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Simulation of grain selection during single crystal casting of a Ni-base superalloy
Journal of Alloys and Compounds 586 (2014) 220–229
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Simulation of grain selection during single crystal casting of a Ni-base superalloy Ning Wang a,b, Lin Liu a,⇑, Sifeng Gao c, Xinbao Zhao d, Taiwen Huang a, Jun Zhang a, Hengzhi Fu a a
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China CHALCO Research Institute of Science and Technology, Beijing 100082, China c School of Metallurgical Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China d Xi’an Thermal Power Research Institute Co., Ltd., Xi’an 710032, China b
a r t i c l e
i n f o
Article history: Received 21 June 2013 Received in revised form 27 September 2013 Accepted 5 October 2013 Available online 18 October 2013 Keywords: Ni-base single crystal superalloy Directional solidification Grain selection Crystal orientation Simulation
a b s t r a c t The grain selection process during single crystal casting of a Ni-base superalloy DD403 in spiral grain selector is simulated by a macro-scale ProCAST coupled a meso-scale Cellular Automaton Finite Element (CAFE) model. And the simulation results are validated by experimental observations. It is found that the grain orientations can be optimized in starter block and the length of starter block could be reduced to about 26.0 mm. A single crystal can be rapidly selected after the solidification front climbing 400° along the spiral passage. It is proposed that the coupling effect of the heat flow direction, the preferred growth direction and the geometrical restriction of spiral wall makes contribution to the crystal selection in spiral passage. An investigation into the grain orientation selection in grain selectors with different geometries reveals that crystal orientation can be optimized by increasing the length of starter block or decreasing its width. However, no obvious relationship is found between the crystal orientation and the parameters of spiral passage. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Ni-base single-crystal (SX) superalloys are extensively used as blades in aero-engines and industry gas turbines for its excellent high temperature strength and creep resistance [1–5]. The superior mechanical properties of Ni-base superalloys are derived largely from the microstructure and crystal orientation [6–11]. One benefit of SX blades is that the creep life of SX blades can be improved significantly due to the removal of grain boundaries that exist in a polycrystalline morphology, such as equiaxed or columnar [12–17]. Another benefit of SX blades is that the preferred h0 0 1i crystallographic solidification direction, which coincides with the minimum in Young’s modulus, is oriented parallel to the casting axis [18,19]. However, a slight deviation of axial orientation from h0 0 1i direction can result in a significant decrease in creep performance [11]. Consequently, it is of great importance to direct the h0 0 1i of the SX as close as possible to the axial orientation during SX casting to improve the creep resistance along the longitudinal direction of a SX blade. In general, the single crystal structure is produced through competitive grain growth by directional solidification technology [20]. Mostly, the grain boundaries are removed entirely by adding ⇑ Corresponding author. Tel.: +86 29 88492227; fax: +86 29 88494080. E-mail address: [email protected] (L. Liu). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.10.036
a ‘grain selector’ to the very base of the wax mould, typically in the form of a spiral grain selector, which consists of a starter block and a spiral selector [21], see Fig. 1. To improve the production efficiency and yield rate of SX blades, numerous efforts on the grain selection during SX casting have been made over the last few decades by simulations and experiments [22–26]. The simulation analysis taking into account the shape of a two-dimensional (2-D) ‘‘pigtail’’ by Esaka et al. [22] revealed that the evolutions of grain structures and crystal orientations during SX casting significantly depend on the geometries of the starter block (length L and width D, see Fig. 2). The yield rate of well-oriented single crystal increases with increasing the ratio of the length to the width of starter block. However, the increase of starter block length inevitably decreases the height of spiral during the production of turbine blades. Besides, a simplified 2-D model is not sufficient to investigate the grain selection in 3-D spirals. Recently, Dai et al. [23] simulated and analyzed the competitive growth and grain selection in the selector with emphasis on the geometric parameters of the spiral (spiral angle h, spiral thickness dT and spiral rotation diameter Ds, see Fig. 2), using a coupled ProCAST&CAFE model. The results showed that the grain selection in spiral become more efficient with the decreasing of the spiral angle or spiral thickness, or increasing the spiral rotation diameter. However, the grain orientations cannot be optimized during the selection process in the spiral. While the results of Meng et al. [24] showed that the grain orientation could be further optimized
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N. Wang et al. / Journal of Alloys and Compounds 586 (2014) 220–229 Table 1 Parameters of starter block designed in this study. Group 1 L/mm D/mm
5
10
20
30 15
35
40
50
60
Group 2 D/mm L/mm
5
10
15
20 35
25
30
35
40
50
Table 2 Parameters of spiral grain selector designed in this study. Group 1 h/° dT/mm Ds/mm Group 2 h/° dT/mm Ds/mm Fig. 1. Photograph of a single crystal sample with a spiral grain selector after macro-etching.
Group 3 h/° dT /mm Ds /mm
15
20
25
30
35
2
3
4
5
6
17
20
23
25
27
40 5 25 30 7 25 30 5 31
45
50
8
9
35
41
55
60
65
70
of the grain selector. Dai et al. [25] proposed that the geometrical restriction is a dominant factor in the process of grain selection. Gao et al. [26] observed the competitive dendritic growth in spiral passage by experimental methods and verified that the geometrical blocking of narrow passage attributes to the grain selection. Nevertheless, research on the mechanism of grain selection in the spiral should not be limited to the geometrical restriction. It has been established that the competitive growth during directional solidification depends on the relative orientation of grains and their relation with the direction of maximum temperature gradient (the direction of heat flow) [27]. And that the crystal orientation determines the dendritic growth direction, while the growth direction of cellular crystal almost depends on the heat flow direction [28]. In view of the dominant role that the heat flow plays in the competitive grain growth during directional solidification, it is speculated that the heat flow also makes contribution to the grain selection in the spiral passage. However, little attention has been paid to the influence of heat flow on the competitive growth and grain selection in the spiral passage. Based on such facts, this article is devoted to investigate the relationship between the crystal orientations and the geometries of the grain selector. In addition, the influence of heat flow will be taken into account when analyzing the mechanism of grain selection in the spiral passage. The SX casting process is simulated by a coupled ProCAST&CAFE model. The geometries of the starter block and the spirals grain selector designed in this study are shown in Tables 1 and 2, respectively. Fig. 2. Schematic diagram of starter block and spiral grain selector showing the parameters used in this study. 2. Experimental procedure
during the competitive growth in the spiral, in the case of that the spiral angle are larger than about 50°. Due to the contradictory conclusions above, it is necessary to get further insight into the relationship between the crystal orientation and the geometries of the spiral grain selector. Furthermore, to enhance the understanding of grain selection and to provide the capability to design and optimize a spiral grain selector for newly developed alloys and components, it is of interest to investigate the mechanism of grain selection in the spiral passage for the attempt to improve the efficiency and reliability
The material used in this study was the first generation SX Ni-base superalloy DD403. The chemical composition of DD403 is listed in Table 3. The SX castings were performed using a modified Bridgman directional casting furnace schematically shown in Fig. 3. It consisted of a vacuum-induction melting unit, a thermal retardation unit and a cooling zone. Prior to casting, the ceramic mould was mounted on a water-cooled copper chill plate and the furnace chamber was evacuated to a partial pressure of approximately 103 bar. Then, the mould was preheated to 1550 °C above the melting point of DD403 alloy by graphite heating elements. After melting of the ingot, the charge was poured into the preheated mould at the pouring temperature of 1460 °C and held for 2 min to stabilize the melt. Finally, the ceramic mould was withdrawn from the furnace at a pre-determined withdrawal velocity of 100 lm/s.
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After SX casting, Electron Back-Scattering Diffraction (EBSD) technology was applied to acquire orientation image maps and determine the grain texture distributions in the starter block and spiral passage. For the EBSD analysis, a ZEISS SUPRA 55 SEM equipped with HKL system and Channel 5 analysis software was used.
3. Simulation details 3.1. Directional solidification process modeling The directional solidification process was modeled by a macroscopic 3-D finite element analysis software namely ProCAST (a trademark of ESI Group, Paris). Fig. 4 illustrates the FEM mesh model of the casting system. To increase computation efficiency,
Table 3 Nominal composition of alloy DD403 used in this study. Element
Cr
Co
W
Mo
Al
Ti
Ni
wt.%
9.5
5.0
5.2
3.8
5.9
2.1
Bal.
the furnace model was built with a boundary 2-D mesh. Corresponding to the modified Bridgman furnace shown in Fig. 3, the 2-D furnace mesh was regarded as an insulated enclosure (the insulator in Fig. 4) and consisted of two heating zones (primary heater and secondary heater in Fig. 4), a thermal baffle and a cooling zone. The casting blade and ceramic mould were built with solid 3-D meshes. The ceramic mould was mounted on a water-cooled copper chill base. In the present model, the relative motion between the mould and the furnace was achieved through the upward movement of the enclosure at a velocity of 100 lm/s, as shown in Fig. 4. During directional solidification, the 3-D casting mesh contacted with the 2-D furnace mesh through thermal radiation (shown in Fig. 4). In this model, the radiation was performed with a complex radiation algorithm (called view factors calculation), in which the reflections, obstructions and shadowing effects were taken into account. During the process that the mould was withdrawn from the chamber, the view factors were continuously updated. 3.2. Heat transfer model The directional solidification process mainly refers to three kinds of heat transfer patterns: the thermal conduction in materials and between different materials that contact each other, the radiation within the insulator as shown in Fig. 4 and convection heat transfer. In this study, convection heat transfer was ignored. According to the energy conversation, heat transfer in the alloy during the directional solidification process can be formulated as follows:
qc
@T @ @T @ @T @ @T @fs þ þ þ qA ¼ k k k þ QR @t @x @x @y @y @z @z @t
ð1Þ
where q is the alloy density, c the specific heat capacity, T the temperature, t the time, k the coefficient of thermal conductivity, A the latent heat and fs the solid fraction, QR the thermal radiation quantity, x, y, z the coordinate. Based on the law of Stefen–Boltzman, the thermal radiation quantity QR in vacuum can be written as: Fig. 3. Schematic diagram of the furnace chamber.
Q R ¼ reðT 4 T 4a Þ
ð2Þ
where r is the Stefan–Boltzmann constant, e the emissivity, T the surface temperature, and Ta the ambient temperature and namely the inner wall temperature of the furnace. 3.3. Nucleation model The calculated thermal profiles by the macro-scale ProCAST were then used as input in the meso-scale CAFE model to predict the grain structure with special consideration of the crystallographic anisotropy of grains and the growth kinetics of dendrite tips. In the present study, the heterogeneous nucleation that occurred randomly at the surface of chill plate was modeled by a continuous nucleation distribution called Gaussian distribution of nucleation sites [29]. The continuous nucleation distribution, dn/ d(DT), can be described as:
" 2 # dn nmax 1 DT DT max exp ¼ pffiffiffiffiffiffiffi dðDTÞ 2 DT r 2pDT r
Fig. 4. FEM mesh model of the casting system.
ð3Þ
where dn is the grain density increase, which is induced by an increase in the undercooling, d(DT). DTmax is the mean undercooling, DTr the standard deviation, and nmax the maximum density of nuclei obtained by the integral of the Gaussian distribution.
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The nmax is an important input parameter which is imperative for the CAFE simulation as a nucleation boundary condition. To obtain the value, the grain density at the surface of chill plate was examined quantitatively with EBSD techniques. Under the above experimental condition, the areal density was equal to 1.65 108 (number of nuclei/m2) and this value was used as the nucleation boundary condition nmax at the chill surface for CAFE simulations. 3.4. Grain growth model The preferred orientation of Ni-base superalloys with a facecentered cubic crystal structure is h1 0 0i crystallographic orientation. It is assumed that the crystallographic orientation of a new nucleus nucleated at the surface of chill plate is random, and the growth directions of the trunks and arms coincide with h0 0 1i crystallographic orientation of the parent nucleus. In castings, the dendrite growth is dominated by the undercooling near the dendrite tip. The total undercooling of the dendrite tip, DT, is generally the sum of four contributions [31]:
DT ¼ DT C þ DT T þ DT K þ DT R
ð4Þ
where DTC, DTT, DTK and DTR are the undercooling contributions associated with solute diffusion, thermal diffusion, attachment kinetics and curvature, respectively. For most metallic alloys, in the case of directional solidification, the last three contributions that appear in Eq. (4) are small. The growth of the dendrite is primarily controlled by solute diffusion, and the growth kinetics of both columnar and equiaxed morphologies can be calculated with the aid of Kurz–Giovanola–Trivedi (KGT) model [32]. During the process of simulation, the growth rate of dendrite tip was simplified as:
v ¼ a2 DT 2 þ a3 DT 3
ð5Þ
where a2 and a3 are constants, determined by alloy composition according to the KGT model. A further detailed descriptions of the CAFE model were given in Refs. [30,33–37]. 4. Results and discussion 4.1. Competitive grain growth in starter block Fig. 5a shows the predicted grain structure at the longitudinal section of the starter block. The different colors of the predicted grain structure represent the minimum deviation angle between the h0 0 1i direction of the grain and the direction of the casting axis. Fig. 6a is the corresponding experimental observation of longitudinal section of the starter block. Both Figs. 5a and 6a show that, as solidification proceeds, the equiaxed crystal grains
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progressively evolve into parallel columnar grains with the competitive dendritic growth in starter block. Figs. 5b–g and 6b–g present the orientation image maps and the corresponding h0 0 1i pole figures at different cross sections of starter block respectively observed by CAFE simulation and EBSD techniques. As for the grain orientation selection, the h0 0 1i pole figures at different cross sections of starter block in Figs. 5b–g and 6b–g both indicate that the grain orientation selection occurs with increasing the distance from the chill plate and the grains with favorable growth direction gradually overgrow the other grains. When the distance from the chill plate reaches 15.5 mm (see Figs. 5e and 6e), the favorably h0 0 1i oriented grains predominate in starter block. When reaching 36.0 mm (Figs. 5g and 6g), almost all deviations are less than 10°. Only a few deviation angles are between 10° and 20°. Meanwhile, the distribution range of the deviation angles at each height of starter block in Fig. 5 is found to be the same with the corresponding height in Fig. 6. This result indicates that the CAFE model has a good performance on prediction of the grain orientation selection in starter block. Fig. 7 shows the simulated average deviation angles between h0 0 1i direction of grains and the direction of the casting axis at different heights from the chill plate. It is found that the average deviations decrease with increasing the distance from the chill plate. When the distance reaches 26.0 mm, the average deviation is decreased to 9.1°. As for the grain number selection, it is found that the grain number decreases and the grain size increases with the increase of the distance from chill plate. The quantitative relationship between the grain density and the distance from the chill plate is shown in Fig. 8. It is revealed that the simulation results of grain number selection agree well with the experiment results. The grain density decreases dramatically when the distance from the chill plate is less than about 6.0 mm. This is because of that there are fierce competitions between those grains with various orientations in the primary period of solidification. In this stage, the grains with large deviation angles are eliminated rapidly and the grain orientations are preliminarily optimized. Then, the competitions between the grains are relieved and the grain density decreases slowly with the increase of distance. When the distance reaches 26.0 mm, the grain density tends to be stabilized at about 106 m2. And the grain density is found to be reduced in two orders of magnitude during the competitive growth in starter block with a height of about 36.0 mm. When the distance is higher than 26.0 mm, the average deviation is decreased to 9.1° and the grain density tends to be stabilized. Therefore, the length of starter block could be reduced to about 26.0 mm for the productivity of SX casting components. However, the proposed value is reasonable only on the premise that the single crystal blade whose deviation is bellow 10° is defined as the qualified blade.
Fig. 5. Predicted grain structures of the longitudinal section of starter block (a); orientation image maps and corresponding h0 0 1i pole figures of cross-sections at 0.5 mm (b); 3.0 mm (c); 6.0 mm (d); 15.5 mm (e); 26.0 mm (f); 36.0 mm (g) from the chill plate.
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Fig. 6. Experimental observations of longitudinal section of the starter block (a); EBSD orientation image maps and corresponding h0 0 1i pole figures of cross-sections at 0.6 mm (b); 2.9 mm (c); 6.2 mm (d); 15.4 mm (e); 25.8 mm (f); 36.1 mm (g) from the chill plate.
three grains remain (Fig. 9c). Finally, two of the grains are blocked during the competitive growth in the spiral passage from section c to d. Only one single grain exists at section d (Fig. 9d). So far, the single crystal selection is completed below the position of about one pitch in the spiral passage.
Fig. 7. Simulation results of the average deviations between h0 0 1i direction of grains and the casting axis at different heights from the chill plate.
Fig. 8. Grain density as a function of the distance from chill plate.
4.2. Grain selection in spiral grain selector The grain selection behavior in the spiral grain selector and the efficiency of the selectors with respect to different spiral designs will be discussed in the following. As an example, Fig. 9 shows how a single crystal is selected in one of the spiral grain selectors (the spiral angle is 30° and the spiral thickness is 5 mm) during directional solidification. Fig. 9a–d are the predicted orientation image maps at different cross sections of the spiral and the corresponding h0 0 1i pole figures. As illustrated in Fig. 9a, there are a few favorably h0 0 1i oriented grains at the entrance of spiral after the competitive growth in the starter block. During the initial selection in the spiral passage from section a to b, the grain numbers drastically decrease, just as shown in Fig. 9b. When the process of solidification reaches section c, only
4.2.1. Effect of geometrical restriction on grain selection By tracking the grain selection in Fig. 9, it is found that the grain A near the inner wall of the spiral passage is finally selected as the single crystal. To further reveal the mechanism of grain selection in the spiral, Fig. 10 shows the simulated microstructures of the longitudinal section at the bottom of the spiral passage and the top view of the grain structure evolutions in the spiral selector. The characters A1, A, B and C in Fig. 10b and c represent different orientation grains, respectively. From Fig. 10b, it is found that at the bottom of spiral, the grains far away from the inner wall of the spiral passage are geometrically blocked by the outer wall of the spiral passage, and there is enough space for the grain A1 located near the inner wall of the spiral passage to develop new dendrites. The top view of the grain structures in Fig. 10c shows that the grain A near the inner wall of the spiral passage eventually overgrows the grain B and C near the outer wall of spiral passage and is selected as the final single crystal. Therefore, it is proposed that the geometrical blocking of narrow passage attributes to the grain selection in the spiral. This agrees well with the results of Dai et al. [25], Gao et al. [26] and Seo et al. [38]. 4.2.2. Effect of heat flow on grain selection Except for geometrical blocking, it is speculated that the heat flow also makes contribution to the grain selection in the spiral passage. For the intention of clear observation, the length of starter block is decreased to 1.0 mm to magnify the impact of heat flow on the competitive grain growth in spiral. Fig. 11a shows the CAFE simulated grain structures in the spiral selector. The microstructure evolutions indicate that the grain A2 near the inside-underside of the spiral passage occupies a dominant position and survives finally. The superiority of the inside grains has been discussed above, and the following is an investigation into the predominance of the underside grains and the influence of heat flow on the grain selection in spiral grain selector. Fig. 11b shows the temperature contour between 90° and 180° (spiral climbing angle) of the spiral passage at t = 96.2 s. It is necessary to state that Fig. 11b is presented in the view which contrarotates 90° from the view of Fig. 11a, for the intention of clearly showing the heat flow direction. In order to present the average direction of heat flow at this moment in the spiral passage, the following four steps (as illustrated in Fig. 11b) are taken: draw the tangent line at the midpoint of each temperature contour respectively; draw the corresponding perpendicular of each tangent line; connect these perpendiculars sections one by one to constitute the direction of heat flow; finally, the tangent line at the midpoint of
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Fig. 9. Predicted orientation image maps and corresponding h0 0 1i pole figures of cross-sections at (a) 0 mm; (b) 3 mm; (c) 6 mm; and (d) 10 mm from the base of spiral.
Fig. 10. Schematic diagram of spiral grain selector (a), predicted grain structures of section I–I (b) and the top view of simulated grain structures in the grain selector (c), the structures in the circle indicate that the grain located near inner wall of the spiral passage is selected as the final SX.
Fig. 11. The relationship between the heat flow and grain selection behavior, CAFE simulated grain structures in the spiral selector (a), temperature contour between 90° and 180° (spiral climbing angles) of spiral selector at t = 96.2 s (b), simulated grain structures of longitudinal section I–I (c1)(d1), section II–II (c2)(d2) and section III–III (c3)(d3) between 90° and 180° of spiral.
the direction of heat flow is defined as the average direction of heat flow. Because the heat dissipation of the spiral passage changes
with the special geometrical shape, the heat flow direction in the spiral passage is no longer in parallel with the casting axis, but
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inclines to the spiral climbing direction. Therefore, at a specific position of the spiral passage, the average direction of the heat flow is just as shown in Fig. 11b. The microstructures of the longitudinal section I, section II and section III (see Fig. 11a) between 90° and 180° of the spiral selector are shown in Fig. 11(c1), (c2) and (c3), respectively. Fig. 11(d1), (d2) and (d3) are the corresponding schematic diagrams of grain boundaries. It is indicated that the grain A2 located near the underside of spiral passage is selected as the final single crystal. The boundary between the selected grain A2 and one of the adjacent grain B2 is parallel to the average direction of heat flow. Similarly, the boundary between the selected grain A2 and another adjacent grain C2 develops along the direction of heat flow in the spiral passage. The findings of Fu et al. [27] showed that the grains with their preferred growth direction (h0 0 1i in Ni-base superalloy) nearer to maximum temperature gradient (the direction of heat flow) will grow faster than those with their preferred growth direction far away from maximum temperature gradient during directional solidification. Zheng et al. [39] considered that the main grain selection mechanism of the spiral selector is that the easy growth direction (preferred growth direction) of the cubic crystal coupled with the spiral structure of the selector. Therefore, it is considered that the heat flow direction and preferred growth direction make great influence on the competitive grain growth. In this study, the grains with their easy growth direction h0 0 1i nearer the spiral heat flow direction, for example, the grain A2 and B2 (with their h0 0 1i deviation 20° and 21° from the axial orientation respectively) as shown in Fig. 11, gradually overgrow those far-away-grains along the spiral passage and dominate in the spiral passage. In addition, the experiment results of Lu et al. [20] showed that the whole sample with bi-crystal microstructure could be obtained when the two seeds were with the same primary dendrites orientation paralleled to the heat flow direction. Since the h0 0 1i of the grain A2 and B2 (deviation angles are 20° and 21°, respectively) in Fig. 11 are quite close and parallel to the heat flow direction, they have the same growth advantage in the direction of heat flow. Therefore, the boundary between them develops parallel to the average direction of the heat flow at their position, as shown in Fig. 11(d1), (d2) and (d3). When the boundary between the grain A2 and B2 extends and encounters the passage wall, the upside grain B2 is eliminated, while the underside grain A2 survives and develops new dendrites. Eventually, the grain A2 grows into the cavity and becomes the single crystal texture. Therefore, it is proposed that the coupling effect of the heat flow direction, the preferred growth direction and the geometrical restriction of the spiral wall makes contribution to the crystal selection in the spiral passage.
Fig. 12. The minimum required climbing angles for single crystal selection in spiral grain selectors as a function of the spiral angle h.
4.2.3. Efficiency of the grain selectors The mechanism of grain selection in the spiral grain selector has been discussed above and the following is an investigation into the efficiency of the selectors with respect to different spiral designs. Fig. 12 shows the minimum required climbing angles for single crystal selection in spiral grain selectors as a function of spiral angle h, illustrating that one single crystal can be rapidly selected after the solidification climbing 400° along the spiral passage. The effective grain selection in the spiral is considered to be mainly attributed to the coupling effect of the heat flow direction and the geometrical restriction of the spiral wall. In addition, it is found from Fig. 12 that there is no obvious relationship between the minimum required climbing angles for single crystal selection and the spiral angles. 4.3. Relationship between geometries of grain selector and crystal orientation 4.3.1. Geometries of starter block The relationship between the SX crystallographic orientation and the geometries of starter block is investigated with a 3-D model of grain selector. Fig. 13a and b shows the effects of the length L and the width D of starter block on the SX orientation, respectively. It is found that the deviation of h0 0 1i direction of single crystal from the casting axis decreases by increasing the length of starter block or decreasing its width. Moreover, the relation between the SX orientation and L/D is shown in Fig. 13c. It is indicated that the SX orientation is optimized quickly with the increase of L/D and approaches a constant value when L/D is greater than 2. The simulation results by Esaka et al. [22] with a 2-D ‘‘pigtail’’ model also indicated that the yield rate of well-oriented single crystal increases with increasing the ratio of the length to the width of starter block. However, in the study of Esaka et al. [22], the yield rate approaches a constant value when L/D is just greater than 1, which is much smaller than the value 2 in the present study. For Ni-base superalloys, the fast growing dendritic orientation is h0 0 1i [40,41]. During the process of directional solidification, the favorably h0 0 1i oriented grains can overgrow the unfavorably oriented grains. With increasing the length of starter block, there will be more opportunities for grain competitive selection to take place, which contributes a lot to the optimization of the grain orientations in starter block. The grain texture evolutions shown in Figs. 5 and 6 above have made a good illustration of the effect of the length of starter block on the grain orientations optimization in starter block. Moreover, the grain orientations at the top of starter block make significant effect on the final SX orientation [26]. Therefore, the single crystal orientation can be optimized by increasing the length of starter block. With decreasing the width of starter block, the specific surface area of the ceramic mould is increased and the cooling rate during solidification is improved. Greater cooling rate will increase the growth rate of the dendrites at the solid–liquid interface. As reported by Ardakani et al. [42], an increase of growth rate leads to a larger difference in the undercoolings between the tips of the well-oriented and misoriented dendrites. This difference will result in rapid elimination of the misoriented dendrite by the secondary dendrites developing from the well-oriented dendrite. Thus, the h0 0 1i direction of the final SX will be aligned more closely along the casting axis. However, the ratio of the length L to the width D of starter block is not the greater the better. When L/D is greater than 2, the orientation of single crystal approaches a constant value. The reason of this trend is the following. In the preliminary stage when L/D is less than 2, the misoriented grains are rapidly eliminated by competitive grain growth. Then, the competitions between the grains in starter block are relieved immensely and the grain orientations
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Fig. 13. Effects of the length L (a), the width D (b) and L/D of starter block (c) on SX orientation, respectively.
are optimized slowly with the increase of L/D. In this situation, the continued increase of L/D is almost of no avail. 4.3.2. Geometries of spiral grain selector In order to investigate the grain orientation selection in the spiral passage, grain structures at different cross sections of the spiral grain selector were examined by simulation and experiment method. Fig. 14a illustrates the predicted grain structure in one of the spiral grain selectors (the spiral angle is 60° and the spiral
thickness is 5 mm). Fig. 14b1–d1 are the h0 0 1i pole figures of different cross-sections, and Fig. 14b2–d2 are the corresponding deviations between the h0 0 1i direction of grains and the casting axis. It is shown in Fig. 14a that one single crystal is quickly selected below the position of one pitch in the spiral passage. From Fig. 14b1 and b2, it can be seen that a few grains grow into the spiral selector after the competitive growth in the starter block and the deviation angles of the grains at the entrance of the spiral mainly concentrate in the range of 0–15°. When solidification in the spiral
Fig. 14. Predicted grain structures in the spiral grain selector (a), h0 0 1i pole figures of cross-sections at (b1) 0 mm; (c1) 16 mm; (d1) 30 mm from the base of spiral and the corresponding deviations between h0 0 1i of the grains and the casting axis (b2)–(d2).
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Fig. 15. Effects of spiral angle h (a), spiral thickness dT (b) and spiral rotation diameter Ds (c) on the SX orientation.
passage reaches section c, the grains whose deviation angles distribute in 5–10° are eliminated. While the relatively misoriented grains (deviations in 10–15°) remain. Then, the solidification proceeds to section d and the well-oriented grains (deviations in 0– 5°) are overgrown by the grain with a deviation angle of 13.5°. Finally, this fortunate grain (deviation of 13.5°) grows up into the cavity as the final single crystal cast. Therefore, it is inferred that the grain orientation selection in the spiral passage is random and the misoriented grains can overgrow the well-oriented grains. To confirm this, the deviation angles between h0 0 1i direction of the final single crystal and the direction of casting axis relative to different parameters of the spiral grain selector are given in Fig. 15. It is illustrated that there is no significant change of deviation angles with the increase of spiral angle h, spiral thickness dT and spiral rotation diameter Ds. In addition, as shown in Fig. 15, the grain orientations randomly distribute in the range of 0–18° which is consistent with the distribution range of 0–20° at the top of starter block shown in Figs. 5 and 6. Therefore, it is concluded that during single crystal casting in spiral grain selector, the spiral is just to ensure only one single crystal finally survive and the grain orientations cannot be optimized during the grain selection in the spiral. This can be attributed to the following reasons. The grains with different deviations randomly distribute at the entrance of the spiral as shown in Fig. 14b1 and b2. Base on the geometrical blocking mechanism, no matter the dendrites of grains at the entrance of the spiral are well-oriented or misoriented, those grains near outer wall of the spiral passage will be eliminated by the outer passage wall and the grains near inner wall of the spiral passage will have enough space to grow by branching new dendrites. Base on the heat flow mechanism, the grains with their easy growth direction h0 0 1i nearer the heat flow direction in the spiral passage will
overgrow those far-away-grains. However, the heat flow direction inclines to the spiral climbing direction, so the well-oriented grains whose h0 0 1i nearer the casting axis have no advantage during the competitive growth in spiral passage. Instead, the misoriented grains whose h0 0 1i off the casting axis but nearer the spiral heat flow direction may survive and grow into the cavity to be the final SX cast. 5. Conclusions Grain selection in spiral grain selectors is simulated by a coupled ProCAST&CAFE model and validated experimentally with different spiral geometries. The predicted results are in good agreement with the experimental ones. The following conclusions can be drawn from this work: (1) During the grain selection process in starter block, the preferred h0 0 1i-oriented grains will overgrow the misoriented grains with the increase of the distance from chill plate. When the distance reaches 26.0 mm, the grain density tends to be stabilized at about 106 m2 and the average deviations of grain orientations are decreased below 10°. This result indicates that the length of starter block could be reduced to about 26.0 mm for the productivity of SX casting components. (2) During the grain selection process in spiral, the grain near the inside-underside of spiral passage is selected as the final crystal and a single crystal can be rapidly selected after the solidification front climbing 400° along the spiral passage. The boundary between the selected grain and its adjacent grains is parallel to the average direction of heat flow. It is proposed that the coupling effect of the heat flow direction,
N. Wang et al. / Journal of Alloys and Compounds 586 (2014) 220–229
the preferred growth direction and the geometrical restriction of the spiral wall makes contribution to the crystal selection in the spiral passage. (3) The SX orientation can be optimized by increasing the length of starter block or decreasing its width. While the SX orientation approaches a constant value when the ratio of the length to the width is greater than 2. The results also reveal that there is no obvious relationship between the crystal orientation and the parameters of spiral passage. Acknowledgments The authors are grateful to the financial support of the National Basic Research Program of China (Nos. 2010CB631202 and 2011CB610406), the National Natural Science Foundation of China (Nos. 50931004 and 51101120) and the Aeronautical Science Foundation of China (No. 2010ZE53047). References [1] S. Tin, T.M. Pollock, J. Propul. Power 22 (2006) 361–374. [2] X.B. Zhao, L. Liu, C.B. Yang, Y.F. Li, J. Zhang, Y.L. Li, H.Z. Fu, J. Alloys Comp. 509 (2011) 9645–9649. [3] C.T. Liu, J. Ma, X.F. Sun, J. Alloys Comp. 491 (2010) 522–526. [4] G. Liu, L. Liu, C. Ai, B.M. Ge, J. Zhang, H.Z. Fu, J. Alloys Comp. 509 (2011) 5866– 5872. [5] K. Zhao, Y.H. Ma, L.H. Lou, J. Alloys Comp. 475 (2009) 648–651. [6] L.N. Wang, Y. Liu, J.J. Yu, Y. Xu, X.F. Sun, H.R. Guan, Z.Q. Hu, Mater. Sci. Eng. A 505 (2009) 144–150. [7] S.A. Sajjadi, H.R. Elahifar, H. Farhangi, J. Alloys Comp. 455 (2008) 215–220. [8] A. Picasso, A. Somoza, A. Tolley, J. Alloys Comp. 479 (2009) 129–133. [9] A. Wanger, B.A. Shollock, M. Mclean, Mater. Sci. Eng. A 374 (2004) 270–279. [10] N. D’Souza, M.G. Ardakani, A. Wagner, J. Mater. Sci. 37 (2002) 481–487. [11] R.A. MacKay, R.D. Maier, Metall. Trans. A 13 (1982) 1747–1754. [12] T. Murakumo, T. Kobayashi, Y. Koizumi, H. Harada, Acta Mater. 52 (2004) 3737–3744. [13] B.C. Wilson, G.E. Fuchs, Metall. Mater. Trans. A 41 (2010) 1235–1245. [14] A. Suzuki, M.F.X. Gigliotti, B.T. Hazel, D.G. Konitzer, T.M. Pollock, Metall. Mater. Trans. A 41 (2010) 947–956.
229
[15] H.J. Dai, H.B. Dong, H.V. Atkinson, P.D. Lee, Solid State Phenom. 139 (2008) 129–134. [16] N. D’Souza, P.A. Jennings, X.L. Yang, H.B. Dong, P.D. Lee, M. McLean, Metall. Mater. Trans. B 36 (2005) 657–666. [17] R.C. Reed, T. Tao, N. Warnken, Acta Mater. 57 (2009) 5898–5913. [18] G.J.S. Higginbotham, Mater. Sci. Technol. 2 (1986) 442–460. [19] S. Tin, T.M. Pollock, W.T. King, K.A. Green, in: T.M. Pollock et al. (Eds.), Superalloys 2000, TMS, Warrendale, PA, 2000, pp. 201–210. [20] Q. Lu, J.G. Li, T. Jin, Y.Z. Zhou, X.F. Sun, Z.Q. Hu, Acta Metall. Sin. 47 (2011) 641– 648. [21] R.C. Reed, The Superalloys Fundamental and Applications, Cambridge University Press, Cambridge, UK, 2006. pp. 124. [22] H. Esaka, K. Shinozuka, M. Tamura, Mater. Sci. Eng. A 413–414 (2005) 151– 155. [23] H.J. Dai, H.B. Dong, N. D’Souza, J.-C. Gebelin, R.C. Reed, Mater. Trans. A 42 (2011) 3439–3446. [24] X.B. Meng, Q. Lu, J.G. Li, T. Jin, X.F. Sun, J. Zhang, Z.Q. Chen, Y.H. Wang, Z.Q. H, J. Mater. Sci. Technol. 28 (2012) 214–220. [25] H.J. Dai, N. D’Souza, H.B. Dong, Metall. Mater. Trans. A 42 (2011) 3430–3438. [26] S.F. Gao, L. Liu, N. Wang, X.B. Zhao, J. Zhang, H.Z. Fu, Metall. Mater. Trans. A 43 (2012) 3767–3775. [27] H.Z. Fu, G. He, J.G. Li, Acta Metall. Sin. 33 (1997) 1233–1238. [28] X.B. Zhao, L. Liu, W.G. Zhang, Z.H. Yu, H.Z. Fu, Mater. Chem. Phys. 125 (2011) 55–58. [29] Ph. Thévoz, J.L. Desbiolles, M. Rappaz, Metal. Trans. A 20 (1989) 311–322. [30] Ch.-A. Gandin, M. Rappaz, R. Tintillier, Metal. Trans. A 24 (1993) 467–479. [31] J. Lipton, M.E. Glicksman, W. Kurz, Mater. Sci. Eng. 65 (1984) 57–63. [32] W. Kurz, B. Giovanola, R. Trivedi, Acta Metall. 34 (1986) 823–830. [33] M. Rappaz, Ch.-A. Gandin, Acta Metall. Mater. 41 (1993) 345–360. [34] Ch.-A. Gandin, M. Rappaz, Acta Metal. Mater. 42 (1994) 2233–2246. [35] M. Rappaz, C.A. Gandin, J.L. Desbiolles, Metall. Mater. Trans. A 27 (1996) 695– 705. [36] Ch.-A. Gandin, M. Rappaz, R. Tintillier, Metall. Mater. Trans. A. 25 (1994) 629– 635. [37] Ch.-A. Gandin, J.-L. Desbiolles, M. Rappaz, Ph. Thévoz, Metall. Mater. Trans. A. 30 (1999) 3153–3165. [38] S.M. Seo, I.S. Kim, J.H. Lee, C.Y. Jo, H. Miyahara, K. Ogi, Met. Mater. Int. 15 (2009) 391–398. [39] Q. Zheng, G.C. Hou, W.M. Tian, T. Jin, X.F. Sun, H.R. Guan, Z.Q. Hu, Trans. Nonferrous. Met. Soc. China 11 (2001) 176–178. [40] M.G. Ardakani, N. D’Souza, B.A. Shollock, M. McLean, Metall. Mater. Trans. A 31 (2000) 2887–2893. [41] P.N. Quested, M. Mclean, Mater. Sci. Eng. 65 (1984) 171–180. [42] M.G. Ardakani, N. D’Souza, A. Wagner, B.A. Shollock, M. Mclean, in: K.A. Green et al. (Eds.), Superalloys 2000, TMS, Warrendale, PA, 2000, pp. 219–228.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Simulation of grain selection during single crystal casting of a Ni-base superalloy Ning Wang a,b, Lin Liu a,⇑, Sifeng Gao c, Xinbao Zhao d, Taiwen Huang a, Jun Zhang a, Hengzhi Fu a a
State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China CHALCO Research Institute of Science and Technology, Beijing 100082, China c School of Metallurgical Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China d Xi’an Thermal Power Research Institute Co., Ltd., Xi’an 710032, China b
a r t i c l e
i n f o
Article history: Received 21 June 2013 Received in revised form 27 September 2013 Accepted 5 October 2013 Available online 18 October 2013 Keywords: Ni-base single crystal superalloy Directional solidification Grain selection Crystal orientation Simulation
a b s t r a c t The grain selection process during single crystal casting of a Ni-base superalloy DD403 in spiral grain selector is simulated by a macro-scale ProCAST coupled a meso-scale Cellular Automaton Finite Element (CAFE) model. And the simulation results are validated by experimental observations. It is found that the grain orientations can be optimized in starter block and the length of starter block could be reduced to about 26.0 mm. A single crystal can be rapidly selected after the solidification front climbing 400° along the spiral passage. It is proposed that the coupling effect of the heat flow direction, the preferred growth direction and the geometrical restriction of spiral wall makes contribution to the crystal selection in spiral passage. An investigation into the grain orientation selection in grain selectors with different geometries reveals that crystal orientation can be optimized by increasing the length of starter block or decreasing its width. However, no obvious relationship is found between the crystal orientation and the parameters of spiral passage. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Ni-base single-crystal (SX) superalloys are extensively used as blades in aero-engines and industry gas turbines for its excellent high temperature strength and creep resistance [1–5]. The superior mechanical properties of Ni-base superalloys are derived largely from the microstructure and crystal orientation [6–11]. One benefit of SX blades is that the creep life of SX blades can be improved significantly due to the removal of grain boundaries that exist in a polycrystalline morphology, such as equiaxed or columnar [12–17]. Another benefit of SX blades is that the preferred h0 0 1i crystallographic solidification direction, which coincides with the minimum in Young’s modulus, is oriented parallel to the casting axis [18,19]. However, a slight deviation of axial orientation from h0 0 1i direction can result in a significant decrease in creep performance [11]. Consequently, it is of great importance to direct the h0 0 1i of the SX as close as possible to the axial orientation during SX casting to improve the creep resistance along the longitudinal direction of a SX blade. In general, the single crystal structure is produced through competitive grain growth by directional solidification technology [20]. Mostly, the grain boundaries are removed entirely by adding ⇑ Corresponding author. Tel.: +86 29 88492227; fax: +86 29 88494080. E-mail address: [email protected] (L. Liu). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.10.036
a ‘grain selector’ to the very base of the wax mould, typically in the form of a spiral grain selector, which consists of a starter block and a spiral selector [21], see Fig. 1. To improve the production efficiency and yield rate of SX blades, numerous efforts on the grain selection during SX casting have been made over the last few decades by simulations and experiments [22–26]. The simulation analysis taking into account the shape of a two-dimensional (2-D) ‘‘pigtail’’ by Esaka et al. [22] revealed that the evolutions of grain structures and crystal orientations during SX casting significantly depend on the geometries of the starter block (length L and width D, see Fig. 2). The yield rate of well-oriented single crystal increases with increasing the ratio of the length to the width of starter block. However, the increase of starter block length inevitably decreases the height of spiral during the production of turbine blades. Besides, a simplified 2-D model is not sufficient to investigate the grain selection in 3-D spirals. Recently, Dai et al. [23] simulated and analyzed the competitive growth and grain selection in the selector with emphasis on the geometric parameters of the spiral (spiral angle h, spiral thickness dT and spiral rotation diameter Ds, see Fig. 2), using a coupled ProCAST&CAFE model. The results showed that the grain selection in spiral become more efficient with the decreasing of the spiral angle or spiral thickness, or increasing the spiral rotation diameter. However, the grain orientations cannot be optimized during the selection process in the spiral. While the results of Meng et al. [24] showed that the grain orientation could be further optimized
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N. Wang et al. / Journal of Alloys and Compounds 586 (2014) 220–229 Table 1 Parameters of starter block designed in this study. Group 1 L/mm D/mm
5
10
20
30 15
35
40
50
60
Group 2 D/mm L/mm
5
10
15
20 35
25
30
35
40
50
Table 2 Parameters of spiral grain selector designed in this study. Group 1 h/° dT/mm Ds/mm Group 2 h/° dT/mm Ds/mm Fig. 1. Photograph of a single crystal sample with a spiral grain selector after macro-etching.
Group 3 h/° dT /mm Ds /mm
15
20
25
30
35
2
3
4
5
6
17
20
23
25
27
40 5 25 30 7 25 30 5 31
45
50
8
9
35
41
55
60
65
70
of the grain selector. Dai et al. [25] proposed that the geometrical restriction is a dominant factor in the process of grain selection. Gao et al. [26] observed the competitive dendritic growth in spiral passage by experimental methods and verified that the geometrical blocking of narrow passage attributes to the grain selection. Nevertheless, research on the mechanism of grain selection in the spiral should not be limited to the geometrical restriction. It has been established that the competitive growth during directional solidification depends on the relative orientation of grains and their relation with the direction of maximum temperature gradient (the direction of heat flow) [27]. And that the crystal orientation determines the dendritic growth direction, while the growth direction of cellular crystal almost depends on the heat flow direction [28]. In view of the dominant role that the heat flow plays in the competitive grain growth during directional solidification, it is speculated that the heat flow also makes contribution to the grain selection in the spiral passage. However, little attention has been paid to the influence of heat flow on the competitive growth and grain selection in the spiral passage. Based on such facts, this article is devoted to investigate the relationship between the crystal orientations and the geometries of the grain selector. In addition, the influence of heat flow will be taken into account when analyzing the mechanism of grain selection in the spiral passage. The SX casting process is simulated by a coupled ProCAST&CAFE model. The geometries of the starter block and the spirals grain selector designed in this study are shown in Tables 1 and 2, respectively. Fig. 2. Schematic diagram of starter block and spiral grain selector showing the parameters used in this study. 2. Experimental procedure
during the competitive growth in the spiral, in the case of that the spiral angle are larger than about 50°. Due to the contradictory conclusions above, it is necessary to get further insight into the relationship between the crystal orientation and the geometries of the spiral grain selector. Furthermore, to enhance the understanding of grain selection and to provide the capability to design and optimize a spiral grain selector for newly developed alloys and components, it is of interest to investigate the mechanism of grain selection in the spiral passage for the attempt to improve the efficiency and reliability
The material used in this study was the first generation SX Ni-base superalloy DD403. The chemical composition of DD403 is listed in Table 3. The SX castings were performed using a modified Bridgman directional casting furnace schematically shown in Fig. 3. It consisted of a vacuum-induction melting unit, a thermal retardation unit and a cooling zone. Prior to casting, the ceramic mould was mounted on a water-cooled copper chill plate and the furnace chamber was evacuated to a partial pressure of approximately 103 bar. Then, the mould was preheated to 1550 °C above the melting point of DD403 alloy by graphite heating elements. After melting of the ingot, the charge was poured into the preheated mould at the pouring temperature of 1460 °C and held for 2 min to stabilize the melt. Finally, the ceramic mould was withdrawn from the furnace at a pre-determined withdrawal velocity of 100 lm/s.
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After SX casting, Electron Back-Scattering Diffraction (EBSD) technology was applied to acquire orientation image maps and determine the grain texture distributions in the starter block and spiral passage. For the EBSD analysis, a ZEISS SUPRA 55 SEM equipped with HKL system and Channel 5 analysis software was used.
3. Simulation details 3.1. Directional solidification process modeling The directional solidification process was modeled by a macroscopic 3-D finite element analysis software namely ProCAST (a trademark of ESI Group, Paris). Fig. 4 illustrates the FEM mesh model of the casting system. To increase computation efficiency,
Table 3 Nominal composition of alloy DD403 used in this study. Element
Cr
Co
W
Mo
Al
Ti
Ni
wt.%
9.5
5.0
5.2
3.8
5.9
2.1
Bal.
the furnace model was built with a boundary 2-D mesh. Corresponding to the modified Bridgman furnace shown in Fig. 3, the 2-D furnace mesh was regarded as an insulated enclosure (the insulator in Fig. 4) and consisted of two heating zones (primary heater and secondary heater in Fig. 4), a thermal baffle and a cooling zone. The casting blade and ceramic mould were built with solid 3-D meshes. The ceramic mould was mounted on a water-cooled copper chill base. In the present model, the relative motion between the mould and the furnace was achieved through the upward movement of the enclosure at a velocity of 100 lm/s, as shown in Fig. 4. During directional solidification, the 3-D casting mesh contacted with the 2-D furnace mesh through thermal radiation (shown in Fig. 4). In this model, the radiation was performed with a complex radiation algorithm (called view factors calculation), in which the reflections, obstructions and shadowing effects were taken into account. During the process that the mould was withdrawn from the chamber, the view factors were continuously updated. 3.2. Heat transfer model The directional solidification process mainly refers to three kinds of heat transfer patterns: the thermal conduction in materials and between different materials that contact each other, the radiation within the insulator as shown in Fig. 4 and convection heat transfer. In this study, convection heat transfer was ignored. According to the energy conversation, heat transfer in the alloy during the directional solidification process can be formulated as follows:
qc
@T @ @T @ @T @ @T @fs þ þ þ qA ¼ k k k þ QR @t @x @x @y @y @z @z @t
ð1Þ
where q is the alloy density, c the specific heat capacity, T the temperature, t the time, k the coefficient of thermal conductivity, A the latent heat and fs the solid fraction, QR the thermal radiation quantity, x, y, z the coordinate. Based on the law of Stefen–Boltzman, the thermal radiation quantity QR in vacuum can be written as: Fig. 3. Schematic diagram of the furnace chamber.
Q R ¼ reðT 4 T 4a Þ
ð2Þ
where r is the Stefan–Boltzmann constant, e the emissivity, T the surface temperature, and Ta the ambient temperature and namely the inner wall temperature of the furnace. 3.3. Nucleation model The calculated thermal profiles by the macro-scale ProCAST were then used as input in the meso-scale CAFE model to predict the grain structure with special consideration of the crystallographic anisotropy of grains and the growth kinetics of dendrite tips. In the present study, the heterogeneous nucleation that occurred randomly at the surface of chill plate was modeled by a continuous nucleation distribution called Gaussian distribution of nucleation sites [29]. The continuous nucleation distribution, dn/ d(DT), can be described as:
" 2 # dn nmax 1 DT DT max exp ¼ pffiffiffiffiffiffiffi dðDTÞ 2 DT r 2pDT r
Fig. 4. FEM mesh model of the casting system.
ð3Þ
where dn is the grain density increase, which is induced by an increase in the undercooling, d(DT). DTmax is the mean undercooling, DTr the standard deviation, and nmax the maximum density of nuclei obtained by the integral of the Gaussian distribution.
N. Wang et al. / Journal of Alloys and Compounds 586 (2014) 220–229
The nmax is an important input parameter which is imperative for the CAFE simulation as a nucleation boundary condition. To obtain the value, the grain density at the surface of chill plate was examined quantitatively with EBSD techniques. Under the above experimental condition, the areal density was equal to 1.65 108 (number of nuclei/m2) and this value was used as the nucleation boundary condition nmax at the chill surface for CAFE simulations. 3.4. Grain growth model The preferred orientation of Ni-base superalloys with a facecentered cubic crystal structure is h1 0 0i crystallographic orientation. It is assumed that the crystallographic orientation of a new nucleus nucleated at the surface of chill plate is random, and the growth directions of the trunks and arms coincide with h0 0 1i crystallographic orientation of the parent nucleus. In castings, the dendrite growth is dominated by the undercooling near the dendrite tip. The total undercooling of the dendrite tip, DT, is generally the sum of four contributions [31]:
DT ¼ DT C þ DT T þ DT K þ DT R
ð4Þ
where DTC, DTT, DTK and DTR are the undercooling contributions associated with solute diffusion, thermal diffusion, attachment kinetics and curvature, respectively. For most metallic alloys, in the case of directional solidification, the last three contributions that appear in Eq. (4) are small. The growth of the dendrite is primarily controlled by solute diffusion, and the growth kinetics of both columnar and equiaxed morphologies can be calculated with the aid of Kurz–Giovanola–Trivedi (KGT) model [32]. During the process of simulation, the growth rate of dendrite tip was simplified as:
v ¼ a2 DT 2 þ a3 DT 3
ð5Þ
where a2 and a3 are constants, determined by alloy composition according to the KGT model. A further detailed descriptions of the CAFE model were given in Refs. [30,33–37]. 4. Results and discussion 4.1. Competitive grain growth in starter block Fig. 5a shows the predicted grain structure at the longitudinal section of the starter block. The different colors of the predicted grain structure represent the minimum deviation angle between the h0 0 1i direction of the grain and the direction of the casting axis. Fig. 6a is the corresponding experimental observation of longitudinal section of the starter block. Both Figs. 5a and 6a show that, as solidification proceeds, the equiaxed crystal grains
223
progressively evolve into parallel columnar grains with the competitive dendritic growth in starter block. Figs. 5b–g and 6b–g present the orientation image maps and the corresponding h0 0 1i pole figures at different cross sections of starter block respectively observed by CAFE simulation and EBSD techniques. As for the grain orientation selection, the h0 0 1i pole figures at different cross sections of starter block in Figs. 5b–g and 6b–g both indicate that the grain orientation selection occurs with increasing the distance from the chill plate and the grains with favorable growth direction gradually overgrow the other grains. When the distance from the chill plate reaches 15.5 mm (see Figs. 5e and 6e), the favorably h0 0 1i oriented grains predominate in starter block. When reaching 36.0 mm (Figs. 5g and 6g), almost all deviations are less than 10°. Only a few deviation angles are between 10° and 20°. Meanwhile, the distribution range of the deviation angles at each height of starter block in Fig. 5 is found to be the same with the corresponding height in Fig. 6. This result indicates that the CAFE model has a good performance on prediction of the grain orientation selection in starter block. Fig. 7 shows the simulated average deviation angles between h0 0 1i direction of grains and the direction of the casting axis at different heights from the chill plate. It is found that the average deviations decrease with increasing the distance from the chill plate. When the distance reaches 26.0 mm, the average deviation is decreased to 9.1°. As for the grain number selection, it is found that the grain number decreases and the grain size increases with the increase of the distance from chill plate. The quantitative relationship between the grain density and the distance from the chill plate is shown in Fig. 8. It is revealed that the simulation results of grain number selection agree well with the experiment results. The grain density decreases dramatically when the distance from the chill plate is less than about 6.0 mm. This is because of that there are fierce competitions between those grains with various orientations in the primary period of solidification. In this stage, the grains with large deviation angles are eliminated rapidly and the grain orientations are preliminarily optimized. Then, the competitions between the grains are relieved and the grain density decreases slowly with the increase of distance. When the distance reaches 26.0 mm, the grain density tends to be stabilized at about 106 m2. And the grain density is found to be reduced in two orders of magnitude during the competitive growth in starter block with a height of about 36.0 mm. When the distance is higher than 26.0 mm, the average deviation is decreased to 9.1° and the grain density tends to be stabilized. Therefore, the length of starter block could be reduced to about 26.0 mm for the productivity of SX casting components. However, the proposed value is reasonable only on the premise that the single crystal blade whose deviation is bellow 10° is defined as the qualified blade.
Fig. 5. Predicted grain structures of the longitudinal section of starter block (a); orientation image maps and corresponding h0 0 1i pole figures of cross-sections at 0.5 mm (b); 3.0 mm (c); 6.0 mm (d); 15.5 mm (e); 26.0 mm (f); 36.0 mm (g) from the chill plate.
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Fig. 6. Experimental observations of longitudinal section of the starter block (a); EBSD orientation image maps and corresponding h0 0 1i pole figures of cross-sections at 0.6 mm (b); 2.9 mm (c); 6.2 mm (d); 15.4 mm (e); 25.8 mm (f); 36.1 mm (g) from the chill plate.
three grains remain (Fig. 9c). Finally, two of the grains are blocked during the competitive growth in the spiral passage from section c to d. Only one single grain exists at section d (Fig. 9d). So far, the single crystal selection is completed below the position of about one pitch in the spiral passage.
Fig. 7. Simulation results of the average deviations between h0 0 1i direction of grains and the casting axis at different heights from the chill plate.
Fig. 8. Grain density as a function of the distance from chill plate.
4.2. Grain selection in spiral grain selector The grain selection behavior in the spiral grain selector and the efficiency of the selectors with respect to different spiral designs will be discussed in the following. As an example, Fig. 9 shows how a single crystal is selected in one of the spiral grain selectors (the spiral angle is 30° and the spiral thickness is 5 mm) during directional solidification. Fig. 9a–d are the predicted orientation image maps at different cross sections of the spiral and the corresponding h0 0 1i pole figures. As illustrated in Fig. 9a, there are a few favorably h0 0 1i oriented grains at the entrance of spiral after the competitive growth in the starter block. During the initial selection in the spiral passage from section a to b, the grain numbers drastically decrease, just as shown in Fig. 9b. When the process of solidification reaches section c, only
4.2.1. Effect of geometrical restriction on grain selection By tracking the grain selection in Fig. 9, it is found that the grain A near the inner wall of the spiral passage is finally selected as the single crystal. To further reveal the mechanism of grain selection in the spiral, Fig. 10 shows the simulated microstructures of the longitudinal section at the bottom of the spiral passage and the top view of the grain structure evolutions in the spiral selector. The characters A1, A, B and C in Fig. 10b and c represent different orientation grains, respectively. From Fig. 10b, it is found that at the bottom of spiral, the grains far away from the inner wall of the spiral passage are geometrically blocked by the outer wall of the spiral passage, and there is enough space for the grain A1 located near the inner wall of the spiral passage to develop new dendrites. The top view of the grain structures in Fig. 10c shows that the grain A near the inner wall of the spiral passage eventually overgrows the grain B and C near the outer wall of spiral passage and is selected as the final single crystal. Therefore, it is proposed that the geometrical blocking of narrow passage attributes to the grain selection in the spiral. This agrees well with the results of Dai et al. [25], Gao et al. [26] and Seo et al. [38]. 4.2.2. Effect of heat flow on grain selection Except for geometrical blocking, it is speculated that the heat flow also makes contribution to the grain selection in the spiral passage. For the intention of clear observation, the length of starter block is decreased to 1.0 mm to magnify the impact of heat flow on the competitive grain growth in spiral. Fig. 11a shows the CAFE simulated grain structures in the spiral selector. The microstructure evolutions indicate that the grain A2 near the inside-underside of the spiral passage occupies a dominant position and survives finally. The superiority of the inside grains has been discussed above, and the following is an investigation into the predominance of the underside grains and the influence of heat flow on the grain selection in spiral grain selector. Fig. 11b shows the temperature contour between 90° and 180° (spiral climbing angle) of the spiral passage at t = 96.2 s. It is necessary to state that Fig. 11b is presented in the view which contrarotates 90° from the view of Fig. 11a, for the intention of clearly showing the heat flow direction. In order to present the average direction of heat flow at this moment in the spiral passage, the following four steps (as illustrated in Fig. 11b) are taken: draw the tangent line at the midpoint of each temperature contour respectively; draw the corresponding perpendicular of each tangent line; connect these perpendiculars sections one by one to constitute the direction of heat flow; finally, the tangent line at the midpoint of
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Fig. 9. Predicted orientation image maps and corresponding h0 0 1i pole figures of cross-sections at (a) 0 mm; (b) 3 mm; (c) 6 mm; and (d) 10 mm from the base of spiral.
Fig. 10. Schematic diagram of spiral grain selector (a), predicted grain structures of section I–I (b) and the top view of simulated grain structures in the grain selector (c), the structures in the circle indicate that the grain located near inner wall of the spiral passage is selected as the final SX.
Fig. 11. The relationship between the heat flow and grain selection behavior, CAFE simulated grain structures in the spiral selector (a), temperature contour between 90° and 180° (spiral climbing angles) of spiral selector at t = 96.2 s (b), simulated grain structures of longitudinal section I–I (c1)(d1), section II–II (c2)(d2) and section III–III (c3)(d3) between 90° and 180° of spiral.
the direction of heat flow is defined as the average direction of heat flow. Because the heat dissipation of the spiral passage changes
with the special geometrical shape, the heat flow direction in the spiral passage is no longer in parallel with the casting axis, but
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inclines to the spiral climbing direction. Therefore, at a specific position of the spiral passage, the average direction of the heat flow is just as shown in Fig. 11b. The microstructures of the longitudinal section I, section II and section III (see Fig. 11a) between 90° and 180° of the spiral selector are shown in Fig. 11(c1), (c2) and (c3), respectively. Fig. 11(d1), (d2) and (d3) are the corresponding schematic diagrams of grain boundaries. It is indicated that the grain A2 located near the underside of spiral passage is selected as the final single crystal. The boundary between the selected grain A2 and one of the adjacent grain B2 is parallel to the average direction of heat flow. Similarly, the boundary between the selected grain A2 and another adjacent grain C2 develops along the direction of heat flow in the spiral passage. The findings of Fu et al. [27] showed that the grains with their preferred growth direction (h0 0 1i in Ni-base superalloy) nearer to maximum temperature gradient (the direction of heat flow) will grow faster than those with their preferred growth direction far away from maximum temperature gradient during directional solidification. Zheng et al. [39] considered that the main grain selection mechanism of the spiral selector is that the easy growth direction (preferred growth direction) of the cubic crystal coupled with the spiral structure of the selector. Therefore, it is considered that the heat flow direction and preferred growth direction make great influence on the competitive grain growth. In this study, the grains with their easy growth direction h0 0 1i nearer the spiral heat flow direction, for example, the grain A2 and B2 (with their h0 0 1i deviation 20° and 21° from the axial orientation respectively) as shown in Fig. 11, gradually overgrow those far-away-grains along the spiral passage and dominate in the spiral passage. In addition, the experiment results of Lu et al. [20] showed that the whole sample with bi-crystal microstructure could be obtained when the two seeds were with the same primary dendrites orientation paralleled to the heat flow direction. Since the h0 0 1i of the grain A2 and B2 (deviation angles are 20° and 21°, respectively) in Fig. 11 are quite close and parallel to the heat flow direction, they have the same growth advantage in the direction of heat flow. Therefore, the boundary between them develops parallel to the average direction of the heat flow at their position, as shown in Fig. 11(d1), (d2) and (d3). When the boundary between the grain A2 and B2 extends and encounters the passage wall, the upside grain B2 is eliminated, while the underside grain A2 survives and develops new dendrites. Eventually, the grain A2 grows into the cavity and becomes the single crystal texture. Therefore, it is proposed that the coupling effect of the heat flow direction, the preferred growth direction and the geometrical restriction of the spiral wall makes contribution to the crystal selection in the spiral passage.
Fig. 12. The minimum required climbing angles for single crystal selection in spiral grain selectors as a function of the spiral angle h.
4.2.3. Efficiency of the grain selectors The mechanism of grain selection in the spiral grain selector has been discussed above and the following is an investigation into the efficiency of the selectors with respect to different spiral designs. Fig. 12 shows the minimum required climbing angles for single crystal selection in spiral grain selectors as a function of spiral angle h, illustrating that one single crystal can be rapidly selected after the solidification climbing 400° along the spiral passage. The effective grain selection in the spiral is considered to be mainly attributed to the coupling effect of the heat flow direction and the geometrical restriction of the spiral wall. In addition, it is found from Fig. 12 that there is no obvious relationship between the minimum required climbing angles for single crystal selection and the spiral angles. 4.3. Relationship between geometries of grain selector and crystal orientation 4.3.1. Geometries of starter block The relationship between the SX crystallographic orientation and the geometries of starter block is investigated with a 3-D model of grain selector. Fig. 13a and b shows the effects of the length L and the width D of starter block on the SX orientation, respectively. It is found that the deviation of h0 0 1i direction of single crystal from the casting axis decreases by increasing the length of starter block or decreasing its width. Moreover, the relation between the SX orientation and L/D is shown in Fig. 13c. It is indicated that the SX orientation is optimized quickly with the increase of L/D and approaches a constant value when L/D is greater than 2. The simulation results by Esaka et al. [22] with a 2-D ‘‘pigtail’’ model also indicated that the yield rate of well-oriented single crystal increases with increasing the ratio of the length to the width of starter block. However, in the study of Esaka et al. [22], the yield rate approaches a constant value when L/D is just greater than 1, which is much smaller than the value 2 in the present study. For Ni-base superalloys, the fast growing dendritic orientation is h0 0 1i [40,41]. During the process of directional solidification, the favorably h0 0 1i oriented grains can overgrow the unfavorably oriented grains. With increasing the length of starter block, there will be more opportunities for grain competitive selection to take place, which contributes a lot to the optimization of the grain orientations in starter block. The grain texture evolutions shown in Figs. 5 and 6 above have made a good illustration of the effect of the length of starter block on the grain orientations optimization in starter block. Moreover, the grain orientations at the top of starter block make significant effect on the final SX orientation [26]. Therefore, the single crystal orientation can be optimized by increasing the length of starter block. With decreasing the width of starter block, the specific surface area of the ceramic mould is increased and the cooling rate during solidification is improved. Greater cooling rate will increase the growth rate of the dendrites at the solid–liquid interface. As reported by Ardakani et al. [42], an increase of growth rate leads to a larger difference in the undercoolings between the tips of the well-oriented and misoriented dendrites. This difference will result in rapid elimination of the misoriented dendrite by the secondary dendrites developing from the well-oriented dendrite. Thus, the h0 0 1i direction of the final SX will be aligned more closely along the casting axis. However, the ratio of the length L to the width D of starter block is not the greater the better. When L/D is greater than 2, the orientation of single crystal approaches a constant value. The reason of this trend is the following. In the preliminary stage when L/D is less than 2, the misoriented grains are rapidly eliminated by competitive grain growth. Then, the competitions between the grains in starter block are relieved immensely and the grain orientations
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Fig. 13. Effects of the length L (a), the width D (b) and L/D of starter block (c) on SX orientation, respectively.
are optimized slowly with the increase of L/D. In this situation, the continued increase of L/D is almost of no avail. 4.3.2. Geometries of spiral grain selector In order to investigate the grain orientation selection in the spiral passage, grain structures at different cross sections of the spiral grain selector were examined by simulation and experiment method. Fig. 14a illustrates the predicted grain structure in one of the spiral grain selectors (the spiral angle is 60° and the spiral
thickness is 5 mm). Fig. 14b1–d1 are the h0 0 1i pole figures of different cross-sections, and Fig. 14b2–d2 are the corresponding deviations between the h0 0 1i direction of grains and the casting axis. It is shown in Fig. 14a that one single crystal is quickly selected below the position of one pitch in the spiral passage. From Fig. 14b1 and b2, it can be seen that a few grains grow into the spiral selector after the competitive growth in the starter block and the deviation angles of the grains at the entrance of the spiral mainly concentrate in the range of 0–15°. When solidification in the spiral
Fig. 14. Predicted grain structures in the spiral grain selector (a), h0 0 1i pole figures of cross-sections at (b1) 0 mm; (c1) 16 mm; (d1) 30 mm from the base of spiral and the corresponding deviations between h0 0 1i of the grains and the casting axis (b2)–(d2).
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Fig. 15. Effects of spiral angle h (a), spiral thickness dT (b) and spiral rotation diameter Ds (c) on the SX orientation.
passage reaches section c, the grains whose deviation angles distribute in 5–10° are eliminated. While the relatively misoriented grains (deviations in 10–15°) remain. Then, the solidification proceeds to section d and the well-oriented grains (deviations in 0– 5°) are overgrown by the grain with a deviation angle of 13.5°. Finally, this fortunate grain (deviation of 13.5°) grows up into the cavity as the final single crystal cast. Therefore, it is inferred that the grain orientation selection in the spiral passage is random and the misoriented grains can overgrow the well-oriented grains. To confirm this, the deviation angles between h0 0 1i direction of the final single crystal and the direction of casting axis relative to different parameters of the spiral grain selector are given in Fig. 15. It is illustrated that there is no significant change of deviation angles with the increase of spiral angle h, spiral thickness dT and spiral rotation diameter Ds. In addition, as shown in Fig. 15, the grain orientations randomly distribute in the range of 0–18° which is consistent with the distribution range of 0–20° at the top of starter block shown in Figs. 5 and 6. Therefore, it is concluded that during single crystal casting in spiral grain selector, the spiral is just to ensure only one single crystal finally survive and the grain orientations cannot be optimized during the grain selection in the spiral. This can be attributed to the following reasons. The grains with different deviations randomly distribute at the entrance of the spiral as shown in Fig. 14b1 and b2. Base on the geometrical blocking mechanism, no matter the dendrites of grains at the entrance of the spiral are well-oriented or misoriented, those grains near outer wall of the spiral passage will be eliminated by the outer passage wall and the grains near inner wall of the spiral passage will have enough space to grow by branching new dendrites. Base on the heat flow mechanism, the grains with their easy growth direction h0 0 1i nearer the heat flow direction in the spiral passage will
overgrow those far-away-grains. However, the heat flow direction inclines to the spiral climbing direction, so the well-oriented grains whose h0 0 1i nearer the casting axis have no advantage during the competitive growth in spiral passage. Instead, the misoriented grains whose h0 0 1i off the casting axis but nearer the spiral heat flow direction may survive and grow into the cavity to be the final SX cast. 5. Conclusions Grain selection in spiral grain selectors is simulated by a coupled ProCAST&CAFE model and validated experimentally with different spiral geometries. The predicted results are in good agreement with the experimental ones. The following conclusions can be drawn from this work: (1) During the grain selection process in starter block, the preferred h0 0 1i-oriented grains will overgrow the misoriented grains with the increase of the distance from chill plate. When the distance reaches 26.0 mm, the grain density tends to be stabilized at about 106 m2 and the average deviations of grain orientations are decreased below 10°. This result indicates that the length of starter block could be reduced to about 26.0 mm for the productivity of SX casting components. (2) During the grain selection process in spiral, the grain near the inside-underside of spiral passage is selected as the final crystal and a single crystal can be rapidly selected after the solidification front climbing 400° along the spiral passage. The boundary between the selected grain and its adjacent grains is parallel to the average direction of heat flow. It is proposed that the coupling effect of the heat flow direction,
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the preferred growth direction and the geometrical restriction of the spiral wall makes contribution to the crystal selection in the spiral passage. (3) The SX orientation can be optimized by increasing the length of starter block or decreasing its width. While the SX orientation approaches a constant value when the ratio of the length to the width is greater than 2. The results also reveal that there is no obvious relationship between the crystal orientation and the parameters of spiral passage. Acknowledgments The authors are grateful to the financial support of the National Basic Research Program of China (Nos. 2010CB631202 and 2011CB610406), the National Natural Science Foundation of China (Nos. 50931004 and 51101120) and the Aeronautical Science Foundation of China (No. 2010ZE53047). References [1] S. Tin, T.M. Pollock, J. Propul. Power 22 (2006) 361–374. [2] X.B. Zhao, L. Liu, C.B. Yang, Y.F. Li, J. Zhang, Y.L. Li, H.Z. Fu, J. Alloys Comp. 509 (2011) 9645–9649. [3] C.T. Liu, J. Ma, X.F. Sun, J. Alloys Comp. 491 (2010) 522–526. [4] G. Liu, L. Liu, C. Ai, B.M. Ge, J. Zhang, H.Z. Fu, J. Alloys Comp. 509 (2011) 5866– 5872. [5] K. Zhao, Y.H. Ma, L.H. Lou, J. Alloys Comp. 475 (2009) 648–651. [6] L.N. Wang, Y. Liu, J.J. Yu, Y. Xu, X.F. Sun, H.R. Guan, Z.Q. Hu, Mater. Sci. Eng. A 505 (2009) 144–150. [7] S.A. Sajjadi, H.R. Elahifar, H. Farhangi, J. Alloys Comp. 455 (2008) 215–220. [8] A. Picasso, A. Somoza, A. Tolley, J. Alloys Comp. 479 (2009) 129–133. [9] A. Wanger, B.A. Shollock, M. Mclean, Mater. Sci. Eng. A 374 (2004) 270–279. [10] N. D’Souza, M.G. Ardakani, A. Wagner, J. Mater. Sci. 37 (2002) 481–487. [11] R.A. MacKay, R.D. Maier, Metall. Trans. A 13 (1982) 1747–1754. [12] T. Murakumo, T. Kobayashi, Y. Koizumi, H. Harada, Acta Mater. 52 (2004) 3737–3744. [13] B.C. Wilson, G.E. Fuchs, Metall. Mater. Trans. A 41 (2010) 1235–1245. [14] A. Suzuki, M.F.X. Gigliotti, B.T. Hazel, D.G. Konitzer, T.M. Pollock, Metall. Mater. Trans. A 41 (2010) 947–956.
229
[15] H.J. Dai, H.B. Dong, H.V. Atkinson, P.D. Lee, Solid State Phenom. 139 (2008) 129–134. [16] N. D’Souza, P.A. Jennings, X.L. Yang, H.B. Dong, P.D. Lee, M. McLean, Metall. Mater. Trans. B 36 (2005) 657–666. [17] R.C. Reed, T. Tao, N. Warnken, Acta Mater. 57 (2009) 5898–5913. [18] G.J.S. Higginbotham, Mater. Sci. Technol. 2 (1986) 442–460. [19] S. Tin, T.M. Pollock, W.T. King, K.A. Green, in: T.M. Pollock et al. (Eds.), Superalloys 2000, TMS, Warrendale, PA, 2000, pp. 201–210. [20] Q. Lu, J.G. Li, T. Jin, Y.Z. Zhou, X.F. Sun, Z.Q. Hu, Acta Metall. Sin. 47 (2011) 641– 648. [21] R.C. Reed, The Superalloys Fundamental and Applications, Cambridge University Press, Cambridge, UK, 2006. pp. 124. [22] H. Esaka, K. Shinozuka, M. Tamura, Mater. Sci. Eng. A 413–414 (2005) 151– 155. [23] H.J. Dai, H.B. Dong, N. D’Souza, J.-C. Gebelin, R.C. Reed, Mater. Trans. A 42 (2011) 3439–3446. [24] X.B. Meng, Q. Lu, J.G. Li, T. Jin, X.F. Sun, J. Zhang, Z.Q. Chen, Y.H. Wang, Z.Q. H, J. Mater. Sci. Technol. 28 (2012) 214–220. [25] H.J. Dai, N. D’Souza, H.B. Dong, Metall. Mater. Trans. A 42 (2011) 3430–3438. [26] S.F. Gao, L. Liu, N. Wang, X.B. Zhao, J. Zhang, H.Z. Fu, Metall. Mater. Trans. A 43 (2012) 3767–3775. [27] H.Z. Fu, G. He, J.G. Li, Acta Metall. Sin. 33 (1997) 1233–1238. [28] X.B. Zhao, L. Liu, W.G. Zhang, Z.H. Yu, H.Z. Fu, Mater. Chem. Phys. 125 (2011) 55–58. [29] Ph. Thévoz, J.L. Desbiolles, M. Rappaz, Metal. Trans. A 20 (1989) 311–322. [30] Ch.-A. Gandin, M. Rappaz, R. Tintillier, Metal. Trans. A 24 (1993) 467–479. [31] J. Lipton, M.E. Glicksman, W. Kurz, Mater. Sci. Eng. 65 (1984) 57–63. [32] W. Kurz, B. Giovanola, R. Trivedi, Acta Metall. 34 (1986) 823–830. [33] M. Rappaz, Ch.-A. Gandin, Acta Metall. Mater. 41 (1993) 345–360. [34] Ch.-A. Gandin, M. Rappaz, Acta Metal. Mater. 42 (1994) 2233–2246. [35] M. Rappaz, C.A. Gandin, J.L. Desbiolles, Metall. Mater. Trans. A 27 (1996) 695– 705. [36] Ch.-A. Gandin, M. Rappaz, R. Tintillier, Metall. Mater. Trans. A. 25 (1994) 629– 635. [37] Ch.-A. Gandin, J.-L. Desbiolles, M. Rappaz, Ph. Thévoz, Metall. Mater. Trans. A. 30 (1999) 3153–3165. [38] S.M. Seo, I.S. Kim, J.H. Lee, C.Y. Jo, H. Miyahara, K. Ogi, Met. Mater. Int. 15 (2009) 391–398. [39] Q. Zheng, G.C. Hou, W.M. Tian, T. Jin, X.F. Sun, H.R. Guan, Z.Q. Hu, Trans. Nonferrous. Met. Soc. China 11 (2001) 176–178. [40] M.G. Ardakani, N. D’Souza, B.A. Shollock, M. McLean, Metall. Mater. Trans. A 31 (2000) 2887–2893. [41] P.N. Quested, M. Mclean, Mater. Sci. Eng. 65 (1984) 171–180. [42] M.G. Ardakani, N. D’Souza, A. Wagner, B.A. Shollock, M. Mclean, in: K.A. Green et al. (Eds.), Superalloys 2000, TMS, Warrendale, PA, 2000, pp. 219–228.