- Email: [email protected]
Prediction of freckle formation in directionally solidified CMSX-4 superalloy
Accepted Manuscript Prediction of freckle formation in directionally solidified CMSX-4 superalloy Qiudong Li, Jun Shen, Yilong Xiong, Ling Qin, Xiao'an Yue PII: DOI: Reference:
S0167-577X(18)30907-8 https://doi.org/10.1016/j.matlet.2018.06.002 MLBLUE 24442
To appear in:
Materials Letters
Received Date: Accepted Date:
14 May 2018 2 June 2018
Please cite this article as: Q. Li, J. Shen, Y. Xiong, L. Qin, X. Yue, Prediction of freckle formation in directionally solidified CMSX-4 superalloy, Materials Letters (2018), doi: https://doi.org/10.1016/j.matlet.2018.06.002
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.
Prediction of freckle formation in directionally solidified CMSX-4 superalloy Qiudong Li, Jun Shen*, Yilong Xiong, Ling Qin, Xiao’an Yue State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China ABSTRACT Freckle defects appearing on the industrial gas turbine blade reduce the high temperature mechanical properties. It is necessary to predict the freckle formation on the castings before the directional solidification. In this paper, the relationship of fluid flow and crystal growth during the vertical directional solidification was analysed. Based on the analysis, a simple method considering the solidification conditions and concaved solidification interface was proposed to predict the freckle formation. The method was verified with specimens and dummy blade under the experimental environments. The validation results show that the method can predict where the freckle may appear on a casting with a large size and complex shape for directionally solidified CMSX-4 superalloy. Keywords: Solidification; Defects; Metals and alloys; Freckle. 1. Introduction Power generation mode based on the industry gas turbine for its high efficiency and less pollution to the environments is favored. However, the wide application is limited by the production of single crystal or directionally solidified blades for the increasing freckling tendency. Freckle defects is caused by the thermal solute convection in the mushy zone [1-5], and reduces the high temperature mechanical properties. Thus, before the production of castings, it is necessary to find a way to predict freckle
*
Corresponding authors. E-mail address: [email protected] (J. Shen). 1
formation so as to take effective measures to suppress freckles. So far, the methods [3, 6, 7] based on the Rayleigh number taking alloy composition and solidification parameter into account can predict the freckle formation well. However, the precise prediction depends on the simulations coupling with the thermal field, solute field, and fluid field. The works of simulations are huge, the specimens used in the simulations are usually simple, and the specimen sizes are far less than the real castings. Therefore, the prediction methods are difficult to be widely applied. Recently, Pustal et al. [8] proposed a method which can predict where the freckles will appear on the specimen with a varying cross-section. But a number of parameters are needed and the process is complex. The aim of this paper is to find a simple way to predict where the freckles may appear on the castings with a large size and complex shape. The previous experimental results were employed to validate the prediction method. Then, the method was applied to predict freckle formation in directionally solidified specimen and dummy blade. 2. Development of model
Fig. 1. The relationship of fluid flow and crystal growth during the vertical directional solidification with a concaved solidification interface.
2
During the directional solidification of CMSX-4 superalloy, it is widely accepted that the thermal solute convection will appear. Meanwhile, for the less lateral heat dissipation, the solidification interface is usually concaved with an angle θ as shown in Fig. 1. According to the investigations of Copley et al. [1] and Li et al. [9], due to the tilted solidification interface, a force arising from the density difference in the horizontal direction will act on the interdendritic liquid. Thus, the interdendritic liquid will have a tendency to flow towards the surface as shown in Fig. 1. α is the angle between the flow of the interdendritic liquid with the solidification interface. Combing with the Fig. 1, Eq. (1) can be obtained from Flemings’ criterion [10] predicting freckle formation qualitatively. V cos V T V T 2 = V sin 1 R R R T
(1)
Where V is the flow velocity of the interdendritic liquid, and given by the Darcy’s law as shown in Eq. (2); T is the thermal gradient; ε is the cooling rate; and R is the growth speed of dendrite.
g cos K g K g K 2 V sin fL fL fL
(2)
Inserting Eq. (2) into Eq. (1), Eq. (3) is derived.
V T
g K sin 2 1 fL R
(3)
Where K, the permeability in the mushy zone, can be represented by the liquid fraction fL and primary dendrite arms λ1 as shown in Eq. (4) [11]. K K f L K 1
(4)
Then, Eq. (5) can be obtained by inserting Eq. (4) into Eq. (3).
V T
g
K f L K 1 sin 2 1 fL
R
3
(5)
For the Eq. (5),
, the alloying effect, the solidification conditions and the slope
effect are taken into account. The aim of this paper is to find a simple way to prediction the freckle formation, and the solidification behavior and thermophysical properties of the alloys are not fully understood. Therefore, some simplifications were done. One of the simplifications is to neglect the gravitational effect and alloying effect for the same alloy and gravity. The second one is to neglect the angle α, for the α between the flow of the interdendritic liquid with the solidification interface is not understood so far [12]. And it is reasonable to assume the angle be smaller than θ [13]. Accordingly, the Eq. (5) can be simplified to the Eq. (6) which takes the solidification conditions and the concaved solidification interface into account.
V T
K 1 sin 2 cons tan t R
(6)
For the superalloy, the λ1 can be represented by Eq. (7) [14]. Thus, the Eq. (8) for predicting freckle formation is obtained by inserting Eq. (7) into Eq. (6).
1 G 1/2 R1/4
(7)
V T
(8)
I
G 1 R 1.5 sin 2 cons tan t
For a directionally solidified casting, where there is a large value I, there will be a larger freckling tendency. The parameters such as thermal gradient G, the growth speed of dendrite R, the angle θ between the solidification interface and horizontal, and the value I can be easily obtained by the commercial finite element software ProCAST. The detailed simulations with the ProCAST have been shown in the previous investigations [15, 16] of the authors. 3. Results and discussions 3.1 Validation of prediction method
4
Fig. 2. Initiation positions of freckles under the different conditions [9].
Fig. 3. Initiation positions of freckles. (a and c) Experimental results [9, 16], (b and d) predictive results. (a and b) without graphite block, (c and d) with graphite block. In order to verify the prediction method proposed, the experimental results in the previous investigations of [9, 16] the authors was employed. All the experiments was carried out in the conventional Bridgman furnace under the various experimental conditions (including withdrawal rate, heater temperature, and specimen size). The initiation positions of freckles are shown in Fig. 2 [9]. It is evident that the freckles usually initiate in the region about 2-4 mm above the platform. One of the experimental results (in Fig. 3a) is taken as the example, and the corresponding predictive result is shown in Fig. 3(b). The predictive result shows that freckles are more likely to appear on the bottom of platform
5
A. The actual initiation position is about 2-4 mm above the predictive one. This also indicates that the prediction method is not applicable to the freckle prediction in the region where the height is not enough. This is also the reason why the predictive results is not consistent with the experiment results in top region B (in Fig. 3b) of the specimen. Thus, the prediction method proposed in this paper can predict where the freckles will appear on the castings expect the regions with a not enough height. 3.2 Application of prediction method In the study [16] of authors, a graphite block was used to improve the local cooling condition, and the freckles was suppressed absolutely (in Fig. 3c). The corresponding predictive result is shown in Fig. 3(d). The value I is evidently reduced in the platform, meaning that the freckling tendency will reduced. It is consistent with the experimental result shown in Fig. 3c. In addition, due to the shortcoming of the prediction method as discussed above, the freckles will not appear on the top region of the specimen, regardless of the large value I. In order to verify whether the prediction method proposed can be used to predict freckle formation in the actual blade, a dummy blade was designed and directionally solidified. The predictive result and experimental result were shown in Fig. 4. As the predictive result shown in Fig. 4(a), the freckles will be more likely to appear in the region C and region D of the dummy blade. It is consistent with the experimental result shown in Fig. 4(b), Fig. 4(c) and Fig. 4(d). Thereby, the prediction method proposed in this study can be applied to predict freckle formation in the casting with a large size and complex shape.
6
Fig. 4. Locations of freckles in dummy blade. (a) Predictive result, (b) (c) (d) experimental results. 4. Conclusions In this paper, the relationship of fluid flow and crystal growth during the vertical directional solidification with a concaved solidification interface was analysed. And then, a method considering the solidification conditions and concaved solidification interface was obtained to predict the freckle formation. The validation results show that the method can be applied to predict where the freckle may appear on a casting with a large size and complex shape. Acknowledgements This work was supported by the National Basic Research Program of China [Grant No.2013CB035703]. References [1] S.M. Copley, A.F. Giamei, S.M. Johnson, M.F. Hornbecker, Metall. Trans. 1 (1970) 2193-2204. [2] S. Boden, S. Eckert, G. Gerbeth, Mater. Lett. 64 (2010) 1340-1343. [3] L. Yuan, P.D. Lee, Acta Mater. 60 (2012) 4917-4926. [4] A. Saad, C.A. Gandin, M. Bellet, N. Shevchenko, S. Eckert, Metall. Mater. Trans. A 46 (2015) 4886-4897. [5] F. Wang, D. Ma, J. Zhang, A. Bührig-Polaczek, J. Alloys Compd. 620 (2015) 24-30.
7
[6] W. Yang, K.M. Chang, W. Chen, S. Mannan, J. DeBarbadillo, Metall. Mater. Trans. A 32 (2001) 397-406. [7] C. Beckermann, J.P. Gu, W.J. Boettinger, Metall. Mater. Trans. A 31 (2000) 2545-2557. [8] B. Pustal, D. Ma, N. Warnken, E. Subasic, J. Jakumeit, A. Bührig-Polaczek, IOP Conf. Ser.: Mater. Sci. Eng. 117 (2016) 012060. [9] Q. Li, J. Shen, L. Qin, S. Gao, J. Alloys Compd. 691 (2017) 997-1004. [10] R. Mehrabian, M. Keane, M. Flemings, Metall. Mater. Trans. B 1 (1970) 1209-1220. [11] P.K. Sung, D.R. Poirier, S.D. Felicelli, Metall. Mater. Trans. A 32 (2001) 202-207. [12] P. Auburtin, T. Wang, S. Cockcroft, A. Mitchell, Metall. Mater. Trans. B 31 (2000) 801-811. [13] W.H. Yang, J.J. Debarbadillo, K. Morita, T. Suzuki, W. Chen, K.M. Chang, JOM 56 (2004) 56-61. [14] T.M. Pollock, W.H. Murphy, Metall. Mater. Trans. A 27 (1996) 1081-1094. [15] L. Qin, J. Shen, G. Yang, Q. Li, Z. Shang, Mater. Des. 116 (2017) 565-576. [16] Q. Li, J. Shen, L. Qin, Y. Xiong, Mater. Charact. 130 (2017) 139-148. Figure captions Fig. 1. The relationship of fluid flow and crystal growth during the vertical directional solidification with a concaved solidification interface. Fig. 2. Initiation positions of freckles under the different conditions [9]. Fig. 3. Initiation positions of freckles. (a and c) Experimental results [9, 16], (b and d) predictive results. (a and b) without graphite block, (c and d) with graphite block. Fig. 4. Locations of freckles in dummy blade. (a) Predictive result, (b) (c) (d) experimental results.
8
1. A method was proposed to predict where freckle may appear on a real casting. 2. Prediction method takes the concaved solidification interface into account. 3. Prediction method is based on the relationship of fluid flow and crystal growth.
9
S0167-577X(18)30907-8 https://doi.org/10.1016/j.matlet.2018.06.002 MLBLUE 24442
To appear in:
Materials Letters
Received Date: Accepted Date:
14 May 2018 2 June 2018
Please cite this article as: Q. Li, J. Shen, Y. Xiong, L. Qin, X. Yue, Prediction of freckle formation in directionally solidified CMSX-4 superalloy, Materials Letters (2018), doi: https://doi.org/10.1016/j.matlet.2018.06.002
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.
Prediction of freckle formation in directionally solidified CMSX-4 superalloy Qiudong Li, Jun Shen*, Yilong Xiong, Ling Qin, Xiao’an Yue State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China ABSTRACT Freckle defects appearing on the industrial gas turbine blade reduce the high temperature mechanical properties. It is necessary to predict the freckle formation on the castings before the directional solidification. In this paper, the relationship of fluid flow and crystal growth during the vertical directional solidification was analysed. Based on the analysis, a simple method considering the solidification conditions and concaved solidification interface was proposed to predict the freckle formation. The method was verified with specimens and dummy blade under the experimental environments. The validation results show that the method can predict where the freckle may appear on a casting with a large size and complex shape for directionally solidified CMSX-4 superalloy. Keywords: Solidification; Defects; Metals and alloys; Freckle. 1. Introduction Power generation mode based on the industry gas turbine for its high efficiency and less pollution to the environments is favored. However, the wide application is limited by the production of single crystal or directionally solidified blades for the increasing freckling tendency. Freckle defects is caused by the thermal solute convection in the mushy zone [1-5], and reduces the high temperature mechanical properties. Thus, before the production of castings, it is necessary to find a way to predict freckle
*
Corresponding authors. E-mail address: [email protected] (J. Shen). 1
formation so as to take effective measures to suppress freckles. So far, the methods [3, 6, 7] based on the Rayleigh number taking alloy composition and solidification parameter into account can predict the freckle formation well. However, the precise prediction depends on the simulations coupling with the thermal field, solute field, and fluid field. The works of simulations are huge, the specimens used in the simulations are usually simple, and the specimen sizes are far less than the real castings. Therefore, the prediction methods are difficult to be widely applied. Recently, Pustal et al. [8] proposed a method which can predict where the freckles will appear on the specimen with a varying cross-section. But a number of parameters are needed and the process is complex. The aim of this paper is to find a simple way to predict where the freckles may appear on the castings with a large size and complex shape. The previous experimental results were employed to validate the prediction method. Then, the method was applied to predict freckle formation in directionally solidified specimen and dummy blade. 2. Development of model
Fig. 1. The relationship of fluid flow and crystal growth during the vertical directional solidification with a concaved solidification interface.
2
During the directional solidification of CMSX-4 superalloy, it is widely accepted that the thermal solute convection will appear. Meanwhile, for the less lateral heat dissipation, the solidification interface is usually concaved with an angle θ as shown in Fig. 1. According to the investigations of Copley et al. [1] and Li et al. [9], due to the tilted solidification interface, a force arising from the density difference in the horizontal direction will act on the interdendritic liquid. Thus, the interdendritic liquid will have a tendency to flow towards the surface as shown in Fig. 1. α is the angle between the flow of the interdendritic liquid with the solidification interface. Combing with the Fig. 1, Eq. (1) can be obtained from Flemings’ criterion [10] predicting freckle formation qualitatively. V cos V T V T 2 = V sin 1 R R R T
(1)
Where V is the flow velocity of the interdendritic liquid, and given by the Darcy’s law as shown in Eq. (2); T is the thermal gradient; ε is the cooling rate; and R is the growth speed of dendrite.
g cos K g K g K 2 V sin fL fL fL
(2)
Inserting Eq. (2) into Eq. (1), Eq. (3) is derived.
V T
g K sin 2 1 fL R
(3)
Where K, the permeability in the mushy zone, can be represented by the liquid fraction fL and primary dendrite arms λ1 as shown in Eq. (4) [11]. K K f L K 1
(4)
Then, Eq. (5) can be obtained by inserting Eq. (4) into Eq. (3).
V T
g
K f L K 1 sin 2 1 fL
R
3
(5)
For the Eq. (5),
, the alloying effect, the solidification conditions and the slope
effect are taken into account. The aim of this paper is to find a simple way to prediction the freckle formation, and the solidification behavior and thermophysical properties of the alloys are not fully understood. Therefore, some simplifications were done. One of the simplifications is to neglect the gravitational effect and alloying effect for the same alloy and gravity. The second one is to neglect the angle α, for the α between the flow of the interdendritic liquid with the solidification interface is not understood so far [12]. And it is reasonable to assume the angle be smaller than θ [13]. Accordingly, the Eq. (5) can be simplified to the Eq. (6) which takes the solidification conditions and the concaved solidification interface into account.
V T
K 1 sin 2 cons tan t R
(6)
For the superalloy, the λ1 can be represented by Eq. (7) [14]. Thus, the Eq. (8) for predicting freckle formation is obtained by inserting Eq. (7) into Eq. (6).
1 G 1/2 R1/4
(7)
V T
(8)
I
G 1 R 1.5 sin 2 cons tan t
For a directionally solidified casting, where there is a large value I, there will be a larger freckling tendency. The parameters such as thermal gradient G, the growth speed of dendrite R, the angle θ between the solidification interface and horizontal, and the value I can be easily obtained by the commercial finite element software ProCAST. The detailed simulations with the ProCAST have been shown in the previous investigations [15, 16] of the authors. 3. Results and discussions 3.1 Validation of prediction method
4
Fig. 2. Initiation positions of freckles under the different conditions [9].
Fig. 3. Initiation positions of freckles. (a and c) Experimental results [9, 16], (b and d) predictive results. (a and b) without graphite block, (c and d) with graphite block. In order to verify the prediction method proposed, the experimental results in the previous investigations of [9, 16] the authors was employed. All the experiments was carried out in the conventional Bridgman furnace under the various experimental conditions (including withdrawal rate, heater temperature, and specimen size). The initiation positions of freckles are shown in Fig. 2 [9]. It is evident that the freckles usually initiate in the region about 2-4 mm above the platform. One of the experimental results (in Fig. 3a) is taken as the example, and the corresponding predictive result is shown in Fig. 3(b). The predictive result shows that freckles are more likely to appear on the bottom of platform
5
A. The actual initiation position is about 2-4 mm above the predictive one. This also indicates that the prediction method is not applicable to the freckle prediction in the region where the height is not enough. This is also the reason why the predictive results is not consistent with the experiment results in top region B (in Fig. 3b) of the specimen. Thus, the prediction method proposed in this paper can predict where the freckles will appear on the castings expect the regions with a not enough height. 3.2 Application of prediction method In the study [16] of authors, a graphite block was used to improve the local cooling condition, and the freckles was suppressed absolutely (in Fig. 3c). The corresponding predictive result is shown in Fig. 3(d). The value I is evidently reduced in the platform, meaning that the freckling tendency will reduced. It is consistent with the experimental result shown in Fig. 3c. In addition, due to the shortcoming of the prediction method as discussed above, the freckles will not appear on the top region of the specimen, regardless of the large value I. In order to verify whether the prediction method proposed can be used to predict freckle formation in the actual blade, a dummy blade was designed and directionally solidified. The predictive result and experimental result were shown in Fig. 4. As the predictive result shown in Fig. 4(a), the freckles will be more likely to appear in the region C and region D of the dummy blade. It is consistent with the experimental result shown in Fig. 4(b), Fig. 4(c) and Fig. 4(d). Thereby, the prediction method proposed in this study can be applied to predict freckle formation in the casting with a large size and complex shape.
6
Fig. 4. Locations of freckles in dummy blade. (a) Predictive result, (b) (c) (d) experimental results. 4. Conclusions In this paper, the relationship of fluid flow and crystal growth during the vertical directional solidification with a concaved solidification interface was analysed. And then, a method considering the solidification conditions and concaved solidification interface was obtained to predict the freckle formation. The validation results show that the method can be applied to predict where the freckle may appear on a casting with a large size and complex shape. Acknowledgements This work was supported by the National Basic Research Program of China [Grant No.2013CB035703]. References [1] S.M. Copley, A.F. Giamei, S.M. Johnson, M.F. Hornbecker, Metall. Trans. 1 (1970) 2193-2204. [2] S. Boden, S. Eckert, G. Gerbeth, Mater. Lett. 64 (2010) 1340-1343. [3] L. Yuan, P.D. Lee, Acta Mater. 60 (2012) 4917-4926. [4] A. Saad, C.A. Gandin, M. Bellet, N. Shevchenko, S. Eckert, Metall. Mater. Trans. A 46 (2015) 4886-4897. [5] F. Wang, D. Ma, J. Zhang, A. Bührig-Polaczek, J. Alloys Compd. 620 (2015) 24-30.
7
[6] W. Yang, K.M. Chang, W. Chen, S. Mannan, J. DeBarbadillo, Metall. Mater. Trans. A 32 (2001) 397-406. [7] C. Beckermann, J.P. Gu, W.J. Boettinger, Metall. Mater. Trans. A 31 (2000) 2545-2557. [8] B. Pustal, D. Ma, N. Warnken, E. Subasic, J. Jakumeit, A. Bührig-Polaczek, IOP Conf. Ser.: Mater. Sci. Eng. 117 (2016) 012060. [9] Q. Li, J. Shen, L. Qin, S. Gao, J. Alloys Compd. 691 (2017) 997-1004. [10] R. Mehrabian, M. Keane, M. Flemings, Metall. Mater. Trans. B 1 (1970) 1209-1220. [11] P.K. Sung, D.R. Poirier, S.D. Felicelli, Metall. Mater. Trans. A 32 (2001) 202-207. [12] P. Auburtin, T. Wang, S. Cockcroft, A. Mitchell, Metall. Mater. Trans. B 31 (2000) 801-811. [13] W.H. Yang, J.J. Debarbadillo, K. Morita, T. Suzuki, W. Chen, K.M. Chang, JOM 56 (2004) 56-61. [14] T.M. Pollock, W.H. Murphy, Metall. Mater. Trans. A 27 (1996) 1081-1094. [15] L. Qin, J. Shen, G. Yang, Q. Li, Z. Shang, Mater. Des. 116 (2017) 565-576. [16] Q. Li, J. Shen, L. Qin, Y. Xiong, Mater. Charact. 130 (2017) 139-148. Figure captions Fig. 1. The relationship of fluid flow and crystal growth during the vertical directional solidification with a concaved solidification interface. Fig. 2. Initiation positions of freckles under the different conditions [9]. Fig. 3. Initiation positions of freckles. (a and c) Experimental results [9, 16], (b and d) predictive results. (a and b) without graphite block, (c and d) with graphite block. Fig. 4. Locations of freckles in dummy blade. (a) Predictive result, (b) (c) (d) experimental results.
8
1. A method was proposed to predict where freckle may appear on a real casting. 2. Prediction method takes the concaved solidification interface into account. 3. Prediction method is based on the relationship of fluid flow and crystal growth.
9