Precipitation Strengthening in Titanium Alloys from First Principles Investigation

doi:10.11900/0412.1961.2022.00096

Acta Metall Sin

2024, Vol. 60

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

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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

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CHENG Kun, CHEN Shuming, CAO Shuo, LIU Jianrong, MA Yingjie, FAN Qunbo, CHENG Xingwang, YANG Rui, HU Qingmiao. Precipitation Strengthening in Titanium Alloys from First Principles Investigation. Acta Metall Sin, 2024, 60(4): 537-547.

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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

Received: 07 March 2022

ZTFLH:

TG139

Fund: National Natural Science Foundation of China(52071315);National Natural Science Foundation of China(U2106215);National Natural Science Foundation of China(52001307);National Science and Technology Major Project(J2019-VI-0012-0126);China Postdoctoral Science Foundation(2019M661149)

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

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	CHENG Kun
	CHEN Shuming
	CAO Shuo
	LIU Jianrong
	MA Yingjie
	FAN Qunbo
	CHENG Xingwang
	YANG Rui
	HU Qingmiao

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https://www.ams.org.cn/EN/10.11900/0412.1961.2022.00096 OR https://www.ams.org.cn/EN/Y2024/V60/I4/537

Fig.1 Schematic representation of the spherical precipitation particle distributed homogenously in the matrix (R—radius of precipitate, L—spacing between precipitation phase particles)

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	-

Table 1 Lattice parameters (a, c) of the α and β phases of pure Ti in comparison with available values from experimental measurements and other theoretical calculations^[20~24]

Fig.2 Lattice parameters of binary Ti-xM (M = Al, V, Cr, Mn, Fe, Co, Ni, Zr, Nb, Mo, Ta, W) against the composition x (atomic fraction)
(a) a of the α phase
(b)

c / a

of the α phase
(c) a of the β phase

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	-

Table 2 Elastic constants of the α and β phases of pure Ti in comparison with available values from experimental measurements and other theoretical calculations^{[20-22,28-30]}

Fig.3 Polycrystalline elastic moduli of the α phase of binary Ti-xM (M = Al, V, Cr, Mn, Fe, Co, Ni, Zr, Nb, Mo, Ta, W) against x
(a) bulk modulus (B)
(b) shear modulus (G)
(c) Young's modulus (Y)

Fig.4 Polycrystalline elastic moduli of the β phase of binary Ti-xM (M = Al, V, Cr, Mn, Fe, Co, Ni, Zr, Nb, Mo, Ta, W) against x
(a) bulk modulus
(b) shear modulus
(c) Young's modulus

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

Table 3 Parameters for the fitting of the shear modulus G and composition x relationship of binary Ti-xM alloy (For the α phase, G-x is fitted with

G = 62.49 + m x

，

x ≤ 0.15

. For the β phase, G-x is fitted with

G = 18.69 + m x + n x 2

x ≤ 0.30

. The intercepts in the fitting equations (62.49 GPa and 18.69 GPa) are respectively the shear moduli of the α and β phases of pure Ti)

Table 4 Shear modulus Mo-equivalencies (

γ M

) of various alloying elements in the α and β phases of Ti

Fig.5 Shear moduli of α phase (a) and β phase (b) of Ti-Al-V alloy from direct EMTO-CPA calculations (gray column) and the error of the shear modulus evaluated with modulus Mo-equivalency (cyan column)

Fig.6 Strength increment ( $Δ σ$ ) induced by the modulus strengthening effect as a function of the radius (R) and volume fraction (f) of the precipitation particle in Ti-Mo alloy with β phase composition of 5%Mo

Fig.7 $Δ σ$ induced by the precipitation strengthening against x of the β phase of the α + β dual phase Ti-xM alloy (M = V, Cr, Mn, Fe, Co, Ni, Nb, Mo, Ta, W) with R = 100 nm and f = 20%

Table 5 Element partitions, f and R of α phase precipitate^[31], and G calculated with the experimental compositions of the α and β phases of Ti55521 alloys under various heat treatments

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

Table 6 Calculated strength increment

Δ σ

induced by precipitation strengthening and experimental yield strength (

σ 0.2

) of Ti55521 alloy after various heat treatments

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