Deformation mechanisms and compressive response of NbTaTiZr alloy via machine learning potentials

LIU Hongyang; CHEN Bo; CHEN Rong; KANG Dongdong; DAI Jiayu

doi:10.7498/aps.74.20250738

Abstract

Refractory multi-principal element alloys (RMPEAs)have become a hotspot in materials science research in recent years due to their excellent high-temperature mechanical properties and broad application prospects. However, the unique deformation mechanisms and mechanical behaviors of the NbTaTiZr quaternary RMPEA under extreme conditions such as high temperature and high strain rate are still unclear, limiting its further design and engineering applications. In order to reveal in depth the dynamic response of this alloy on an atomic scale, this study develops a high-accuracy machine learning potential (MLP) for the NbTaTiZr quaternary alloy and combines it with large-scale molecular dynamics (MD) simulations to systematically investigate the effects of crystallographic orientation, strain rate, temperature, and chemical composition on the mechanical properties and microstructural evolution mechanisms of the alloy under compressive loading. The results show that the NbTaTiZr alloy exhibits significant mechanical and structural anisotropy during uniaxial compression. The alloy exhibits the highest yield strength when loaded along the [111] crystallographic direction, while it shows the lowest yield strength when compressed along the [110] direction, where twinning is more likely to occur. Under compression along the [100] direction, the primary deformation mechanisms include local disordering transitions and dislocation slip, with 1/2$ \left\langle{111}\right\rangle $ dislocations being the dominant type. When the strain rate increases to 10¹⁰ s^–1, the yield strength of the alloy is significantly enhanced, accompanied by a notable increase in the proportion of amorphous or disordered structures, indicating that high strain rate loading suppresses dislocation nucleation and motion while promoting disordering transitions. Simulations at varying temperatures indicate that the alloy maintains a high strength level even at temperatures as high as 2100 K. Compositional analysis further indicates that increasing the atomic percentage of Nb or Ta effectively enhances the yield strength of the alloy, whereas an increase in Ti or Zr content adversely affects the strength. By combining MLP with MD methods, this study elucidates the anisotropic characteristics of the mechanical behavior and the strain rate dependence of disordering transitions in the NbTaTiZr RMPEA under combination of high strain rate and high temperature, providing an important theoretical basis and simulation foundation for optimizing and designing novel material under extreme environments.

Keywords:

Authors and contacts

1.
College of Science, National University of Defense Technology, Changsha 410073, China
2.
Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha 410073, China
3.
Hunan Research Center of the Basic Discipline for Physical States, National University of Defense Technology, Changsha 410073, China

Corresponding author: CHEN Bo, chenbochain@nudt.edu.cn ; DAI Jiayu, jydai@nudt.edu.cn

Funds: Project supported by the Science and Technology Innovation Program of Hunan Province, China (Grant No. 2021RC4026).

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References

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Cited By

图 1 32原子超胞　(a) BCC; (b) FCC; (c) HCP结构示意图

Figure 1. Schematic of 32-atom supercell: (a) BCC; (b) FCC; (c) HCP structure.

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图 2 训练集中(a)单原子能量、(b)受力、(c)维里应力的分布; DP和DFT在(d)能量、(e)受力、(f)维里应力预测值的相关性

Figure 2. (a) Atomic energy, (b) forces, (c) distribution of virial stress; correlation between DP and DFT for (d) energy, (e) forces and (f) virial stress.

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图 3 在300 K, 10⁹ s^–1条件下, NbTaTiZr沿[100]晶向压缩的各性质随压缩应变的变化规律　(a) 压缩应力; (b) 能量和体积; (c) 位错密度; (d) 相结构. (e) 不同应变下的径向分布函数

Figure 3. Evolution of properties for NbTaTiZr under uniaxial compression along the [100] crystalline orientation as a function of compressive strain at 300 K and a strain rate of 10⁹ s^–1: (a) Compressive stress; (b) energy and volume; (c) dislocation density; (d) phase structure. (e) Radial distribution functions at different strain levels.

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图 4 300 K, 10⁹ s^–1沿[100]晶向压缩结构时, 应变分别为15.78%, 15.96%, 17.27%, 24.16%, 30%时的位错密度(a1)—(e1)和相结构分布(a2)—(e2). 蓝色代表BCC, 红色代表HCP, 绿色代表FCC, 灰色代表其他结构

Figure 4. Dislocation density (a1)–(e1) and phase structure distribution (a2)–(e2) in NbTaTiZr under uniaxial compression along the [100] orientation at 300 K and a strain rate of 10⁹ s^–1, shown at compressive strains of 15.78%, 15.96%, 17.27%, 24.16%, and 30%. Blue represents BCC, red represents HCP, green represents FCC, and grey represents other structures.

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图 5 沿不同晶向压缩的应力应变曲线(a), (b)和相结构的变化规律(c), (d)　(a), (c) 沿[110]晶向; (b), (d) 沿[111]晶向

Figure 5. Stress-strain curves (a), (b) and structural evolution (c), (d) under uniaxial compression along the different orientations: (a), (c) [110] orientations; (b), (d) [111] orientations.

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图 6 300 K, 10⁹ s^–1条件下沿[110]晶向压缩, 应变不同时的原子结构(a1)—(a4)和剪应变分布(b1)—(b4)　(a1), (b1) 8.3%; (a2), (b2) 8.6%; (a3), (b3) 8.9%; (a4), (b4) 14.9%

Figure 6. Atomic structures (a1)—(a4) and shear strain distribution (b1)—(b4) in NbTaTiZr under uniaxial compression along the [110] orientation at 300 K and 10⁹ s^–1 for varying strains: (a1), (b1) 8.3%; (a2), (b2) 8.6%; (a3), (b3) 8.9%; (a4), (b4) 14.9%.

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图 7 300 K, 10⁹ s^–1沿[111]晶向压缩结构时, 应变分别为16.7%, 17.4%, 18.7%, 24%, 30%时的位错密度(a1)—(e1)和相结构分布(a2)—(e2), 其中蓝色代表BCC, 红色代表HCP, 绿色代表FCC, 灰色代表其他结构　(a1), (a2) 16.7%; (b1), (b2) 17.4%; (c1), (c2) 18.7%; (d1), (d2) 24%; (e1), (e2) 30%

Figure 7. Dislocation density (a1)–(e1) and phase structure distribution (a2)–(e2) in NbTaTiZr under uniaxial compression along the [111] orientation at 300 K and a strain rate of 10⁹ s^–1 for varying strains, and blue represents BCC, red represents HCP, green represents FCC, and grey represents other structures: (a1), (a2) 16.7%; (b1), (b2) 17.4%; (c1), (c2) 18.7%; (d1), (d2) 24%; (e1), (e2) 30%.

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图 8 (a), (b) 10⁸ s^–1和10¹⁰ s^–1应变率下的应力应变曲线和位错密度; (c), (d) 10⁸ s^–1和10¹⁰ s^–1应变率下相比例随应变的变化

Figure 8. (a), (b) Stress-strain curves and dislocation density at strain rates of 10⁸ s^–1 and 10¹⁰ s^–1; (c), (d) phase proportion versus strain at 10⁸ s^–1 and 10¹⁰ s^–1.

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图 9 [100], [110]和[111]晶向在10⁸ s^–1, 10⁹ s^–1, 10¹⁰ s^–1应变率条件下的屈服强度(a)和无序结构比例(b); 10⁸ s^–1, 10¹⁰ s^–1应变率条件下[110]晶向(c)和 [111]晶向(d)的位错密度随应变的变化

Figure 9. Yield strength (a) and disordered structure proportion (b) under [100], [110], and [111] crystal orientations at strain rates of 10⁸ s^–1, 10⁹ s^–1, and 10¹⁰ s^–1; dislocation density versus strain for [110] orientation (c) and [111] orientation (d) at strain rates of 10⁸ s^–1 and 10¹⁰ s^–1.

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图 10 应变为28%时, 位错组态在应变率10⁸ s^–1(a1)—(a3)和10¹⁰ s^–1(b1)—(b3)下的分布, 灰色原子表示无序原子　(a1), (b1) [100]晶向; (a2), (b2) [110]晶向; (a3), (b3) [111]晶向

Figure 10. Dislocation configurations at 28% strain under strain rates of 10⁸ s^–1 (a1)–(a3) and 10¹⁰ s^–1 (b1)–(b3), and the gray atoms indicate disordered atomic configurations: (a1), (b1) [100] crystallographic orientations; (a2), (b2) [110] crystallographic orientations; (a3), (b3) [111] crystallographic orientations.

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图 11 不同元素含量的压缩应力应变曲线　(a) Nb, (b) Ta, (c) Ti, (d) Zr

Figure 11. Compressive stress-strain curves for different content of element: (a) Nb, (b) Ta, (c) Ti, (d) Zr.

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图 12 300—2100 K温度范围内改变单一元素含量对屈服强度的影响　(a) Nb; (b) Ta; (c) Ti; (d) Zr

Figure 12. Effects of varying the content of a single element on yield strength across the 300—2100 K temperature range: (a) Nb; (b) Ta; (c) Ti; (d) Zr.

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表 1 DP模型预测值和DFT计算结与实验值的比较

Table 1. Comparison of DP model predictions with DFT calculations and experimental values.

Method T_m/K C₁₁/GPa C₁₂/GPa C₄₄/GPa B/GPa G/GPa μ

NbTaTiZr DP 2361 170 129 30 142 32 0.43

Exp/DFT 2440 (3.2%)
179 (5.0%)
134 (3.7%)
33 (10%)
151 (6.0%)
27 (18.5%)
0.42 (2.4%)

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