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Yuki Muto, Kazuki Kammuri, Junji Miyake, [Machiko Ode](https://orcid.org/0000-0002-9500-5466), Tetsusei Kurashiki, Hiroaki Mori

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[Numerical Analysis to Evaluate the Effect of Cooling Rates on Microstructures in Casted Cu-Ni-Si Alloys by Phase-Field Simulation](https://mdr.nims.go.jp/datasets/c3d2936b-728d-4acf-a882-02c4b7969fac)

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Numerical Analysis to Evaluate the Effect of Cooling Rates on Microstructures in Casted Cu-Ni-Si Alloys by Phase-Field SimulationNumerical Analysis to Evaluate the Effect of Cooling Rates on Microstructures inCasted Cu-Ni-Si Alloys by Phase-Field SimulationYuki Muto1,+1,+2, Kazuki Kammuri1, Junji Miyake2, Machiko Ode3, Tetsusei Kurashiki4 andHiroaki Mori41Kurami Branch, Technology Development Center, JX Advanced Metals Corporation, Koza-gun, Kanagawa 253-0101, Japan2First Division, JX Advanced Metals Research Institute for Technology & Strategy Co., Ltd., Tokyo 105-0001, Japan3Structural Thermodynamics Group, Research Center for Structural Materials, National Institute for Materials Science (NIMS),Tsukuba 305-0047, Japan4Graduate School of Engineering, Osaka University, Suita 565-0871, JapanCorson (Cu-Ni-Si) alloys were unidirectionally solidified via the Mizuta method under air or water cooling. To replicate the microstructureof a Corson alloy during solidification, phase-field (PF) simulations were performed, and the numerical results were compared with theexperimental findings. The comparison between the air- and water-cooling conditions revealed that the primary dendrite trunks were thinner, andthe secondary dendrites were longer and more developed under air-cooling conditions. These results were consistent with the experimentalobservations. Furthermore, the secondary dendrite arm spacings were evaluated via PF simulations, and the calculated results were consistentwith the experimental observations. The interface energy and its anisotropy adopted in the present PF simulations were reasonable for the Corsonalloy when compared with the values reported in other studies. [doi:10.2320/matertrans.MT-M2024098](Received July 4, 2024; Accepted September 15, 2024; Published November 25, 2024)Keywords: Corson alloy, unidirectional solidification, microstructure, phase-field, secondary dendrite arm spacing, cooling condition1. IntroductionCopper alloys are widely used in electronic connectorsand semiconductor lead-frames. Recently, the demand forthe miniaturization of such electronic components, along withhigh reliabilities, increased, particularly for use in mobilephones and other electronic devices. These trends aresignificant driving forces in the development of high-strengthand electrical-conductivity copper alloys. Therefore, precip-itation-hardening copper alloys have received considerableattention for use in these applications compared to solid-solution-hardening phosphor bronzes.Among precipitation-hardening copper alloys, Corsonalloys, which contain Ni and Si as the main alloyingelements, are primarily used because of their excellentbalances of strength, electrical conductivity, and bendformability [1–3]. Corson alloys with higher Ni and Sicontents, in particular, exhibit higher strengths because oftheir high-volume fractions of the precipitate Ni2Si [4]. Thesealloys contribute to the further miniaturization and higherreliabilities and degrees of design of connectors, lead frames,and other electronic devices [5]. Therefore, Corson alloyscontaining higher amounts of Ni and Si are indispensablematerials in the forthcoming information society.Hot cracking is a significant issue for copper alloys [6, 7],but most research regarding hot cracking has been conductedusing steel and aluminum alloys. In such studies, severalmodels have been proposed to assess susceptibility to hotcracking [8, 9]. The basic theory is that the temperature rangewhere residual liquid healing does not occur is crucial inexplaining hot cracking. As the capacity for liquid healing isstrongly influenced by the dendritic shape, understanding thedendritic growth behavior during solidification is necessaryin evaluating hot cracking susceptibility [9]. Nevertheless,very few studies regarding copper alloys have been reportedin this field of research [10–14]. For example, Oya et al.focused on Cu-Sn and Cu-Zn alloys to investigate the effectsof the microstructures and additive elements on the hotcracking susceptibilities of the alloys. However, quantitativeevaluation is insufficient in predicting hot cracking, andfurthermore, no study on Corson alloys have been reported.Therefore, quantitatively evaluating hot cracking susceptibil-ities of Corson alloys is critical.Recently, numerous studies have been conducted regardingthe in-situ observation of the solidified microstructure [15,16]. For example, Yasuda et al. reported the in-situ obser-vation of Fe-C alloys during solidification using synchrotronX-rays radiation at SPring-8 [16]. Although these in-situobservation methods are extremely useful, they are not viablefor conducting laboratory-scale experiments, and they arealso inadequate for large-scale casting experiments. Consid-ering the experimental limitation, a quantitative, low-costinvestigation of the effects of the solidification conditionson the dendritic growth behavior can only be performed bypredicting the solidified microstructure using simulationmethods. Previously, we experimentally investigated thesolidified microstructures of Corson alloys and analyzed theprimary and secondary dendrite arm spacings (P- and S-DASs, respectively) after the completion of solidification[17]. In this study, the experimental data reported in ourprevious study are used to theoretically predict the P- and S-DASs of Corson alloys.The numerical analysis of solidification microstructuresbegan in the 1990s. Kobayashi conducted the first phase-field(PF) simulation to calculate dendrite growth during solid-ification by introducing a parameter, denoted the PF, thatindicated the phase state [18]. The PF method is suitable+1Graduate student, Osaka University+2Corresponding author, E-mail: muto.yuki.wv9@jx-nmm.comMaterials Transactions, Vol. 65, No. 12 (2024) pp. 1464 to 1472©2024 The Japan Institute of Metals and Materialshttps://doi.org/10.2320/matertrans.MT-M2024098for predicting dendrite growth because introducing the PFparameter eliminates the necessity of following the interfaceand easily represents complex microstructural changes.Owing to these advantages, numerous studies and system-atizations using the PF method have been conducted onmicrostructure formation during the solidification of variousmaterials [19–32]. For example, the S-DASs of aluminumand ferrous alloys were evaluated via 2D PF simulations, andthe relationships between the S-DASs and cooling rate wereanalyzed [19–21]. Thereafter, the increase in computingpower and development of efficient calculation methodsenabled the calculation of the large-scale 3D dendrite growthof Al-Si alloy [22]. These 3D PF calculations were alsoapplied to other alloys, such as Al-Cu and Fe-Mn alloys,which enabled more detailed evaluations of their micro-structures during solidification [23–25]. Recently, an inverseanalysis method was proposed to determine the anisotropiesof solid-liquid interface energies by combining PF simu-lations and machine learning [26, 27], where the estimatedanisotropy of an Fe-Mn alloy was 0.021 [27].However, there are few research reports on the applicationof the PF method to the solidification microstructures ofcopper alloys. The only report on copper-based alloys [33]is limited to Cu-Sn alloys, which are conventional solid-solution-strengthened copper alloys. In this study, theinfluence of the solidification rate on the partition coefficientwas assessed, but crucial microstructural characteristics suchas P-DAS and S-DAS, were not analyzed. Furthermore, PFparameters related to the anisotropy of interface energy werenot provided.We have conducted the first experimental observations ofthe solidification microstructures to predict hot crackingsusceptibility using precipitation-strengthened copper alloys(Corson alloys) [17]. The present study aims to replicatethese experimentally observed microstructures using the PFmethod to demonstrate whether it can be utilized for alloysunder the actual manufacturing solidification conditions ofpractical copper alloys for the first time. By comparing P-DAS and S-DAS from both experiments and PF computa-tions, we estimate the calculation parameters for the interfaceenergy and reproduce the effect of cooling rate on thesolidification microstructures of Corson alloys. Finally, wewill evaluate whether the obtained parameters and simulatedmicrostructures can be utilized in future research to predicthot cracking in precipitation-hardened copper alloys.2. Phase-Field MethodIn the PF method [28, 32, 34, 35], the phase-field, º isintroduced to represent the phase state. When calculatingthe solidification microstructure of a single solid phase, forexample, the phase-field is set º = 0 for the solid phase,º = 1 for the liquid phase and, 0 < º < 1 for the solid/liquidinterface, respectively. The solid/liquid interface in the PFmodel has a finite width, allowing the PF to continuouslychange, which enables numerical differentiation.The PF equation is derived to minimize the free energy ofthe system (F(º)), which is set by integrating the free energydensity ( f ), as shown in eq. (1). The free energy density forsolidification is composed of the chemical free energy density( fchem) and interface free energy density ( fintf ), as shown ineq. (2).FðºÞ ¼ZfðºÞdV ð1Þf ¼ fchem þ fintf ð2Þwherefchem ¼ ºfl þ ð1� ºÞfs;fintf ¼4·©©2³2ðrºÞ2 þ ºð1� ºÞ� �:fl and fs are the free energy of liquid and solid phases, © isthe interface width and · is the solid/liquid interface energy.As the PF variable is a non-conservative quantity, the PFequation with an anisotropic interface energy is expressed as[28, 32],@º@t¼ �M¤F¤º¼ M�ð· þ · 00Þ r2º � ³22©2ð1� 2ºÞ� �� ³©ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiºð1� ºÞpðfl � fsÞ�ð3Þ· ¼ �·ð1� ·4 cos 4ªÞ ð4Þwhere ·AA is the second derivative of the interface energywith respect to ª.M is the interface mobility and related to theinterface kinetic coefficient ® as follows,M1�M©8�Smil½Dijl ��1ðcjs � cjl Þ¼ ® ð5ÞWhen the solidification condition can be considered adiffusion-controlled reaction, in other words, when theinterface kinetic coefficient is effectively infinite, the mobilityis expressed as,M�1 ¼ ©8�Smil½Dijl ��1ðcjs � cjl Þ ð6Þwhere ¦S is the entropy at the interface temperature, mil is theliquidus slope (mil < 0), Dijl is the interdiffusion coefficientof the liquid, and cjs and cjl are the composition of eachcomponent in the solid and liquid phases, respectively. Notethat if ® is sufficiently large, the calculation results do notdepend on M because the interface motion is controlled bysolute-diffusion.As the interface motion depends on the concentration andtemperature fields, the PF equation is coupled with theconcentration and/or temperature field equations. The timeevolution equation for concentration can be expressed by thefollowing diffusion equation incorporating the anti-trappingcurrent commonly used in the PF method [35].@ci�@t¼ r ðð1� ºÞdirci�l Þ þ ¡i�@º@trºjrºj� �ð7Þ¡i� ¼ ©³ðci�l � ci�s Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiºð1� ºÞpð8Þwhere di is diagonal matrix of the interdiffusion coefficientrepresenting the diffusion matrix. di means eigenvalue of Dijlwhen Dijl is diagonalized by using transformation matrix P.Numerical Analysis to Evaluate the Effect of Cooling Rates on Microstructures in Casted Cu-Ni-Si Alloys by Phase-Field Simulation 1465ci+ and ¡i+ represent by using P as ci+ = Pci and ¡i+ = P¡i,where ci and ¡i are the composition and antitrapping currentcoefficient of component i. Because of high diffusivity ofheat compared to solute, temperature field was simulated inone-dimensional calculation with lager mesh size than thatof concentration by the following equation [36, 37]. Thedirection was set as parallel to the that of temperaturegradient.@T@t¼ 1Cp�rðPFl­ l þ PFs­ sÞrTþ Hl@PFl@tþHs@PFs@t� ��ð9Þwhere Cp is the average heat capacity, PFl, PFs are theaverage fraction, ­ l, ­s are the heat diffusivity, and Hl, Hs arethe enthalpy of liquid and solid phase in each temperaturegrid cell.The cooling rate of conventional casting process issufficiently slow to satisfy a local-equilibrium condition.This condition requires the constraint of equal diffusionpotentials for the phases within the interface to minimize thelocal Gibbs energy. In this study, the thermodynamic drivingforce, fs ¹ fl = ¦G, in the PF equation is calculated usingthe commercial thermodynamic database of Cu-based alloysto satisfy the equal diffusion potentials and their concen-trations as follows [34],�G ¼ 1vmð®0s � ®0l Þ ð10Þwhere vm is molar volume and ®0s , ®0l are the diffusionpotentials of the solid and liquid phases.3. Casting Method with Various Cooling Rates Based onthe Mizuta MethodTo evaluate the effect of the cooling rate on the castingmicrostructure, Corson alloy ingots were prepared using acasting method denoted the Mizuta method [38]. The detailsof the experimental setup are described in a previous study[17].In the Mizuta method, a copper alloy is melted in acrucible via induction heating. The crucible containing thecopper alloy was air- or water-cooled. The ingots wereunidirectionally solidified from the wall of the cylindricalcrucible toward the center, the temperatures at several pointsparallel to the solidification direction were measured, and themicrostructures were observed using an optical microscopeat a location corresponding to the temperature measurementpoints. The casting microstructures and cooling curveswere obtained under three types of water- and air-coolingconditions using various observation positions.The compositions of the ingots were Cu-4.8mass%Ni-1.1mass%Si and Cu-4.7mass%Ni-1.1mass%Si for waterand air cooling, respectively. Figure 1 shows the coolingcurves obtained in this experiment, where the distancerepresents that from the crucible wall to the position oftemperature measurement. The cooling rate decreased as thedistance from the crucible wall increased. Figure 2 presentsthe microstructural observations under each cooling con-dition, where the white arrows indicate the direction towardthe center of the crucible. The dendrites grew from the wallto the center of the crucible, and the cooling rate stronglyinfluenced both the primary and secondary dendrite micro-structures. In the final stage of casting, the secondary armsof air-cooled dendrites were coarsened. Based on theseobservations, the P- and S-DASs were evaluated, and theyare summarized in Table 1.4. Numerical Analysis of Microstructures during Cast-ing by Phase-Field Method4.1 Simulation conditionIn this study, PF calculations were performed usingthe commercial software MICRESS (version 7.1) [34].MICRESS employs the API provided by the thermodynamiccalculation software Thermo-Calc (version 2022b) [39],which allowed users to access their thermodynamic andmobility databases. The present computations incorporatefree energy data from TCCU5, TCS Cu-Based AlloysDatabase, and kinetic data from MOBCU5, TCS Cu-BasedAlloys Mobility Database.While 2D and 3D calculations are not identical, this studyemployed 2D calculations due to their lower computationalcosts. This is because we consider that 2D PF simulationsprovide reasonable results for evaluating the effects of thecooling condition on the S-DASs by comparing the simulatedand experimental results. Several studies have shown that2D calculations can accurately predict the experimental S-DAS [19, 20, 40]. Additionally, one of these studies [40]demonstrated that the S-DASs predicted via 3D and 2D PFcalculations are almost the same. Consequently, as weconsidered that the deviation from the experimental valuesis not significant even when using 2D calculations, weutilized 2D PF simulations in this study.Figure 3 illustrates the simulation conditions employed inreproducing the microstructures generated via unidirectionaldendritic solidification, as obtained using the Mizuta method.The calculation domain was denoted by the x- and z-directions, as shown in Fig. 3.Fig. 1 Cooling curves obtained using the Mizuta method at each positionfrom the crucible wall under water and air cooling [17].Y. Muto et al.1466Considering that a single columnar dendrite can representthe whole experimental microstructure, the size of thecalculation domain was the P-DAS and approximately 20times the S-DAS in the x- and z-directions, respectively. Theinitial temperature at the bottom of temperature domain was0.5K lower than the equilibrium liquid temperature. Temper-ature conditions were set to reproduce experimental results.In our previously paper on the experiment [17], we placedtwo thermocouples along the growth direction of columnardendrites. The thermocouple temperature on the mold sidewas directly input for the temperature at the bottom of thecalculation domain, and the temperature in the calculationdomain is computed using the eq. (9), as shown in Section 2.Mesh size of temperature simulation was set as 100 µm. Thethermophysical properties in the equation, enthalpy, H, andspecific heat capacity, Cp, are referenced from thethermodynamic database, TCCU5. The thermal conductivity,­, was preliminary calculated to reproduce the measuredtemperature by the second thermocouple. The comparisonbetween experimental and simulated cooling curves wasshown in Fig. 4.An initial nucleus, which was represented as a dendrite tipthat had grown to the point of temperature measurement, wasplaced at the center of the bottom of the calculation domain.The angle between the preferred growth direction of theinitial solid and the direction of the temperature gradient wasset to 0°, and the boundary conditions were set as periodicand adiabatic in the x- and z-directions, respectively. Thiscalculation was focused on single-dendrite growth within theexperimentally observed microstructure.The PF simulations were performed by moving thecalculation domain in the z-direction following the dendritetip. In the initial stage of the calculation, the calculationdomain was fixed until the dendrite tip approached the top ofthe domain. The calculation domain was then moved suchthat the distance between the dendrite tip and top of thedomain was maintained at 50 or 385 µm under water- or air-cooling, respectively. The computational domain was moveduntil the tip velocity reached a steady state, and the stage atwhich the tip velocity stabilized and the stage prior weredenoted the steady and unsteady state, respectively. Afterentering the steady state, the calculation domain was fixed,and dendrite coarsening process was calculated. Thiscalculation setup was used to avoid an unsteady state in theearly stages of the calculation to compare the experimentaland calculated microstructures.The physical properties and simulation parameters usedin the calculations are shown in Table 2 and Table 3,respectively. To reduce the computational cost, the drivingforce was calculated by linearizing the phase diagramobtained using the TCCU5 with the average concentrationin each phase. The linearization routine was applied atintervals of 0.1 and 1.0 s under water and air cooling,respectively. Three meshes were set at each interface, and theappropriate time step was automatically calculated by thesoftware. The interface properties, such as the solid-liquidinterface energy and its anisotropy, are not well-defined andvary depending on the alloy system. In this study, theseproperties of the Corson alloy were estimated to reproducethe experimental microstructure through pre-calculationsFig. 2 Microstructural observations under an air-cooling condition of (a)5mm and water-cooling conditions of (b) 5 and (c) 15mm. The whitearrows indicate the solidification directions. Reprinted with permissionfrom Ref. [17].Table 1 Primary and secondary dendrite arm spacings [17]. The number inparentheses indicate the standard deviations.Numerical Analysis to Evaluate the Effect of Cooling Rates on Microstructures in Casted Cu-Ni-Si Alloys by Phase-Field Simulation 1467under water cooling. The chemical composition used inpre-calculations was set as Cu-4.5mass%Ni-1.07mass%Si(the target composition in the experiment), and the interfaceenergy and its anisotropy were varied within the ranges of1.0 © 10¹5 to 3.0 © 10¹5 J/cm2 and 0.010 to 0.027,respectively. The ranges for the estimation were determinedbased on existing research, and the respective experimentaland calculated interface energy of pure copper were 1.77 ©10¹5 J/cm2 [41] and 1.957 © 10¹5 J/cm2 [42]. The aniso-tropy of the interface energy estimated via or used in thePF simulations ranges from 0.005 to 0.05 [25, 27, 42–48].These estimated interface properties were adopted in thesubsequently performed calculations, and a large interfacekinetic coefficient was used to calculate the interface mobilityby eq. (6). The anisotropy of the interface mobility was notintroduced.4.2 Simulation resultsThe properties of the solid-liquid interface considerablyinfluence the formation of solidification microstructures. Ahigher interface energy generally inhibits secondary armformation, resulting in columnar structures. Meanwhile, aninterface energy with a sufficiently large anisotropy isindispensable in generating well-defined dendritic micro-structures. Figure 5 shows a representative calculationexample from preliminary calculations. The effect of theinterface energy on the microstructure of the Corson alloywas evaluated. These calculations indicated that secondarydendrite arms were well developed at an interface energy of1.0 © 10¹5 J/cm2, whereas they were hardly generated at3.0 © 10¹5 J/cm2. Varying the interface energy and itsanisotropy within the above ranges reveals that respectivevalues of 1.0 © 10¹5 J/cm2 and 0.013 could reproduce theexperimentally observed S-DAS. Comparing these interfaceproperties to those from other studies, the interface energyin this study was lower than the experimental value of pureFig. 3 Pattern diagram of the phase-field (PF) simulation condition.Fig. 4 Comparison between experimental and simulated cooling curves at15mm away from the crucible wall under water and air cooling.Table 2 Physical properties used in the phase-field simulations.Table 3 Phase-field simulation parameters.Y. Muto et al.1468copper of 1.77 © 10¹5 J/cm2 [41] and its anisotropy waslower than those (0.02–0.03) used in other PF simulationsof ferrous alloys [25, 27, 48]. The determined interfaceproperties were utilized in subsequent PF simulations.Figure 6 shows the dendrite tip temperatures and solid-ification rate, as calculated via the PF simulations. In theinitial stage of the calculation, dendrite growth was veryslow, and the dendrite tip temperature decreased. Thesolidification rate then increased rapidly, the dendrite tiptemperature reached a minimum, and the undercooling fromthe steady temperature was approximately 1K. In the steadystage, the solidification rate remained constant, as shown inFig. 6(b), or it exhibited a constant slope, as shown inFig. 6(a) and (c). The changes in the calculated dendritemicrostructures over time under water cooling (5mm) areshown in Fig. 7. The figure panels show the microstructuresat 0.7, 0.9, and 5.0 s after initiating the calculations. In theunsteady state, the secondary dendritic branches only beganto develop in the middle of the dendrite, as shown inFig. 7(1). When the dendrite tip temperature was approx-imately 1K lower than that of the steady state, the secondarydendritic branches were well-developed, as shown inFig. 7(2). The experimental results shown in Fig. 2 wereconsidered for stable dendrite growth. Therefore, thecalculated microstructure for comparison with the exper-imental results was selected from the steady stage, as shownin Fig. 7(3).Under water cooling at 5 and 15mm and air cooling at5mm, the steady states began after 5, 8, and 110 s,respectively. The longer the distance of dendrite growthwas, the more likely the tip temperature is to deviate from theexperimentally measured value. Therefore, to accuratelyevaluate the S-DAS using this simulation, coarsening processwas calculated by fixing the calculation domain at the time ofthe initiation of the steady state.Figure 8 shows the results after coarsening process underwater or air cooling at 5mm. The solid fraction shown inFig. 8(2) and (3) were 0.7 and 0.8, respectively. The resultsof PF simulation indicated that the primary dendrite trunkswere thinner, and the secondary dendrites increased in lengthunder air cooling compared to those of the respective primaryand secondary dendrites under water cooling. This wasconsistent with the experimental results shown in Fig. 2, andthis result suggested that this simulation could reproduce theeffects of the cooling conditions on the shape of the dendrites.As dendrite coarsening process progressed, the trunks of theprimary and secondary dendrites thicken.Fig. 5 Effects of interface energy on the pre-calculations at interfaceenergies of (1) 1.0 © 10¹5, (2) 1.77 © 10¹5, and (3) 3.0 © 10¹5 J/cm2,with an anisotropy of 0.013.Fig. 6 Solidification rates and the dendrite tip temperature in the PFsimulations under water-cooling conditions at (a) 5 and (b) 15mm and anair-cooling condition at (c) 5mm.Numerical Analysis to Evaluate the Effect of Cooling Rates on Microstructures in Casted Cu-Ni-Si Alloys by Phase-Field Simulation 1469The S-DAS was evaluated using the results calculated at asolid fraction of 0.8 and compared with the experimentalvalue. The calculated S-DAS was evaluated based on thedistribution of the Ni concentration. The Ni concentration ona line parallel to the z-direction at a solid fraction of 0.8 underair cooling at 5mm is shown in Fig. 9. The method ofevaluating S-DAS was based on the measurement proceduresof the Japan Institute of Light Metals [49]. The points atwhich the Ni concentration decreased to less than 5wt% wereidentified as the solidification phases, and the S-DAS wasdetermined by dividing the length of the line (Fig. 9) by thenumber of secondary dendritic branches. The S-DAS wasevaluated in an area far from the top of the calculated domainto avoid the boundary effects at the top of the domain.Figure 10 compares the experimentally obtained and PF-simulated S-DASs. The horizontal axis represents the coolingrate because the experimental S-DAS can be expressed as amultiplier approximation of the cooling rate [17]. The S-DASs obtained via the PF simulations are consistent with theexperimentally obtained values.Based on these results, it was concluded that themicrostructure formed during the casting of a Corson alloycould be accurately predicted using the PF method byconsidering various parameters.5. ConclusionsCalculations were performed to reproduce the micro-structure of a Corson alloy during casting using the PFmethod. The microstructures were obtained from unidirec-tionally solidified ingots produced using the Mizuta methodunder several cooling conditions. The results are summarizedas follows,(1) The PF simulation was conducted using the commercialMICRESS software (version 7.1). The calculationdomain was moved with the dendrite tip until thesteady state was reached, and coarsening process wascalculated to yield microstructures that could becompared to the experimental observations.(2) Comparing the simulated results obtained under airor water cooling confirmed that the primary dendritetrunks were thinner and the secondary dendrites werelonger and well-developed under air cooling, whichsuccessfully reproduced the experimental results.(3) The S-DAS determined via PF simulation was evaluatedusing the Ni concentration profile, and the results wereconsistent with the experimental observations.(4) The interface properties used in the PF simulations ofthe Corson alloy were compared to those reported inother studies, and the interface energy used in this studywas lower than the experimental value of pure copper,Fig. 7 Result of PF simulations of the dendrite structures at (1) 0.7, (2) 0.9,and (3) 5.0 s under water-cooling condition at 5mm.Fig. 8 Results of the PF simulations of the dendrite structures at varioussolidification rates: (a) water- and (b) air-cooling at 5mm: (1) the initialstructure used in simulating the coarsening process, and the structures atsolid fraction (fs) = (2) 0.7 and (3) 0.8.Y. Muto et al.1470and its anisotropy was lower than those used in other PFsimulations of ferrous alloys.The capacity of this simulation method to predict thedendrite microstructure using its temperature history duringsolidification was critical in predicting the hot crackingsusceptibility. However, to predict the hot cracking suscepti-bility during casting, it is insufficient only to correctlysimulate solidified microstructure. Thus, further investiga-tions of the hot-cracking susceptibility shall be conductedusing simulation methods.AcknowledgmentsI would like to thank M. Segawa at the ITOCHU Techno-Solutions Corporation for their useful instructions andassistance with the PF simulations using the MICRESSversion 7.1 software.REFERENCES[1] M.G. Corson: Copper Alloy Systems with Variable Alpha Range andTheir Use in the Hardening of Copper, Proc. Inst. Metals Div., AIME,(1927) pp. 435–450.[2] S.A. Lockyer and F.W. Noble: Precipitate structure in a Cu-Ni-Si alloy,J. Mater. 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