49 12 Vol.49 No  ACTA METALLURGICA SINICA Dec pp II.

49 12 Vol.49 No.12 2013  12 1521 1531 ACTA METALLURGICA SINICA Dec. 2013 pp.1521 1531 ÆÅ ÍÏ Ð µ II. Þ 1) 1) ÅØ 2) 1) «1) ÔÚ 1) 1) Ô Å ÈÉ» ë̺, 100084 2) Ï Ü¹ ( Ñ) Û ÐËÁ, Ï 110043 Ä Î Î ÑÖ. ÞÄ EBSD Í, Î µ Ç Î, Î Ø Ô ³Ù Î µø. Î Î À Ö : µ ÉÑÖÔ ÑÖ. Á ¹ÊÈ ± Î Î ÑÖ. Ö (MCA), ± Î µ Ç Îɾ. Ä Î Ì Î Ø È Æ Î µ, ½ Í É¾ ±, Ù Ñ. Þ Í Ä, Ð ± Î¾Ú Ò ÑÖ, Î. Đ, ξÚ, Î Ø, EBSD ÒÃÅ TG132 ÆÈÜ A Æ Û 0412 1961(2013)12 1521 11 SIMULATION AND EXPERIMENTAL STUDIES ON GRAIN SELECTION BEHAVIOR OF SINGLE CRYSTAL SUPERALLOY II. Spiral Part ZHANG Hang 1), XU Qingyan 1), SUN Changbo 2), QI Xiang 1), TANG Ning 1), LIU Baicheng 1) 1) Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 2) Shenyang Liming Aero Engine Group Corporation Ltd., Shenyang 110043 Correspondent: XU Qingyan, associate professor, Tel: (010)62795482, E-mail: scjxqy@tsinghua.edu.cn Supported by National Basic Research Program of China (No.2011CB706801), National Natural Science Foundation of China (No.51171089), National Science and Technology Major Project (Nos.2011ZX04014 052 and 2012ZX04012 011) Manuscript received 2013 04 25, in revised form 2013 08 02 ABSTRACT The spiral selector is the key part for producing single crystal (SX) blades and ensures the integrity of crystal, which mainly includes starter block and spiral part. In this work, the influence of spiral part on the grain selection process was studied. Both of the metallography results and EBSD results proved that the prior location and the special orientation of the second dendrite arms were important for the grains competitive growth during the directional solidification process. Based on the experimental results, two geometrical restrict mechanisms of grain selection were proposed. They were the competitive stimulating effect on the second dendrite arms in horizontal direction, which was resulted from the spiral arc shape, and the growing blocking effect on the primary dendrites in vertical direction, which was resulted from the take off angle of the spiral part. These models could successfully explain the grain selecting effects of the spiral part. The modified cellular automaton * Ä Äº 2011CB706801, Ý À Ä 51171089, ÄÕ 2011ZX04014 052 Ô 2012ZX04012 011 Í ¼Þ : 2013 04 25, ¼Þ : 2013 08 02 Ñ ¹Á : Ð,, 1985 Ã, ² DOI: 10.3724/SP.J.1037.2013.00214

1522  49 (MCA) technology was used to simulate the grains competitive growth in spiral part. The changes of grains structure and orientation as the grain growing on were studied. The simulated and experimental results were compared and agreed well. Based on the simulated and experimental results, Influences of structural parameters on the grain selection behavior were proposed. The criteria for designing spiral part were also presented. KEY WORDS numerical simulation, grain selection behavior, grain orientation, EBSD Ç ÚÏ ² Î Ï Æ ÚÏ ¾. Ï Í Ó Ï² ÊµÓ ÂÏÚ ±. Ï Ê º º µºõ º Â Í [1], ² 4 Â Ï Ê Ö¼ ß Ï ( Ï Ï ). Ï Ý Ò Ï² µ. Ï, µ Ý Í Æ, µ Å. ËÄ À ËÛ Ï Å Å ¾. Ç Àß ³³ 90 Ä ß ßÄ», Å ßÇ [2,3] ºÏ È [4 6] ÚÅ Å [7,8]. Gandin Õ Rappaz [9 13] (CA) ÚÝ (FE) ¼ Ç Ï ÅĐ ¾ À, ¾Å» ProCAST Å Ç Þ. ØÅ [14 18] ²Ó Ç À Å ÇÒ,, [14 16,19,20] Ý Á (CA FD) ¼ Ç Ï ÅÕ ¾ À Æ. Ó Á± Ó Ö Ï Å. Carter [21] Å ²ºÏ ±Ù Å Ó. Esaka [22] À¾ Šݺ Ï Í ² ϲ Ó. Epishin [23] ² Ï Ï Ê ÏÊ ÎÅ. Seo [24] ProCAST À 3 Ï Ï Ï¾Đ ÎÊ ² Å. Ë [25,26] À ÚÆ É (EBSD) ξ ² Ï ÑÐÊ Å. Dai [27 29] ProCAST ÀÅ Í Ï, ¾Đ ÎÊ ², Æ ² Ï Ò. Jiang [30] ² Ni 3 Al ÚÅ Ï ÏÊ Å. Meng [31,32] ProCAST ² Ï Ê À Æ, ¾Đ Î Ê ². À [33] EBSD Î À Å Þ Ï È, ¾ Ï È «Ò Ï Ê. Å CA FD ¼, ÊÓ» ÚÏ Î Ç ÀÏ, ²ÚÏ Ï ÏÊ À Æ. EBSD Î, Å Ï Í Ù, Æ ² Ï Û Ó Ò, ¾ Ï. 1 Ì 1.1 Î «Ø Ï ÍÚ Û 3 Á : Ï Õ. Í Ó Ï² ¾, Ð 1 ˱. Ê Í : h s, d s, θ, d w., h s, d s Õ θ º Æ (1): h s = πd s tanθ (1) Ï Ï 2 Á, Ï Ï É ½Ó, È¾Ê Õ Ï, ÐÀ Ý ÐÙÙ ĐÞ Ë Ï ² ÈÊ ; Ì Ï ÈÊ Ð, Í ÕË È, ÐÀÝ 1 ÁÏ Ï Ï, Ý 2 Á ÁÏ, Ï Ï. Î Ï º 1 ˱. Ð 2 Û Ä 1 Î Ì Fig.1 Structure and designing parameters of spiral selector (φ diameter of starter block, h b height of starter block, h s pitch of spiral part, d s diameter of spiral part, θ take off angle, d w diameter of spiral line) Ý 1 ¹ λ Table 1 Structural parameters of spiral selectors (d w= 5 mm) Group h s, mm d s, mm θ, deg G1 14 8 29.1 G2 10 8 21.7 Note: θ can be calculated by Eq.(1)

12 : ØÍ ĐØõ Í ÍĐ Ð Ìà II. µ 1523 Ï Ð. Î È Ù Ï Ò Ù. EBSD ¼ Å Ï Ù. ² Ï Ê Å, Ü ¾ 90 Ù 1 Á, ¾ Zeiss (Axio Imager A1m) Å Ø Ê Å (OM) Å; Ì ¼² ÏÊ, ¾ JEOL 6301F Å» Æ Ê EBSD À.  РР3 ˱. Ï º 2 ˱. Ä 2 Î Fig.2 Molding pattern of the spiral selector (R c radius of chill, r m radius of casting mould) (a) molding pattern (top view) (b) picture of the wax pattern 1.2 Ç 1.2.1 Æ EBSD Û ÐÝ ÑÐ, Ê ß Ï Ù µ ±ß 15. ± Ù Ö Ï, µ Õ ± Ù Á Ï. Ð 4 Ë±Û Þ ¾ Î. ÚÐ 4b Ú», Ï ÈÊ, ; µöë ÈÕ Ï ±» ± È. É Ç ÏÊ, Ï ± Ê Þ ÈÖ, µöë ÈÕ Ó Ï Õ Ò ¼±, Ð 4c Õ d ˱. É Ç Ï Ê, ÐÀ Ý ÁÏ Æ, ÈÛÚÏ. Ð 5 Ë±Û EBSD Ï Ù Ë Ð. ß Ï ²ÀÐ,, Ð 5a ˱. ÜÏ ÈÊ, È Ï ÂÄ È, ÐÀ ÚÏ ¾ Á, Ð 5f. 1.2.2 Đ Ù Ü Ï Ï È Ï Ì È, Ð 4 Õ 5 ˱. Ð 6 Û ÈÏ È Ï. È ±È [100] Õ [010] È, Ù ºÏ ± È È, È. ÚÐ 6a Ú», Ï A ÕÏ B ±È [100] È, ± ±Ï Ñ µ,. ÜÂÏ ² È, 90 ¼Ð, Ï È Ð 6b ˱., Ï A ÕÏ B Ò ÝË Ö. Ï A È [100] ± È, µè [010] ±ßÄ È, ¾ÕÛ È. µï B [100] ± ß «µ È. ÚÐ 6 Ú», Ï A Ö Ë ÈÕ, µ Ý ÐÙµ, Ý«ßÏ ± È. µï B ÖË Ó, Ý Ý ÙµµÐÀ. Ú Å, Å Î EBSD Ù Ë Ú», ÊÔ Í, ÊÂÏ ±» È, µ² Ï Ê, ÕË Ï Ï. ÖË ÈÕ Ï Ý 2 ¹ ³Ñ Table 2 Corresponding table of height (distance between the top surface of starter block and the position where the corresponding section was cut) and sections in the spiral part (d w=5 mm) Section G1 Height, mm G2 S1 1 1 Ä 3 Fig.3 Schematic of the sections positions of the spiral part (S1 S6: the sections of different heights; h 1 h 6 : the corresponding heights of sections) S2 4 4 S3 7.5 6.5 S4 11 9 S5 14.5 11.5 S6 18 14

J 8 * P F g y = r } u ), d D _ 2Pr w lh v W k2. v l 5 v /,, P W, f% P *{ 1524 L F 49 i L[X^TW _Ij K. w *e jm d /,, P W AA W f A44 Q, j W Z 5$0%. l 7 w, Pr, P r {001} j+?!4fy 3 j1"u 4 G1 Fig.4 Micrographs of microstructures at different sections in spiral part of G1 (a) S1 (b) S2 (c) S3 (d) S4 (e) S5 (f) S6 L j+?!4f 3 V t"r k 5 G2 EBSD Fig.5 EBSD grains orientation images of different sections in spiral part of G2 (a) S1 (b) S2 (c) S3 (d) S4 (e) S5 (f) S6

12 \ k : t U B t K) =B U h U? 5 ;F } TK b II. ) = 1525 L +? OV D" O"U 6 Fig.6 Micrographs of extending growth at the lower edge of spiral part (a) S2 (b) S3 L 7 +? OV V3 k {001} Fig.7 Pole figures of {001} crystal face at upper edges and lower edges of spiral (TD transverse direction, RD rolling direction) W4 l&"dg. vbp_,, P ÆW[X jw ={, x{o S4 A4 `[Sw 1 IW. ), P ÆW[XjW =/, x{o S6 A4 O 1 IW. 2hvl 5f v/, {o S6 A4, `[1S vwk2. v <7 v/,, PZm _ W a* [X ns, ; *^ &Æ W [XL Y%{, P. 2 3T #/&h? Lf < VDg,, A4 Pq, D E_ : W,f% P, y>:7w a*f [X; rs, Pq, oe W P4{ C) :7 [X. & < Vb$R 3f D, `_, DWa IMYD W C. 2.1 %J Qm } m I I= S v 'i "ob W R {, ", luu# z 5# (z 15 #) ):=%, _ %{ 15, d5# W a* P., " RYns w`r s C 3, g)kr, [25] f% a* P, D vw A. w F:EY 5# W, f% a * P qd C, &, "R3,y</jo, l 8 S%, ^F+i.%& y br 3z# [g } Æ ~ A4 & %. O Yj W F, x W k W " q S a * P }, R j " y_ AAW m. &'W lu P 5# [001] z 5# ):= %, w ^, f% ( [010] q [100] 5#) 7 7 Q. &' W & < P2 R, ", l 8b F A A4. rs, P W P [010] q [100] 5#, f% o!{l P, w * v{ s D U C, : 7 W, f% P 4 { C. &Ij W F/ W a* P. W, q /, f% a * P. x W &< P,, 2 Y 90 0}, rs, P W,f%Z 7 P, W Yn*r, l 8b S% B A4F W q. ^FW MrS, Pq, DE, ^W Ynl r. RY jw: _54W rs, Pq, DE, 8Y#e N P=% h v P{oOYH4eP, j) a* PF f,u);

1526  49 Ä 8 Î µ Ç Ü Ò Fig.8 2D projected schematic diagrams of grains second dendrite arm competition growth in spiral part (a) the positions of sections (b) schematic of grain competition Ï ÈÖ ºÏ (d w ), «ÌÖË Ó Õ È Ï È ² È, Ý Ï È Ý Ùµ. Ë Ï Ò Ö. É Ç Ê, Ï ² È, µï ÈÕÛ Ï Õ ÍË «. Ü Èß ÓÐ 8b C, Ï ÕÛ È. µ Ó Ï ÈË. ʵÜÏ ² ÈÓßÐ 8b D, Ï Ú Á, µ½ëúï ¾. ºËÉ ¹ Ê ½ ÊÏ ± È. º ÖË ÈÕ Ï È Ý Ùµ, Å ÈÛÐÀ ÚÏ ¾. º, Ï ±Ù Ð Í Ó Ï Ï Ã, º ² Ý Î Õ Æ. 2.2 ±Â ÉÑÐ Ñ II «Ë ÚÉÑÓ Ï Ê, ÊÏ È, ² Ï Ò, Ï Û Âß µº Ï [22]. Ð 9 Û Ï Ï Ý± Ð. Ü Ö (θ 1 ), È H, Ï ÕÏ. Ð 9b ˱, Ü ¼±Û θ 2, È H, Ï Ñ, Ç Ï Ï² È. Ü ¼±Û θ 3, Ä 9 θ 1 < θ 2 < θ 3 ÏÑÖ Fig.9 Schematic diagrams of geometry restricting and obsoleting effect of spiral take off angle (θ 1, θ 2, θ 3 different take off angles; H a certain growth height; h the height that grains were eliminated by competition growth; a the width of growth passageway in 2D) (a) inclined growing channel with the angle of θ 1 (b) inclined growing channel with the angle of θ 2 (c) inclined growing channel with the angle of θ 3 È H, Ï Ñ, Ï È, º ² È. Ð 9c, Ü È ß Ó h(h < H), Ï, Ç Ï Ï² È. Ú ÅÚ», Ê Đ ²À µï ² a. ² ÝÑÐ, ܺ H > a tanθ, Ò ß»Å, ÇÝÖË È Ï ( Ï ). ² ± Ý, Ðܺ h s > H; Û Ú ß Æ Í Ç Ï Å µ

12 : ØÍ ĐØõ Í ÍĐ Ð Ìà II. µ 1527 Ý ºÏ È Ä ÝËÁ, Ó Ï². Ë Ê h s Ð Öß d w tanθ, º ËÉ ÚÏ ¾. ± Ò Ï È ÁÅ. º ¹ (θ) Đ (h s ) (d w ) ¼ Ʋ ϲ Ó ; Ï Ý ÐÙµ ( Ë È Ï ) Ï ¾. ºËÉ ¹ Ð 5 Đ 7 ˱ ÈÏ È Ï. Ë, ± ÊÒ Õ ± Ò Ï ÁÅ. ¹ Ê Í ² ºÏ ± È ÊÒ ²ºÏ ± Ò. ± Ï ÂÒ, Ú (d s ) (θ) (h s ) (d w ) Ó Ï². 2.3 Î ±¼³ Ð º ÇÒ ¹ ¼ (MCA), Õ Ï È ÕÅ, ² Ï ÏÊ Æ À. ÏÒ Ê Û Í, Ü Ø ¾ À Ò Ú ½Ô Ï ¾. Ç Ï ¾Ê CA ºÚ (2) Ê : Γ τ=1 ζ t i,j,k = x=t, T,C,V... f(x t i,j,k ) f t τ t (ζ t n t i l,j m,k n,l [ L,L], m [ M,M],n [ N,N]) (2) (2), ζi,j,k t Û t Û (i, j, k) Ú Î ; f(x) Û t Û (i, j, k) Ú Û CA Ë ; x t i,j,k, Ú Û T( ), T( ), C(Đ É ), V( ) ; Γ º± Ò Ö±; L, M, N º±Ý Ò Ö±; Γ, L, M, N Û¹. ²ßÝ Á (FD), ¹ Ú ÒÛ, Ψ ÛÖÚ Ý. Ψ = L+M +N (3) (3), Ü Ψ 1, ËÒ Û von Neumann º ; Ü Ψ 2, ËÒ Û º ; Ψ 3, ËÒ ÛËÝ. CA º  Æ, µ Ú (3) ÚÐË Ü. δl Û Ú Ý È, À Æ Õ Ë Ý Ë Ò (Ψ 3) ÑÐ, Ø Ò È l(ψ) º : l(ψ) 3 δl (4) l(ψ) λ 1 (5), λ 1 ÛºÏ ±. Ä Å, Õ Í, Ú Ò ½Ô Ï Ï ¾. À Ø Ò È Ðº (5). µ À Ú ÈËÂÛ δl λ 1 /3. ± Ç Ï ºÏ Ñ λ 1 «Û 0.3 mm [34], Å º Ï Ñ Û 0.32 mm ( Ð 4 ˱). À Ï È Ï, Ú Ý È δl «ÙÛ 10 4 m. 3 Ì» 3.1 Î ±ÂÐ Ù Å ² Ï Ï ÈÊ À Æ. À Ø ÖÚƼ, Å Ú ÒÛ 0.6 mm 0.6 mm 0.6 mm, Ø ¾ Æ Ú ÒÛ 0.15 mm 0.15 mm 0.15 mm. Û ÂÅ ÚÏ ÚÅ DD6. À º 3 ˱. Ð 10 Û Þ Ï Í À. Ð Ï ÏĐÏ È I È Ï Å. ÐÀÖË È Ï È, ½ËÚÏ ¾. Ð 5 ÕÐ 10 Ú Ô, À ½Ô ± Ï È Ï, µ Î Ú Ð ½Ô ºÏ ½½, Ï À ± È ; À Æ ÏÐ ½Ô Ï, Ï Î È Ï. Ð 11 Û Ï Ù Ë Ð. Ð Ú Ô, ÜÏ Ê, Ï [001] Ù Đ z µ ѱ ß 15, Ü Ð Öß 14.5 mm, µ Ôß 0, Ï Ù Ú Ó. 3.2 Î ßÀ ± Ê ½ À ² Í Đ ÏÒ Ê Å. ÚÐ 10 ÕÐ 11 Ú», Ê Ï, Ï [001] Ù Đ z (Þ ½ ) µ 15 Ý 3 DD6 ÛÆ ß [25,35] Table 3 Thermophysical parameters of DD6 superalloy [25,35] Parameter Value Liquidus, K 1672 Solidus, K 1615 Specific heat, kj/(kg K) 0.773 Density, kg/m 3 8780 Latent heat, kj/kg 99

1528  49 Ä 10 G1 Ý Î Ì Fig.10 Simulation results of grain structure of different sections in spiral part of G1 (a) S1 (b) S2 (c) S3 (d) S4 (e) S5 (f) S6 Ý 4 Á Ç ¹ λ Table 4 Structure parameters of spiral selectors for simulation calculation (d w=5 mm, h s=14 mm) Ä 11 Ý Î [001] Ø z Fig.11 Simulation results of angles between [001] orientation and z direction of some sections in spiral part (a) S1 (b) S3 (c) S5. Ï ÓÝ 2 : (1) Æ ÚÏ Ù Đ z µ ±ß 15 ; (2) Æ ÚÏ Ð Í ( 1 2 h s ). ² Ó (1), Ú Ï Å Ú», Ü Ç Ú, Ê Ï Ú¹. Ü [001] Ù º, [010] Õ [100] ± ËÛÓ Ï Ï ¾, Æ Ú Ï Ð. º 4 à À Æ Ï Í, Ï Ú Í. Õ ± É, ²º ¾ ºÓ 10 Æ, Æ Ú Ï ÚÏÙ. Ð 12 ĐÐ 13 ¼Û M2 Í Ï Ç Ï Å Đ Ö Ð. ÚÐÚ», Group d s, mm θ, deg M1 8 29.1 M2 10 24.7 M3 12 20.4 M4 14 17.7 Å Ú Ç ÝÞ. µð 13c, Đ Ö, ¾ Å½Æ Ö, Ð Ü Ú˱. ²Â ŽÆÖ ÆÏ½Ó È, «ßÚÏ Ï Ï. ²ÂÖ ĐÇ ÃÝ, Í Ä. µê Úß Ú Õ ±, ËÚ Þ Á; Ö ²Ö, Ë. µ Ú Õ ± «ß Ï Ï. ÚÏ ¾Û, Ì ¼± Ú. Ð 14 Û M2 Ç Ï ¾ À Æ. Ð ²ÐÃ Ç Û 30%, 50%, 65%Õ 75% ¾, ÜÇ Öß 50%, Ï ÈßÓ, Ó ± È Ï. Ð 14c Ú½, ÖË Ï È Ý Ùµ, ʵ Ì

12 : ØÍ ĐØõ Í ÍĐ Ð Ìà II. µ 1529 Ä 12 M2 Æ Ä Å Fig.12 Simulation results of directional solidification temperature fields of M2 group (f s solidification ratio, t time) (a) f s=30%, t=630 s (b) f s=50%, t=840 s (c) f s=65%, t=1200 s (d) f s=75%, t=1350 s Ä 14 M2 Æ ½ Å Fig.14 Simulation results of directional solidification microstructure growth of M2 group (a) f s=30%, t=630 s (b) f s=50%, t=840 s (c) f s=65%, t=1200 s (d) f s=75%, t=1350 s Ä 13 M2 Æ Î Õ µ Fig.13 Changes of mushy zones during the directional solidification process of M2 group (a) f s=30%, t=630 s (c) f s=65%, t=1200 s (b) f s=50%, t=840 s (d) f s=75%, t=1350 s Ï, ¾ÐÀ ÈËÚÏ ¾. ² d s Ç ¾ À Æ Ê ², Ð 15 ˱. ÜÏ Ê Ð, Û d s, Ï ÈÑÐÂ, ÚÏ ¾ Ð. Ð Ú Ô, Ü d s Ö, ÚÏ½Ë ÐÉ. Õ Ï ±É, ² d s Ï Ê À Æ, ¾ ÅÚÏ½Ë Ð Õ d s Æ. Ð 16 ÛÚÏ½Ë Ð Å Ð. Ð ½,, ½ ß d s /2. ½ ¾Ù ÈÜ : Ü Ï ÚÏ Ð, ÆÐ Ð ÛÚÏ½Ë ; Ä ÚÏ½Ë Õ Ü Â Î Ð 16 ²Ð, µ½ëð Ë ± ¾Ù. ½ º±, Ü d s, Ú Ï½Ë Ð (²ÐÚÏ½Ë ) ÝË ; ¾Ù º±, d s Ï ÚÏ Ð Ú ¾Ù. Ð 16 Ú Ô, ÚÏ ¾ ½ËÐ Ý : Ä 15 Î Æ ½ Å Fig.15 The simulation results of directional solidification microstructure growth of spiral selector with different parameters (a) d s=8 mm (c) d s=12 mm (b) d s=10 mm (d) d s=14 mm (1) d s Ö, ÚÏ½Ë ¼±, ²ÐÐ. Ü d s Ú 8 mm Ö 14 mm, ÚÏ½Ë Ñ Ú 314.9 (²Ð Û 12.2 mm) 204.6 (²Ð Û 8.0 mm). Ð 17 ÛÚÏ½Ë Ñ Đ d s ÆÐ. (1) Ë Å : h s, Ü d s Ö, Ä (1), θ ¼±. Ä Ï È I, d s ÖÝ«ß ÊÏ ± È, Ï ß, ÚÏ½Ë Ð ;, Ä Ï È II, θ ¼±, Ò, ÚÏ½Ë Ð., h s, Ö d s ±¼± θ, ÈÒ, ÚÏ½Ë Ð. (2) d s Ö, ÚÏ½Ë ¾Ù. Ü d s Ú 8 mm Ö 14 mm, ÚÏ½Ë ¾ÙÚ 93.4 Ö 155.3, Ð 16 ˱. µ, d s Ö ÚÏ½Ë Ð Á. (2) Ë Å : ÚÏ È

1530  49 Ä 16 ÙÎ¼Ê Fig.16 Schematic of height of single crystal formed (h s= Spiral angle, deg 360 315 270 225 14 mm, d w=5 mm) 14.0 12.2 10.5 180 7 8 9 10 11 12 13 14 7.0 15 d s, mm Ä 17 ÙÎ¼Ê Ð d s Fig.17 Relationship between d s and the single crystal average appearing height I Õ II ÅÚ», Ï Ùµ Ï ÐÙµÕÏ ±Ù Ùµ Ú. Ü d s Ö, ± ÊÒ ( I), Ý ±Ù Ù µ Ï Ú ßÄ «ÌÏ ¾ нËÚÏ ¾;, ± Ò ( II), ÝÐÙµ Ï Ú ßÄ È¾ Ð½Ë ÚÏ ¾. Â Ò É Ñ, Ï È É, µúï½ë ¾Ù. ½¼, Ü d s ±,  º Ò ¼, Ý Ý ± ÈÙµÕ Ð Ù µ Ï, Ú ÌÏ, ½ËÚÏ ¾, 8.7 Height, mm Ï Ï É, ÚÏ½Ë ¾Ù. 4 ¾ (1) EBSD Å Î, Æ Ï Ð Ï Í Ï Ù, Å Ï Ï Ï È Û, ÝÐÙµÕÙ Ùµ Ï Å. Ä Î, Ï È ÁÅ, ¹ ± ÊÒ ( I) Õ ± Ò ( II) Ê ÇÒ. (2) ßÏ È Ê Å, Ú À. ² Ï Ê À Æ, Æ Ç Ï Ç Å Đ Ö ¾. Å Å, Í Ú Þ, Ú «ß ÚÏ ¾., Ö À Æ, ²ÚÏ½Ë Ð Ó. ÚÏ È,, ÏÒ, ÚÏ½Ë Ð, Ú Ü¼± Ú. Û Ý Ï Ùµ É, Ï Ú ½Ëо٠Ö. ± Ð ÚÕ ± Ó. Þ ÆÈ [1] Goulette M J, Spilling P D, Arthey R P. In: Kortovich C S, Bricknell R H, eds., Superalloys 1984, Warrendale, PA: TMS, 1984: 167 [2] Kurz W, Fisher D J, translated by Mao X M, Bao G Q. Fundamentals of Solidification. Xi an: Northwestern Polytechnical University Press, 1987: 20 (Kurz W, Fisher D J Ë, ¼,. Æ. «: «Æ ÕÀ Æ, 1987: 20) [3] Glicksman M E. Principles of Solidification an Introduction to Modern Casting and Crystal Growth Concepts. New York: Springer Science Business Media, 2011: 305 [4] Kurz W, Fisher D J. Acta Mater, 1981; 29: 11 [5] Kurz W, Giovanola B, Trivedi R. Acta Metall, 1986; 34: 823 [6] Oldfield W. Mater Sci Eng, 1973; 11: 211 [7] Reed R C. The Superalloys Fundamentals and Applications. Cambridge, UK: Cambridge University Press, 2006: 121 [8] Shi C X, Zhong Z Y. Acta Metall Sin, 2010; 46: 1281 ( Ã, Æ Ó. Ä À, 2010; 46: 1281) [9] Gandin C A, Rappaz M, Tintillier R. Metall Mater Trans, 1994; 25A: 629 [10] Gandin C A, Rappaz M. Acta Mater, 1997; 45: 2187 [11] Gandin C A, Rappaz M. Acta Metall Mater, 1994; 42: 2233 [12] Gandin C A, Desbiolles J L, Rappaz M, Thevoz P. Metall Mater Trans, 1999; 30A: 3153 [13] Rappaz M, Gandin C A. Acta Metall Mater, 1993; 41: 345 [14] Tang N, Xu Q Y, Liu B C. Spec Cast Nonferrous Alloys, 2011; 31: 1028 ( È, ÒË, ÆÊ. ÁÎ Ü ÙÄ, 2011; 31: 1028) [15] Pan D, Xu Q Y, Liu B C. Acta Metall Sin, 2010; 46: 294 (Ê, ÒË, ÆÊ. Ä À, 2010; 46: 294) [16] Yu J, Xu Q Y, Cui K, Liu B C. Acta Metall Sin, 2007; 43: 731 (Þ, ÒË, Ð Õ, ÆÊ. Ä À, 2007; 43: 731) [17] Guo Y G, Li S M, Liu L, Fu H Z. Acta Metall Sin, 2008;

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