Lattice-distortion dependent yield strength in high entropy alloys

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Abstract

High entropy alloys (HEAs) have attracted great attention due to their impressive properties induced by the severe lattice distortion in comparison to the conventional alloys. However, the effect of severe lattice distortion on the mechanical properties in face-centered-cubic (FCC) and body-centered-cubic (BCC) structured HEAs is still not fully understood, which are critically important to the fundamental studies as well as the industrial applications. Herein, an analytical model for predicting the solid-solution strengthening and the yield stress in FCC and BCC HEAs accounting for the lattice distortion is presented. Both the calculated solid-solution strengthening and the yield strength are compared to the experimental results, to verify the rationality of the built theoretical model. The numerical predictions considering the severe lattice-distortion effect agree well with the experimental results for both FCC and BCC HEAs, in terms of the yield strength and the solid-solution strengthening. Based on theoretical model, the constructed contour line of solid-solution strengthening can be used to evaluate the effect of elemental type on yield strength of HEAs, which provides guideline for discovering and screening the advanced HEAs. Furthermore, it has been identified the atomic-radius mismatch and solid-solution strengthening do not increase directly as the number of components increases in HEAs based on the theoretical analysis. In the Alx-Cr-Co-Fe-Ni-Mn HEA system, the atomic-radius mismatch and shear-modulus mismatch induced by the added Al element govern the solid-solution strengthening, but this situation disappears in the Alx-Hf-Nb-Ta-Ti-Zr HEA system. It is further confirmed that the effect of the atomic-radius mismatch on the solid-solution strengthening is obviously higher than effect of the shear-modulus mismatch, dominating the yield strength. These results provide an insight into the effect of severe lattice distortion on the yield strength, and demonstrate a theoretical framework for identifying the desired compositions to create the excellent HEAs.

Introduction

High entropy alloys (HEAs) break the traditional alloy design concepts where the traditional alloys are composed of one or rarely two dominant elements. HEAs are essentially composed of five or more principal elements in equimolar or near-equimolar ratios, with each elemental composition between 5 and 35 atomic percent [[1], [2], [3], [4], [5], [6], [7], [8], [9]]. Even though HEAs possess the complex compositions, they are typically keen on the formation of single solid-solution structures, such as face-centered-cubic (FCC), body-centered-cubic (BCC), or hexagonal-close-packed (HCP) structures, owing to the fact that their high-mixing entropy can decrease the Gibbs free energy and retard the formation of intermetallic [[10], [11], [12], [13], [14], [15]]. The multi-component HEAs have drawn great attention due to their remarkable mechanical potentials, such as outstanding tensile strength and fracture toughness at cryogenic temperatures [16], wonderful thermal stability [17,18], resistance to wear and corrosion [3,7,19,20], and great fatigue and creep properties [2,5,7,10], which conventional metal materials can't afford. These excellent properties qualify that the HEAs can be applied in a wide range of fields.

It is established that the mechanical property of HEAs is strongly dependent on the microstructure. Therefore, recent paper [[21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]] are devoted to enhancing the link between the microstructure and performance in HEAs, and improving the mechanical properties by adjusting the microstructure. For example, with various Al and Ti compositions, a series of AlxCo1.5CrFeNi1.5Tiy HEAs were designed in the previous work [21]. Compared with the traditional wear-resistant steels, the wear resistance of the Co1.5CrFeNi1.5Ti and Al0.2Co1.5CrFeNi1.5Ti HEAs are at least two times better with the similar hardness [22]. This trend is attributed to the excellent anti-oxidation property and resistance to thermal softening in HEAs [21]. The valence electron concentration plays an important role in phase formation, based on the valence electron concentration, an effective method is proposed to design HEA constituents for balancing strength and ductility by selecting ideal elements [23], it is found high valence electron concentration is beneficial to forming FCC phases that improve ductility, while a low valence electron concentration is conducive in forming BCC phases with enhanced strength. By making use of the state-of-the-art TEM characterization technique, dislocation reactions in a plastically-deformed FCC HEA was conducted [24]. It is found the low stacking fault energy results in the widely-dissociated dislocation cores, which, subsequently, causes the significant work hardening with a large hardening rate. In addition, the effect of the temperature on the stacking fault energy for FeCrCoNiMn has been studied in previous research using quantum mechanical first-principles methods [25]. The results show a large positive temperature factor for the stacking fault energy, which could explain the observed twinning induced plasticity effect at sub-zero temperatures and the transformation induced plasticity effect at cryogenic conditions in FeCrCoNiMn [25]. Moreover, the molecular-dynamics simulation is also employed in studying the plastic-deformation mechanism of HEAs in recent years. The kinetics of the strain-induced phase transformation from FCC to BCC phases in the single-crystal and nanocrystalline HEA is investigated in the previous work, it is found that the low stacking fault energy plays a key role in affecting the plasticity of HEA [26]. Combining elasticity-based theory and material inputs computed by ab initio methods, a predictive theory for the yield strength in FCC HEAs is presented [27,28]. Further, a predictive model on the intrinsic yield strength of HEAs is presented within the framework of the Peierls-Nabarro model [31]. Combining the mechanical testing and the literature data, a solid-solution strengthening model containing the athermal component and the thermally-activated component is developed to describe the yield stress of refractory HEAs [32]. Through different research methods, the previous studies have made a great progress in revealing the close correlation between the microstructures and properties of HEAs [[21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]].

Due to the difference in atomic size and shear modulus between different principal elements, noteworthy lattice-distortion are produced in HEAs. It has been demonstrated that the strain in the HEA lattice is greater than that of pure Ni, the magnitude of this strain was similar to that observed in some of the binary Ni–33Cr and ternary Ni-37.5Co–25Cr alloys and cannot be considered anomalously large in previous research [33]. As shown in Fig. 1, Fig. 2a, there is almost no lattice distortion in the perfect FCC and BCC structure with only one element. As the addition of the other element with different atomic size and atomic shear-modulus, the severe lattice distortion occurs in both the binary alloy and the five-principal-element HEAs (see Fig. 1, Fig. 2c). However, the effect of the additional element on the lattice distortion is unclear, and the strengthening mechanism produced by the severe lattice distortion is still not fully understood in theoretical perspectives [[34], [35], [36]].

The purpose of this study is to explore theoretically the severe lattice-distortion effect on the strength of HEAs. In order to achieve this purpose, a theoretical model is developed by introducing the distorted unit cell. Moreover, the grain-size distribution effect is coupled in the present proposed model to more precisely predict the yield strength. The proposed model is applied to describe the severe lattice-distortion effect and predict the yield strength of HEAs. The numerical predictions are in good agreement with the experimental results in terms of both the yield strength and the solid-solution strengthening in various HEAs. Furthermore, the impacts of the Al atomic fraction on the solid-solution strengthening and mismatch degree in the Alx-Co-Cr-Fe-Ni-Mn and Alx-Hf-Nb-Ta-Ti-Zr HEAs are discussed. The present research demonstrate that the atomic-radius mismatch in HEAs and medium-entropy alloys are not significant but similar to that in binary alloys theoretically. The contour plots on the shear modulus and atomic radius effects in solid-solution strengthening of various HEAs can provide help for discovering and screening the high strength of advanced HEAs. The meaningful model is expected to provide a theoretical method to explore the severe lattice-distortion effect and discover advanced higher-strength HEAs in the future.

Section snippets

Lattice-distortion effect

As is known to all, the solid-solution strengthening of metals and alloys originates from the elastic interactions between the local stress fields of solute atoms and the mobile dislocations. In the dilute alloys with a low solute concentration, the solute atoms are almost surrounded by the solvent atoms, resulting in that the local lattice distortions caused by the solute atoms are greatly slight. Hence, the lattice-friction stress is pretty small for the dilute alloys. For the dilute solid

Severe lattice distortion on yield stress in FCC HEA

In order to verify the accuracy and rationality of the model, the predicted tensile strength mentioned above are compared with the experimental results in the Al0.3CrCoFeNi HEA [13]. According to the previous study [46], the Hall-Petch coefficient, k, in the Al0.3CrCoFeNi HEA in Eq. (7) is 824 MPa μm0.5. As for the solid-solution strengthening based on the constructed theoretical model, the atomic radius and the shear modulus of each element are shown in Table 1. Fig. 3a shows the tensile

Discussion

The previous study shows the atomic-radius mismatch enhances with increasing the number of incorporated principal elements in HEAs [53]. However, it is demonstrated that the lattice strain in CoCrFeMnNi is not significant but similar to that in CrNi and CoCrNi lately [33]. Fig. 8a shows the atomic-radius mismatch in various BCC HEAs based on Eq. (3). It is found that the increasing incorporated principal elements does not necessarily increase the atomic-radius mismatch in HEAs, which is against

Conclusions

The theoretical model coupling the lattice distortion with grain-size distribution is presented to describe the solid-solution strengthening and yield strength in FCC and BCC structured HEAs. The simulated results are in good agreement with the experimental data obtained for the solid-solution strengthening and the yield strength in various HEAs. It has been confirmed the atomic-radius mismatch and solid-solution strengthening can be irrelevant to the increasing number of components in HEAs. In

CRediT authorship contribution statement

Li Li: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Writing - review & editing. Qihong Fang: Formal analysis, Methodology, Resources, Supervision, Writing - review & editing. Jia Li: Investigation, Writing - review & editing, Funding acquisition. Bin Liu: Writing - review & editing, Project administration, Funding acquisition. Yong Liu: Writing - review & editing, Project administration, Funding acquisition. Peter K. Liaw: Resources, Writing - review

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to deeply appreciate the support from the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51621004), the NNSFC (11772122, 51871092, 51625404, 51771232, and 51671217), the Fundamental Research Funds for the Central Universities (531107051151), and the National Key Research and Development Program of China (2016YFB0700300). The research is supported by Hunan Provincial Innovation Foundation for Postgraduate (CX2018B156

References (53)

  • R. Sriharitha et al.

    Alloying, thermal stability and strengthening in spark plasma sintered AlxCoCrCuFeNi high entropy alloys

    J. Alloys Compd.

    (2014)
  • K.Y. Tsai et al.

    Sluggish diffusion in Co-Cr-Fe-Mn-Ni high-entropy alloys

    Acta Mater.

    (2013)
  • H. Luo et al.

    Corrosion behavior of an equiatomic CoCrFeMnNi high-entropy alloy compared with 304 stainless steel in sulfuric acid solution

    Corrosion Sci.

    (2018)
  • T. Fujieda et al.

    CoCrFeNiTi-based high-entropy alloy with superior tensile strength and corrosion resistance achieved by a combination of additive manufacturing using selective electron beam melting and solution treatment

    Mater. Lett.

    (2017)
  • M.H. Chuang et al.

    Microstructure and wear behavior of AlxCo1.5CrFeNi1.5Tiy high-entropy alloys

    Acta Mater.

    (2011)
  • M.M. Serna et al.

    MC complex carbide in AISI M2 high-speed steel

    Mater. Lett.

    (2009)
  • R. Chen et al.

    Composition design of high entropy alloys using the valence electron concentration to balance strength and ductility

    Acta Mater.

    (2018)
  • X.D. Xu et al.

    Transmission electron microscopy characterization of dislocation structure in a face-centered cubic high-entropy alloy Al0. 1CoCrFeNi

    Acta Mater.

    (2018)
  • S. Huang et al.

    Temperature dependent stacking fault energy of FeCrCoNiMn high entropy alloy

    Scripta Mater.

    (2015)
  • J. Li et al.

    Transformation induced softening and plasticity in high entropy alloys

    Acta Mater.

    (2018)
  • C. Varvenne et al.

    Theory of strengthening in fcc high entropy alloys

    Acta Mater.

    (2016)
  • C. Varvenne et al.

    Solute strengthening in random alloys

    Acta Mater.

    (2017)
  • B. Schuh et al.

    Mechanical properties, microstructure and thermal stability of a nanocrystalline CoCrFeMnNi high-entropy alloy after severe plastic deformation

    Acta Mater.

    (2015)
  • F. Otto et al.

    The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy

    Acta Mater.

    (2013)
  • L. Zhang et al.

    The effect of randomness on the strength of high-entropy alloys

    Acta Mater.

    (2019)
  • F.G. Coury et al.

    Solid-solution strengthening in refractory high entropy alloys

    Acta Mater.

    (2019)
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