transverse static magnetic field during directional solidification,focusing on the formation of freckle.Our experimental and numerical simulation results indicate that the TEMC circulation at sample scale under transverse static magnetic field leads to the enrichment of solute Al on one side of the sample.The TEMC and the solute enrichment degree increase with the increase of magnetic field when the magnetic field increases to 0.5 T.The enrichment degree of solute elements under magnetic field is affected by temperature gradient and growth rate.The non-uniform distribution of solute Al in the radial direction of the sample results in the non-uniform distribution of primary dendrite arm spacing(PDAS).Moreover,the applied magnetic field can lead to freckle formation and its number increases with the increase of magnetic field.The change of freckle is consistent with the anisotropy TEMC caused by the anisotropy of primary dendrite or primary dendrite network under magnetic field.Finally,the mechanism of synergism effect of the anisotropy TEMC,the distribution of solute Al and the PDAS on freckle formation and evolution is studied during directional solidification under magnetic field.     

凝固速度对奥氏体不锈钢定向凝固组织及其固液界面稳定性的影响

本文研究了凝固速率对1Cr18Ni9Ti不锈钢定向凝固组织及其固液界面稳定性转变规律的影响.结果表明,在某特一定的温度梯度下,随着凝固速度的增加,定向凝固的固液界面由平面转变为胞状晶,再转变为树枝晶.研究发现,随着凝固速率的增大,定向凝固组织枝晶形貌逐渐细化,枝晶间距减小.     

Multi-scale modeling of liquid-metal cooling directional solidification and solidification behavior of nickel-based superalloy casting

Liquid-metal cooling(LMC)process can offer refinement of microstructure and reduce defects due to the increased cooling rate from enhanced heat extraction,and thus an understanding of solidification behavior in nickel-based superalloy casting during LMC process is essential for improving mechanical performance of single crystal(SC)castings.In this effort,an integrated heat transfer model coupling meso grain structure and micro dendrite is developed to predict the temperature distribution and microstructure evolution in LMC process.An interpolation algorithm is used to deal with the macro-micro grids coupling issues.The algorithm of cells capture is also modified,and a deterministic cellular automaton(DCA)model is proposed to describe neighborhood cell tracking.In addition,solute distribution is also considered to describe the dendrite growth.Temperature measuring,EBSD,OM and SEM experiments are implemented to verify the proposed model,and the experiment results agree well with the simulation results.Several simulations are performed with a range of withdrawal rates,and the results indicate that 12 mm·min^-1is suitable for LMC process in this work,which can result in a fairly narrow and flat mushy zone and correspondingly exhibited fairly straight grains.The mushy zone length is about 4.8 mm in the steady state and the average deviation angle of grains is about 13.9°at the height 90 mm from the casting base under 12 mm·min^-1withdrawal process.The competitive phenomenon of dendrites at different withdrawal rates is also observed,which has a great relevant to the temperature fluctuation.     

Microstructure Evolution during Solidification of AZ91D Magnesium Alloy in Semisolid

The liquid quenching method was adopted to study the solidification morphology and microstructure of AZglD Mg alloy in semisolid. The results indicate that cooling rate has important effects upon the solidification structures. Under the cooling rate of liquid quenching, primary α-phase grows first by attaching on the original α grains, or independent nucleation and growth. The high cooling rate makes primary α-phase grow in ＂rags＂ or dendrite shape. Eutectic solidification is carried out in terms of both dissociated growth and symbiotic growth. The dissociated growth forms rough and large β-phase at grain boundaries, while symbiotic growth forms eutectic of laminar structure. The small liquid pool inside the original α-phase solidifies basically in the same way as that of intergranular liquid, but owing to less amount of liquid phase, the eutectic solidification is mainly carried out in the dissociated pattern.     

Effects of initial undercooling on microstructure formation and recrystallisation of undercooled melts

The critical undercoolings for the two grain refinement events and the onset of recrystallisation event are determined by detailed analysis of the microstructure evolution of bulk undercooled Ni–20?at.-%Cu alloy melts. The first grain refinement event occurred in the low undercooling range was explained by dendrite remelting. The second grain refinement event occurred in the high undercooling range was due to the combined effects of dendrite remelting stress-induced dendrite breakup during recalescence and recrystallisation during the near-equilibrium solidification stage after recalescence. The micro-stress induced by the solidification contraction during recalescence in the so called ‘first mushy zone’ would lead to distortion and breakup of primary dendrites. The stress-induced broken-up dendrites have sufficient driving force for recrystallisation.     

亚快速单向凝固晶体生长的非稳态演化

晶体生长中的非稳态演化过程一直是凝固领域人们很少涉及的课题，尤其在胞枝转变之后相当宽范围的亚快速凝固更是少人问津，而非稳态过程对材料最终的组织往往产生在影响，本文采和有机物模拟合金研究了低速及亚快速凝固范围界面形态与一次间距的演化规律，并初步探讨了其演化机制。     

AZ91镁合金的凝固冷却速度与二次枝晶间距的定量关系研究

通过设计制作一套可获得不同凝固冷却速度的镁合金熔炼与浇注装置,采用多通道连续温度记录仪,获得了对应不同凝固冷却速度下的AZ91镁合金试样.用定量金相分析之截线法测定了各个试样的二次枝晶间距,并对不同凝固冷却速度下的组织特征做了简要分析.用数学回归的方法得到了AZ91镁合金的凝固冷却速度与二次枝晶间距的定量关系式.