Abstract
The primary dendrite spacing selection in a multicomponent Ni-based superalloy during directional solidification was systematically studied using two-dimensional phase-field simulations. The alloy thermodynamic and kinetic data were obtained from Pandat software with PanNickel database and directly coupled into the multiphase-field model. All the simulations were performed on a GPU server, and an optimized computing scheme using GPU shared memory was adopted. First, the morphology of the solidification front was studied, and the segregation pattern was investigated and compared with the experimental results. Then, the dendritic spacing distribution under a wide range of pulling velocities Vp (10–500 μm s−1) and temperature gradients G (2–200 K mm−1) was obtained and analyzed. The simulation results agree well with analytical model that the primary dendrite spacing scales as \( \varLambda \propto V_{\text{p}}^{ - b} G^{ - c} \). The coefficient b is near a constant value of 0.38 and varies slightly between 0.34 and 0.42, while coefficient c increases monotonously from 0.27 to 0.56 with the increasing G. The predicted dendritic spacing agrees well with the experimental data, but exhibits a major difference when under very low cooling rate (R < 0.1 K s−1). The effect of grain inclination angle θ on the final primary dendritic spacing was also studied, and an abnormal decrease in dendritic spacing was found under low grain orientation where θ < 10°. When the grain inclination angle exceeds 20°, the dendritic spacing increases with θ as the power law.
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References
Versnyder FI, Shank M (1970) The development of columnar grain and single crystal high temperature materials through directional solidification. Mater Sci Eng 6:213
Giamei AF, Tschinkel JG (1976) Liquid metal cooling: a new solidification technique. Metall Trans A 7:1427
Liu L, Huang T, Zhang J, Fu H (2007) Microstructure and stress rupture properties of single crystal superalloy CMSX-2 under high thermal gradient directional solidification. Mater Lett 61:227
Quested P, McLean M (1984) Solidification morphologies in directionally solidified superalloys. Mater Sci Eng 65:171
Whitesell H, Li L, Overfelt R (2000) Influence of solidification variables on the dendrite arm spacings of Ni-based superalloys. Metall Mater Trans B 31:546
Li LC (2002) Microstructural development and segregation effects in directionally solidified nickel-based superalloy PWA 1484. ProQuest Dissertations and Theses, Ph.D. thesis, Auburn University, pp 65–86
Konter M, Thumann M (2001) Materials and manufacturing of advanced industrial gas turbine components. J Mater Process Technol 117:386
Reed RC (2008) The superalloys: fundamentals and applications. Cambridge University Press, Cambridge
Wagner A, Shollock BA, Mclean M (2004) Grain structure development in directional solidification of nickel-base superalloys. Mater Sci Eng A 374:270
Dsouza N, Ardakani M, Wagner A, Shollock B, McLean M (2002) Morphological aspects of competitive grain growth during directional solidification of a nickel-base superalloy, CMSX4. J Mater Sci 37:481. https://doi.org/10.1023/A:1013753120867
Liang Z, Xu Q, Li J, Li S, Zhang J, Liu B, Zhong Z (2002) Experimental research on the near net shape casting process of gamma titanium aluminide turbochargers. Rare Met Mater Eng 31:353
Hunt J (1979) Solidification and casting of metals. In: Proceedings of conference, Sheffield, England, July 1977
Kurz W, Fisher D (1981) Dendrite growth at the limit of stability: tip radius and spacing. Acta Metall 29:11
Gandin CA, Eshelman M, Trivedi R (1996) Orientation dependence of primary dendrite spacing. Metall Mater Trans A 27:2727
Schneider MC, Gu JP, Beckermann C, Boettinger WJ, Kattner UR (1997) Modeling of micro-and macrosegregation and freckle formation in single-crystal nickel-base superalloy directional solidification. Metall Mater Trans A 28:1517
Karma A, Rappel W-J (1996) Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys Rev E 53:R3017
Kim SG, Kim WT, Suzuki T (1999) Phase-field model for binary alloys. Phys Rev E 60:7186
Steinbach I, Pezzolla F (1999) A generalized field method for multiphase transformations using interface fields. Physica D 134:385
Eiken J, Böttger B, Steinbach I (2006) Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys Rev E 73:066122
Tang J, Xue X (2009) Phase-field simulation of directional solidification of a binary alloy under different boundary heat flux conditions. J Mater Sci 44:745. https://doi.org/10.1007/s10853-008-3157-1
Warnken N, Ma D, Drevermann A, Reed RC, Fries S, Steinbach I (2009) Phase-field modelling of as-cast microstructure evolution in nickel-based superalloys. Acta Mater 57:5862
Böttger B, Eiken J, Apel M (2015) Multi-ternary extrapolation scheme for efficient coupling of thermodynamic data to a multi-phase-field model. Comput Mater Sci 108:283
Yang C, Xu Q, Liu B (2017) GPU-accelerated three-dimensional phase-field simulation of dendrite growth in a nickel-based superalloy. Comput Mater Sci 136:133
Takaki T, Ohno M, Shimokawabe T, Aoki T (2014) Two-dimensional phase-field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal. Acta Mater 81:272
Takaki T, Sakane S, Ohno M, Shibuta Y, Shimokawabe T, Aoki T (2016) Primary arm array during directional solidification of a single-crystal binary alloy: large-scale phase-field study. Acta Mater 118:230
Kim SG (2007) A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties. Acta Mater 55:4391
Carré A, Böttger B, Apel M (2013) Implementation of an antitrapping current for a multicomponent multiphase-field ansatz. J Cryst Growth 380:5
Karma A (2001) Phase-field formulation for quantitative modeling of alloy solidification. Phys Rev Lett 87:115701
Wang W, Lee PD, Mclean M (2003) A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection. Acta Mater 51:2971
Diepers H-J, Ma D, Steinbach I (2002) History effects during the selection of primary dendrite spacing. Comparison of phase-field simulations with experimental observations. J Cryst Growth 237:149
Ganesan M, Dye D, Lee P (2005) A technique for characterizing microsegregation in multicomponent alloys and its application to single-crystal superalloy castings. Metall Mater Trans A 36:2191
Parsa AB, Wollgramm P, Buck H, Somsen C, Kostka A, Povstugar I, Choi PP et al (2015) Advanced scale bridging microstructure analysis of single crystal Ni-base superalloys. Adv Eng Mater 17:216
Seo S, Lee J, Yoo Y, Jo C, Miyahara H, Ogi K (2011) A comparative study of the γ/γ′eutectic evolution during the solidification of Ni-base superalloys. Metall Mater Trans A 42:3150
Eiken J, Apel M, Liang SM, Schmid-Fetzer R (2015) Impact of P and Sr on solidification sequence and morphology of hypoeutectic Al–Si alloys: combined thermodynamic computation and phase-field simulation. Acta Mater 98:152
Higuchi K, Fecht HJ, Wunderlich RK (2010) Surface tension and viscosity of the Ni-based superalloy CMSX-4 measured by the oscillating drop method in parabolic flight experiments. Adv Eng Mater 9:349
Elliott AJ, Pollock TM, Tin S, King WT, Huang SC, Gigliotti MFX (2004) Directional solidification of large superalloy castings with radiation and liquid-metal cooling: a comparative assessment. Metall Mater Trans A 35:3221
Heckl A, Rettig R, Cenanovic S, Göken M, Singer R (2010) Investigation of the final stages of solidification and eutectic phase formation in Re and Ru containing nickel-base superalloys. J Cryst Growth 312:2137
Tien J, Gamble R (1971) The suppression of dendritic growth in nickel-base superalloys during unidirectional solidification. Mater Sci Eng 8:152
Beckermann C, Diepers H-J, Steinbach I, Karma A, Tong X (1999) Modeling melt convection in phase-field simulations of solidification. J Comput Phys 154:468
Clarke AJ, Tourret D, Song Y, Imhoff SD, Gibbs PJ, Gibbs JW, Fezzaa K et al (2017) Microstructure selection in thin-sample directional solidification of an Al–Cu alloy: in situ X-ray imaging and phase-field simulations. Acta Mater 129:203
Takaki T, Rojas R, Sakane S, Ohno M, Shibuta Y, Shimokawabe T, Aoki T (2017) Phase-field-lattice Boltzmann studies for dendritic growth with natural convection. J Cryst Growth 474:146
Zhang H, Xu QY, Sun CB, Qi X, Tang N, Liu BC (2013) Simulation and experimental studies on grain selection behavior of single crystal superalloy II. Spiral part. Acta Metall Sin 49:1521
Zhang H, Xu QY, Tang N, Pan D, Liu BC (2011) Numerical simulation of microstructure evolution during directional solidification process in directional solidified (DS) turbine blades. Sci China Technol Sci 54:3191
Matan N, Cox D, Carter P, Rist M, Rae C, Reed R (1999) Creep of CMSX-4 superalloy single crystals: effects of misorientation and temperature. Acta Mater 47:1549
Wang L, Liu Y, Yu J, Xu Y, Sun X, Guan H, Hu Z (2009) Orientation and temperature dependence of yielding and deformation behavior of a nickel-base single crystal superalloy. Mater Sci Eng A 505:144
Liu B, Xu Q, Jing T, Shen H, Han Z (2011) Advances in multi-scale modeling of solidification and casting processes. JOM 63:19
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This research was funded by the National Key Research and Development Program of China (2017YFB0701503), National Science and Technology Major Project (No. 2017ZX04014001) and the National Natural Science Foundation of China (No. 51374137).
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Yang, C., Xu, Q. & Liu, B. Primary dendrite spacing selection during directional solidification of multicomponent nickel-based superalloy: multiphase-field study. J Mater Sci 53, 9755–9770 (2018). https://doi.org/10.1007/s10853-018-2236-1
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DOI: https://doi.org/10.1007/s10853-018-2236-1