Investigation on freckles in directionally solidified CMSX-4 superalloy specimens with abrupt cross section variation

Accepted Manuscript Investigation on freckles in directionally solidified CMSX-4 superalloy specimens with abrupt cross section variation Qiudong Li, Jun Shen, Ling Qin, Shuxin Gao PII:

S0925-8388(16)32741-4

DOI:

10.1016/j.jallcom.2016.09.007

Reference:

JALCOM 38841

To appear in:

Journal of Alloys and Compounds

Received Date: 7 July 2016 Revised Date:

29 August 2016

Accepted Date: 1 September 2016

Please cite this article as: Q. Li, J. Shen, L. Qin, S. Gao, Investigation on freckles in directionally solidified CMSX-4 superalloy specimens with abrupt cross section variation, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.09.007. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Investigation on freckles in directionally solidified CMSX-4 superalloy specimens with abrupt cross section variation Qiudong Li, Jun Shen*, Ling Qin, Shuxin Gao

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State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an, 710072, PR China

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ABSTRACT

The freckle formation was investigated in directionally solidified CMSX-4 superalloy specimen with abrupt cross section variation to better understand that in the real hollow blade. Freckles were usually observed on the specimen surface within a range of 2-15 mm above the platform, and

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the freckles on both sides were slanted to respective edge. The freckling number was reduced with increasing withdrawal rate. Combining with the simulation, freckle formation was analysed. The deceleration of dendrites growth above the platform caused by the abrupt variation in cross section

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leads to an increase in the tendency of the fact that the interdendritic fluid-flow velocity is larger

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than the growth rate, and thus increasing the freckling tendency. The pressure difference in the horizontal direction induced by the concaved solidification interface forces the interdendritic segregated melt to flow toward the surfaces and edges, and slants the freckles. The freckle formation can be suppressed with increasing withdrawal rate for the refined dendrite microstructure.

Keyword: Freckle; Directional solidification; CMSX-4; Abruptly varying cross section

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Corresponding author. Tel.: +86 29 88494708; fax: +86 29 88494080. E-mail address: [email protected] (J. Shen). 1

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1. Introduction

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The reliability and high-efficiency of industrial gas turbine (IGT) are correlated to the single crystal and directionally solidified turbine blades, which can be produced by directional solidification processing with which the transverse grain boundary can be removed. However, the size and

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mass of IGT blade are several larger than that of aero engine turbine blade. Thus, the traditional

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methods, such as high rate solidification (HRS) method, are ineffective in removing solidification defects like freckle defect for the insufficient cooling.

Freckles, macrosegregation defect, consist of randomly oriented grains, shrinkage porosity and eutectic structures [1, 2], deteriorating high temperature mechanical properties [2, 3]. Usually,

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freckles are found in any casting containing columnar dendrite structures such as directional solidification (DS) and single crystal (SC) castings of superalloys [4], Vacuum-Arc Remelting (VAR) [5] and Electroslag Remelting (ESR) processed ingots [6], and large steel ingots [7, 8]. In the case

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of DS or SC castings, freckles generally appear on the surfaces of castings, and are roughly paral-

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lel to the direction of gravity [1, 3, 9-12]. It is now widely accepted that freckles have a relationship with thermosolutal convection in

the mushy zone which is induced by density inversion originating from the interdendritic microsegregation [1, 3, 13-19]. In the directional solidification process of superalloy CMSX-4, the heavy elements like W, Re usually segregate to the dendrite core, while the light elements like Ti, Al are ejected to the interdendritic region. In the case of vertically upward directional solidification, the interdendritic liquid becomes lighter with increasing distance from the dendrites tip in the 2

ACCEPTED MANUSCRIPT mushy zone [1, 4, 8]. As a result, the segregated liquid in the mushy zone will flow up, leading to the remelting and fragment of the dendrite arms, and then freckles may appear finally [1, 3, 8, 13]. The majority of previous studies on freckle formation mainly focused on two fields: the nu-

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merical simulations of transport phenomena during solidification [14, 15, 17, 18, 20-26] and the improvement of Rayleigh number criterion to predict the freckle formation [13, 27-31]. In the two fields, specimens with uniform cross section were usually taken as their experimental subjects.

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However, for the IGT blade, the cross section is non-uniform, especially for the platform which

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possesses the characteristic of abrupt cross section variation, and only limited studies have been conducted with the specimens concerned. In the experiment of Ma et al [11, 12, 32], the specimens with abrupt and moderate cross section variation were directionally solidified, and they reported that the geometry of castings not only has an effect on temperature field, but also changes the res-

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ervoir and flow conditions for thermosolutal convection, thus it is another independent factor affecting the formation of freckles. However, the circular cross section and small size of the platform in their study made it hard to truly reflect freckle formation in practical application.

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In addition, the dendrite growth in the platform of specimens with abrupt cross section varia-

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tion has been concerned by in-situ observation and numerical simulation [33-35], and it is found that the abrupt variation in cross section leads to a great increase of undercooling in front of the lateral secondary dendrite near the bottom of platform. Therefore, the secondary dendrite arm grows much faster in the horizontal direction. However, the relationship between the abrupt variation in cross section and the freckle formation has not been revealed. In this paper, in order to better reflect the real blade, several rectangular section specimens were designed, of which the cross section was varied abruptly, and directionally solidified in the 3

ACCEPTED MANUSCRIPT conventional Bridgman furnace. Then the freckle formation was investigated.

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2. Experimental procedures

2.1. Superalloy and specimen preparation

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Due to its freckle-prone feature [10], superalloy CMSX-4 [36] was chosen in this study and

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the nominal alloy composition (wt.%) is Ni- 9.0Co- 6.0W- 5.6Al- 6.5Cr- 6.5Ta- 3.0Re- 0.1Hf0.6Mo- 1.0Ti. Specimens (see Fig. 1a) with abrupt variation in cross section were directionally solidified to simulate the situation in the platform of blades. The specimen consists of two sections, with the small and large section representing the blade body and tenon, respectively. In this paper,

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five kinds of specimens with a thickness of 20 mm were designed in order to obtain much more reliable results which can reveal the freckle formation in the specimens with abrupt cross section variation as shown in Fig. 1(b). The b2, b3, b4 have a different height above the platforms. The

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width of large section is 20 mm for the b1, while 40 mm for b3 which is the same as b1 in height.

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In particular, b5 was designed to have two platforms.

2.2. Procedure of directional solidification

The ceramic shell moulds (Fig. 2a) used were produced in standard investment casting procedure, and the experiments were carried out in a conventional Bridgman furnace (Fig. 2b). To measure the heater temperature, thermocouple of type D (W-3% Re/W-25% Re) was placed at 4

ACCEPTED MANUSCRIPT defined position T1 as shown in Fig. 2(b). During directional solidification, the superalloy melt was poured into the ceramic shell moulds placed on the chill plate in the furnace, and then pulled down from the heater through the baffle into the cooling chamber (Fig. 2b). The experiment con-

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ditions were listed in Table 1. After the casting trial, specimens were taken out from the shell mould, and subjected to sandblast to remove the residual ceramic particles attached to the surface of specimens. Macro-etching

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agent (a solution of 50 pct H2O2 and 50 pct HCl) was employed to reveal the number (Table 1),

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initiation positions (Fig. 3a), lengths (Fig. 3b) and morphology (Fig. 4 and Fig. 5) of freckles in the directionally solidified specimens. After that, specimens were sectioned transversely (perpendicular to the growth direction) from the position about 2.5 mm above the platforms. Then, the microstructures was revealed with a solution of 15 pct HNO3, 30 pct HF and 55 pct C3H8O3. The

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primary dendrite arm spacings (PDAS) were measured by counting the number N of dendrites in a given area A (λ1 = (A/N)0.5).

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2.3. Simulation of local physical field

To make it easier to understand the freckle formation in the specimens with abrupt cross sec-

tion variation, the finite element software ProCAST was used to qualitatively evaluate the solidification conditions for each specimen. The data of temperature measuring points also provided a basis to set the boundary conditions for simulation. The position of thermocouples are shown in Fig. 1(b). The temperature measuring point T1 was located in the middle of heater, while the T2 was placed on the surface of thermal baffle. 5

ACCEPTED MANUSCRIPT The thermal gradient, GL, at the liquidus and the solidification rate, R, at the liquidus were calculated in the following manner [37]. When each node reaches the liquidus temperature, GL is calculated as the temperature difference between adjacent nodes divided by their distance, and R is

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equal to the distance between adjacent nodes divided by the time that it spends for the liquidus isotherm moving from point to point. The vertical temperature gradient, GV, the vertical solidification rate, RV, influencing the freckle formation and the horizontal solidification rate, RH, were cal-

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culated along with GL and R. The simulation results were combined with experimental results to

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analyse the formation of freckles.

3. Results

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3.1. Experimental Results

Fig. 3 shows the initiation positions and lengths of freckles on the surfaces of specimens. The

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freckles tend to initiate in the region about 2-4 mm above the platform (Fig. 3a), and extend con-

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tinuously about 4-10 mm (Fig. 3b) in variable cross section specimens (in Fig. 1). The macro-etched pictures of specimen for experiment 4# is shown in Fig. 4. As can be seen,

the majority of freckles are concentrated in the large section, and distributed in the region 2-15 mm above the platform. In addition, of the 161 freckles observed, only 4 appear on the surface B and B’, which is a distinct contrast compared with surface A and A’ (in Fig. 4a). It is also noticed that the freckles on the both sides of surface are slanted to respective edge, while the freckles on the middle part of the surface are roughly parallel to the direction of gravity (in Fig. 4b). 6

ACCEPTED MANUSCRIPT Fig. 4(c) shows the macro-etched cross section of specimen about 2.5 mm above the platform, and Fig. 5 shows the macro-etched pictures of specimen for experiment 2# about 1.2 mm depth from the surface of specimen to the interior. It is concluded that the freckles are mainly distributed

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in the surface region. In comparison to the experiment 1# (Fig. 6a), 2# (Fig. 6b) and 3# (Fig. 6c), where all the freckles disappeared after a maximum length of 15mm above the platform, it is interesting that

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freckles for the experiment 9# (Fig. 6d) first vanished as that for 1#, 2# and 3#, but recurred in the

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second platform. It is consistently indicated that the abrupt variation in cross section can be in favor of freckling.

In addition, as listed in Table 1, the freckling numbers were 28, 26 and 18 for the experiment 1#, 2# and 3# with the respective withdrawal rates of 0.7, 1.2 and 1.7 mm/min. It is evidently in-

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dicated that the freckling tendency will be reduced with increasing withdrawal rate. This conclusion was confirmed once again for the experiment 5# and 6#, where the withdrawal rate was increased from 1.2 to 4.2 and the freckling number was significantly reduced from 14 to 1, leading

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to a nearly freckle-free structure. Fig. 7 shows the transverse microstructure about 2.5 mm above

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the platform for experiment 5# and 6#. The dendrites were clearly refined, and the primary dendrite arm spacing was reduced from 497 µm to 287 µm (Fig. 8).

3.2. Simulation Results

According to all of the simulation results, it is found that the distributions of vertical thermal gradient GV and vertical solidification rate RV on the specimens were similar. The simulation result 7

ACCEPTED MANUSCRIPT of experiment 5# was chosen for investigation as shown in Fig. 9. The GV on the small section of specimen is greater than that on the large one. For the large section of specimen, the distribution of vertical thermal gradient consists of 3 regions, including the region O about 0-2 mm above the

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platform, the region P about 2-20 mm above the platform, and the region Q from 20 mm above the platform to the top of specimen. The GV with a value of 1.18 K/mm in region O is lower than that (GV =1.45 K/mm) in region P. While, the GV in region Q is gradually reduced.

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Fig. 10 shows the vertical solidification rate RV and horizontal one RH for experiment 5#. It is

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obviously that solidification rate RV changes from a large value (RV = 1.7 mm/min) to a small one (RV = 1.3 mm/min) on the region 0-4 mm above the platform, and then increases gradually on the upper of specimen (see Fig. 10a). In addition, except that on the top of specimen, the horizontal solidification rate RH on the region 0-4 mm above the platform is clearly larger than that on the

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other region (Fig. 10b).

The simulation results for experiment 2# and 9# is shown in Fig. 11. The distribution of solidification rate is similar to that for experiment 5# (Fig. 10). In addition, in comparison to the

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simulation results for experiment 2# (Fig. 11a), the difference is that the solidification rate RV on

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the bottom of upper platform also changes from a large value (R = 2.8 mm/min) to a small one (R = 1.9 mm/min) as the lower one for specimen 9# (Fig. 11c).

4. Discussion

4.1. Effect of the abrupt variation in cross section

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ACCEPTED MANUSCRIPT At the bottom of large section, there was no solidified metal acting as a heat sink. Thus, the vertical thermal gradient GV was low in the region O. In terms of the region Q, with the directional solidification proceeding, there were much more solidified metal below, but the height of mould

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extending into the heat zone was gradually reduced. As a result, the radiation heat from the heater was also gradually reduced. Thus, the GV in the region Q was gradually reduced, and lower than

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that in the region P.

It is well-known that the freckles are usually observed on a location where the thermal gradi-

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ent is low under the same solidification rate [1, 3, 38]. In the small section of specimen, due to the large thermal gradient (Fig. 9) and the narrow mushy zone which cannot provide a sufficient reservoir to support the interdendritic convection [11, 12], freckles were not found. In comparison to the experimental results (Fig. 3, Fig. 4, and Fig. 6), however, in the large section of specimens, it

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is found that freckles were usually observed in the region where the vertical thermal gradient was larger, while no freckle initiated in the region with a smaller vertical thermal gradient in this study

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(see Fig. 9). Therefore, it is not reasonable that only the thermal gradient are employed to explain

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the freckle formation.

As seen in Fig. 9 and Fig. 10, when the dendrites grew into the platform, the solidification

conditions changed. At the bottom of large section, when the melt temperature was reduced to the liquidus temperature, the melt contacted closely with the shell mould due to the high liquid fraction, and then a small thermal resistance was obtained. Meanwhile, the bottom of large section was facing to the cooling zone and could not be heated directly by the heater during solidification. Therefore, the dendrites grew to spread the platform with a large solidification rate (see Fig. 10a)

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ACCEPTED MANUSCRIPT at the bottom of large section. In addition, there was no solidified metal below acting as a heat sink, and heat dissipation was accomplished mainly through the bottom of mould, the lateral of mould, and the solidified metal in the small section. Thus, the dendrites grew not only in the ver-

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tical direction (parallel to the direction of gravity), but also in the horizontal direction (perpendicular to the direction of gravity) at the bottom of large section (see Fig. 10b).

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As the solidification processed further, the gap between the melt and the shell mould increased for the solidification shrinkage. As a result, the thermal resistance increased, and the in-

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terfacial heat transfer coefficient decreased [37, 39, 40]. Thus, the solidification rate decreased after the rapid growth of dendrites in a short distance (Fig. 10a). It means that the growth rate of dendrites was reduced.

At the bottom of large section, on the one hand, the rapid growth of dendrites resulted in the

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ejection of much more solute, and then the interdendritic liquid became more instable, thus enhancing the interdendritic fluid-flow. At the same time, the solute ejected from the dendrite

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growth in the horizontal direction also contributed to the enhancement of fluid-flow. On the other hand, the growth rate decreased after the rapid growth in a short distance. According to the Flem-

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ings’ criterion, there will be freckle formation when the interdendritic fluid-flow velocity in the direction of crystal growth is greater than the growth rate [41, 42]. Therefore, the freckling tendency increased, and freckles initiated at the region 2-4 mm above the platform in the specimen with abrupt cross section variation (Fig. 3, Fig. 4, and Fig. 6). Along with the mould moving downwards further, the height of mould extending into the heat zone was gradually reduced, and thus the heat absorbed by melt was reduced. Meanwhile, the heat released during the solidification could be absorbed by the increased solidified metal below 10

ACCEPTED MANUSCRIPT acting as a heat sink, and radiated towards the ambience through the increased radiation area. As a result, the solidification rate gradually increased again (Fig. 10a). In addition, according to the study of Trivedi et al, the fluid-flow can be suppressed with the reduced volume of melt [43, 44].

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Thus, the growth rate might be larger than the interdendritic fluid-flow velocity, and the freckle formation was suppressed. Finally, the freckles were usually observed on the surface with a range of 2-15 mm above the platform, and were absent from the other region of large section.

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For the experiment 9#, when the abruptly varying cross section appeared again (see Fig. 6d),

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the solidification condition was varied like that in the specimens with one platform (Fig. 11), thus freckles appeared again in the upper platform of specimen.

In other words, in this study, the freckle tendency was low not only in the small section of specimen but also in the large one. However, the deceleration of dendrites growth above the plat-

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form caused by the abrupt variation in cross section led to an increase in the tendency of the fact that the interdendritic fluid-flow velocity is larger than the growth rate, then in-creasing the freck-

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ling tendency.

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4.2. Slant of freckles

Fig. 12 schematically shows the forces acting on small cells of liquid and the flow direction

in the mushy zone where the solidification interface is tipped at the bottom of the platform. In rectangular section specimen with abrupt cross section variation, the solidification interface was concaved (Fig. 12a) due to the less lateral heat dissipation, and there existed a difference in height of solidification interface not only between the surface and the interior of specimen, but also between 11

ACCEPTED MANUSCRIPT the side and middle of surface. According to the study with the transparent analog system of Copley et al, when the solidification interface is tipped, a force arising from the density difference in the horizontal direction will act on the segregated interdendritic liquid [1]. Therefore, the cell 1

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and 2 near the symmetry plane C experienced not only the force Fz that drove the segregated interdendritic liquid to flow upward, but also the Fy and Fx, which were perpendicular to the surface A and B, respectively. So the segregated interdendritic liquid in the interior had a tendency to flow

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towards the surface A and B, and finally, the freckles appeared on the surface of specimens. For

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the cell 3 and 4 in the surface A, the force Fy was absent due to the effect of shell mould, and the force Fx, coupled with Fz, caused the segregated interdendritic liquid to flow towards the edges. Nevertheless, the cell 5 at the middle of surface A where the solidification interface was nearly horizontal would move upward and parallel to the direction of gravity for the reason that only the

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force Fz was acting. The preceding discussion provides a reason why the freckles on both sides were slanted to respective edge, while the freckles on the middle part of the surface were roughly parallel to the direction of gravity for specimens with abrupt cross section variation as shown in

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Fig. 4, and Fig. 6.

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In comparison to the cylinder specimens of Giamei et al [3], the force Fz was the only one driving the fluid-flow because of the horizontal solidification interface in the surface like that of the cell 5. So the freckles were roughly parallel to the direction of gravity, and distributed uniformly around the specimen. However, when the specimens were non-uniformly heated like that in the study of Ma et al [32] which were arranged in a circle around a central rod, the solidification interface in the surface were tilted, and then the flow from one side to the other side of specimen happened, thus freckles exclusively appeared on the “shadow side” of the specimens, while no 12

ACCEPTED MANUSCRIPT freckles were observed on the other side.

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4.3. Effect of withdrawal rate

In the case of specimens with uniform cross section, Ma et al [38] reported that the freckle formation will be suppressed with the increase of withdrawal rate. Because, a refined microstruc-

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ture with reduced primary dendrite arm spacing, which results in a low permeability in the mushy

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zone, will be obtained due to the increased cooling rate. Therefore, freckling tendency will be reduced for the reason that the resistance to interdendritic fluid-flow owing to the low permeability is difficult to be overcome by the driving force induced by density inversion. In this study, for the specimen with abrupt cross section variation, a refined microstructure with reduced primary den-

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drite arm spacing was also obtained (Fig. 7 and Fig. 8) with increasing withdrawal rate. In addition, with increasing withdrawal rate, the shortened local solidification time also contributed to the

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5. Conclusions

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suppressing of freckling [1]. Thus, the freckling number was reduced.

In this paper, the specimens with abrupt cross section variation were directionally solidified

to reflect the situation in that of turbine blade. The conclusions are as follows: (1) The abrupt variation in cross section results in a deceleration of dendrite growth in the platform, and then increases the tendency of the fact that interdendritic fluid-flow velocity is greater than the growth rate, thus increasing the freckling tendency. 13

ACCEPTED MANUSCRIPT (2) The pressure difference in the horizontal direction induced by the concaved solidification interface forces the interdendritic segregated melt to flow toward the surfaces and edges, and then slants the freckles.

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(3) The freckle formation can be suppressed with increasing withdrawal rate for the refined dendrite microstructure.

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Acknowledgements

This work was supported by the National Basic Research Program of China under Grant No.2013CB035703.

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ACCEPTED MANUSCRIPT 365-379. [44] R. Trivedi, J. Park, J. Cryst. Growth 235 (2002) 572-588. Figure captions:

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Fig. 1. Specimens used in the experiments with a thickness of 20 mm: (a) a three-dimensional schematic diagram, (b) sizes of specimens.

Fig. 2. The ceramic shell mould (a) and the schematic diagram of the main structure of Bridgman

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furnace (b) used in the experiments.

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Fig. 3. Statistical results: (a) the initiation positions of freckles on the surfaces of specimens, (b) the lengths of freckles.

Fig. 4. Distribution and morphology of freckles: (a) (b) on the surface of specimen for experiment 4#, (c) in the cross section 2.5 mm above the platform.

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Fig. 5. Morphology of freckles at different position for experiment 2#: (a) the schematic location of each layer, (b) the surface of specimen, (c) the first layer beneath the surface, (d) the second layer beneath the surface, (e) the third layer beneath the surface, (f) the fourth layer about 1.2 mm

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beneath the surface.

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Fig. 6. Distribution of freckles on the surface of specimens for experiment: (a) 1#, (b) 2#, (c) 3#, (d) 9#.

Fig. 7. Micro-etched cross-sections about 2.5mm above the platform for experiment (a) 5# and (b) 6#.

Fig. 8. The primary dendrite arm spacing measured at the cross-sections about 2.5mm above the platform for experiment 5# and 6#. Fig. 9. The vertical thermal gradient GV evaluated by simulation for experiment 5#. 17

ACCEPTED MANUSCRIPT Fig. 10. The vertical solidification rate RV (a) and horizontal solidification rate RH (b) evaluated by simulation for experiment 5#. Fig. 11. Simulation results for experiment (a and b) 2# and (c and d) 9#. (a and c) the vertical

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solidification rate RV, (b and d) the horizontal solidification rate RH. Fig. 12. Schematic showing forces acting on small cells of liquid and the flow direction indicated by the dashed arrows in the mushy zone where the solidification interface is tipped in the platform:

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(a) 3D sketch map, (b) top view.

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Table

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Table 1 Experimental conditions and the number of freckles.

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ACCEPTED MANUSCRIPT Table 1 Experimental conditions and the number of freckles Specimen

Heater

Size

Temperature

(see Fig.1b)

(K)

1#

b4

2#

Number

(mm/min)

Freckles

1973

0.7

28

b4

1973

1.2

26

3#

b4

1973

1.7

18

4#

b3

1973

1.2

17

5#

b3

1823

1.2

6#

b3

1823

4.2

7#

b2

1973

1.2

8#

b1

1973

1.2

9#

b5

1973

1.2

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Withdrawal Rate

14 1

23 5

29

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No.

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Fig. 1. Specimens used in the experiments with a thickness of 20 mm: (a) a three-dimensional schematic diagram,

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(b) sizes of specimens

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Fig. 2. The ceramic shell mould (a) and the schematic diagram of the main structure of Bridgman furnace (b) used

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in the experiments.

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Fig. 3. Statistical results: (a) the initiation positions of freckles on the surfaces of specimens, (b) the lengths of

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freckles.

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cross section 2.5 mm above the platform.

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Fig. 4. Distribution and morphology of freckles: (a) (b) on the surface of specimen for experiment 4#, (c) in the

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Fig. 5. Morphology of freckles at different position for experiment 2#: (a) the schematic location of each layer, (b) the surface of specimen, (c) the first layer beneath the surface, (d) the second layer beneath the surface, (e) the

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third layer beneath the surface, (f) the fourth layer about 1.2 mm beneath the surface.

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Fig. 6. Distribution of freckles on the surface of specimens for experiment: (a) 1#, (b) 2#, (c) 3#, (d) 9#.

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Fig. 7. Micro-etched cross-sections about 2.5mm above the platform for experiment (a) 5# and (b) 6#.

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Fig. 8. The primary dendrite arm spacing measured at the cross-sections about 2.5mm above the platform for

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experiment 5# and 6#.

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Fig. 9. The vertical thermal gradient GV evaluated by simulation for experiment 5#.

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Fig. 10. The vertical solidification rate RV (a) and horizontal solidification rate RH (b) evaluated by simulation for

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experiment 5#.

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Fig. 11. Simulation results for experiment (a and b) 2# and (c and d) 9#. (a and c) the vertical solidification rate RV,

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(b and d) the horizontal solidification rate RH.

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Fig. 12. Schematic showing forces acting on small cells of liquid and the flow direction indicated by the dashed arrows in the mushy zone where the solidification interface is tipped in the platform: (a) 3D sketch map, (b) top

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view.

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1. Freckles appear at the surface of specimens 2-15mm above the platform. 2. Freckles on both sides are slanted to respective edge. 3. The abrupt variation in cross section increases the freckling tendency. 4. The concaved solidification interface slants the freckles. 5. Freckle formation can be suppressed with increasing withdrawal rate.