3D Phase Field Simulation of Factors Influencing the Microstructure Morphology of Lamellar Ti-6Al-4V Alloy
ZHANG Yao1, QI Min2, SUN Jia3, WU Ting1, MA Yingjie2, WANG Hao1(), YANG Rui2
1.Interdisciplinary Center for Additive Manufacturing, School of Materials and Chemistry, University of Shanghai for Science and Technology, Shanghai 200093, China 2.Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China 3.Yunnan Tin New Material Company Limited, Kunming 650106, China
Cite this article:
ZHANG Yao, QI Min, SUN Jia, WU Ting, MA Yingjie, WANG Hao, YANG Rui. 3D Phase Field Simulation of Factors Influencing the Microstructure Morphology of Lamellar Ti-6Al-4V Alloy. Acta Metall Sin, 2024, 60(9): 1265-1278.
Ti-6Al-4V, a typical dual-phase titanium alloy, has mechanical properties largely determined by its microstructures. However, the absence of three-dimensional (3D) information regarding the relative orientation relationships of grain boundary α, α lamellae, and α side branches, hinders precise microstructure control. In this study, using thermodynamic data from Pandat and Thermo-Calc, along with kinetic data from DICTRA, the 3D morphology of α lamellae in Ti-6Al-4V alloy was simulated via the phase field method. This study simulated the influence of interfacial energy anisotropy on the growth of α lamellae at a heat treatment temperature of 820°C and analyzed the corresponding solute field. The findings reveal that interface energy anisotropy considerably affects the morphology of α lamellae. When the anisotropy of the interface energy increased from 0.4:0.1:1.0 to 0.8:0.1:1.0, the α lamellae transformed from a thick rod shape to a slender needle shape. Higher anisotropy levels lead to accelerated growth rates of α lamellae. Variation in interface anisotropy, primarily affect the density and growth rate of α lamellae, while their growth direction remains consistent. Additionally, the width of individual lamellae progressively widens under different interface anisotropies. The phase-field simulation results align closely with experimental findings. Notably, the 3D simulation results of α lamellae organization offer more detailed insights into the side branches of α lamellae than two-dimensional (2D) SEM images. In 3D simulation, it can be observed the growth morphology of side branches at different positions of grains. The results indicate that the angle between the main lamellae and the side branches includes experimental observations of 30° and random angles.
Fund: National Natural Science Foundation of China(U2241245,91960202);Aeronautical Science Foundation of China(2022Z053092001);National Key Laboratory Foundation of Science and Technology on Materials under Shock and Impact(6142902220301);Opening Project of National Key Laboratory of Shock Wave and Detonation Physics(2022JCJQLB05702)
Corresponding Authors:
WANG Hao, professor, Tel: (021)55270108, E-mail: haowang7@usst.edu.cn
Fig.1 Lamellae morphologies of three different interface energy anisotropy ratios under different heat treatment temperatures at the same time (The color scale in the simulation results represents the numerical value of the order parameter, the same in figures below. kx —characterize the magnitude of interface energy in the x-direction) (a1) kx = 0.4, 780oC (a2) kx = 0.6, 780oC (a3) kx = 0.8, 780oC (b1) kx = 0.4, 820oC (b2) kx = 0.6, 820oC (b3) kx = 0.8, 820oC (c1) kx = 0.4, 860oC (c2) kx = 0.6, 860oC (c3) kx = 0.8, 860oC
Fig.2 Morphology evolutions of lamellae growth at different moments (t) (The heat treatment temperature is 820oC, αGB—grain boundary allotriomorphs) (a) t = 50 s (b) t = 100 s (c) t = 500 s (d) t = 1000 s
Fig.3 Evolution of α side branch morphologies on the same z-x section (y = 252.85Δx, unit length Δx = 5 × 10-8 m) at different moments (The dashed box represents the growth status of the same layer at different time) (a) t = 100 s (b) t = 200 s (c) t = 300 s (d) t = 400 s (e) microstructure of Ti-4211 heat-treated at 1050oC for 1 h, furnace cooled to 830oC and annealed for 1 h, and water-quenched from 830oC to room temperature[10]
Fig.4 Morphologies of α side branches at different z-x sections at t = 2000 s (Unit length Δx = 5 × 10-8 m; the angle involved in the figure is the angle between the main layer and the side branches; Figs.4a-c are equivalent to Figs.4a1-c1, respectively) (a, a1) y = 23.85Δx (b, b1) y = 128.5Δx (c, c1) y = 252.85Δx (d) 2D slice layer α morphology[10]
Fig.5 Morphologies of α lamellae at different z-y sections at t = 500 s (The growth pattern of visible layers in the dashed box inside Fig.5a1 is extremely regular, and the phenomenon of layer twisting and discontinuity appears in the dashed circular box of Fig.5b1; Figs.4a-c are equivalent to Figs.4a1-c1, respectively) (a, a1) x = 255.8Δx (b, b1) x = 128.5Δx (c, c1) x = 1.2Δx
Fig.6 Volume fractions of α phase as a function of evolution time at 820℃
Fig.7 Morphologies of α lamellae under different interface energy anisotropy ratios at 820oC(ky and kz are used to characterize the magnitude of interface energy in the y and z directions, respectively) (a) kx:ky:kz = 0.4:0.1:1.0 (b) kx:ky:kz = 0.6:0.1:1.0 (c) kx:ky:kz = 0.8:0.1:1.0 (d-f) side views of Figs.7a-c, repectively
Fig.8 Lamellae growth morphologies of z-y cross-section under different interface energy anisotropy conditions at t = 1000 s (a) kx:ky:kz = 0.4:0.1:1.0 (b) kx:ky:kz = 0.6:0.1:1.0 (c) kx:ky:kz = 0.8:0.1:1.0
Fig.9 Growth morphologies of lamellae on different x-z sections of grains under kxconditions of 0.4 (a1-c1), 0.6 (a2-c2), and 0.8 (a3-c3), respectively at t = 1000 s (a1-a3) x = 255.8Δx (b1-b3) x = 128.5Δx (c1-c3) x = 1.2Δx
Fig.10 Solute distributions of Al and the local magnifications under different interface energy anisotropy conditions at 820oC for 100 s (XAl—molar fraction of Al) (a) kx:ky:kz = 0.4:0.1:1.0 (b) kx:ky:kz = 0.6:0.1:1.0 (c) kx:ky:kz = 0.8:0.1:1.0
Fig.11 Solute distributions of V and the local magnifications under different interface energy anisotropy conditions (XV—molar fraction of V) (a) kx:ky:kz = 0.4:0.1:1.0 (b) kx:ky:kz = 0.6:0.1:1.0 (c) kx:ky:kz = 0.8:0.1:1.0
Fig.12 Growth of lamellae structure at t = 50 s (a) overall lamellae perspective (b) enlarged image of details of lamellae structure
Fig.13 Growth of lamellae structure at t = 100 s (a) overall lamellae perspective (b) morphology of side branches inside the rectangular box
Fig.14 Lamellae morphologies at t = 100 s with various interface energy anisotropies (a) kx:ky:kz = 0.4:0.1:1.0 (b) kx:ky:kz = 0.6:0.1:1.0 (c) kx:ky:kz = 0.8:0.1:1.0 (d-f) 3D views corresponding to Figs.12a-c, respectively
Fig.15 z-y section morphologies at different positions of grains at t = 2000 s under the condition of kx:ky:kz = 0.6:0.1:1.0 (The angles marked in the figure are the angles formed by measuring the side branches of the three layers near the root, middle, and tip of the same main lamellae and the main layer along their respective length directions, respectively) (a) x = 230Δx (b) x = 235Δx (c) x = 240Δx
1
Greenfield M A, Margolin H. The mechanism of void formation, void growth, and tensile fracture in an alloy consisting of two ductile phases [J]. Metall. Trans., 1972, 3: 2649
2
Yoder G R, Cooley L A, Crooker T W. Observations on microstructurally sensitive fatigue crack growth in a widmanstätten Ti-6Al-4V alloy [J]. Metall. Trans., 1977, 8A: 1737
3
Yoder G R, Cooley L A, Crooker T W. Quantitative analysis of microstructural effects on fatigue crack growth in widmanstätten Ti-6A1-4V and Ti-8Al-1Mo-1V [J]. Eng. Fract. Mech., 1979, 11: 805
4
Hall I W, Hammond C. Fracture toughness and crack propagation in titanium alloys [J]. Mater. Sci. Eng., 1978, 32: 241
5
Banerjee R, Bhattacharyya D, Collins P C, et al. Precipitation of grain boundary α in a laser deposited compositionally graded Ti-8Al-xV alloy—An orientation microscopy study [J]. Acta Mater., 2004, 52: 377
6
Chong Y, Bhattacharjee T, Tsuji N. Bi-lamellar microstructure in Ti-6Al-4V: Microstructure evolution and mechanical properties [J]. Mater. Sci. Eng., 2019, A762: 138077
7
Ma Y J, Liu J R, Lei J F, et al. Influence of fatigue crack tip plastic zone on crack propagation behavior in TC4ELI alloy [J]. Chin. J. Nonferrous Met., 2009, 19: 1789
Yang M, Wang G, Teng C Y, et al. 3D phase field simulation of effect of interfacial energy anisotropy on sideplate growth in Ti-6Al-4V [J]. Acta Metall. Sin., 2013, 48: 148
Wang Y Z, Ma N Y, Chen Q, et al. Predicting phase equilibrium, phase transformation, and microstructure evolution in titanium alloys [J]. JOM, 2005, 57(9): 32
10
Sun J, Qi M, Zhang J H, et al. Formation mechanism of α lamellae during β→α transformation in polycrystalline dual-phase Ti alloys [J]. J. Mater. Sci. Technol., 2021, 71: 98
11
Huang X N, Ding S B, Yue W. Cryogenic treatment on Ti6Al4V alloy fabricated by electron beam melting: Microstructure and mechanical properties [J]. J. Mater. Res. Technol., 2022, 20: 3323
12
Wang G, Xu D S, Yang R. Phase field simulation on sideplates formation in Ti-6Al-4V alloy [J]. Acta Phys. Sin, 2009, 58(suppl.1) : S343
Shi R P, Choudhuri D, Kashiwar A, et al. α phase growth and branching in titanium alloys [J]. Philos. Mag., 2022, 102: 389
14
Shi R P, Li D, Antonov S, et al. Origin of morphological variation of grain boundary precipitates in titanium alloys [J]. Scr. Mater., 2022, 214: 114651
15
Shi R P, Zhou N, Niezgoda S R, et al. Microstructure and transformation texture evolution during α precipitation in polycrystalline α/β titanium alloys—A simulation study [J]. Acta Mater., 2015, 94: 224
16
Ginzburg V L, Landau L D. On the theory of superconductivity [A]. Translation in Collected Papers of L.D. Landau [C]. Oxford: Pergamon, 1965: 546
17
Allen S M, Cahn J W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening [J]. Acta Metall., 1979, 27: 1085
18
Cahn J W, Hilliard J E. Free energy of a nonuniform system. I. Interfacial free energy [J]. J. Chem. Phys., 1958, 28: 258
19
Langer J S. Models of pattern formation in first-order phase transitions [A]. Directions in Condensed Matter Physics [M]. Singapore: World Scientific, 1986: 165
20
Hohenberg P C, Halperin B I. Theory of dynamic critical phenomena [J]. Rev. Mod. Phys., 1977, 49: 435
21
Wang Y, Chen L Q, Khachaturyan A G. Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap [J]. Acta Metall. Mater., 1993, 41: 279
22
Chen L Q. A computer simulation technique for spinodal decomposition and ordering in ternary systems [J]. Scr. Metall. Mater., 1993, 29: 683
23
Khachaturyan A G. Theory of structural transformations in solids [M]. New York: Wiley-Interscience Publications, 1983: 574
24
Sun J, Li X X, Zhang J H, et al. Phase field modeling of formation mechanism of grain boundary allotriomorph in β→α phase transformation in Ti-6Al-4V alloy [J]. Acta Metall. Sin., 2020, 56: 1113
Kim S G, Kim W T, Suzuki T. Phase-field model for binary alloys [J]. Phys. Rev., 1999, 60E: 7186
26
Zhang J H. The influences of stresses and defects on the variant selection and texture during phase transformation in Ti-6Al-4V alloy [D]. Shenyang: Institute of Metal Research, Chinese Academy of Sciences, 2016
Zhu J Z, Liu Z K, Vaithyanathan V, et al. Linking phase-field model to CALPHAD: Application to precipitate shape evolution in Ni-base alloys [J]. Scr. Mater., 2002, 46: 401
28
Andersson J O, Agren J. Models for numerical treatment of multicomponent diffusion in simple phases [J]. J. Appl. Phys., 1992, 72: 1350
29
Chen Q, Ma N, Wu K S, et al. Quantitative phase field modeling of diffusion-controlled precipitate growth and dissolution in Ti-Al-V [J]. Scr. Mater., 2004, 50: 471
30
Zhang J H, Qi M, Xu H S, et al. A phase-field model for simulating the growth of α sideplates with branching in titanium alloy [J]. J. Mater. Sci. Technol., 2022, 123: 154
31
Ma N, Yang F, Shen C, et al. Modeling formation of α sideplates in alpha/beta Ti-alloys—Effect of interfacial energy anisotropy and coherency elastic strain energy [A]. Ti-2007 Science and Technology [C]. Sendai: The Japan Institute of Metals, 2007: 287
32
Sun Z C, Guo S S, Yang H. Nucleation and growth mechanism of α-lamellae of Ti alloy TA15 cooling from an α + β phase field [J]. Acta Mater., 2013, 61: 2057
