PHASE-FIELD MODELING OF γ PRECIPITATION IN MULTI-COMPONENT NI-BASE SUPERALLOYS

Transcription

1 PHASE-FIELD MODELING OF γ PRECIPITATION IN MULTI-COMPONENT NI-BASE SUPERALLOYS Tomonor Ktashma 1, De-Ha Png 1, Jncheng Wang, and Hrosh Harada 1 1 Natonal Insttute for Materals Scence; 1--1 Sengen, Tsukuba, Ibarak, , Japan Northwestern Polytechncal Unversty; No. 17 West Youy Road, X an, Shaanx, 71007, P.R. Chna Keywords: Phase-Feld Modelng, Mult Component, Phase Transformaton, Atom Probe Analyss. Abstract To smulate γ precptaton n mult-component N-base superalloys usng the phase-feld method, the Gbbs free energy of the γ and γ phases was lnked to the CALPHAD method. The free energy curve and phase equlbrum compostons n ths work showed good agreement wth results obtaned usng Thermo-Calc calculaton, ndcatng that the model was successfully coupled wth the CALPHAD method. Usng ths couplng method, the γ precptaton n a quaternary N-Al-Re- Ta and a thrd-generaton N-base superalloy TMS-75 systems were smulated. These one-dmensonal smulatons demonstrated the dffuson-controlled γ precptaton under local equlbrum wth precptaton nteractons. Accordng to our atom probe mcroanalyses, ther smulated composton evolutons were reasonable. Such a mcrostructure modelng technque can contrbute to alloy desgn, process desgn and even lfetme assessment of hgh-temperature turbne blades currently n servce. Introducton Modelng the mcrostructure evoluton of N-base superalloys s of consderable mportance for alloy desgn, process desgn and lfetme assessment of turbne components, e.g. n a vrtual turbne [1]. Phase-feld smulaton has been a powerful tool to predct mcrostructure evoluton n N-Al systems [-8]. Nevertheless, few reports have descrbed ts γ precptaton n multcomponent N-base superalloys, even though recent practcal Nbase superalloys ncorporate over 10 elements, such as Al, Cr, Mo, Re, and Ta [9-11]. The addton of refractory elements, especally Re, confers sold soluton strengthenng at hgh temperature. However, the small dffusvty of such refractory elements renders t dffcult to predct the elemental dstrbutons n γ and γ phases and the sze dstrbuton of γ precptates at the thermal equlbrum state. Therefore, to enable predcton of mcrostructure morphology n mult-component superalloys, development of a knetc-modelng technque for multcomponent systems s of consderable mportance. Dffuson Controlled Transformaton (DICTRA) software has been used to predct the growth rate of a smple-shaped precptate for the mult-component systems n one-dmensonal calculaton [1]. However, accompanyng the nteracton of precptates across the γ phase s dffcult because the nterface energes, such as nterphase doman boundary (IPB) and ant-phase boundary (APB) energes, are not taken nto account n the DICTRA. On the other hand, the phase-feld model s more attractve to predct complcated morphology evoluton because of the characterstcs of the so-called dffuse nterface model. One reason for the mult-component dffculty n phase-feld modelng s the complexty of dervng the chemcal-free-energy surface n the mult-component system, especally for order/dsorder phase transformaton. In phase-feld modelng, the chemcal free energy s an mportant factor that determnes the drvng force and path of the mcrostructure evoluton. As for a bnary N-Al superalloy system, some descrptons of the chemcal free energy functon have been reported, e.g., usng the Landau-type polynomal form, the KKS model, and a lnk to the CALPHAD method [-8]. However, few descrptons of the mult-component N-base superalloy have been proposed [13,14]. In ths study, a new phase-feld modelng technque that can address γ precptaton n mult-component superalloys was developed. Ths was acheved usng the sngle functon formalsm of γ / γ Gbbs free energy drectly n the CALPHAD method for the chemcal free energy n the phase-feld method. Usng ths couplng method, the γ precptaton for a quaternary N-Al-Ta-Re superalloy and a thrd-generaton N-base superalloy TMS-75 (N-6Al-1Co-3Cr-Mo-5Re-6Ta-6W-0.1Hf, wt%) were smulated n one dmenson. The temporal evoluton of element compostons durng the growth and coalescence of γ precptates was dscussed usng results of atom probe analyses. Modelng A thermodynamc descrpton of the γ (fcc-a1) and γ (L1 ) phases n the bnary N-Al system was obtaned by Ansara et al. usng a four-sublattce model [15]. The Gbbs energy of the γ phase was descrbed by separatng t nto dsordered and ordered contrbutons n a sngle functon to allow ndependent evaluaton of both γ and γ phase parameters. Zhu et al. [5] proposed a model drectly lnkng a phase-feld model wth exstng thermodynamc databases usng the CALPHAD method for the bnary N-Al system. Ths method was extended to mult-component systems usng the four-sublattce model. The ste fracton of each alloyng element (= Al, Co, Cr, Mo, N, Re, Ta and W) on each sublattce s s denoted as y (s). The molar Gbbs energy for the γ and γ phases s expressed usng the followng equatons [15,16]: 819

2 fcc,or,l1 G fcc = c G RT > c > k> m n c n= 0 c c c k L c fcc, L ln c ( c c ) fcc,,k n ΔG ord (s) ( y ) (s) L1 (s) L1 (s) ( y ) = ΔG ( y ) ΔG ( y = c ) ord G, (1) Δ, () Δ G (s) ( y ) = L1 (1) () (3) (4) L1 y y yk yl ΔGkl k l RT 4 s s > y (s) ln (s) ( y ) 1 (s) (s) n L1 y L, n = 0 (s) (s) n ( y y ) y, (3) where,, k and l can be Al, Co, Cr, Mo, Re, Ta, W and N on any of the sublattces. c s a mole-fracton of element, R s the gas constant and T s the temperature. G fcc s a molar Gbbs energy of element wth the structure of fcc. The frst four terms of Eq. (1) correspond to the Gbbs energy of the dsordered γ phase; ord Δ G (y (s) ) s the orderng energy of the γ phase as a functon of the ste fractons. Δ G L1 kl was expressed n terms of the nterchange bond energes (e.g., U between and atoms), as Δ G = U U U U U U a, (4) L1 kl k l k where a kl s a correcton varable for some compounds [16]. All varables n Eqs. (1), (3), and (4) are obtanable from the CALPHAD-type assessment [15-18]. Blavette et al. demonstrated by an atom probe study that the parttonng behavor between the N-ste and the Al-ste n the γ phase depends greatly on the alloyng elements [19]. Therefore, the order parameter of each element was newly ntroduced for the mult-component system. Accordng to the Landau-Lfshtz rule [5, 0, 1], the order parameter of four nterpenetratng smple cubc sublattces had three components that can be represented by the ste fracton n each sublattce. The order parameters and the composton for each element are defned as 1 3 (1) () (3) (4) ( y y y y ) 4c (1) () (3) (4) ( y y y y ) 4c (1) () (3) (4) ( y y y y ) 4c (1) () (3) (4) ( y y y y ) 4 η =, (5a) η =, (5b) η =, (5c) c =, (5d) where η (=1,, 3, = Al, Co, Cr, Mo, Re, Ta, W), c (= Al, Co, Cr, Mo, Re, Ta, W) respectvely ndcate the order parameter and the composton felds. By combnng Eqs. (1)-(5), the molar Gbbs energy of the γ and γ phases for the mult-component system can be descrbed usng the varables of the order parameter l kl kl and composton felds for elements Al, Co, Cr, Mo, Re, Ta, W and N. mult The total stress-free chemcal free energy F sys n the multcomponent system ncludes the local free energy densty and the nterface energy, gven as [] F mult sys V 1 V m G fcc,or,l1 α β ( c ) 3 = 1 ( ) η dv, (6) where V m s the molar volume, whch was assumed to be constant. In addton, α and β respectvely sgnfy the gradent energy coeffcents for the compostons and order parameters. For ths study, to retan smplcty, the composton-dependent elastc energy stemmng from the elastc nhomogenety s not ncluded. The temporal evoluton of the element compostons and order parameters are obtanable by solvng the followng equatons: c δf = M ~, (7) t δc = = Al, Co, Cr, Mo, Re, Ta, W, η δf = L, (8) t δη = Al, Co, Cr, Mo, Re, Ta, W, = 1,, 3 where M ~ s the so-called chemcal moblty wth N as the dependent speces, and L s the structural relaxaton coeffcent. The chemcal moblty M ~ for the γ phase s related to the atomc mobltes of the consttuent elements, as ( δl c )( δ l c ) M ~ = c M, (9) l l γ l γ where δ l and δ l are the Kronecker s delta and M l s obtanable from the moblty database [3, 4]. The chemcal moblty for the γ phase was assumed to be dentcal to that of the γ phase. As for parameter L, t was determned as M ~ AlAl=L a 0 /16 [5], such that the nterface mgraton velocty was manly controlled by the dffuson moblty, because the structural relaxaton was much faster than the dffuson, wth lattce parameter 10 a 0 = m. Assumng the gradent energy coeffcent α 16 to be zero, β = J m / mol for N-Al-Re-Ta system, 15 and β = J m / mol for TMS-75 were chosen by fttng the nterfacal energy to 10 mj m, whch was close to the expermental and smulated values reported n a N-Al system [7,6,7], although very few accurate expermental nterface energy data for bnary and mult-component N-base superalloy systems are avalable. The assumpton that the composton gradent coeffcent s zero was a smplfcaton ntroduced by Vathyanathan et al. [4]. A Sem-Implct-Fourer-Spectral- 80

3 Method [8] was used for numercal analyses wth a perodcal boundary condton. The grd number and grd sze were set respectvely to 56 and 0.5 nm. At the nucleaton stage, small cells of 3 nm dameter n the feld were transformed to γ phases wth the values of equlbrum order parameters after unform random values were generated and compared to a certan value. Expermental Procedures For ths study, TMS-75 alloy, a thrd-generaton N-base sngle crystal superalloy developed by the Natonal Insttute for Materals Scence (NIMS) Japan, was nvestgated usng atomprobe analyss n ths study. Its nomnal composton s N-6Al- 1Co-3Cr-Mo-5Re-6Ta-6W-0.1Hf n weght %, whereas N- 13.7Al-1.6Co-3.6Cr-1.3Mo-1.7Re-.1Ta-.0W-0.01Hf n atomc % [10,11]. Bar-shaped samples (10mm dameter, 10mm length) were cast nto sngle crystal form by drectonal soldfcaton wth the longtudnal axs wthn 5 o from the [100] pole n the standard stereographc trangle. One bar sample was soluton treated for 1 h at 1300 o C, then by 4 h at 130 o C n the argon gas; then ar-cooled. The soluton-treated bar sample was then machned nto two plate-type samples, whch were 0mm 9mm mm. Subsequently, they were aged at 1100 o C for 15 mn or 4 h n ar. They were then water quenched. To avod preparng atom-probe tps wth the oxdzed mcrostructure, the cross-secton mcrostructure of the heat-treated plate-type sample was observed usng scannng electron mcroscopy (SEM). The γ depleton and mcrostructure nhomogenety n a sample that was heat-treated at 1100 o C for 4 h were observed n the range of maxmum 30 μ m from the surface. Square rods of approxmately 0.mm 0.mm 10mm were cut from the bulk of the heat-treated sample wthout the oxdzed mcrostructure. These rods were electropolshed wth 5% perchlorc acd and 75% acetc acd to sharp needle-shaped specmens ntally, wth subsequent treatment n % perchlorc acd n butoxyethanol. Atom-probe analyses were performed at a tp temperature of about 50K under ultrahgh vacuum (< Pa) wth a pulse fracton of 0. and a pulse repetton rate of 1500 Hz. wth that of the Thermo-Calc calculaton, whch ndcates that the free energy surface n the mult-component system was successfully derved by lnkage to the CALPHAD method. Therefore, the drvng force and path of the mcrostructure evoluton are obtanable n the phase-feld method accordng to the CALPHAD method, even n a complex hgher-component system. Usng the free energy lnkng to the CALPHAD method, a onedmensonal smulaton for the γ precptaton of a N-16.5at% Al-1at%Re-at%Ta superalloy at 1100 o C was carred out as shown n Fg.. Ta and Re were rch n the γ and γ phases, respectvely. After nucle formed, the precptates were supersaturated wth Al of 0.19, as presented n Fg. (b). Fg. (c) shows that the supersaturaton then decreased contnuously. The local equlbrum of Re at the γ / γ nterface, as demonstrated by results of atom probe studes [9, 30], was confrmed n Fg. (c). In Fgs. (b) and (c), precptate B s closer to C than to A. However, precptates A and B subsequently merged and decreased the nterface energy, as presented n Fg. (d) because the doman of precptate A was dentcal to that of B, whereas those of B and C dffered, not formng an APB. The APB energy was usually hgh: twce as large as the IPB energy. Regardng the coalescence of precptates A and B, after two spkes of Re, denoted by D and E, came near each other, a narrow γ channel formed wth a supersaturated Re composton, whch pled up as a result of D and E, thereby promptng a hgher Re spke, presented as F n Fg. (d). Moreover, the small dffusvty of Re made the spke F decrease slowly n the γ phase. The phase compostons then gradually reached the equlbrum composton. The spke of the element composton accompaned by the precptate coalescence, such as that shown by F n Fg. (d), was probably common for alloyng elements, although the dffuson rate of the spke depended largely on the element dffusvty. Results and Dscusson Phase-Feld Smulaton of the N-Al-Re-Ta System Fgure 1 presents a comparson of the Gbbs energy usng the equlbrum order parameters obtaned under the condton of G η =0 (=Al, Ta, Re, =1,, 3), wth the result obtaned usng the Thermo-Calc calculaton of the total Gbbs free energy. Accordng to the result, the free energy of the γ phase was lower than that of the γ phase from to 0.18 of C Al. The free energy curve lnkng to the CALPHAD method agreed well Fgure 1 Comparson of free energy obtaned n ths work wth the calculated result obtaned usng Thermo-Calc software. 81

4 Fgure Temporal evoluton of Al, Re, and Ta composton profles n a N-16.5at% Al-1at%Re-at%Ta superalloy at 1100 o C. Co Cr Mo W Al Ta Re V f γ Calculaton (ths work) γ Observaton γ by Yokokawa et al.[11]. γ [10] Table 1 Comparson of the predcted and the observed γ and γ phase compostons of TMS-75 at 1100 o C. 8

5 In Fg. (f), the phase compostons at x=10nm n the γ phase and at x=115nm n the γ phase were N-18.4at%Al-0.47at%Re-.87at%Ta and N-13.8at%Al-1.70at%Re-0.79at%Ta, respectvely. These values agreed well wth the equlbrum compostons calculated usng Thermo-Calc software, whch were N-18.5at%Al-0.450at%Re-.86at%Ta for the γ phase and N- 13.8at%Al-1.77at%Re-0.79at%Ta for the γ phase. Consequently, the present model demonstrated γ precptaton wth the growth and nteracton of precptates n the quaternary system, by couplng wth thermodynamc descrpton n the CALPHAD method. In the next secton, a practcal alloy, TMS- 75, s smulated. Phase-Feld Smulaton and Atom Probe Analyss of TMS-75 A thrd-generaton N-base superalloy, TMS-75 contans Al, Co, Cr, Mo, Re, Ta, W, and Hf. Its nomnal composton s N-6Al- 1Co-3Cr-Mo-5Re-6Ta-6W-0.1Hf n weght %, and N-13.7Al- 1.6Co-3.6Cr-1.3Mo-1.7Re-.1Ta-.0W-0.01Hf n atomc % [10,11]. For smplfcaton, Hf was excluded from present calculatons. At frst, γ volume fracton, γ and γ phase compostons were compared between the calculated predcton and expermental observatons as shown n Table 1. Accordng to Murakumo et al.[10], the observed γ volume fracton of TMS-75 was about 0.55 at 1100 o C. On the other hand, the present CALPHAD predcted 0.51 of the volume fracton for ths alloy. Yokokawa et al. [11] measured the γ and γ phase compostons usng an electron probe x-ray mcroanalyzer (EPMA), followed by water quenchng after heat treatment at 1100 o C as shown n Table 1. Both the predcted and measured compostons and parttonng behavor show good agreement, even though the phase-equlbrum nformaton for hgher component systems are determned from the extrapolaton of bnary, ternary and quaternary systems n the CALPHAD method. The observed γ composton of Co s slghtly larger than the predcted one. W s preferred to partton nto much more γ phase n the calculated result. In ths alloy, Al and Ta were rch n the γ phases, whereas Co, Cr, Mo, Re, and W were rch n the γ phase. To nvestgate the temporal evoluton of alloyng element compostons expermentally, mcrostructural observaton and atom-probe mcroanalyses of TMS-75 were performed. Fgure 3 shows mcrostructures of TMS-75 after heat treatment at 1100 o C for 15 mn (a) or 4 h (b). In the alloy heat treated for 15 mn, fne sphercal γ precptates were observed because the growth of γ phases at ths stage was manly controlled by the ncreasng sotropc nterfacal energy. In the alloy that had been heat treated for 4 h depcted n Fg. 3(b), the morphology of grown γ precptates was algned cubodally along a certan orentaton. (b). In the alloy that was heat treated for 15 mn, small γ precptates, where the Al mole fracton s about 0., were easly detected. At the γ / γ nterface denoted by I, the local equlbrum was sgnfcantly observed, especally for Re. addton, Al and Ta n a narrow γ channel next to small precptates shown by arrows G and H n Fg. 4 (a) were depleted. On the other hand, Co and Cr and other refractory elements such as Mo, Re, and W supersaturated n ts γ phase. In Fg. 4(b), the local equlbrum was stll observable at the nterfaces ndcated by arrows of J and K because that the γ phase remaned under the growth process at ths stage,.e. the system had not reached a thermodynamc equlbrum state. These phenomena were smulated usng the phase-feld method. Fgure 5 shows snapshots of smulated temporal evoluton of alloyng element composton profles n TMS-75 at 1100 o C. At the ntal stage after nucleaton, Al n a narrow γ channel shown by an arrow L n Fg. 5(a) was depleted. The γ formers, such as Co, Cr, Mo, Re, and W, supersaturated n the γ phase. In the γ growth process presented n Fg. 5(b), almost all elements at the nterfaces of small precptates had almost equlbrum compostons, except for Re and W. On the other hand, at the nterface of γ and large γ phases shown by an arrow M, a local equlbrum was confrmed for all elements. In Fgs. 5(c) and 5(d), a small γ phase shrank and dsappeared, as shown by an arrow N. Such a so-called Ostwald-rpenng process was observed n the smulaton. Its Re profle was very characterstc, lke a spnnng top as presented n Fg. 5(c) because the Re s local equlbra at γ / γ nterfaces of both sdes of the precptate merged. Therefore, the smulated temporal evoluton of composton profles at the γ / γ nterface agreed well qualtatvely wth the expermental observatons, consderng the smplcty of ts mult-component model. In general, t s dffcult to detect, expermentally, such temporal evoluton of compostons durng γ coalescence and Ostwald-rpenng process. Such mult-component smulaton s necessary to predct the mcrostructure evoluton. It s noteworthy that the present smulated system ncorporated no composton-dependent elastc energy stemmng from the elastc nhomogenety for smplfcaton. Such elastc energy would affect mcrostructure morphology such as the γ precptate algnment, precptate dsperson, and precptate shapes. Moreover, the smulated system sze s smaller than the real one because of the computatonal scheme and model lmts. Therefore, the growth rate of the γ phase does not correspond quanttatvely to expermental results. Such ncorporaton of elastc energy effects and ncrease of the length scale are our next obectves. Nevertheless, t was concluded from results of ths study that the present modelng technque s very useful to desgn new alloys as well as process condtons. In Fgure 4 shows the composton profles obtaned usng atomprobe analyses for these alloys: heat-treated for 15 mn (a) or 4 h 83

6 (a) (b) Fgure 3 SEM mages of TMS-75 after heat treatment at 1100 o C for 15mn (a) or 4 h (b). Fgure 4 Composton profles of TMS-75 obtaned usng atom-probe analyses: heat treated at 1100 o C for 15mn (a) or for 4 h (b). 84

7 Fgure 5 Temporal evoluton of alloyng-element composton profles n TMS-75 at 1100 o C. 85

8 Conclusons New mult-component phase-feld modelng coupled wth the CALPHAD method was developed by adoptng the γ / γ sngle formalsm of the Gbbs free energy n the CALPHAD for the chemcal free energy n the phase-feld method. Usng ths couplng method, the γ phase precptaton n a quaternary N- Al-Re-Ta system and a thrd-generaton superalloy TMS-75 was smulated. These smulatons demonstrated the local equlbrum at γ / γ nterfaces, growth of γ precptates, precptate nteractons such as coalescence, and the Ostwald-rpenng process. The smulated temporal evoluton of composton profles was qualtatvely reasonable, compared to expermental observatons usng atom-probe analyses. Ths modelng technque can contrbute to alloy desgn, process desgn and lfetme assessment of hgh-temperature turbne blades currently n servce. Acknowledgement The authors acknowledge Mr. Tomohto Kmura at Shbaura Insttute of Technology, Japan for assstance wth experments. References 1. T. Yokokawa, H. Saek, Y. Fukuyama, T. Yoshda, and H. Harada, The vrtual gas turbne system for alloy assessment, Superalloys 004, D.Y. L, and L.Q. Chen, Computer smulaton of morphologcal evoluton and raftng of γ partcles n Nbased superalloys under appled stresses, Scrpta Materala, 37 (1997), Y. Wang, D. Baneree, C.C. Su, and A.G. Khachaturyan, Feld knetc model and computer smulaton of precptaton of L1 ordered ntermetallcs from F.C.C sold soluton, Acta Materala, 46 (1998), V. Vathyanathan, and L.Q. Chen, Coarsenng of ordered ntermetallc precptates wth coherency stress, Acta Materala, 50 (00), J.Z. Zhu, Z.K. Lu, V. Vathyanathan, and L.Q. Chen, Lnkng phase-feld model to CALPHAD: applcaton to precptate shape evoluton n N-base superalloys, Scrpta Materala, 46 (00), J.Z. Zhu, T. Wang, A.J. Ardell, S.H. Zhou, Z.K. Lu, and L.Q. Chen, Three-dmensonal phase-feld smulatons of coarsenng knetcs of γ partcles n bnary N-Al alloys, Acta Materala, 5 (004), J.C. Wang, M. Osawa, T. Yokokawa, H. Harada, and M. Enomoto, Modelng the mcrostructural evoluton of N-base superalloys by phase feld method combned wth CALPHAD and CVM, Computatonal Materals Scence, 39 (007), Y.H. Wen, B. Wang, J.P. Smmons, and Y. Wang, A phasefeld model for heat treatment applcatons n N-based alloys, Acta Materala, 54 (006), Y. Kozum, T. Kobayash, T. Yokokawa, J.X. Zhang, M. Osawa, H. Harada, Y. Aok, and M. Ara, Development of next generaton N-base sngle crystal superalloys, Superalloys 004, T. Murakumo, T. Kobayash, Y. Kozum, and H. Harada, Creep behavour of N-base sngle-crystal superalloys wth varous γ volume fracton, Acta Materala, 5 (004), T. Yokokawa, M. Osawa, K. Nshda, T. Kobayash, Y. Kozum, and H. Harada, Parttonng behavor of platnum group metals on the γ and γ phases of N-base superalloys at hgh temperatures, Scrpta Materala, 49 (003), John Agren, Computer smulatons of dffusonal reactons n complex steels, ISIJ Internaonal, 3 (199), U. Grafe, U. Bottger, J. Taden, and S.G. Fres, Couplng of multcomponent thermodynamc databases to a phase feld model: applcaton to soldfcaton and sold state transformatons of superalloys, Scrpta Materala, 4 (000), Toshyuk Koyama, Phase-feld smulaton of the mcrostructure changes n N and Co base superalloys, (Paper presented at the JSME 19th Computatonal Mechancs Conference, Nagoya, Japan, 3-5 November, 006). [n Japanese] 15. I. Ansara, N. Dupn, H.L. Lukas, and B. Sundman, Thermodynamc assessment of the Al-N system, Journal of Alloys and Compounds, 47 (1997), N. Dupn, I. Ansara, and B. Sundman, Thermodynamc reassessment of the ternary system Al-Cr-N, Calphad, 5 (001), A.T. Dnsdale, SGTE data for pure elements, Calphad, 15 (1991), Ursula R. Kattner, The thermodynamc modelng of multcomponent phase equlbra, JOM, 49 (1997),

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