Elsevier

Computational Materials Science

Volume 152, September 2018, Pages 169-177
Computational Materials Science

Revealing the local lattice strains and strengthening mechanisms of Ti alloys

https://doi.org/10.1016/j.commatsci.2018.05.028Get rights and content

Highlights

  • The strengthening mechanisms of HCP Ti-X are studied by first-principles calculations.

  • The mechanical and chemical contributions to the local lattice strains are distinguished.

  • The power-law-scaled yield strength in terms of EWF and grain size is validated in Ti-Al alloys.

Abstract

In this work, effects of solute atoms (X) on lattice parameters, bulk modulus, enthalpy of formation, lattice distortion energy, electron work function (EWF) and bonding morphology/strength of HCP Ti95X are comprehensively studied by first-principles calculations. Here, X includes the α-stabilizer Al, and the β-stabilizer Cr, Mo, V and Nb, which are commonly combined in the high-strength Ti7333 and Ti5553 alloys. Attributing to various atomic size and number of valence electrons of these solute atoms, the mechanical (lattice distortion) and the chemical (solute atom) contributions to the local lattice strains are clearly distinguished in terms of lattice distortion energy and bonding charge density. It is found that the equilibrium volume of Ti95X decreases linearly with the increased HCP volume of each solute atom. The less change of volume yields minimum lattice distortion energy. Moreover, a higher value of Δρ caused by the electron redistributions of solute atoms than the matrix indicates an improved bonding strength via the coupling effects of lattice distortion and valence electrons. The bonding strength of Ti95X increases in the order of Ti-Al < Ti-Cr < Ti-V < Ti-Nb < Ti-Mo. According to the available measured yield strength of Ti-Al alloys, the proposed a power-law-scaled relationship in terms of EWF and grain size results in the predicted yield strength agree well with those experimental data. This work provides an atomic and electronic basis for the solid solution strengthening and grain refinement hardening mechanisms, paving a path accelerating the development of advanced high-strength Ti alloys.

Introduction

Titanium alloy is widely used in various fields especially aerospace due to its excellent mechanical and machining properties such as high specific strength, good corrosion resistance and high heat resistance [1], [2], [3]. Recent years, β and near-β Ti alloys are considered as essential structural materials for aeronautical applications, attributing to their high yield strength, better fatigue and crack propagation resistance [4], [5], [6], [7], [8]. For example, Ti–5Al–5Mo–5V–3Cr (Ti-5553, wt%) being a recently developed beta Ti alloy gradually replaces Ti–10V–2Fe–3Al (Ti-1023) alloy, which is processed into the landing gear components for higher strengths, wider processing windows and higher hardenability [9], [10], [11], [12], [13]. Meanwhile, near β-Ti alloys Ti-7Mo-3Al-3Nb-3Cr (Ti-7333) have gained increased attention for aerospace applications due to their unique combination of high strength, reasonable ductility, excellent hardenability, good anti-fatigue performance and excellent corrosion resistance [7], [14], [15]. It is understood that the main deformation mechanisms of β-Ti alloys include twinning, dislocation slip, and martensitic phase transformation, all of which are related to the stability of the β phase [16], [17]. Particularly, in the HCP structure, the basal plane serves as either the principle or the secondary slip plane, yielding basal plane stacking fault energy a highly desirable property tailored by alloying [18], [19]. Twinning is another important deformation mechanism besides slip. Unfortunately, the twinning mechanisms in HCP metals/alloys are still unclear despite extensive studies [20], [21], [22], [23], which could be attribute to the changes of the energy pathway for twinning [24], [25] and the local strain/stress [26] affected by different solute atoms.

Optimization of lattice misfit/distortion has been an extremely attractive approach in the development of advanced structural materials [6], [27], [28], [29], [30], [31], [32]. Efforts have been made to reveal the relationship between electronic structure and mechanical properties of materials, with emphasis on developing models of fracture and deformation [33]. For a given HCP structure, the selection of the dominant slip system during deformation is known to be an electronic property since the electronic structure controls the relative energies of stacking faults in the basal and prismatic planes, determining the preferred dissociation plane for the dislocations [34]. It is understood that the c/a ratio is an important parameter dominating the slip system (slide plane and direction) of deformation twins in HCP structure [35] In particular, the adjustment of c/a ratio could activate various twinning systems, thus to improve the number of independent slip systems [35], [36]. Accordingly, the lattice parameters and the lattice misfit have become important indicators characterizing not only the partitioning behaviors but also the solid solution strengthening effects of solute atoms [30], [31], [32].

Besides solid solution strengthening [3], [37], grain refinement hardening [38], [39] is another traditional strengthening mechanisms, both of which are conventionally utilized to enhance the strength as well as retaining or imparting the ductility by the elastic interaction between the respective lattice strains of the solute atoms and the structural defects [3]. Through utilizing the modern experimental and/or computational tools, the solutes-defect interactions [40], [41], [42] could be understood at the atomic/electronic level, providing an insight into the detailed bonding structures dominated properties and a physics-based model [39], [43]. The relationship between electronic structure and mechanical properties of materials is under extensive investigations with emphasis on developing atomistic models of fracture and deformation [33], [43], [44], [45], [46], [47], [48], [49], [50]. Therefore, the fundamental understanding of the effect of solute atoms on the deformation behavior of Ti alloys is critical to improve their strength and ductility in the development of the advanced high-strength Ti alloys.

In this work, effect of solute atoms (X = Al, Cr, Mo, Nb, and V) on lattice parameters, bulk modulus, enthalpy of formation, lattice distortion energy, electron work function (EWF) and bonding morphology/strength of HCP Ti95X are comprehensively studied by first-principles calculations. Here, these solute atoms commonly combined in the high-strength Ti7333 and Ti5553 alloys are selected as case studies. Efforts are made to reveal the atomic and electronic basis for the solid-solution strengthening and grain refinement hardening of high-strength Ti alloys through an integrated first-principles calculations and EWF study. The power law scaled yield strength in terms of EWF and grain size is proposed and validated in the Ti-Al alloys, yielding a good agreement between the theoretical and the experimental data. This work provides an insight into the atomic and electronic basis for the strengthening mechanisms of Ti alloys and paves a path accelerating the development of advanced high-strength Ti alloys.

Section snippets

Methodology

First-principles calculations at 0 K are conducted by employing the Vienna ab initio simulation package (VASP) [51], [52] with the generalized gradient approximation (GGA) [53] for the exchange-correction functional of Perdew-Burke-Ernzerhof (PBE [54]) and the projector augmented wave (PAW) [55] for the electron-ion interaction. The plane wave cutoff energy is set to 1.3 times of the maximum energy of each element (ENCUT = 1.3 ∗ ENMAX), and the energy convergence criterion of the electronic

Results and discussions

Fig. 1 shows the properties of Ti95X from the BM4 EOS fitting, which is also summarized in Table 1 in detail. It is presented that our calculated equilibrium values of energy, equilibrium volume, and bulk modulus of Ti-X alloys match well with available experimental and theoretical results. Based on the energy-volume curve presented in Fig. 1(a), the local lattice distortions caused by the solute atoms at the equilibrium state could be revealed in terms of equilibrium volume, lattice misfit,

Conclusions

In summary, the α-stabilizer Al, and β-stabilizer Cr, Mo, V and Nb, which are commonly combined in the high-strength Ti7333 and Ti5553 alloys, are selected to reveal the local lattice strain and the strengthening mechanisms of HCP Ti alloys. Lattice parameters, bulk modulus, enthalpy of formation, lattice distortion energy, electron work function, and bonding morphology/strength of Ti95X are comprehensively studied by first-principles calculations. It is found that the equilibrium volume of Ti95

Acknowledgements

This work was financially supported by National Key Research and Development Program of China (2016YFB0701304 and 2016YFB0701303), National Natural Science Foundation of China (51690163), and Fundamental Research Funds for the Central Universities in China (G2016KY0302). First-principles calculations were carried out on the clusters at the Northwestern Polytechnical University.

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