第一性原理研究钛合金中的沉淀强化

doi:10.11900/0412.1961.2022.00096

金属学报

2024, Vol. 60

Issue (4): 537-547 DOI: 10.11900/0412.1961.2022.00096

研究论文

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第一性原理研究钛合金中的沉淀强化

程坤¹^,², 陈树明¹^,², 曹烁¹, 刘建荣¹, 马英杰¹, 范群波³, 程兴旺³, 杨锐¹, 胡青苗¹(

)

1 中国科学院金属研究所师昌绪先进材料创新中心沈阳 110016
2 中国科学技术大学材料科学与工程学院沈阳 110016
3 北京理工大学材料学院冲击环境材料技术重点实验室北京 100081

Precipitation Strengthening in Titanium Alloys from First Principles Investigation

CHENG Kun¹^,², CHEN Shuming¹^,², CAO Shuo¹, LIU Jianrong¹, MA Yingjie¹, FAN Qunbo³, CHENG Xingwang³, YANG Rui¹, HU Qingmiao¹(

)

1 Shi -changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
2 School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China
3 National Key Laboratory of Science and Technology on Materials Under Shock and Impact, School of Materials Science and Technology, Beijing University of Technology, Beijing 100081, China

引用本文:

程坤, 陈树明, 曹烁, 刘建荣, 马英杰, 范群波, 程兴旺, 杨锐, 胡青苗. 第一性原理研究钛合金中的沉淀强化[J]. 金属学报, 2024, 60(4): 537-547.
Kun CHENG, Shuming CHEN, Shuo CAO, Jianrong LIU, Yingjie MA, Qunbo FAN, Xingwang CHENG, Rui YANG, Qingmiao HU. Precipitation Strengthening in Titanium Alloys from First Principles Investigation[J]. Acta Metall Sin, 2024, 60(4): 537-547.

全文: PDF(1616 KB) HTML

摘要:

为研究合金化对沉淀强化行为的影响，采用第一性原理方法计算了二元Ti-xM (M = Al、V、Cr、Mn、Fe、Co、Ni、Zr、Nb、Mo、Ta、W)合金弹性模量随成分的变化，提出了弹性模量Mo当量概念，以高效计算复杂成分钛合金(如Ti-Al-V合金以及Ti55521)的弹性模量；结合弹性模量及Russell-Brown沉淀强化模型，研究了二元Ti-xM (M = V、Cr、Mn、Fe、Co、Ni、Nb、Mo、Ta、W)合金以及Ti55521合金中的沉淀强化。结果显示，在体积分数及沉淀相颗粒尺寸相同的情况下，Co、Fe、W、Mo、Ni、Mn沉淀强化作用较强，Cr、Nb、Ta强化作用居中，V强化作用最弱。随合金元素含量x增加，沉淀强化作用均有所增强。热机械处理Ti55521合金经短时时效后，沉淀强化作用有所减弱，但长时时效后，沉淀强化效果增强。

关键词 ：第一性原理, 钛合金, 弹性模量, 沉淀强化, 强度

Abstract：

Titanium alloys have shown wide application potential in the areas such as aerospace and marine because of their comprehensive properties, including high specific strength, ductility, corrosion resistance, and damage tolerance. Given the rapid development of new-generation advanced military hardware toward large scale, high-speed, light-weight, and structure-complicated titanium alloys experience increasingly harsh application environments. Thus, developing novel high-strength and high-toughness titanium alloys is an important direction in the field of titanium research. To date, the compositional design of titanium alloys is performed within the framework of some empirical rules without involving strengthening and toughening mechanisms. This kind of approach can hardly achieve an accurate and efficient material design. Based on the abovementioned background, the effect of alloying on the precipitation strengthening of the α + β dual-phase titanium alloy was studied by using the first-principles exact muffin-tin orbital method in combination with a coherent potential approximation. High-strength and high-toughness titanium alloys obtain its high strength through precipitation strengthening in the β-phase matrix with α-phase precipitates. The influence of alloying on the precipitation strengthening is crucial to the understanding and prediction of alloy strength and rational alloy design. In the present work, the elastic moduli and lattice constants of a serial binary titanium alloy Ti-xM (M = Al, V, Cr, Mn, Fe, Co, Ni, Nb, Mo, Ta, W) against the composition x were calculated using the first-principles method. Based on which, the elastic moduli of the titanium alloy with a complex composition (such as Ti-Al-V and Ti55521) were evaluated using the concept of elastic Mo equivalency. Subsequently, the precipitation strengthening of binary titanium alloys and the Ti55521 alloy was evaluated by using the elastic modulus within the framework of the modulus strengthening model. Result shows that alloying elements, such as Co, Fe, W, Mo, Ni, and Mn, have the strongest precipitation strengthening effect for the same particle size and volume fraction of α precipitates, followed by Cr, Nb, and Ta, whereas V is the weakest. The strengthening effect increases with the content of alloying element. For the Ti55521 alloy prepared by using a thermal mechanical process, subsequent short-time aging weakens the precipitation strengthening effect compared with long-time aging.

Key words： first principles titanium alloy elastic modulus precipitation strengthening strength

收稿日期: 2022-03-07

ZTFLH:

TG139

基金资助:国家自然科学基金(52071315);国家自然科学基金(U2106215);国家自然科学基金(52001307);国家科技重大专项项目(J2019-VI-0012-0126);国家博士后基金项目(2019M661149)

通讯作者: 胡青苗，qmhu@imr.ac.cn，主要从事工程合金计算设计方面的研究

Corresponding author: HU Qingmiao, professor, Tel: (024)23971813, E-mail: qmhu@imr.ac.cn

作者简介: 程坤，男，1996年生，硕士生

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https://www.ams.org.cn/CN/10.11900/0412.1961.2022.00096 或 https://www.ams.org.cn/CN/Y2024/V60/I4/537

图1 基体内均匀分布的球形沉淀相示意图

Phase	Method	$a$ / nm	$c / a$
α	EMTO	0.2933	1.611
	VASP^[20]	0.2924	1.595
	VASP^[21]	0.2931	1.584
	VASP^[22]	0.2946	1.584
	Exp.^[23]	0.2951	1.585
β	EMTO	0.3261	-
	VASP^[20]	0.3252	-
	VASP^[22]	0.3264	-
	Exp.^[24]	0.3281	-

表1 纯Ti α和β相的晶格常数(a、c)与实验值和其他理论值的比较[20~24]

图2 二元钛合金Ti-xM (M = Al、V、Cr、Mn、Fe、Co、Ni、Zr、Nb、Mo、Ta、W)的晶格常数随成分x的变化

Phase	Method	$C 11$	$C 12$	$C 13$	$C 33$	$C 44$	$C 66$
α	EMTO	201.6	44.2	54.4	222.6	49.3	78.7
	VASP^[20]	204.0	59.1	77.0	192.9	45.9	72.5
	VASP^[21]	176.6	84.5	77.0	190.2	41.5	46.1
	VASP^[22]	171.6	86.6	72.6	190.6	41.1	42.5
	Exp.^[28]	176.1	86.9	68.3	190.5	50.8	44.6
	Exp.^[29]	162.4	92.0	68.5	180.7	46.6	35.2
	Exp.^[30]	155.0	91.0	79.0	173.0	65.0	32.0
β	EMTO	102.2	103.6	-	-	65.9	-
	VASP^[20]	76.6	121.9	-	-	30.0	-
	VASP^[22]	87.8	112.2	-	-	39.8	-

表2 纯Ti中α和β相的弹性常数与实验值和其他理论值的比较[20~22,28~30] (GPa)

图3 二元钛合金Ti-xM (M = Al、V、Cr、Mn、Fe、Co、Ni、Zr、Nb、Mo、Ta、W)的α相多晶弹性模量随x的变化

图4 二元钛合金Ti-xM (M = Al、V、Cr、Mn、Fe、Co、Ni、Zr、Nb、Mo、Ta、W)的β相多晶弹性模量随x的变化

M	α	β
M	$m$	$m$	$n$
Al	0.87 ± 1.29	38.84 ± 4.57	107.37 ± 18.26
V	-116.97 ± 0.42	103.95 ± 3.96	-142.15 ± 15.85
Cr	-254.92 ± 11.39	161.50 ± 6.75	-255.07 ± 26.99
Mn	-279.12 ± 3.47	198.59 ± 9.37	-270.81 ± 37.46
Fe	-225.56 ± 8.13	227.59 ± 9.73	-288.98 ± 38.94
Co	-167.85 ± 8.85	240.66 ± 7.59	-353.45 ± 30.36
Ni	-110.81 ± 5.70	216.68 ± 6.73	-353.20 ± 26.90
Zr	-19.07 ± 0.35	38.28 ± 3.52	-61.30 ± 14.07
Nb	-90.08 ± 0.76	148.00 ± 5.10	-212.12 ± 20.40
Mo	-200.39 ± 1.61	207.58 ± 9.16	-308.80 ± 36.65
Ta	-48.13 ± 1.72	145.14 ± 4.63	-161.78 ± 18.53
W	-162.35 ± 1.68	215.07 ± 8.60	-239.50 ± 34.42

表3 二元Ti-xM合金剪切模量G对M含量x的拟合系数

表4 不同合金元素在α及β相中的剪切模量Mo当量系数(γM)

图5 Ti-Al-V合金α相和β相剪切模量EMTO-CPA计算值(灰色方柱)以及该计算值与采用模量Mo当量方法的估算值的绝对误差(青色方柱)

图6 β相成分为5%Mo的Ti-Mo合金中，模量强化强度增量(Δσ)随沉淀相粒子半径(R)和体积分数(f)的变化

图7 在沉淀相R = 100 nm、f = 20%时，二元α + β双相Ti-xM (M = V、Cr、Mn、Fe、Co、Ni、Nb、Mo、Ta、W)合金的模量强化强度增量Δσ随x的变化

表5 不同热处理条件下，Ti55521合金中的元素分配、α相体积分数及颗粒尺寸[31]，以及根据实验获得的α、β相成分计算得到的剪切模量

State	$Δ σ$	$σ 0.2$ (exp.)
TMP	237.8 ± 42.8	980 ± 15
Aged I	161.1 ± 80.3	1080 ± 18
Aged II	364.3 ± 148.3	1200 ± 12

表6 不同热处理制度下沉淀强化强度增量Ti55521合金的Δσ计算值及屈服强度实验值(σ0.2) (MPa)

1	Boyer R R. An overview on the use of titanium in the aerospace industry[J]. Mater. Sci. Eng., 1996, A213: 103
2	Lütjering G, Williams J C. Titanium[M]. 2nd Ed., Berlin: Springer, 2007: 431
3	Banerjee D, Williams J C. Perspectives on titanium science and technology[J]. Acta Mater., 2013, 61: 844 doi: 10.1016/j.actamat.2012.10.043
4	Zhang B, Tian D, Song Z M, et al. Research progress in dwell fatigue service reliability of titanium alloys for pressure shell of deep-sea submersible[J]. Acta Metall. Sin., 2023, 59: 713 doi: 10.11900/0412.1961.2022.00441
4	张滨, 田达, 宋竹满等. 深潜器耐压壳用钛合金保载疲劳服役可靠性研究进展[J]. 金属学报, 2023, 59: 713
5	Yang R, Ma Y J, Lei J F, et al. Toughening high strength titanium alloys through fine tuning phase composition and refining microstructure[J]. Acta Metall. Sin., 2021, 57: 1455 doi: 10.11900/0412.1961.2021.00353
5	杨锐, 马英杰, 雷家峰等. 高强韧钛合金组成相成分和形态的精细调控[J]. 金属学报, 2021, 57: 1455
6	Yan S C. Numerical simulation for the isothermal forging processes of complex structural component of Ti-1023 alloy[D]. Xi'an: Northwestern Polytechnical University, 2005
6	闫世成. Ti-1023合金复杂结构件等温锻造过程的数值模拟[D]. 西安: 西北工业大学, 2005
7	Ivasishin O M, Markovsky P E, Matviychuk Y V, et al. A comparative study of the mechanical properties of high-strength β-titanium alloys[J]. J. Alloys Compd., 2008, 457: 296 doi: 10.1016/j.jallcom.2007.03.070
8	Coakley J, Vorontsov V A, Jones A G, et al. Precipitation processes in the beta-titanium alloy Ti-5Al-5Mo-5V-3Cr[J]. J. Alloys Compd., 2015, 646: 946 doi: 10.1016/j.jallcom.2015.05.251
9	Kelly P M. Progress report on recent advances in physical metallurgy: (C) The quantitative relationship between microstructure and properties in two-phase alloys[J]. Int. Metall. Rev., 1973, 18: 31 doi: 10.1179/imr.1973.18.1.31
10	Melander A, Persson P Å. The strength of a precipitation hardened AlZnMg alloy[J]. Acta Metall., 1978, 26: 267 doi: 10.1016/0001-6160(78)90127-X
11	Russell K C, Brown L M. A dispersion strengthening model based on differing elastic moduli applied to the iron-copper system[J]. Acta Metall., 1972, 20: 969 doi: 10.1016/0001-6160(72)90091-0
12	Zhang S Z, Cui H, Li M M, et al. First-principles study of phase stability and elastic properties of binary Ti-xTM (TM= V, Cr, Nb, Mo) and ternary Ti-15TM-yAl alloys[J]. Mater. Des., 2016, 110: 80 doi: 10.1016/j.matdes.2016.07.120
13	Benoit M, Tarrat N, Morillo J. Density functional theory investigations of titanium γ-surfaces and stacking faults[J]. Modell. Simul. Mater. Sci. Eng., 2013, 21: 015009
14	Hutchinson C R, Gouné M, Redjaïmia A. Selecting non-isothermal heat treatment schedules for precipitation hardening systems: An example of coupled process-property optimization[J]. Acta Mater., 2007, 55: 213 doi: 10.1016/j.actamat.2006.07.028
15	Vitos L. Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications[M]. 2nd Ed., London: Springer, 2007: 14
16	Hill R. The elastic behaviour of a crystalline aggregate[J]. Proc. Phys. Soc., 1952, 65A: 349
17	Martin R M. Electronic Structure: Basic Theory and Practical Methods[M]. New York: Cambridge University Press, 2004: 119
18	Vitos L, Abrikosov I A, Johansson B. Anisotropic lattice distortions in random alloys from first-principles theory[J]. Phys. Rev. Lett., 2001, 87: 156401 doi: 10.1103/PhysRevLett.87.156401
19	Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple[J]. Phys. Rev. Lett., 1996, 77: 3865 doi: 10.1103/PhysRevLett.77.3865 pmid: 10062328
20	Zhou W C, Sahara R, Tsuchiya K. First-principles study of the phase stability and elastic properties of Ti-X alloys (X = Mo, Nb, Al, Sn, Zr, Fe, Co, and O)[J]. J. Alloys Compd., 2017, 727: 579 doi: 10.1016/j.jallcom.2017.08.128
21	Yu H, Cao S, Youssef S S, et al. Generalized stacking fault energies and critical resolved shear stresses of random α-Ti-Al alloys from first-principles calculations[J]. J. Alloys Compd., 2021, 850: 156314 doi: 10.1016/j.jallcom.2020.156314
22	Ikehata H, Nagasako N, Furuta T, et al. First-principles calculations for development of low elastic modulus Ti alloys[J]. Phys. Rev., 2004, 70B: 174113
23	Barret C S, Massalski T B. Structure of Metals: Crystallographic Methods, Principles and Data[M]. 3rd Ed., New York: Pergamon Press, 1980: 654
24	Lynch J F, Tanaka J. Thermodynamics of the solid solution of hydrogen in β-titanium alloys: β-TiMo and β-Ti/Re[J]. Acta Metall., 1981, 29: 537 doi: 10.1016/0001-6160(81)90077-8
25	Sun K, Yuan X Z, Wu E D, et al. Neutron diffraction study of the deuterides of Ti-Mo alloy[J]. Physica, 2006, 385-386B: 141
26	Denton A R, Ashcroft N W. Vegard's law[J]. Phys. Rev., 1991, 43A: 3161
27	Zhao Y F, Fu Y C, Hu Q M, et al. First-principles investigations of lattice parameters, bulk moduli and phase stabilities of Ti_1- _x V _x and Ti_1- _x Nb _x alloys[J]. Acta Metall. Sin., 2009, 45: 1042
27	赵宇飞, 符跃春, 胡青苗等. Ti_1- _x V _x 及Ti_1- _x Nb _x 合金晶格参数、体模量及相稳定性的第一原理研究[J]. 金属学报, 2009, 45: 1042
28	Fisher E S, Renken C J. Single-crystal elastic moduli and the hcp→bcc transformation in Ti, Zr, and Hf[J]. Phys. Rev., 1964, 135: A482 doi: 10.1103/PhysRev.135.A482
29	Simmons G, Wang H. Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook[M]. 2nd Ed., Cambridge: MIT Press, 1971: 323
30	Trinkle D R, Jones M D, Hennig R G, et al. Empirical tight-binding model for titanium phase transformations[J]. Phys. Rev., 2006, 73B: 094123
31	Ahmed M, Li T, Casillas G, et al. The evolution of microstructure and mechanical properties of Ti-5Al-5Mo-5V-2Cr-1Fe during ageing[J]. J. Alloys Compd., 2015, 629: 260 doi: 10.1016/j.jallcom.2015.01.005

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