Numerical Simulation of Grain Growth of Directionally Solidified DZ4125 Alloyunder Varied Blade Orientations

Bingxing Wang, Yue Xia+, Guohuai Liu, Chao Yin, Zhaodong Wang and Guodong Wang

The State Key Laboratory of Rolling and Automation (RAL), Northeastern University, Shenyang 110819, China

The ProCAST simulation software is used to simulate the temperature field and the mushy zone of the blade under different bladeorientations, and then grain growth was investigated based on them. It is found that the temperature field and the mushy zone of the bladesamples in the parallel orientation are stably horizontally distributed at the same height, while the perpendicular orientation has a degree ofinclination. In the heat preservation zone, the sample temperature close to the furnace wall is higher than that of the sample temperature near thecenter (referred to here as the Center-Side), and the temperature field is inclined upwards. However, in the cooling zone, the temperature field isinclined downwards because the temperature near the furnace wall (referred to here as the Wall-Side) is lower than that of the Center-Side. Thegrain growth of the blades with parallel orientation is superior as single crystal blade castings are formed. The blade samples in a perpendicularorientation have a certain heterocrystal tendency. The grain growth of the mutated cross-section of the blade samples is summarized usingvariable cross-section samples. Heterocrystals are used to be formed at the edge plate of complex structure, the mutation section and the end ofspiral crystal separator. [doi:10.2320/matertrans.MT-M2019383]

(Received December 27, 2019; Accepted March 27, 2020; Published July 25, 2020)

Keywords: orientation relationship, directional solidification, temperature field, mushy zone, grain growth

1. Introduction

Ni-based superalloy are used for turbineblade of aircraft jetengines because of their excellent creestress rupture, thermomechanical fatigue capabilities.1) Directional Solidification(DS) technology is widely utilized for manufacturingcomponents with columnar or single crystal structure thatalign a particular crystallographic axis to the growth directionto improve the high temperature properties of nickelsuperalloy.2­4) However, the grain defects of different degreeswas caused by uneven heat exchange with the furnacewall due to the complex structure of the blade during thedirectional solidification process. Numerical simulation, atechnology can directly reflect the directional solidificationprocess which has been increasingly applied to the develop-ment of single-crystal superalloy turbine blades.5)

Many researchers have studied the temperature field andgrain growth of blades formed with directional solidification.Using the CA-FD method, Lee et al.6) simulated the dendriticgrowth process under different parameters and studied theadverse effects of blade mutations cross-section on thegrowth of a single crystal. Kermanpur and Varahram et al.7)

simulated the grain growth of a single crystal turbine bladeunder the condition of liquid metal cooling directionalsolidification process using the CA-FE method. In particular,the influence of process parameters on the growth and defectsof single-crystal tissue was examined. Yu et al.8) establisheda radiation heat transfer model between the blade and thefurnace wall, which accounted for the influence of thegeometric size of the furnace body. The temperature fielddistribution of the blade was then simulated under differentdrawing speeds. Gao9) studied the directional solidificationtemperature field of a nickel-based single crystal blade. Theresults showed that when the drawing speed reached a certainvalue, the blade isotherm became concave, and inclined tothe thin side of the blade. Yang et al.10) studied the

temperature field of the blade platform during the directionalsolidification process and found that the probability ofheterocrystal grains formation increased with the increasedisotherm inclination angle. Liang et al.11) studied thedirectional solidification process under the condition of asingle blade and predicted the microstructure of a singlecrystal. Process parameters such as drawing speed wereconsidered in the model. The results indicate that theisothermal curvature at the solid-liquid interface frontincreases with increased drawing speed, and the temperaturegradient increases accordingly. Saitou and Hirata12) used atwo-dimensional model to calculate the relationship betweenthe shape of the solid-liquid interface and the growthconditions in the HRS directional solidification furnace. Itwas pointed out that the solid-liquid interface presented acertain curvature in the stable stage. Yu et al.13,14) usedcommercial finite element analysis software to study thedirectional solidification process and the associated temper-ature field of a single crystal blade. In addition, therelationship between temperature gradient and castingdefects, such as heterocrystal grain was examined from amacroscopic perspective. The key to successful directionalsolidification technology is to control the influence ofradiative heat transfer on the temperature field in order toobtain a well-organized single crystal blade. However, themajority of research focused on the directional solidificationprocess parameters rarely mention the influence of bladeorientation on the directional solidification temperature field,which further affects the grain growth.

In this paper, the three-dimensional CAD programSolidWorks is used to set the blade sample model withdifferent orientations. The blade temperature field, the mushyzone and grain growth at different blade orientations arecalculated by the ProCAST simulation software during thedirectional solidification process. The present paper focuseson the evolution of the grains at the complex mutation cross-section of the blade platform and uses a simplified model toexplain the formation of heterocrystal grains in order to+Corresponding author, E-mail: yxia024@163.com

Materials Transactions, Vol. 61, No. 8 (2020) pp. 1663 to 1670©2020 The Japan Institute of Metals and Materials

provide a theoretical basis for the preparation of optimalblade products.

2. Experimental Setup and Procedure

A simple model is established to simulate the directionalsolidification process, as shown in Fig. 1. The modelincludes a graphite sleeve, a heat insulation baffle, a water-cooled ring, and a water-cooled copper plate under thesample. The graphite sleeve with 450/400mm (inside/outside diameter), and 500mm in height is used to heatand insulate the model. In the actual industrial productionprocess, shielding of the surrounding magnetic field is alsoone of its important roles. The heat insulation baffle blocksthe heat exchange between the upper heat preservation zoneand the lower cooling zone. The thickness of the baffle is

25mm. The figure shows the simply structures of the water-cooled ring and water-cooled copper plate which circulatecooling water internally and play an important role in thedirectional solidification apparatus.

In order to study the effect of blade orientation in thedirectional solidification furnace on the grain growth, twogroups of models were created and awere referred to hereas parallel orientation and perpendicular orientation. Theseorientations are shown in Fig. 2. The blade bodies are110mm high and 40mm wide, and the samples are spaced90° apart. Figure 2(a) shows the perpendicular orientationassembly. The blade bodies are held relatively perpendicularto the graphite sleeve. Figure 2(b) shows the parallelorientation assembly. In this case, the blade body is relativelyparallel to the graphite sleeve, and the different positions inthe same height of the blade body are approximately the sameas the furnace wall distance.

The superalloy used in this paper is DZ4125, a nickel-based directionally solidified superalloy which widely usedin China. DZ4125 has excellent high-temperature oxidationresistance, creep resistance, and rupture life. The specificalloy components and their mass fraction are given inTable 1.

The pouring temperature was fixed at 1550°C and washeated in 1550°C, holding for 180 s with a withdraw velocityof 5mm/min. The water-cooled ring and the water-cooledcopper plate in the cooling zone were held at a constanttemperature of 20°C. The molded shell, casting, and water-cooled copper plate move simultaneously during the drawingprocess. The model was divided into total 467161 grids byusing MeshCAST module in the ProCAST simulationsoftware (The size of the grid unit in important parts with2mm © 2mm © 2mm, such as the blades. In less importantregions, the grid size was 10mm © 10mm © 10mm). Thephysical parameters of DZ4125 alloy are imported into thematerial database of ProCAST, the main physical propertiesof the DZ4125 superalloy15) are shown in Table 2.

Fig. 1 Schematic diagram of the simplified model of directional solid-ification.

Fig. 2 Schematic diagram of different blade orientations.

Table 1 Chemical composition of nickel-based directionally solidified superalloy DZ4125.

B. Wang et al.1664

3. Calculation Method

In the process of directional solidification drawing, theheat transfer is mainly divided into two forms. One is thelocal contact heat transfer between the water-cooled copperplate and the mullite structural shell. The other is the radiativeheat transfer between the sample column and othercomponents, including other sample columns, heatingfurnace walls, and the water-cooled ring. In the heat transferprocess, the energy conservation law must be satisfied. Themathematical representation of the heat transfer model is:

μC@T

@t¼ ­

@2T

@x2þ @2T

@y2þ @2T

@z2

� �þ μL

@fS@t

þQnet ð1Þ

where μ is the material density, c is the specific heat capacityof the material, T is the material temperature, t is time, ­ isthe thermal conductivity of the material, L is the latent heatof the material crystallization, and fS is the solid fraction. Itcan be seen from eq. (1) that the heat transfer process iscomposed of three parts, the contact heat conduction term,the internal heat source term caused by latent heat ofcrystallization, and the Qnet radiative heat transfer term.

Radiative heat transfer is the core problem in the wholeprocess of the directional solidification process. Accordingto the Stefan-Boltzmann law,16) the radiant heat transferbetween the surfaces of a gray body is:

Qnet ¼A1·ðT 4

1 � T 42 Þ�

1� ¾1

¾1þ 1

¤1;2þ A1

A2

� 1� ¾2

¾2

� ð2Þ

where, ¤1,2 in eq. (2) can be expressed as:

¤1;2 ¼CV

A1

ZA2

ZA1

cos ª2 cos ª1³R2

dA1 dA2 ð3Þ

In these equations, · is the Stefan Boltzmann constant, A1,2 isthe gray body surface area, CV is the visible coefficient ongray body surface (0 is invisible, 1 is visible), ª1,2 is the anglebetween the normal line of gray body surface and the centerline of the surfaces, R is the center distance between twosurfaces, ¤1,2 is radiation angle coefficient, T1,2 is the surfaceelement temperature, and ¾1,2 is the surface elementgrayscale.

The preferred orientation of the DZ4125 dendrite growthwas ©100ª. The CAFE module in the ProCAST simulationsoftware was used to establish the grain growth model. TheRappaz model of continuous nucleation is consistent with anormal distribution used by the grain nucleation.17) The graindensity at the solid-liquid interface front was characterized bya Gaussian distribution function:

dn

dð�T Þ ¼nmaxffiffiffiffiffiffi2³

p�T·

exp � 1

2

�T �� �T

�T·

� �2" #

ð4Þ

where, n is the nucleation density, nmax is the maximumnucleation density, "T is the undercooling, "T· is thestandard deviation of the undercooling distribution, � �T is theaverage nucleation undercooling.

The number of grains for a certain degree of undercoolingcan be calculated using eq. (5):

nð�TtÞ ¼Z �Tt

0

dn

dð�T Þ dð�T Þ ð5Þ

where ¦Tt is the level of undercooling.A kinetic model of grain growth was established at the

solid-liquid interface, namely the dendrite tip growth front.18)

The model was composed of four parts which can beexpressed as:

�T ¼ �Tc þ�Tr þ�Tk þ�Tt ð6Þ

Table 2 Directionally solidified superalloy DZ4125 main thermophysical parameters.

Numerical Simulation of Grain Growth of Directionally Solidified DZ4125 Alloy under Varied Blade Orientations 1665

where, "Tc is the component undercooling; "Tr is thecurvature undercooling, "Tk is the dynamic undercooling,"Tt is the thermodynamic undercooling.

The cell capture method was used for grain growth, and thekinetic growth model was integrated to obtain the followingpolynomial:

v ¼ a2�T 2 þ a3�T 3 ð7Þwhere v is the dendrite tip growth rate, a2 and a3 are graingrowth coefficients.

4. Results and Discussion

4.1 Effects of different blade orientation on temperaturefield and mushy zone

Figure 3 contains a schematic diagram of the temperaturefield of two different orientations at the same time andsolidification fraction. For the perpendicular orientation inFig. 3(a), the temperature field at the upper part of the bladeand at the lower part of the blade are inclined in differentdirections. For the parallel orientation shown in Fig. 3(b), thetemperature field isotherm tends to stabilize and flatten.Moreover, under closer examination of the complex structureof the blade platform, the inclined temperature field of theperpendicular orientation case results in different temperaturefields at the mutation cross-section, which is apt to generate

defects. The overall temperature field at the platform of theparallel orientation has a smooth transition, especially at thecomplex structure of the blade body.

To examine the perpendicular orientation of the temper-ature field inclination, a simplified model was establishedusing a cylindrical sample. Here, the sample is a round barwith a diameter of 18mm, a height of 110mm. The numberof modules is 4. The other simulation conditions are thesame as those used for the blade sample simulations. Thesimulation results are shown in Fig. 4.

The temperature field distribution of the cylindrical samplepassing through the heat insulation baffle was selected. It wasfound that in the upper part of the heat insulation baffle,known as the heat insulation zone, the temperature of theWall-Side was higher than the Center-Side. For this reason,the temperature field presents an upward inclination. In thecooling zone, the temperature of the Wall-Side sample islower than that of the Center-Side, and the temperature fieldis inclined downward. In order to clearly explain thedistribution of the temperature field, the radiation dissipationangle is used.

In the process of directional solidification, the samplecooling is primarily achieved in two ways: First, the water-cooled copper plate provides an upward cooling effect, butdue to the barrier of the mullite structure and the smallstructure of the spiral grain selector, the cooling effect is verysmall. The second cooling effect is provided by the water-cooled ring. The water-cooled temperature of 20­30°C isalways maintained by the water-cooled ring and therefore hasa large temperature difference with the sample resulting in agood radiative cooling effect. In the calculation of radiativeheat transfer, the selected temperature measurement point isvisually separated from the water-cooled copper plate and theheat insulation baffle. The visible included angle is calledthe radiative heat dissipation angle. The larger the radiationangle, the stronger the radiation ability. As shown in Fig. 5,two points A and B at the same height above the heatinsulation baffle are selected. By drawing the angle betweenthe heat insulation baffle and the water-cooled copper plate, itis found that the angle ¡ < ¢. Therefore, the radiative heatdissipation capacity at point A is lower than that of point B,Fig. 3 Temperature field of different orientation blades.

Fig. 4 Temperature field distribution of the cylindrical sample.

B. Wang et al.1666

which causes the temperature near point A to be higher thanat point B. Under the heat insulation baffle, the parallel pointsC and D are examined. The angle between the heat insulationbaffle and the cooling copper plate is such that £ > ¤. Asa result, the temperature near Point C is lower than thetemperature at point D.

In a similar fashion, the more uniform temperature field ofthe parallel orientation can be explained. In this case, theblade surface of the parallel orientation is parallel to thefurnace wall, and all points on the same horizontal surface areequidistant from the furnace wall. Therefore, the radiationheat transfer angle formed through the water-cooled ring isthe same resulting in consistent heat transfer. Additionally,since the blade is relatively thin, the heat transfer differencein thickness could be ignored.

Aiming at the mushy zone of the blade sample, thecomplex structure of the blade was studied. Due to theinclination of the temperature field in the perpendicularorientation, the advancing direction of the mushy zonedeviates from the preferred orientation. This effect becomesincreasingly obvious in the complex structure of the blade.The mushy zone of the different blade orientation is shown inFig. 6, when the solidification fraction is 28.3%. Here, thesolid-liquid interface moves to the complex structure of theblade. When the blade is in the perpendicular orientation, themushy zone has an inclined angle. This indicates that theCenter-Side mutation cross-section solidifies earlier than theWall-Side mutation cross-section, damaging the overallstructure of the blade. This can also lead to the formationof heterocrystal grains or change the growth direction of thecolumnar crystals. In the parallel blade orientation, the mushyzone moves more stable in the complex structure. In thiscase, the distance from each point on the plane to the water-cooled ring is equal. As a result, no obvious uneven heatdissipation phenomenon, leading to improved results.

4.2 Grain growth behavior of different blade orientationThe study of the blade temperature field and mushy zone

provides a reference for exploring the blade grain growthbehavior. The fluctuation of the temperature field and themushy zone affects the grain formation and growth,particularly in the mutation cross-section. Therefore, thegrain growth status of the different orientations was studied.Two types of grain growth models were observed for the

perpendicular and parallel blade orientations with the variableinsulation temperature of 1550°C. The simulation results areshown in Fig. 7. The results show that the tendency ofheterocrystal grains to form is increased in the blade sampleswith a perpendicular orientation. Because the temperaturefield and mushy zone of the blade sample of theperpendicular orientation have a certain inclination, thereare different temperature gradients at a given height, whichfacilitates the formation of heterocrystal grains. Particularlyat the mutation cross-section of blades, heterocrystalnucleation occurs more readily. For the parallel orientation,no heterocrystal tendency was observed at the complexplatform or the mutation cross-section of the blade. This isbecause the temperature field distribution of the blade samplewith parallel orientation is relatively stable without excessiveinclination. The original grains screened from the end of thespiral grain selector gradually grow in the direction of heatflux until the complete blade casting is filled.

In order to demonstrate the growth behavior of the grainsat the mutation cross-section more clearly, a variable cross-section sample was introduced for detailed analysis. Thestructure of the variable cross-section sample is similar to thatof the cylindrical sample Following a transition section, themain body of the variable section sample is cuboid, there is avariable cross-section platform every 20mm. The widths of

Fig. 5 Schematic diagram of radiation dissipation angle in the drawingprocess.

Fig. 6 Mushy zone of different orientation of blade.

Numerical Simulation of Grain Growth of Directionally Solidified DZ4125 Alloy under Varied Blade Orientations 1667

these variable-sections platform are 3, 6, 9, 12mm frombottom to top, and the thickness of the variable cross-sectionplatform is equal to 5mm. The sample height is equal to thecylindrical sample.

Figure 8 shows one of the variable cross-section platformsof the sample (platform width is 6mm and thickness is5mm). The time taken by dendrites on the Center-Side togrow from the initial point A to the inflection point of thevariable cross-section platform is given by t1. The filling timeof the original secondary transverse dendrites from theinflection point of the variable-section platform to Point B ist2. When the liquidus is at the position shown in Fig. 8(a),point B at the platform is not nucleated due to insufficientundercooling. The time interval where Point B changes fromliquidus temperature to grain nucleation is t3. The followingrelationships exist: When t1 + t2 < t3, the time taken forthe original grain to grow from Point A to the fully filledvariable-section platform is less than the time taken for theundercooled heterocrystal nucleation. Therefore, no hetero-crystal grains are generated, and the original grain continuesto grow. When t1 + t2 > t3, the nucleation time from theliquidus to the new grain at Point B is faster than the timerequired for the original grain to fill the variable cross-sectionplatform. Therefore, the heterocrystal grains at the variable-section platform continue to grow along the direction of heat

flux. During the competitive growth of the original grains,some of the heterocrystal grains are replaced by the originalgrains, and conversely, some of the heterocrystal grainsreplace the original grains. Figure 8(b) shows a schematicdiagram of the heterocrystal grains growth in the variablecross-section platform.

Figure 9 is a schematic diagram of the grain growth in thesecond section of the variable cross-section sample. Whenthe grain growth is close to the variable cross-sectionplatform, the sample trunk is completely filled by the originalgrain, as shown in Fig. 9(a). As the drawing processcontinues, the original grains grow in the direction of theheat flux and reach the second variable cross-sectionplatform. As shown in Fig. 9(b), the original grains grow atthe variable cross-section platform corner opposite from thefurnace wall.

As the process continues, many new heterocrystalnucleations occur at the corners of the platform, as shownin Fig. 9(c). These heterocrystal grains grow gradually, andthere is competitive growth between the heterocrystal grainsuntil the variable cross-section platform is completely filledtogether with the original grains, as shown in Fig. 9(f ). In thesubsequent directional solidification process, the Wall-Sideplatform is filled with original grains. Because the temper-ature field is inclined from the Wall-Side to Center-Side, thereis no possibility of heterocrystal nucleation and growth onthis platform. During this process, the heterocrystal grainsfrom the Center-Side pass through the upper surface of theplatform and enter the sample trunk, competing with theoriginal grains for growth. This part of the process is shownin Fig. 9(g). As the directional solidification continues, theheterocrystal grains gradually replace the original grain, asshown in Fig. 9(h).

4.3 Position of heterocrystal grains in the bladeSimulation software was used to simulate the grain growth

of the blade samples. The selected samples were arranged ina perpendicular orientation, and the results are shown in

Fig. 7 Grain growth of blade samples in different orientation at 1550°C.

Fig. 8 Schematic diagram of grain growth at the variable cross-sectionplatform.

B. Wang et al.1668

Fig. 10. In order to better express the position whereheterocrystal grains are likely to be formed, the tendency ofheterocrystal formation was increased by reducing the heatinsulation temperature to 1530°C. The left side of the bladesample is the Center-Side, and the right side is the nearfurnace wall side. As shown in Fig. 10(a), Point A is locatedon the complex structure platform of the blade. Due to theinclination of the temperature field, alloy liquid undercoolingnucleation first occurs on the Center-Side, forming theheterocrystal grains. The same behavior also exists at themutation cross-section at Point B. In Fig. 10(b), the newlyformed heterocrystal grain gradually replaces the originalgrain and fills in the blade. At Point C, at the end of the spiral

grain selector, multiple grains grow together due to the poorcrystal screening of the selector. Therefore, there are threepositions on the blade where the heterocrystal grains easilygenerate: the complex structure platform, the mutation cross-section, and the end of the spiral grain selector.

5. Conclusions

(1) The temperature field and mushy zone of blades underdifferent orientations were simulated and calculated. Arelatively stable temperature field and mushy zone ofthe blade sample with parallel orientation were easilyobtained at the same horizontal height. Conversely, the

Fig. 9 Schematic diagram of grain growth in the second variable-section platform.

Fig. 10 the positions of heterocrystal grains in blade sample at 1530°C.

Numerical Simulation of Grain Growth of Directionally Solidified DZ4125 Alloy under Varied Blade Orientations 1669

temperature field blade sample with a perpendicularorientation had a certain inclination.

(2) Based on a radiative heat transfer calculations and theheat dissipation angle, the temperature field and relativeposition between the sample and the furnace body wereanalyzed. In the heat insulation zone, it was found thatthe sample surface temperature at a given height washigher on the Wall-Side than the Center-Side. In thecooling zone, the sample surface temperature at Center-Side was higher than Wall-Side.

(3) For the parallel orientation, the blade sample easilyobtains a complete single crystal structure. This is aresult of the stable temperature field and mushy zone inthe parallel orientation. Using a variable cross-sectionsample, the grain growth behavior in the directionalsolidification process was further studied, and thegrowth state of the original grain passing through thevariable-section platform is summarized. The hetero-crystal formation positions of blade samples wereanalyzed. It was found that the most likely positionsof heterocrystal grains formation are the complexstructure platform, the mutation cross-section, and theend of the spiral grain selector.

Acknowledgments

This research was jointly supported by the NationalKey Research and Development Program of China(2016YFB0301201).

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