Lattice-distortion dependent yield strength in high entropy alloys
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)
- et al.
Microstructures and properties of high-entropy alloys
Prog. Mater. Sci.
(2014) - et al.
Corrosion of AlxCoCrFeNi high-entropy alloys: Al-content and potential scan-rate dependent pitting behavior
Corrosion Sci.
(2017) - et al.
Fatigue behavior of a wrought Al0. 5CoCrCuFeNi two-phase high-entropy alloy
Acta Mater.
(2015) - et al.
Fatigue behavior of Al0.5CoCrCuFeNi high entropy alloys
Acta Mater.
(2012) - et al.
A critical review of high entropy alloys and related concepts
Acta Mater.
(2017) - et al.
Microstructural development in equiatomic multicomponent alloys
Mater. Sci. Eng., A
(2004) - et al.
Effect of aluminum on the microstructure and properties of two refractory high-entropy alloys
Acta Mater.
(2014) - et al.
A hexagonal close-packed high-entropy alloy: the effect of entropy
Mater. Des.
(2016) - et al.
Microstructural and mechanical characterization of an equiatomic YGdTbDyHo high entropy alloy with hexagonal close-packed structure
Acta Mater.
(2018) - et al.
High-entropy Al0.3CoCrFeNi alloy fibers with high tensile strength and ductility at ambient and cryogenic temperatures
Acta Mater.
(2017)
Alloying, thermal stability and strengthening in spark plasma sintered AlxCoCrCuFeNi high entropy alloys
J. Alloys Compd.
Sluggish diffusion in Co-Cr-Fe-Mn-Ni high-entropy alloys
Acta Mater.
Corrosion behavior of an equiatomic CoCrFeMnNi high-entropy alloy compared with 304 stainless steel in sulfuric acid solution
Corrosion Sci.
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.
Microstructure and wear behavior of AlxCo1.5CrFeNi1.5Tiy high-entropy alloys
Acta Mater.
MC complex carbide in AISI M2 high-speed steel
Mater. Lett.
Composition design of high entropy alloys using the valence electron concentration to balance strength and ductility
Acta Mater.
Transmission electron microscopy characterization of dislocation structure in a face-centered cubic high-entropy alloy Al0. 1CoCrFeNi
Acta Mater.
Temperature dependent stacking fault energy of FeCrCoNiMn high entropy alloy
Scripta Mater.
Transformation induced softening and plasticity in high entropy alloys
Acta Mater.
Theory of strengthening in fcc high entropy alloys
Acta Mater.
Solute strengthening in random alloys
Acta Mater.
Mechanical properties, microstructure and thermal stability of a nanocrystalline CoCrFeMnNi high-entropy alloy after severe plastic deformation
Acta Mater.
The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy
Acta Mater.
The effect of randomness on the strength of high-entropy alloys
Acta Mater.
Solid-solution strengthening in refractory high entropy alloys
Acta Mater.
Cited by (80)
The shear softening and dislocation glide competition due to the shear-induced short-range order degeneration in CoCrNi medium-entropy alloy
2024, Journal of Materials Science and TechnologyA hierarchical multiscale crystal plasticity model for refractory multi-principal element alloys
2024, International Journal of Mechanical SciencesRecent progress in high-entropy alloys: A focused review of preparation processes and properties
2024, Journal of Materials Research and TechnologyDesigning the composition and optimizing the mechanical properties of non-equiatomic FeCoNiTi high-entropy alloys
2024, Journal of Materials Research and Technology