Two-phase model calculation of diffraction elastic constant of crystal plane at different temperature
XU Haifeng1,3, ZHU Changjun1,2,3, CHEN Kanghua1,2,3, LIU Li1,3
1. Light Alloy Research Institute, Central South University, Changsha 410083, China; 2. National Key Laboratory of Science and Technology for National Defence on High-strength Structural Materials, Central South University, Changsha 410083, China; 3. Collaborative Innovation Center of Advance Nonferrous Structural Materials and Manufacturing, Central South University, Changsha 410083, China
Abstract:Nickel-based superalloy can be regarded as a two-phase material with matrix phase (Ni phase) and mixed phase (Ni3Al phase) (ignoring a few other phases). A two phase model for calculating diffraction elastic constant is established by self-consistent way, combined with Eshelby inclusion theory. The elastic stiffness coefficient of two-phase single crystal at high temperature is obtained by quasi harmonic Debye theory and first principle calculation, and the diffraction elastic constants of related crystal surfaces of nickel base superalloy at different temperatures are calculated by substituting the model. The accuracy of the model is verified by the small error between the calculated results and the experimental measurements reported in the literature.
许海峰, 祝昌军, 陈康华, 刘力. 不同温度下晶面衍射弹性常数的两相模型计算[J]. 粉末冶金材料科学与工程, 2020, 25(2): 91-97.
XU Haifeng, ZHU Changjun, CHEN Kanghua, LIU Li. Two-phase model calculation of diffraction elastic constant of crystal plane at different temperature. Materials Science and Engineering of Powder Metallurgy, 2020, 25(2): 91-97.
[1] AKINIWA Y, MACHIYA S, KIMURA H, et al.Evaluation of material properties of SiC particle reinforced aluminum alloy composite using neutron and X-ray diffraction[J]. Materials Science & Engineering A, 2006, 437(1): 93-99. [2] KRÖNER E. Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls[J]. Zeitschrift Für Physik A Hadrons and Nuclei, 1958, 151(4): 504-518. [3] BLANCO M A, FRANCISCO E, LUANA V.GIBBS: Isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model[J]. Computer Physics Communications, 2004, 158(1): 57-72. [4] ESHELBY J D.The determination of the elastic field of an ellipsoidal inclusion, and related problems[J]. Proceedings of the Royal Society of London, 1957, 241(1226): 376-396. [5] NOYAN I C, COHEN J B.Residual Stress: Measurement by Diffraction and Interpretation[M]. New York, USA: Springer, 2013. [6] VOIGT W.Lehrbuch der Kristallphysik[M]. Teubner, Liepzig, 1996. [7] CROSSON, ROBERT S, LIN, JIA-WEN.Voigt and reuss prediction of anisotropic elasticity of dunite[J]. Journal of Geophysical Research Atmospheres, 2014, 76(2): 570-578. [8] 林政, 刘旻. 材料弹性常数之新探[M]. 北京: 科学出版社, 2011. LIN Zheng, LIU Min.New Research on Elastic Constants of Materials[M]. Beijing: Science Press, 2011. [9] 黄争鸣. 复合材料细观力学引论[M]. 北京: 科学出版社, 2004. HUANG Zhengming.Introduction to Microstructure of Composites[M]. Beijing: Science Press, 2004. [10] MORI T, TANAKA K.Average stress in matrix and average elastic energy of materials with misfitting inclusions[J]. Acta Metallurgica, 1973, 21(5): 571-574. [11] HUTCHINSON J W.Elastic-plastic behaviour of polycrystalline metals and composites[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1970, 319(1537): 247-272. [12] 黄克智. 固体本构关系[M]. 北京: 清华大学出版社, 1999. HUANG Kezhi.Solid Constitutive Relations[M]. Beijing: Tsinghua University Press, 1999. [13] SEGALL M D, LINDAN P J D, PROBERT M J, et al. First-principles simulation: Ideas, illustrations and the CASTEP code[J]. Journal of Physics: Condensed Matter, 2002, 14(11): 2717-2744. [14] OTERO-DE-LA-ROZA A, ABBASI-PÉREZ D, VÍCTOR L A. Gibbs 2: A new version of the quasiharmonic model code. II. Models for solid-state thermodynamics, features and implementation[J]. Computer Physics Communications, 2011, 182(10): 2232-2248. [15] SHANG S L, WANG Y, KIM D E, et al.First-principles thermodynamics from phonon and Debye model: Application to Ni and Ni3Al[J]. Computational Materials Science, 2010, 47(4): 1040-1048. [16] FRANCISCO E, RECIO J M, BLANCO M A, et al.Quantum-mechanical study of thermodynamic and bonding properties of MgF2[J]. J Phys Chem A, 1998, 102: 1595-1601. [17] FRANCISCO E, BLANCO M A, SANJURJO G.Atomistic simulation of SrF2 polymorphs[J]. Physical Review B, 2001, 63(9): 385-392. [18] CALVERT L D, VILLARS P.Pearson’s Handbook of Crystallographic Data for Intermetallic Phases[M]. Materials Park, OH, USA: ASM International, 1991. [19] PRIKHODKO S V, YANG H, ARDELL A J, et al.Temperature and composition dependence of the elastic constants of Ni3Al[J]. Metallurgical and Materials Transactions A (Physical Metallurgy and Materials Science), 1999, 30(9): 2403-2408. [20] ALERS G A, NEIGHBOURS J R, SATO H.Temperature dependent magnetic contributions to the high field elastic constants of nickel and an Fe-Ni alloy[J]. Journal of Physics & Chemistry of Solids, 1960, 13(1/2): 40-55. [21] WAGNER J N, HOFMANN M, WIMPORY R, et al.Microstructure and temperature dependence of intergranular strains on diffract to metric macroscopic residual stress analysis[J]. Materials Science and Engineering A, 2014, 618: 271-279.