Numerical Simulation of Solidification Structures of Ag­28Cu­1Ni Alloy throughContinuous Casting Based on Three-Dimensional CAFE Method

Jiheng Fang, Xi Liu, Yuman Fan, Ming Xie+, Yongtai Chen, Youcai Yang, Yunzhao Duan and Song Chen

Department of Materials, Kunming Institute of Precious Metals, No. 988 Science and Technology Road, 650106, China

Microstructure evolution of Ag­28Cu­1Ni alloy during the continuous casting process was simulated based on 3D-CAFE method, and theeffect of the mean nucleation undercooling and the distance from the bottom of the ingot to the cross section on the solidification structure werestudied. Furthermore, the effects of pouring temperature, heat transfer coefficient and pulling speed on solidification structure were alsoinvestigated. The results show that the simulated results are in agreement with the experimental results. The solidification structure consists offour parts, including region of surface fine grain, zone of columnar grain, transition zone of CET (columnar to equiaxed grain transition) andregion of center equiaxed grain. The higher the mean undercooling, the larger the columnar dendrite zone. The ¦Tv,max = 5K is determined asan important simulation parameter to simulate the microstructure evolution. As the cross-section increases from the bottom of the ingot, thecolumnar crystal regions gradually expand. Moreover, lowering the pouring temperature, increasing the heat transfer coefficient or improving thepulling speed have the beneficial effect on grain refinement. Under the optimal process conditions, the largest proportion of equiaxed grains andthe finer grain size is present in the solidified structure. [doi:10.2320/matertrans.MT-M2020024]

(Received January 21, 2020; Accepted March 31, 2020; Published June 25, 2020)

Keywords: CAFÉ, microstructure evolution, the mean nucleation undercooling, process parameters, continuous casting

1. Introduction

The proportion of columnar grains to equiaxed grainsduring solidification processes can reflect the distributionuniformity degree of solute elements in solidificationmicrostructure. And the solidification structure of the castingdetermines the mechanical properties and forming quality ofthe casting.1,2) Therefore, it is of actual significance to studythe solidification microstructure.

Cellular Automation-Finite Element model (CAFE) is thefirst computational model of solidification structure thatcombines macroscopic heat flow calculation with micro-scopic grain growth.3,4) Based on the theory of grainnucleation, the dynamics theory of dendrite growth, CETtransformation criterion and other crystallographic theory.The process of nucleation, growth and evolution of grainswere simulated by establishing the models of grain nucleationand growth. Finally, an accurate evaluation on the micro-structure and mechanical properties of different parts for theworkpiece is achieved.5,6) Gandin and Rappaz proposedthree-dimensional CAFE algorithm in 1999.6) The CAFEmethod belongs to a deterministic method that can calculatethe temperature field, flow field and solute field of thesolidification process.7­9) Besides, it can also be used tosimulate the competitive growth of dendrites, the morpho-logical changes of columnar crystals and equiaxed crystals,the segregation and the transformation of columnar crystalsto equiaxed grains (CET).10­12) Gandin et al.13,14) coupledthe cellular automaton method (CA) with the finite elementmethod (FE) to simulate the evolution process of thesolidification structure for the AlSi alloy and predict thepreferred growth of the columnar crystals in the outerequiaxed grains of ingot, the competitive growth betweencolumnar crystals, and the transformation of columnar crystalto equiaxed crystal, the simulation results agree with the

experimental observation. Bu et al.15) used the CAFE modelcombined with finite element and cellular automata tosimulate and predict the solidification structure of Al­Cualloy by adding the solid-phase diffusion coefficient ofvacancy formation energy. The results can accurately reflectthe distribution, proportion and size of equiaxed andcolumnar crystals. There are few reports on the simulationof solidification structure about precious metals. However,solidification simulation for precious metals can significantlyreduce the cost of experiments and quickly obtain the optimalprocess parameters.

Ag­28Cu­1Ni alloy is one of the most widely usedelectronic filler metals due to its excellent fluidity,permeability and brazing properties.16­18) In the process ofcontinuous casting, the process parameters (such as pouringtemperature, heat transfer coefficient, pulling speed, etc.)have great influence on the quality of the casting blank, andit is costly to find the best process parameters through theexperiment. The computational simulation provides a low-cost, high-efficiency approach for the improvement andresearch of the process.19) Furthermore, the Gaussiandistribution parameters directly affect grain size, and theproportion of columnar grains to equiaxed grains during thesimulation. In addition, Gaussian distribution parametersare interactive and vary with casting shape and size, castingtemperature, and cooling conditions. Thus, it is necessary tostudy the influence of Gaussian distribution parameters onsolidification simulation, which is beneficial to the simulationof 3D microstructure more quickly and accurately.20)

Therefore, the solidification structure of Ag­28Cu­1Nialloy was simulated by the 3D CAFE program in Procastsoftware, and the effects of the pouring temperature, theheat transfer coefficient, the pulling speed and the meannucleation undercooling (Gauss distribution parameter) onthe solidification structure are analyzed, and the optimaltechnological parameters are obtained, which can providepractical value for industrial production.+Corresponding author, E-mail: 921539423@qq.com

Materials Transactions, Vol. 61, No. 7 (2020) pp. 1230 to 1238©2020 The Japan Institute of Metals and Materials

2. Establishment of CA-FE Model

2.1 Microscopic model2.1.1 Model of heterogeneous nucleation

The stage of solidification nucleation adopts Rappaz’s thedeterministic nucleation model based on gaussian distribu-tion.21) The model holds that the characteristics of thenucleation should be a continuous curve rather than a discretedistribution, and the nucleation position is described by acontinuous distribution function ("T );

nð�T Þ ¼ nmax

�T·ffiffiffiffiffiffi2³

pZ �T

0

expð�T ��TmaxÞ2

2�T 2·

� �dð�T Þ ð1Þ

Where n("T ) is the grain density when the undercoolingis ¦T, nmax is the maximum nucleation density obtained fromthe integration of normal distribution from 0 to infinity,"Tmax is the maximum nucleation undercooling, ¦T· is thestandard deviation of nucleation undercooling.2.1.2 Growth kinetics model of dendrite tip

During the solidification process, grain growth is affectednot only by the dynamic undercooling but also by thecomposition undercooling. The total undercooling of thedendrite tip is described by the following equation:22)

�T ¼ �Tc þ�Tt þ�Tk þ�Tr ð2Þwhere "T is the total undercooling of the dendrite tip, "Tc,"Tt, "Tk and "Tr are the undercooling contributionsassociated with solute diffusion, thermal diffusion, attach-ment kinetics, and solid-liquid interface curvature,respectively. For most metallic alloys, the last threecontributions are small, and the solute undercoolingpredominates. Thus, the growth kinetics of both columnarand equiaxed microstructures can be calculated with the aidof the KGT model.23) In the actual simulation process, inorder to accelerate the computation course, the KGT modelis fitted and the following equation is gained.24)

vð�T Þ ¼ a2�T 2 þ a3�T 3 ð3ÞWhere a2 and a3 are the coefficients of the polynomial of

dendrite tip growth rate, "T is the total undercooling of thedendrite tip.

2.2 Macroscopic model2.2.1 Calculation of thermophysical properties

The parameters of thermophysical properties includedensity, specific heat, enthalpy, latent heat, heat transfercoefficient, liquid viscosity and so on,25) which are usuallycalculated by a simple two-hybrid model:26)

p ¼X

ixipi þ

Xi

Xj>i

xixjX

v�v

ijðxi � xjÞv ð4ÞWhere P is the characteristic of phase; Pi is the

characteristic of pure elements in the phase; �vij is a binary

interaction parameter; xi, xj is the mole fraction of the elementin the phase, mol/L; v is a variable for determining the binaryinteraction parameters �v

ij, 0 ¯ v ¯ 2.2.2.2 The governing equation

Considering the three-dimensional transient flow and heattransfer of molten metal, a governing equation based onmass, momentum and energy balance is established. At thesame time, considering the influence of gravity, the gravity

term is added to the momentum equation so that the equationcan be applied to the mushy region and the solid phaseregion.27,28) Its governing equation is as follows:(1) Mass conservation equation

@μ

@tþ @ðμuÞ

@xþ @ðμvÞ

@yþ @ðμwÞ

@z¼ 0 ð5Þ

(2) Momentum conservation equation

μ

f1

@u

@tþ μ

f21

u@u

@xþ v

@v

@yþ w

@w

@z

� �

¼ � @P

@xþ μgxþ @

@x

u

f1

@u

@x

� �þ @

@y

u

f1

@u

@y

� �

þ @

@z

u

f1

@u

@z

� �� u

K

� �U ð6Þ

(3) Energy conservation equation

μ@H

@tþ μ

@H

@Tu@T

@xþ v

@T

@yþw

@T

@z

� �

¼ @

@xkT

@T

@x

� �þ @

@ykT

@T

@y

� �þ @

@zkT

@T

@z

� �ð7Þ

and,

HðT Þ ¼Z T

0

CpðT ÞdT þ Lð1� fsÞ ð8Þ

Where μ for density, kg/m3; t for time, s; u, v and wrepresent the velocity vectors of x, y and z respectively, m/s;K ¼ K0½¤31=ð1� ¤1Þ2�, (K is the permeability of the solid-liquid two-phase region, m2, ¤1 is the volume fraction of theliquid phase and Ko is the parameter related to the dendritesize of the two-phase region); f1 for the liquid fraction; fs forthe for the solid fraction; P for pressure, Pa; U for theabsolute viscosity, Pa·S; gx is the gravity component of x,m/s2; KT represents the thermal conductivity, W/(m·K); Hfor enthalpy, J/kg; L for solidifying latent heat, J/kg; Trepresents the node temperature, K; Cp is specific heatcapacity, J/(kg·K).

2.3 Coupling the FE and CA modelThe aim of this work is to combine the FE and CA

calculations in a single model to predict simultaneously theeffects of the latent heat release on the calculated thermalhistory and the microstructure evolution (as a function of thethermal field). For this purpose, interpolation coefficients aredefined between nodal points of FE mesh and CA cells asillustrated in Fig. 1. The CA cell, ½, with its centre infiniteelement I, has non-zero interpolation coefficients P½i, P½j, andP½k with FE nodes i, j, and k, respectively. Combined withthe known FE nodes and interpolation coefficients, thetemperature of the CA cells in the grid can be determined.The same interpolation coefficients are used to sum up, atnodal points, the latent heat released by nucleation andgrowth, and the thickening of the dendritic microstructurescalculated at the scale of CA cells.

3. The Determination of the Calculation Model and theSimulation Parameters

3.1 Modeling and meshingIn order to calculate the extended process of the simulated

Numerical Simulation of Solidification Structures of Ag­28Cu­1Ni Alloy through Continuous Casting 1231

crystalline region over time, the Mile (mix Lagrangian andEulerian algorithm) method was used to calculate thetemperature distribution at the starting stage of the Ag­28Cu­1Ni ingot during continuous casting. The principle ofthe Mile method is illustrated in Fig. 2.

First of all, the casting region is divided into region 1 andregion 2, and a number of zero-thickness foldable units areplaced between the contact interfaces of the two regions. Asthe continuous casting process starts, the position of theregion 1 stays at initial position, and the region 2 movesdown at a set traction speed. In order to maintain thecontinuity of temperature and velocities between two regions,a number of unit layers with an initial zero thickness aregiven, and it is assumed that each unit layer can reach acertain thickness value. When the ingot moves down to theset thickness, a new element layer is unfolded, the layers aregradually “unfolded”, similar to the unfolding of anaccordion, and finally forming the whole ingot. In the fixedarea 1, the Eulerian algorithm is used to calculate the flowand heat transfer of the liquid metal, and the thermo-mechanical coupling of moving region 2 and 3 are calculatedby the Lagrangian algorithm.30,31)

The calculation model in this paper is depicted in Fig. 3.Parts I, II, III and V correspond to parts 1, 2, 3 and 5 inFig. 2. Between the II and III sections, the number for thefoldable layers of elements is defined as 40, and the thickness

of each layer after the expansion is set to 0.2mm. The meshof the casting area III in the model is a dynamic mesh, andthe other areas is a fixed mesh, as shown in Fig. 3(b). Thediameter of the ingot is 30mm, and the crystallizer V is madeof pure copper and the pull rod IV is made of 45# steel(carbon steel). In order to reduce the computation time andimprove the calculation precision, the parameters of the meshare as follows: the total number of nodes is 83176, and thenumber of tetrahedral elements is 543187.

3.2 Setting of boundary conditionsAs shown in Fig. 3(a):

(1) Set the fixed temperature condition at the top of theregion I, that is, the pouring temperature;

(2) The fixed heat exchange conditions are set in thecontact surface of region I, II and region V, and thecontact surface between the region II and region IV;

(3) When the region II and III away from the part of thecrystallizer, the heat exchange condition of the surfaceis set to air cooling h = 20W/(m·K). Moreover, theheat exchange conditions between the regions II and IIIis controlled by an external C language program;

(4) According to the process parameters of continuouscasting, the heat exchange conditions between theexternal surface of crystallizer V and the cooling waterare determined. The determination conditions are asfollows:

In the crystallizer, the average heat flux density is used toindicate the intensity of convective heat transfer:32)

q ¼ μwcwW�T

Sð9Þ

The heat transfer coefficient and average heat flux densityhave the following relationship:

h ¼ q

Ts � Twð10Þ

q is the average heat flux density of the crystallizer, W/m2;μw is the density of cooling water, kg/m3; cw is the heatcapacity of cooling water, J/(kg·k); W is the flow of cooling

Fig. 2 The principle of Mile method.

(a) (b)

Fig. 3 Meshing of computational domain ((a) original mesh, (b) stretchingmesh).

Fig. 1 Relation between FE mesh and CA cells.29)

J. Fang et al.1232

water, m3/s; ¦T is the water temperature difference in theimport and export of the crystallizer, K; S is the effectivecontact area of liquid metal and crystallizer, m2.

3.3 The determination of simulation parametersThe General Research for Nonferrous Metals provides

pure silver (99.99mass%), pure nickel (99.9mass%) andelectrolytic copper (99.9mass%) as raw materials forexperiment. An Ag­28Cu­1Ni (mass%) ingot with dimen-sion of )30mm prepared by continuous casting process, andthe schematic diagram of the directional solidificationapparatus is shown in Fig. 4. The melting temperature rangeof the directional solidification process in vacuum environ-ment is 1113³1173K, the holding time is 15min, the pullingspeed interval is 1 © 10¹2³2.5 © 10¹2m/s, the coolingwater flow is 200³500L/h, and the cooling water temper-ature is 22°C. The experimental and simulated samples weretaken along a cross section of 800mm from the bottom ofthe ingot. The cross section of the alloy are ground andpolished, and then eroded by an etching agent (volume ratioNH3·HO2:H2O2:HO2 = 1:1:1) to obtain the metallographicstructure.

During solidification simulation, the pouring temperature,heat transfer coefficient and pulling speed were obtainedthrough actual measurement, and the simulation conditionswere consistent with the actual experimental conditions. Thecooling condition is the water cooling mode in thecrystallizer, and the heat transfer coefficient varies with thechange of the water flow rate. The process conditions ofcasting temperature, heat transfer coefficient and pullingspeed on the microstructure evolution of Ag­28Cu­1Niingots are listed in Table 1.

In addition, the physical parameters used in the numericalsimulation of Procast software are shown in Table 2. Mostof the physical parameters are calculated by JmatProsoftware, and a small part is obtained through theliterature.33­35) The kinetic parameters of dendritic tipgrowth are defined a2 = 2.13716 © 10¹6m/(s·K3) and a3 =1.11035 © 10¹7m/(s·K3), which are calculated by liquidusslope, equilibrium partition coefficient, liquid phase diffusioncoefficient and Gibbs-Thomson coefficient.

4. Results and Discussion

4.1 Experimental resultsThe microstructure of the continuous casting Ag­28Cu­

1Ni alloy is shown in Fig. 5. The microstructure of the Ag­28Cu­1Ni ingot is a typical solidified structure, includinga chill crystal region composed of fine equiaxed grains, acolumnar crystal region, and a central equiaxed crystalregion. The diameter of equiaxed grain is in the range of0.5³1.5mm, and the closer to the center of the casting, thelarger the equiaxed grains. There are a large number ofcolumnar crystals around the casting. The width of thecolumnar crystal is less than 1mm and the length is between0.5 and 3mm. Figure 6 is a local macroscopic structure of an

Fig. 4 Schematic diagram of continuous casting device.

Table 1 Process parameters of Ag­28Cu­1Ni ingot during continuouscasting.

Table 2 Physical parameters of Ag­28Cu­1Ni alloy for numericalsimulation.

Fig. 5 Experimental results of Ag­28Cu­1Ni ingot during continuouscasting.

Numerical Simulation of Solidification Structures of Ag­28Cu­1Ni Alloy through Continuous Casting 1233

Ag­28Cu­1Ni ingot. According to the American Society forTesting and Materials standards, NV ¼ 0:8N3=2

A ¼ 0:5659N3L

(NV is the number of grain per unit volume, NA is the numberof grain per unit area, and NL is the number of grain on theunit measuring line). From the Fig. 5, the nucleation densitynv,max = 1.5 © 108m¹3 in the bulk of the liquid andnucleation density ns,max = 1.8 © 105m¹2 at the mold wallare calculated.

4.2 The determination of the mean nucleation under-cooling

The above three-dimensional mathematical model (CAFE)was applied to the continuous casting of Ag­28Cu­1Niingots, which considered non-uniform nucleation and graingrowth of the crystallizer surface and in the bulk of themelt. In the process of microstructure simulation, Gaussiandistribution parameters have critical effects on the solidifiedstructure. The Gaussian distribution parameters (nv(s),max,¦Tv(s),max and ¦Tv(s),·) can be gained by the experiments, butthe errors of these parameters available are always inevitablein testing of practical castings. Thus, it’s absolutely necessaryto investigate the effects of Gaussian distribution parameterson solidified structure, in order to find the appropriateGaussian distribution parameters for calculation, which helpsto improve the accuracy of the simulation results. Gaussiandistribution function both in the bulk and at the surface ofthe ingot are described in Fig. 7, the maximum nucleationdensity (nv(s),max), the standard deviation of nucleationundercooling (¦Tv(s),·) and the mean nucleation undercooling(¦Tv(s),max) were used to represent the undercooling. Thevalue of nv(s),max stands for the maximum number ofheterogeneous nuclei, which can be easily obtained fromthe macroscopic morphology of the solidified structure. Thevalue of ¦Tv(s),· only determines the rate at which theheterogeneous nucleation reaches the maximum density ofgrains. ¦Tv(s),max is the undercooling required for thenucleation of the heterogeneous nucleus. When the under-cooling required for nucleation of the heterogeneous nucleusis reached, the nucleus are activated and begin to nucleateand grow. Furthermore, it is difficult to adjust six nucleationparameters to match each other in microstructure simulation.Consequently, in this study, we focus on the study of themean nucleation undercooling parameter and assume that theother two Gaussian parameters are specific empirical values.Table 3 lists the different Gaussian distribution parametersin the CAFE model. The mean nucleation undercooling(¦Tv,max) is a single variable and other nucleation parameters

are assigned constant. The effect of mean bulk undercoolingon the microstructure of the Ag­28Cu­1Ni alloy arepresented in Fig. 8 so as to determine the mean nucleationundercooling in the bulk of the molten metal. The simulationusing the different process parameters with the pouringtemperature, heat transfer coefficient and the pulling speedfor this simulation are defined as 1173K, 4000W/(m·K) and2 © 10¹2m/s, respectively. Moreover, the above-mentioned

Fig. 6 Local macroscopic structure of Ag­28Cu­1Ni ingot in Fig. 5.

Fig. 7 Nucleation site distributions for nuclei formed at the mould wall(indexed as “s”) and in the bulk of the liquid (indexed as “v”).36)

Table 3 Nucleation parameters varied in the simulation.

(a)

(b)

(c)

Fig. 8 Simulation results of Ag­28Cu­1Ni ingot with the different meannucleation undercooling in the bulk of the liquid: 1.5K (a); 5K (b) and10K (c).

J. Fang et al.1234

simulated microstructure of the cross-section is 800mmdistant from the bottom of the ingot.

In the Fig. 8, the different colors represent differentcrystallographic orientations, and the contact surfaces withcolor and gray areas on the ingot represent the solidificationinterface. The grain size and the growth direction of columnargrains are also presented in Fig. 8. Furthermore, theformation of crystalline regions corresponds to differentmean nucleation undercooling. In Fig. 8(a), a large amountof equiaxed grains nucleate in the bulk of the liquid metal. InFig. 8(b), the microstructure of the Ag­28Cu­1Ni ingotconsists of four different crystalline zones, including regionof surface fine grain, zone of columnar grain, transition zoneof CET and region of center equiaxed crystal. When the meannucleation undercooling is increased to 10K, the columnargrains which originate from nuclei of the periphery at thechill zone can develop up to the center of the Ag­28Cu­1Niingot, as can be seen in Fig. 8(c). Therefore, the nucleationparameter has significant effect on the crystalline zones.Obviously, the higher the mean nucleation undercooling, thelarger the columnar grain zone.

The above phenomena can be explained as follows: thenuclei are activated to nucleate and grow as the undercoolingrequired for heterogeneous nucleation is reached. The lowerthe nucleation undercooling, the stronger the nucleationability of the heterogeneous particles, and the more grainsappear in the solidified structure. Therefore, the ability ofheterogeneous nucleation will be weakened and the numberof grains will be reduced with the increase of the meannucleation undercooling, which is beneficial to the weaken-ing the growth of equiaxed grain as well as the CETtransformation, resulting the enhancement of the nucleationand growth ability of columnar crystal.

The results show that when the mean undercooling is 5 k,the simulation results are in good agreement with the actualexperimental results. The diameter of the equiaxed grain isin the range of 0.5³2mm, the width of columnar crystal isless than 1mm, and the length is in the range of 0.5³3.5mm.The quantitative results of simulated grain size approximatethe experimental results. Accordingly, the mean bulkundercooling, ¦Tv,max = 5K, as the determined nucleationparameter to predict and analyze the microstructure evolutionunder different casting conditions, which extends the abilityto control the solidified structure by controlling pouringtemperature, heat transfer coefficient and pulling speed ofAg­28Cu­1Ni ingot during continuous casting.

4.3 The crystallization process and the simulated micro-structure of Ag­28Cu­1Ni ingot at different distancefrom the bottom surface of ingot

The crystallization process of Ag­28Cu­1Ni alloy isshown in Fig. 9(a)­(e). In the initial stage of the solidificationsimulation, the molten metal on the periphery of the ingot isin contact with the water-cooled crystallizer, resulting in anincrease at the undercooling. The greater undercooling causesmore grains are clearly nucleated on the wall of the casting,these equiaxed grains are small in size and have a randomorientation. In Fig. 9(d)­(e), the columnar crystals areepitaxial from the opposite direction of heat flow, and thegrowth direction is perpendicular to the isothermal lines inthe liquid. Hence, the columnar grains on the surface of theingot tend to be perpendicular to the surface of the mold.Furthermore, the “columnar to equiaxed” transition (CET)can be clearly seen in Fig. 9, which is attributable to thefollowing reasons: the equiaxed grains begin to nucleate andgrow at the expense of columnar grains as the undercoolingin the residual liquid becomes small, thus leading to thetransition from columnar grains to equiaxed grains. In thefinal stage of solidification, the temperature gradient at thecenter of the ingot is reduced, which is not conducive tothe formation of columnar crystals, thereby obtaining theequiaxed crystals.

In addition, we also observed the simulated microstructureof the cross sections at different distances from the bottom ofthe ingot, and the simulation results are showed in Fig. 10. Itcan be observed from Fig. 10(a) that equiaxed grains occupythe entire area, owing to the cross section is closer to thewater-cooled dummy bar, the undercooling of this crosssection greater than the mean undercooling on the other crosssection (500mm, 1000mm). Eventually, the number ofgrains nucleated in the Ag­28Cu­1Ni ingot is rapidlyincreased. Hence, the undercooling decreases as the distance

(a) (b) (c) (d) (e)

Fig. 9 The crystallization process of Ag­28Cu­1Ni ingot during continuous casting at pouring temperature, heat transfer coefficient andpulling speed was determined to be 1173K, 4000W/(m·K) and 2 © 10¹2m/s, respectively. Simulated solidification time: (a) 0.3124 s(b) 1.1341 s (c) 1.2969 s (d) 1.7224 s (e) 2.4912 s.

(a) (b) (c)

Fig. 10 Simulation results show that in different cross sections: thedistance from the bottom of the ingot is 100mm (a), 500mm (b) and1000mm (c).

Numerical Simulation of Solidification Structures of Ag­28Cu­1Ni Alloy through Continuous Casting 1235

between the ingot and the bottom of the ingot increases.Moreover, it can be concluded from Fig. 10 that the columnarcrystal region gradually expands as the distance from thebottom of the ingot increases.

4.4 Effect of process parameters on solidificationstructure

4.4.1 Effect of pouring temperature on solidificationstructure

When the cross section is 800mm from the bottom of theingot, the microstructure simulation of Ag­28Cu­1Ni ingotat different pouring temperatures (1113, 1173, 1233 and1293K) with the identical heat transfer coefficient 4000W/(m·K) and pulling speed of 2 © 10¹2m/s was carried out,and the result is shown in Fig. 11. The chilling zonecomposed of fine equiaxed grains is the largest at the lowerpouring temperature, and the thickness of the chilling layerdecreases with the increase of pouring temperature. However,the percentage of the columnar grains in the entire regionincreases with the increase of pouring temperature. Thestatistical simulation results of Ag­28Cu­1Ni alloy withinthe identical cross section at different casting conditions aredescribed in Table 4. As can be seen from Table 4, theaverage grain radius increases from 5.79 © 10¹7 to 8.26 ©10¹7mm, and the number of the grains decreases from 1262to 757 as the pouring temperature increasing from 1113 to1293K.

When the casting temperature is 1113K (superheat is45K), the smaller temperature gradient of melt is conduciveto the retention of free grains formed from the casting wall,resulting the increase of the nucleus for heterogeneousnucleation. Thus, the proportion of equiaxed grains is larger.

In addition, the smaller temperature gradient of melt willresult in the actual undercooling of molten metal is greaterthan that of the nucleation undercooling, which leads to theincrease of preserved nuclei at the frontier of columnardendritic. Eventually, the CET transformation occurred andthe proportion of equiaxed grains was also improved. Thetransition extent of CET under low superheat is greater thanthat under high superheat. Furthermore, when the pouringtemperature is 1113K, the constitutional undercooling atthe frontier of solid-liquid interface reaches the maximum,which is much greater than that of the undercooling requiredfor heterogeneous nucleation. All nuclei grow almostsimultaneously, thus the grain size of the central equiaxedgrains is more uniform than that of the high superheatconditions.

When the casting temperature is 1293K (superheat is225K), the possibilities of remelting and disappearing forthe free grains from the chilled layer have been improved,reducing the number of nuclei in the melt and restrainingthe growth of equiaxed grains. The increase of the superheatresults in the increase of the thermal gradient, whichpromotes the growth of the columnar dendrites and thedecrease in nucleation rate.

Therefore, in the continuous casting process, lowering thepouring temperature is the most effective way to refine thegrain size and improve the amount of equiaxed grains forAg­28Cu­1Ni ingot.

In addition, the transformation position of CET is movedto the peripheral direction of the casting as the decrease ofsuperheat. Due to the decrease of superheat, the formationtime of the stable chilled layer is prolonged, which isconducive to the separation of more grains from the cast wall.These grains move toward the front of columnar dendrite,resulting in an increase in the number of retained nuclei atthe front of columnar dendrite. These nuclei have been stablygrown before the columnar grains grow, and the CETtransformation is ahead of schedule.4.4.2 Effect of heat transfer coefficient on solidification

structureFigures 12(a)­(d) show the solidification structure of the

simulated Ag­28Cu­1Ni alloy under different heat transfercoefficients. When the heat transfer coefficient is 2000W/(m·K), the solidified structure is occupied by thecolumnar grain between the surface of casting and 2.5mmaway from the surface of casting, and the remaining area ofthe casting consists of equiaxed grains. When the heattransfer coefficient increases from 2000 to 5000W/(m·K),the columnar grains can be observed from the surface ofcasting to the 9mm away from the casting surface. Moreover,the proportion of columnar grain region increases but the

(a) (b) (c) (d)

Fig. 11 The solidified structures under the identical casting conditions atdifferent casting temperatures: 1113K (a); 1173K (b), 1233K (c) and1293K (d).

Table 4 Statistical simulation results of Ag­28Cu­1Ni alloy under theidentical cross section at different casting conditions.

(a) (b) (c) (d)

Fig. 12 The solidified structures of Ag­28Cu­1Ni alloy under the identicalcasting conditions at different heat transfer coefficient: 2000W/(m·K)(a); 3000W/(m·K) (b); 4000W/(m·K) (c) and 5000W/(m·K) (d).

J. Fang et al.1236

proportion of equiaxed crystal region decreases with theincrease of heat transfer coefficient. Further, as shown inTable 4, the average grain radius increases from 6.13 © 10¹7

to 7.32 © 10¹7mm, and the number of the grains decreasesfrom 1264 to 825 as the heat transfer coefficient increasingfrom 2000 to 5000W/(m·K).

The temperature field and flow field during solidificationdetermine the solidification structure, and the temperaturegradient of the solidification front is much larger than thetemperature gradient of the low heat transfer coefficientwhen the heat transfer coefficient is large. The greater thetemperature gradient, the more favorable the growth ofcolumnar grains. Besides, in terms of the flow rate of fluid atthe front of liquidus, the flow rate under the condition of largeheat transfer coefficient is much smaller than that of the lowheat transfer coefficient. The smaller the flow rate of thefluids, the less the generation of dendritic fragments and thetransport of the solute, which is unfavorable to the formationof the undercooled zone and the equiaxed grains. Therefore,the solidification structure is composed of coarse columnargrains under the condition of large heat transfer coefficient.

In terms of solid-liquid phase zone, the low heat transfercoefficient is wider than the high heat transfer coefficient. Thewider the solid-liquid phase zone, the more favorable forthe retention and development of free grains separated fromthe casting wall, which leads to the increase at the numberof nuclei. In addition, in the case where the heat transfercoefficient is low, the smaller the temperature gradient atfront of the liquidus line, the more favorable for theformation of equiaxed grains. Moreover, the flow rate ofthe fluid at the front of the liquidus line increases with thesolidification process under the low heat transfer coefficient.The greater the flow rate of the fluid in the front of theliquidus, the more beneficial to the removal of heat from themelt and the formation of the undercooled zone. Therefore,under the condition of low heat transfer coefficient, largeundercooling can be obtained in the casting, and the smallertemperature gradient is beneficial to the formation ofequiaxed grains. Consequently, when the heat transfercoefficient is small, the proportion of the equiaxed grains inthe solidification structure of the castings is higher.4.4.3 Effect of the pulling speed on solidification

structureThe effects of pulling speed on the solidified structures

of Ag­28Cu­1Ni ingots are shown in Fig. 13. In this case,

the microstructure simulation are implemented at differentpulling speeds (1 © 10¹2, 1.5 © 10¹2, 2 © 10¹2 and 2.5 ©10¹2m/s) with the identical pouring temperature 1173K andthe same heat transfer coefficient 4000W/(m·K). Thecolumnar dendrite zones expand with the increase of pullingspeed. Furthermore, the statistical simulated results ofTable 4 shows the relationship between the number of grainsand the average grain radius with the pulling speed. It can befound from the Table 4 that the average grain radius increasesfrom 5.47 © 10¹7 to 8.05 © 10¹7mm, and the number ofthe grains decreases from 1289 to 771 as the pulling speedincreases from 1 © 10¹2 to 2.5 © 10¹2m/s. The higherpulling speed leads to lower cooling rate for the fixedcooling capacity of the crystallizer, resulting in the increasingof the liquid undercooling. The above factors will inducemuch more grains nucleate on the Ag­28Cu­1Ni ingot,which weakens the growth of columnar grains and leads tograin refinement. Therefore, in order to refine grains andimprove the proportion of fine equiaxed crystals, the pullingspeed should be properly reduced for the Ag­28Cu­1Niingot during continuous casting.4.4.4 Effect of process parameters on distribution of

grain sizeAs can be seen from Fig. 14, the effect of process

parameters on distribution of grain size is different. The heattransfer coefficient has a great influence on the grain sizedistribution, the number of small grains increases and thedistribution range of grain size becomes wider as the increaseof heat transfer coefficient. The distribution range of grainsize is also increased with increasing of pouring temperature,but the amplitude variation is less affected than the heattransfer coefficient. With the increase of the pulling speed,the distribution range of grain size decreased initially andthen increased, and the fluctuation range of the grain size wasbigger than that of the first two cases.

(a) (b) (c) (d)

Fig. 13 The solidified structures of Ag­28Cu­1Ni alloy within theidentical casting conditions at different pulling speeds: 1 © 10¹2m/s(a); 1.5 © 10¹2m/s (b); 2 © 10¹2m/s (c) and 2.5 © 10¹2m/s (d).

(a) (b) (c)

Fig. 14 The distribution of grain size for Ag­28Cu­1Ni ingot at different heat transfer coefficient (a), pouring temperature (b) and pullingspeed (c).

Numerical Simulation of Solidification Structures of Ag­28Cu­1Ni Alloy through Continuous Casting 1237

5. Conclusions

The microstructure evolution of Ag­28Cu­1Ni ingotduring the continuous casting process was simulated basedon CAFE method. For the determined parameters, thesimulated results are agreement with experimental result.The solidified structure consists of four parts, includingregion of surface fine grain, zone of columnar grain,transition zone of CET and region of central equiaxedcrystal. In the modele of microstructure evolution for the Ag­28Cu­1Ni ingot, the nucleation parameters have a significantinfluence on the crystalline zones. Obviously, the higherthe mean nucleation undercooling, the larger the columnarcrystal zone. Besides, the columnar grain regions expandswith the distance from the bottom of the ingot increasing.The effects of pouring temperature, heat transfer coefficientand pulling speed on the microstructure of Ag­28Cu­1Niingot under the steady-state solidification were obtained. Theresults show that with the pouring temperature increasing,the average grain radius increases. Therefore, the reductionof superheat is the most effective way to refine the grain sizeand improve the amount of equiaxed grains. With theincrease of heat transfer coefficient, the proportion ofcolumnar crystal regions increases and the proportion ofequiaxed crystal regions decreases. Furthermore, the averagegrain area and the average grain radius decrease. With thepulling speed increasing, the columnar zone expands andthe number of grains decreases, whereas the mean radius ofgrains increases. Therefore, in order to refine grains andimprove productivity, the pulling speed should be appropri-ately reduced. Furthermore, under the same processparameters, the pulling speed has the greatest effect on thedistribution of grain size. Comparison of solidificationsimulation results under various process conditions, theoptimum process conditions obtained are as follows: the heattransfer coefficient is 2000W/(m·K), the pouring temper-ature is 1113K, and the pulling speed is 1 © 10¹2m/s.

Acknowledgments

This work was supported by the National Key Researchand Development Program of China [Project No.2017YFB0305700], National Natural Science Foundationof China [Project No. U1602271 and U1602275], MajorScience and Technology Projects in Yunnan Province[Project No. 2018ZE011, 2018ZE012, 2018ZE022,2018ZE026 and 2018ZE020] and Yunnan Basic AppliedResearch Program [Project No. 2018FB088].

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