Microstructural evolution and mechanical properties of Al0.3CoCrFeNiSix high-entropy alloys containing coherent nanometer-scaled precipitates

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Microstructural evolution and mechanical properties of Al0.3CoCrFeNiSix high-entropy alloys containing coherent nanometer-scaled precipitates Peng Cheng, Yuhong Zhao *, Xiaotao Xu, Shuai Wang, Yuanyang Sun, Hua Hou School of Materials Science and Engineering, North University of China, Taiyuan, 030051, China

A R T I C L E I N F O

A B S T R A C T

Keywords: High-entropy alloy Microstructure Mechanical properties Strengthening mechanisms

In this work, Al0.3CoCrFeNiSix (x ¼ 0, 0.2, 0.5, 0.8, 1.0 in molar ratio) high-entropy alloys (HEAs) were designed by introducing a non-metallic element Si. The microstructural evolution and its effect on the mechanical properties were discussed. The results suggested that the addition of Si promoted the transition from facecentered cubic (FCC) to body-centered cubic (BCC)/ordered BCC (B2) phases, in which the spherical Cr-rich BCC nanoparticles were coherently dispersed in the Al, Ni-rich B2 matrix. The mechanical properties were improved by adding an appropriate amount of Si. When x increased from 0 to 0.2, the tensile yield strength and ultimate tensile strength increased by 63% and 60%, respectively, while the elongation remained at 56%. The Vickers hardness enhanced from 143 HV (x ¼ 0) to 826 HV (x ¼ 1.0) with increasing Si content, and the specific wear rate reduced by two orders of magnitude accordingly. The strengthening mechanisms were evaluated for this series of HEAs based on the correlation between microstructure and mechanical properties.

1. Introduction High-entropy alloys (HEAs), as a new class of metal materials, have drawn growing attention since Cantor and Yeh et al. [1,2] first proposed that in 2004. By definition, HEAs typically contain multiple principal elements with equal or near-equal molar ratios. HEAs are influenced by high entropy effect tending to generate a simple solid solution, such as face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal closed-packed (HCP) structures, rather than complex multiphase struc­ tures consisting of intermetallic compounds [3–7]. Until now, several reported HEA systems have unique properties superior to traditional alloys, including high strength, high hardness, excellent high-temperature performance, good fatigue, corrosion, oxidation, and wear resistance [7–19]. There are some common strengthening mech­ anisms in HEAs, such as solid solution strengthening, dislocation strengthening, grain boundary strengthening, and precipitation strengthening [20–24]. The phase structure and properties of HEAs are affected by the elemental composition, and more than 30 kinds of elements have been applied [25,26]. HEAs are divided into three types according to the different constituent elements, namely, the late transition metals (LTMs) base FCC HEAs, the early transition metals (ETMs) base BCC refractory HEAs (RHEAs), as well as the Al-TMs HEAs with FCC þ BCC dual-phase

structure. Among them, the single-phase FCC HEAs represented by CoCrFeMnNi (commonly known as Cantor alloy) have excellent fracture toughness and ductility at room and cryogenic temperatures [1,17, 27–29]. The single-phase BCC RHEAs exhibit higher hardness and strength than Ni-based superalloys at ambient and elevated tempera­ tures, such as NbMoTaW and VNbMoTaW RHEAs [30–32]. However, it is difficult for single-phase HEAs to achieve a balance between ductility and strength [2]. In the case of Al-LTMs HEAs, the crystal phase can be altered by adjusting the Al content. The widely reported AlxCoCrFeNi system is a typical representative. It passes from single FCC structure (x < 0.5) to single BCC structure (x > 0.9) and forms coexisting of both structures in the intermediate range [3,33–35]. The BCC phase in the AlxCoCrFeNi system forms a nano-sized two-phase structure through the spinodal decomposition mechanism [3]. The structural diversities generally determine the differences in mechanical properties [33–45]. Considering the strengthening effect of Si on conventional metallic materials such as steel, Zhu et al. [46] discussed the microstructure and properties of AlCoCrFeNiSix alloys. The result indicated that mechanical properties were improved by introducing Si to form a nano-scale cellular structure. Liu et al. [47] and Kumar et al. [48] observed the evolution of crystal structure from FCC to FCC þ BCC with increasing Si concentra­ tion in Al0.5CoCrCuFeNiSix and AlCoCrCuFeNiSix alloys, respectively. Nevertheless, the effect of non-metallic element Si on HEAs is still poorly

* Corresponding author. 3 Xueyuan Road, Taiyuan, Shanxi, 030051, China. E-mail addresses: [email protected] (P. Cheng), [email protected] (Y. Zhao). https://doi.org/10.1016/j.msea.2019.138681 Received 3 September 2019; Received in revised form 8 November 2019; Accepted 11 November 2019 Available online 12 November 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Peng Cheng, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2019.138681

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understood, and the correlation between microstructure and mechanical properties is rarely mentioned and discussed in detail. According to the above discussion, Al0.3CoCrFeNiSix HEAs with different Si concentra­ tions were designed in this work. The microstructural evolution and its effect on the mechanical properties were discussed. Concretely, we demonstrated that the addition of Si to the single-phase FCC Al0.3CoCrFeNi alloy not only promoted the formation of BCC/ordered BCC (B2) phase, but also induced the coherent precipitation of nano­ particles. The strengthening mechanisms were evaluated based on the correlation between microstructure and mechanical properties.

reciprocating amplitude of 5 mm and a normal load of 40 N. Three tests were performed on each sample. The surface roughness and the volume loss were investigated using a surface profilometer (Micro XAM-3D) after tribological testing. The specific wear rate [50,51] for evaluating wear property is defined as: K¼

V FL

(1)

where K is the specific wear rate, V is the volume loss, F is the normal load, and L is the sliding distance. The worn surfaces were analyzed by SEM and EDS.

2. Experimental procedure

3. Results

The Al0.3CoCrFeNiSix (x ¼ 0, 0.2, 0.5, 0.8, 1.0 in molar ratio) HEAs were produced by arc-melting under a Ti-gettered high purity Ar at­ mosphere on a Cu hearth. The raw materials were Al, Co, Cr, Fe, Ni, and Si particles with purity higher than 99.95 wt%. Each ingot was flipped and re-melted at least five times to improve the chemical homogeneity. For convenience, the above five alloys are named Si0, Si0.2, Si0.5, Si0.8, and Si1.0, respectively. The crystal structure of the arc-melted samples was characterized by X-ray diffraction (XRD, Rigaku D/max-rB) using a Cu-Kα radiation scanning from 20� to 80� at a scanning rate of 2� /min, and the lattice parameters were calculated by the external standard method [49]. The microstructure and chemical composition were characterized using scanning electron microscope (SEM, Hitachi SU5000) and transmission electron microscopy (TEM, JEM F200), both of which were equipped with energy dispersive spectroscopy (EDS) detectors. The SEM samples were mechanically polished and then etched in a mixed solution of 25% HNO3 and 75% HCl. The samples for TEM were cut from the ingots and ground to a thickness of about 50 μm using abrasive paper, then polished by twin-jet electropolishing in a solution of 10% HClO4 and 90% C2H5OH cooled to 30 � C. The volume fraction of FCC and BCC/B2 phases was determined by analyzing at least ten SEM images using ImageJ software. Statistical analysis on the vol­ ume fraction and average size of precipitates was conducted with at least ten TEM bright-field images. The precipitate size was defined using an pffiffiffiffiffiffiffiffiffiffiffiffiffiffi area-equivalent diameter (i.e., r ¼ 2 area=π) calculated from the pro­ jected area of spherical particles. The average precipitate size was determined by analyzing more than 500 particles from different regions. The hardness values were tested using a Vickers hardness tester (TMHVS-1000Z) with a load of 500 g and a holding time of 15 s. At least 20 measurements were performed at different areas for each sample, and the average values were applied. Both compression and tension tests were carried out using an Instron 3382 universal testing system with a strain rate of 1 � 10 3 s 1 at ambient temperature. The cylindrical compression samples with a size of Φ3 mm � 6 mm and the dog-bone shaped tensile samples with a gauge dimension of 10 mm (length) � 2 mm (width) � 1.2 mm (thickness) were machined from the ingots respectively. The tensile strain was measured directly using an extensometer. The machine stiffness should be considered in determining the compressive strain. The compression test was performed without any sample to record the force-displacement curve, from which the machine stiffness was obtained. The graphite sheets and high-pressure grease were used to minimize the friction be­ tween the sample and anvil. The true compressive stress-strain curves were presented after correcting the errors produced by the test machine. At least three sets of mechanical (compression/tension) tests were per­ formed under each condition to confirm the reproducibility of the results. The wear behavior of the Al0.3CoCrFeNiSix HEAs was analyzed using a ball-on-block high-speed reciprocating wear tester (MFT-4000) at ambient temperature under dry conditions. The tested samples with a dimension of 20 mm � 10 mm � 5 mm were machined and polished. The counterpart was GCr15 ball with a diameter of 5 mm. The tests were performed at a sliding velocity of 100 mm/min for 30 min with a

3.1. Microstructure analysis The XRD patterns of the Al0.3CoCrFeNiSix alloys are shown in Fig. 1. Only diffraction peaks corresponding to the FCC phase were identified in the alloy without Si. The diffraction peaks related to the BCC phase appear in all Si-containing alloys, and the relative intensity increases with Si content. The (100)B2 superlattice reflection occurring near 2θ � 31� proves the presence of the B2 phase. The inset clearly shows the separation between the BCC and B2 peaks, indicating that the addition of Si results in the formation of a duplex BCC structure. The phase constitution and lattice parameters of the tested alloys are summarized in Table 1. The SEM micrographs of the Al0.3CoCrFeNiSix alloys with various Si contents are shown in Fig. 2. The microstructure of the base alloy (Si0 alloy) was determined as FCC solid solution according to the XRD re­ sults. A typical dendritic structure was observed in the Si0.2 alloy, in which the bright dendritic (DR) region is the FCC phase and the dark interdendritic (ID) region is the BCC/B2 phase. The EDS results and chemical mapping (see Table S1 and Fig. S1 in Supplementary Material) indicate that the DR regions have higher Cr and Fe contents, while the ID regions are rich in Al, Ni, and Si. The estimated volume fraction of the BCC/B2 phase increases with the increase of Si content, as shown in Fig. 2(f). When x ¼ 0.5, the ID region increases and forms a continuous network structure. A large number of side plates (marked by A in Fig. 2 (d and e)) were observed in the Si0.8 and Si1.0 alloys, which were identified as FCC phase based on phase brightness and EDS results. Fig. S2 shows representative TEM images of the Al0.3CoCrFeNiSix alloys, and the corresponding selected area electron diffraction (SAED) patterns taken from different regions are given in the insets. The base alloy displays a single FCC structure and no precipitate can be observed. The bright-field images and diffraction patterns in Fig. S2(b and c) demonstrate that the DR and ID regions in the FCC-dominated Si0.2 and Si0.5 alloys are FCC and BCC/B2 structures, respectively. For the BCCdominated Si0.8 and Si1.0 alloys, the microstructure consisting of the BCC/B2 substrate and the side plates with FCC structure was confirmed, as shown in Fig. S2(d and e). The high-magnification TEM images of the BCC/B2 regions in Fig. 3 show that nano-scale spherical particles with a size of about 60 nm are uniformly distributed in the matrix. The highresolution TEM (HRTEM) image taken from the BCC/B2 region of the Si1.0 alloy is shown in Fig. 4(a). The particles and matrix are BCC and B2 structures, respectively, as indicated by the corresponding Fast Fourier Transform (FFT) images. The magnified image of the interface and corresponding schematic diagram (Fig. 4(d and e)) demonstrate the interfacial coherency between particles and matrix. Fig. S3 shows the elemental distributions recorded from the BCC/B2 region, where Cr is concentrated in the BCC particles while Al and Ni are separated in the B2 matrix. 3.2. Mechanical properties Both compression and tension tests were conducted at ambient 2

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Fig. 1. XRD analysis for the Al0.3CoCrFeNiSix alloys.

compressive yield strength of the Si0.5 and Si0.8 alloys reaches 1039 MPa and 1555 MPa, respectively. However, the plastic strain de­ creases with the increase of Si content, and the brittle fracture occurs at x ¼ 1.0, which is expected because excessive Si addition usually leads to brittleness in silicon steels [52].

Table 1 Lattice parameters of the Al0.3CoCrFeNiSix alloys. Alloy

Phase constitution

Lattice parameters (Å)

Si0 Si0.2

FCC FCC BCC B2 FCC BCC B2 FCC BCC B2 FCC BCC B2

3.588 � 0.003 3.574 � 0.002 2.859 � 0.002 2.867 � 0.008 3.561 � 0.003 2.851 � 0.001 2.862 � 0.004 3.551 � 0.007 2.846 � 0.006 2.855 � 0.002 3.551 � 0.003 2.845 � 0.007 2.856 � 0.005

Si0.5 Si0.8 Si1.0

3.3. Hardness and wear behavior The hardness of the Al0.3CoCrFeNiSix alloys, along with the friction coefficient and specific wear rate under dry sliding wear conditions are shown in Fig. 6. A sharp increase occurs in the hardness value when x is varied from 0.2 to 0.8. At x ¼ 1.0, the hardness value reaches a maximum of 826 HV, which is about 5.8 times that of the base alloy. The friction coefficient and specific wear rate are used to evaluate the wear resistance of the Al0.3CoCrFeNiSix alloys. When x ¼ 0, the friction co­ efficient and specific wear rate are 0.45 and 1.61 � 10 4 mm3N 1m 1, respectively, and both exhibit a similar decreasing tendency with the increase in Si content. The best wear resistance was obtained at x ¼ 1.0, and the friction coefficient and specific wear rate decreased to 0.163 and 1.24 � 10 6 mm3N 1m 1, respectively. The wear resistance was mark­ edly enhanced by the addition of Si and revealed a strong correlation with hardness. To further understand the wear behavior of the Al0.3CoCrFeNiSix alloys, Fig. S4 shows the worn surface morphology after dry sliding wear test. For the Si0 and Si0.2 alloys, deep grooves and wear patches were observed on the worn surface, as well as evident plastic deformation along the grooves. The chemical compositions of the marked points in the worn surface are listed in Table S2. Higher O content was detected on the worn surface, indicating that oxidation occurred during friction and deformation. Compared to the Si0 and Si0.2 alloys, the Si0.5 alloy has a smoother worn surface with shallow grooves. When x � 0.8, large-

temperature to investigate the effect of microstructural evolution on mechanical properties. The true compressive stress-strain curves of Al0.3CoCrFeNiSix alloys are presented in Fig. 5(a). Both Si0 and Si0.2 alloys exhibit excellent ductility with compressing to the displacement limit without fracture. Fig. 5(b) shows the typical engineering tensile stress-strain curves for the two alloys, and the detailed properties of which are listed in Table 2. The tensile yield strength, ultimate tensile strength, and elongation of the base alloy are 180 MPa, 419 MPa, and 63%, respectively. The mechanical properties were improved by adding an appropriate amount of Si. When x increased from 0 to 0.2, the tensile yield strength and ultimate tensile strength increased by 63% and 60%, respectively, while the elongation remained at 56%. The compressive properties of the tested alloys are also summarized in Table 2, from which it was found that the compressive yield strength is comparable to the tensile yield strength with a difference of about 2–5%. The 3

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Fig. 2. SEM micrographs of the Al0.3CoCrFeNiSix alloys: (a) Si0, (b) Si0.2, (c) Si0.5, (d) Si0.8, and (e) Si1.0. (f) The volume fraction of the BCC/B2 phase.

area plastic deformation and grooves disappear, reflecting a slight ma­ terial removal. Fig. S5 shows the typical 3D images of wear tracks and the corresponding cross-section profiles. The width and depth of wear tracks decrease as the Si content increases. The Si0.8 and Si1.0 alloys exhibit relatively small mass loss with a wear depth of less than 1 μm.

compared with the later (68%), can alleviate the lattice distortion en­ ergy [54,55]. This transition is consistent with the previously published result that Si is an effective BCC former and stabilizer [56]. In addition, Guo et al. [57] proposed that valence electron concentration (VEC) is an effective parameter affecting phase stability in HEAs. The work was based on empirical observations suggesting that the FCC phase is stable at VEC �8.0 while the BCC phase will be stable for VEC <6.87. The mixed structure exists in the intermediate range. The variation of VEC value with the Si content is shown in Fig. S6. The VEC value decreases from 7.88 to 7.15 with the increase of Si content, indicating that the addition of Si promotes covalency. Although the current results show a wider range of single FCC phase, the VEC criterion reasonably predicts the tendency to form the BCC phase. It has been observed that the microstructure of the Si-containing alloys consists of FCC þ BCC/B2 dual-phase structure, in which the BCC and B2 structures were always identified together. As shown in Table 3, the negative mixing enthalpy between Al and Ni is larger than that of other atom pairs except for

4. Discussion 4.1. Microstructural evolution The above results demonstrate that the addition of Si has an obvious effect on the microstructure of the Al0.3CoCrFeNiSix HEAs. The base alloy possesses a single-phase FCC structure as expected [3,33,38,53]. When Si is added, other atoms in the lattice are easily replaced by Si atoms with a smaller radius, thus introducing lattice distortion. Based on the atomic packing efficiency, the transition from FCC structure to BCC one, the former of which has higher atomic packing density (74%) 4

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we use a conventional formula to evaluate the solid solution strength­ ening effect caused by Si [74,75]: 3=2

G⋅ε ⋅c1=2 ΔσS ¼ M⋅ S 700

(2)

where G is the shear modulus of Al0.3CoCrFeNi, estimated to be 76.90 GPa [76], c is the molar ratio of Si in the FCC phase, and the Taylor factor M ¼ 3.06, as an approximate conversion from shear stress to normal stress, is introduced [22]. The interaction parameter εS is expressed as: � � � � εG (3) εS ¼ �� 3εα �� 1 þ 0:5εG This includes elastic mismatch (εG) and atomic size mismatch (εα), which are expressed as follows:

εG ¼

1 ∂G G ∂c

(4)

εα ¼

1 ∂a a ∂c

(5)

where a is the lattice constant. The parameter εα can be obtained from Table 1, and the effect of εG is commonly negligible in comparison with εα. Thus, εS and ΔσS can be imputed. The theoretical strength enhancement (Δσ S) due to solid so­ lution strengthening of the Si0.2 alloy is about 11 MPa. This incremental quantity is evidently not enough for explaining the strength difference, suggesting that there are other strengthening mechanisms in the current HEAs. The alloy exhibited good comprehensive mechanical properties at x ¼ 0.2 due to the reasonable mixing of the FCC and BCC/B2 phases. The BCC/B2 phase is generally stronger but more brittle than the FCC phase because the former possesses fewer available slip systems [58]. Thus the formation of the BCC/B2 phase enhanced the strength and hardness while inevitably reducing the plasticity. Similar phenomena were also found in AlxCoCrFeNi alloys with various Al contents which correspond to the transition from FCC to BCC/B2 phases [38]. In fact, both hardness and strength are approximately proportional to the volume fraction of the BCC/B2 phase, indicating that the alloys composed of FCC þ BCC/B2 dual-phase structure can be regarded as “composite” materials. Thus, the strength of alloys is expressed in accordance with the following rule of mixture [77]:

Fig. 3. TEM bright-field images of the BCC/B2 regions in the Si-containing alloys: (a) Si0.2, (b) Si0.5, (c) Si0.8, and (d) Si1.0.

Si-(Co, Cr, Fe, Ni), which provides conditions for the formation of the Al, Ni-rich B2 phase. Generally, the Al content is a decisive factor affecting the formation of Al, Ni-rich phases in AlxCoCrFeNi alloys, because Al serves as a stabilizer for the Al, Ni-rich phases [38,58]. In the current work, the Al content in the base alloy is insufficient to form the Al, Ni-rich phase. When Si is added, the highest negative mixing enthalpy between Si and Ni promotes the segregation of Al, Ni, and Si, resulting in a short-range ordered structure [59–61]. The Cr-rich phase precipitates in the ordered matrix by spinodal decomposition and forms spherical nanoparticles different from the typical modulation structure [3,58, 62–64]. In principle, the elastic strain energy produced during solid transformation determines the morphology of coherent precipitates [65–67]. Thus, the formation of spherical particles may be attributed to specific elastic properties, including elastic inhomogeneity and elastic anisotropy. Similar spinodal structures have been observed in other HEAs, such as AlCoCrFeNi [63,64], AlCoCrCuFeNi [68], AlCrCuFeNi2 [69], and the coherent precipitation of spherical particles could improve mechanical properties.

σ y ¼ σ FCC ⋅VFCC þ σ BCC=B2 ⋅VBCC=B2

(6)

where σ and V are the yield strength and volume fraction of different phases, respectively. Eq. (6) can also be expressed as: � σ y ¼ σ FCC þ σBCC=B2 σ FCC ⋅VBCC=B2 (7) Accordingly, the compressive yield strength measured from Si0 to Si0.8 was described as a function of the volume fraction of the BCC/B2 phase, as shown in Fig. 7. There is a good linear relation between them, which indicates that the composite model provides a basis for the strength increment based on structure transition. For σBCC/B2 in Eq. (6), the strength increment contributed by the coherent precipitation of BCC particles in the B2 matrix should be included. The precipitation strengthening is classified into two mecha­ nisms, particle shearing or Orowan bypassing, according to the inter­ action between precipitates and moving dislocation. The shearing mechanism typically occurs under the condition that the precipitates are coherent with the matrix [24,78]. Two factors, coherency strengthening (ΔσCS) and modulus strengthening (Δσ MS), are considered in calculating the effect of the shearing mechanism, because the total value of (ΔσCS þ ΔσMS) determines the final strength increment from shearing when the precipitate size is larger (>40 nm) [22,24,79,80]. The equations for calculating Δσ CS and Δσ MS as follow [81–86]:

4.2. Strengthening mechanisms There is no doubt that the microstructural evolution caused different mechanical properties of the current HEAs. The Vickers hardness enhanced from 143 HV (x ¼ 0) to 826 HV (x ¼ 1.0) with increasing Si content, and the specific wear rate reduced by two orders of magnitude accordingly. The compressive yield strength of Si0.2, Si0.5, and Si0.8 alloys increased by 0.6, 4.6, and 7.3 times, respectively, compared to the base alloy. Based on the relationship between microstructure and me­ chanical properties, the difference in mechanical properties can be attributed to solid solution strengthening, structure transition, and coherent precipitation strengthening. When Si is added into the solid solution Al0.3CoCrFeNi HEA as the only variable, lattice distortion occurs and the resistance to dislocation movement increases. For the Si0 and Si0.2 alloys, the actual content of Si in the FCC phase increased from 0 to 3.95 at%, so the Si0 alloy could be considered as a solvent matrix for the FCC phase simply [71–73]. Here, 5

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Fig. 4. TEM analysis for the BCC/B2 region: (a) HRTEM image taken from the BCC/B2 region of the Si1.0 alloy along the [012] direction; (b, c) FFT patterns of particles and matrix, respectively; (d, e) a magnified image of the interface in (a) and corresponding schematic diagram, respectively.

Fig. 5. True compressive (a) and engineering tensile (b) stress-strain curves of the Al0.3CoCrFeNiSix alloys at ambient temperature.

� �12 3 rf ΔσCS ¼ M ⋅ αε ⋅ ðGεÞ2 ⋅ 0:5Gb

(8)

3

ΔσMS ¼ M ⋅ 0:0055 ⋅ ðΔGÞ2 ⋅

6

� �12 � �3m 2f r 2 ⋅ G b

1

(9)

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maximum strength increment obtained at the critical particle size r0. Obviously, the theoretically predicted r0 values of the three, 137 nm, 115 nm, and 138 nm, are higher than the experimental size r. Therefore, precipitation strengthening mainly depends on the shearing mechanism due to the small and coherent characteristics of precipitates in the cur­ rent HEAs.

Table 2 Mechanical properties of the Al0.3CoCrFeNiSix alloys. Alloys

Si0 Si0.2 Si0.5 Si0.8 Si1.0

Compressive properties Compressive yield strength

Fracture strength

Plastic strain

MPa

MPa

%

187 299 1039 1555 –

– – 1369 1820 1360

>60 >60 24.3 12.6 6.7

Tensile yield strength

Ultimate tensile strength

Elongation

MPa

MPa

%

180 293

419 671

63 56

5. Conclusions In summary, the microstructure, mechanical properties, and strengthening mechanisms of the Al0.3CoCrFeNiSix HEAs with various Si contents were discussed. The main conclusions are summarized below:

Tensile properties

Si0 Si0.2

(1) The microstructure of the current HEAs changes from a singlephase FCC solid solution structure (x ¼ 0) to a dendritic struc­ ture (0.2 � x � 0.5) with chemical segregation due to the addition of Si. The DR and ID regions are FCC and BCC/B2 phases, respectively, and the volume fraction of the BCC/B2 phase in­ creases with increasing Si content. The side plates of the FCC phase form in the BCC/B2 substrate when x � 0.8. (2) The BCC and B2 structures were always identified together in the Si-containing alloys, in particular, the spherical Cr-rich BCC precipitates with a size of about 60 nm are coherently dispersed in the Al, Ni-rich B2 matrix. The precipitates strengthen the matrix by shearing mechanism due to their small and coherent characteristics. (3) The composite model is suitable for the current HEAs with a linear increase in strength at the expense of ductility. When

where M ¼ 2.73 is the Taylor factor [87], αε ¼ 2.6 (a constant) [82,83], G ¼ 80 GPa is the shear modulus [88], ε � ð2 =3ÞðΔa =aÞ is the con­ strained lattice parameter mismatch [22,84], m ¼ 0.85 (a constant) [85, pffiffiffi 86], b ¼ 3a=2 is the Burgers vector [24,80]. ΔG ¼ 3 GPa is the shear modulus misfit between precipitates (G ¼ 83 GPa for α-Fe [89]) and matrix. f and r are the volume fraction and average size of precipitates, respectively. See the parameters and calculated results in Table 4. In fact, the bypassing and shearing mechanisms occur simulta­ neously and independently of each other, and the smaller of Δσorowan or (ΔσCS þ Δσ MS) is the operative mechanism [90,91]. When the bypassing mechanism occurs, the strength increment, Δσ orowan, is defined as: , ! qffiffi ln 2 23r b 0:4Gb Δσorowan ¼ M⋅ pffiffiffiffiffiffiffiffiffiffiffi⋅ (10) λp π 1 υ rffiffi �rffiffiffiffi 2 π λp ¼ 2 r 3 4f

Table 3 Thermodynamic and physicochemical properties for the constituent elements [70].

� 1

(11)

where υ ¼ 0.3 is Poisson’s ratio [87], and λp is the inter-precipitate spacing. For each alloy, both Δσ orowan and (ΔσCS þ Δσ MS) can be considered as a function of particle size r if the volume fraction f is determined. As shown in Fig. 8, Δσorowan ¼ ðΔσ CS þΔσMS Þ is the

Elements

Al

Co

Cr

Fe

Ni

Si

Radius (pm) VEC

143 3

125 9

125 6

124 8

125 10

117 4

Al (FCC) Co (HCP) Cr (BCC) Fe (BCC) Ni (FCC) Si (diamond)

Al

19 Co

10 4 Cr

11 1 1 Fe

22

19 38 37 35 40 Si

Fig. 6. Hardness, specific wear rate, and friction coefficient of the Al0.3CoCrFeNiSix alloys under dry sliding wear conditions. 7

0

7 2 Ni

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Fig. 7. The linear relation between the compressive yield strength and the volume fraction of the BCC/B2 phase when x is in the range of 0–0.8.

x ¼ 0.2, the tensile yield strength and ultimate tensile strength reach 293 MPa and 671 MPa, respectively, along with an elon­ gation of 56%. The Vickers hardness enhances from 143 HV (x ¼ 0) to 826 HV (x ¼ 1.0) with the increase of Si content, and the specific wear rate reduces by two orders of magnitude accordingly. (4) The strengthening effect of Si addition on the current HEAs is attributed to the transition from FCC to BCC/B2 phases and the

Table 4 Parameters and calculated results in the strength calculations. Alloy

f

r (nm)

ε (%)

b (nm)

ΔσCS (MPa)

ΔσMS (MPa)

Si0.2 Si0.5 Si0.8

0.46 0.52 0.50

56 � 11 63 � 15 65 � 10

0.19 0.26 0.21

0.2483 0.2479 0.2473

677 1224 886

37 41 40

Fig. 8. Strength increment Δσ orowan and (Δσ CS þ ΔσMS) as a function of r. 8

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coherent precipitation of BCC particles in the B2 matrix, while the solid solution strengthening caused by Si is almost negligible.

[17] B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, Science 345 (2014) 1153–1158. [18] Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Metastable high-entropy dualphase alloys overcome the strength-ductility trade-off, Nature 534 (2016) 227–230. [19] B. Schuh, F. Mendez-Martin, B. Volker, E.P. George, H. Clemens, R. Pippan, A. Hohenwarter, Mechanical properties, microstructure and thermal stability of a nanocrystalline CoCrFeMnNi high-entropy alloy after severe plastic deformation, Acta Mater. 96 (2015) 258–268. [20] R.S. Ganji, P. Sai Karthik, K. Bhanu Sankara Rao, K.V. Rajulapati, Strengthening mechanisms in equiatomic ultra-fine grained AlCoCrCuFeNi high-entropy alloy studied by micro- and nanoindentation methods, Acta Mater. 125 (2017) 58–68. [21] Z. Chen, W. Chen, B. Wu, X. Cao, L. Liu, Z. Fu, Effects of Co and Ti on microstructure and mechanical behavior of Al0.75FeNiCrCo high entropy alloy prepared by mechanical alloying and spark plasma sintering, Mater. Sci. Eng. A 648 (2015) 217–224. [22] J.Y. He, H. Wang, H.L. Huang, X.D. Xu, M.W. Chen, Y. Wu, X.J. Liu, T.G. Nieh, K. An, Z.P. Lu, A precipitation-hardened high-entropy alloy with outstanding tensile properties, Acta Mater. 102 (2016) 187–196. [23] I. Basu, V. Ocelík, J.T. De Hosson, BCC-FCC interfacial effects on plasticity and strengthening mechanisms in high entropy alloys, Acta Mater. 157 (2018) 83–95. [24] Y. Ma, Q. Wang, B.B. Jiang, C.L. Li, J.M. Hao, X.N. Li, C. Dong, T.G. Nieh, Controlled formation of coherent cuboidal nanoprecipitates in body-centered cubic high-entropy alloys based on Al2(Ni,Co,Fe,Cr)14 compositions, Acta Mater. 147 (2018) 213–225. [25] M.C. Gao, J.W. Yeh, P.K. Liaw, Y. Zhang, High-entropy Alloys: Fundamental and Applications, Springer International Publishing, Berlin, 2016. [26] M.H. Tsai, J.W. Yeh, High-entropy alloys: a critical review, Mater. Res. Lett. 2 (2014) 107–123. [27] I.V. Kireeva, YuI. Chumlyakov, Z.V. Pobedennaya, I.V. Kuksgausen, I. Karaman, Orientation dependence of twinning in single crystalline CoCrFeMnNi high entropy alloy, Mater. Sci. Eng. A 705 (2017) 176–181. [28] F. Otto, A. Dlouhý, Ch Somsen, H. Bei, G. Eggeler, E.P. George, The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi highentropy alloy, Acta Mater. 61 (2013) 5743–5755. [29] S.J. Sun, Y.Z. Tian, H.R. Lin, H.J. Yang, X.G. Dong, Y.H. Wang, Z.F. Zhang, Achieving high ductility in the 1.7 GPa grade CoCrFeMnNi high-entropy alloy at 77 K, Mater. Sci. Eng. A 740–741 (2019) 336–341. [30] O.N. Senkov, G.B. Wilks, J.M. Scott, D.B. Miracle, Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys, Intermetallics 19 (2011) 698–706. [31] Z. Han, H. Luan, X. Liu, N. Chen, X. Li, Y. Shao, K. Yao, Microstructures and mechanical properties of TixNbMoTaW refractory high-entropy alloys, Mater. Sci. Eng. A 712 (2018) 380–385. [32] B. Kang, J. Lee, H.J. Ryu, S.H. Hong, Ultra-high strength WNbMoTaV high-entropy alloys with fine grain structure fabricated by powder metallurgical process, Mater. Sci. Eng. A 712 (2018) 616–624. [33] W.R. Wang, W.L. Wang, J.W. Yeh, Phases, microstructure and mechanical properties of AlxCoCrFeNi high-entropy alloys at elevated temperatures, J. Alloy. Comp. 589 (2014) 143–152. [34] Y.F. Kao, T.J. Chen, S.K. Chen, J.W. Yeh, Microstructure and mechanical property of as-cast, -homogenized, and -deformed AlxCoCrFeNi(0�x�2) high-entropy alloys, J. Alloy. Comp. 488 (2009) 57–64. [35] H.P. Chou, Y.S. Chang, S.K. Chen, J.W. Yeh, Microstructure, thermophysical and electrical properties in AlxCoCrFeNi (0�x�2) high-entropy alloys, Mater. Sci. Eng. B 163 (2009) 184–189. [36] P. Cui, Y. Ma, L. Zhang, M. Zhang, J. Fan, W. Dong, P. Yu, G. Li, R. Liu, Effect of Ti on microstructures and mechanical properties of high entropy alloys based on CoFeMnNi system, Mater. Sci. Eng. A 737 (2018) 198–204. [37] D. Li, C. Li, T. Feng, Y. Zhang, G. Sha, J.J. Lewandowski, P.K. Liaw, Y. Zhang, Highentropy Al0.3CoCrFeNi alloy fibers with high tensile strength and ductility at ambient and cryogenic temperatures, Acta Mater. 123 (2017) 285–294. [38] J.C. Rao, H.Y. Diao, V. Ocelík, D. Vainchtein, C. Zhang, C. Kuo, Z. Tang, W. Guo, J. D. Poplawsky, Y. Zhou, P.K. Liaw, J.T.M. De Hosson, Secondary phases in AlxCoCrFeNi high-entropy alloys: an in-situ TEM heating study and thermodynamic appraisal, Acta Mater. 131 (2017) 206–220. [39] H. Shahmir, M. Nili-Ahmadabadi, A. Shafiee, T.G. Langdon, Effect of a minor titanium addition on the superplastic properties of a CoCrFeNiMn high-entropy alloy processed by high-pressure torsion, Mater. Sci. Eng. A 718 (2018) 468–476. [40] M.H. Chuang, M.H. Tsai, W.R. Wang, S.J. Lin, J.W. Yeh, Microstructure and wear behavior of AlxCo1.5CrFeNi1.5Tiy high-entropy alloys, Acta Mater. 59 (2011) 6308–6317. [41] M.V. Klimova, D.G. Shaysultanov, S.V. Zherebtsov, N.D. Stepanov, Effect of second phase particles on mechanical properties and grain growth in a CoCrFeMnNi high entropy alloy, Mater. Sci. Eng. A 748 (2019) 228–235. [42] S.W. Wu, G. Wang, Q. Wang, Y.D. Jia, J. Yi, Q.J. Zhai, J.B. Liu, B.A. Sun, H.J. Chu, J. Shen, P.K. Liaw, C.T. Liu, T.Y. Zhang, Enhancement of strength-ductility tradeoff in a high-entropy alloy through a heterogeneous structure, Acta Mater. 165 (2019) 444–458. [43] M.V. Klimova, D.G. Shaysultanov, R.S. Chernichenko, V.N. Sanin, N.D. Stepanov, S. V. Zherebtsov, A.N. Belyakov, Recrystallized microstructures and mechanical properties of a C-containing CoCrFeNiMn-type high-entropy alloy, Mater. Sci. Eng. A 740–741 (2019) 201–210.

Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. 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. Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 51574206, 51574207, 51674226, U1610123, 51701187, 51774254, 51774253); The Science and Technology Major Project of Shanxi Province (No. MC2016-06); Scientific and Technological Inno­ vation Project for Outstanding Talents of Shanxi Province (No. 201805D211036). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.msea.2019.138681. References [1] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 375–377 (2004) 213–218. [2] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Adv. Eng. Mater. 6 (2004) 299–303. [3] W.R. Wang, W.L. Wang, S.C. Wang, Y.C. Tsai, C.H. Lai, J.W. Yeh, Effects of Al addition on the microstructure and mechanical property of AlxCoCrFeNi highentropy alloys, Intermetallics 26 (2012) 44–51. [4] Y. Zhang, G.M. Stocks, K. Jin, C. Lu, H. Bei, B.C. Sales, L.W. Wang, L.K. Beland, R. E. Stoller, G.D. German, M. Caro, A. Caro, W.J. Weber, Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys, Nat. Commun. 6 (2015) 8736. [5] K.M. Youssef, A.J. Zaddach, C. Niu, D.L. Irving, C.C. Koch, A novel low-density, high-hardness, high-entropy alloy with close-packed single-phase nanocrystalline structures, Mater. Res. Lett. 2 (2014) 95–99. [6] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Microstructures and properties of high-entropy alloys, Prog. Mater. Sci. 61 (2014) 1–93. [7] Y. Zhang, Y.J. Zhou, J.P. Lin, G. Chen, P.K. Liaw, Solid-solution phase formation rules for multi-component alloys, Adv. Eng. Mater. 10 (2008) 534–538. [8] J.W. Yeh, Recent progress in high-entropy alloys, Ann. Chimie Sci. Mat� eriaux 31 (2006) 633–648. [9] S. Singh, N. Wanderka, B.S. Murty, U. Glatzel, J. Banhart, Decomposition in multicomponent AlCoCrCuFeNi high-entropy alloy, Acta Mater. 59 (2011) 182–190. [10] X.Z. Gao, Y.P. Lu, B. Zhang, N.N. Liang, G.Z. Wu, G. Sha, J.Z. Liu, Y.H. Zhao, Microstructural origins of high strength and high ductility in an AlCoCrFeNi2.1 eutectic high-entropy alloy, Acta Mater. 141 (2017) 59–66. [11] Z.S. Nong, Y.N. Lei, J.C. Zhu, Wear and oxidation resistances of AlCrFeNiTi-based high entropy alloys, Intermetallics 101 (2018) 144–151. [12] Y. Chen, T. Duval, U. Hung, J. Yeh, H. Shih, Microstructure and electrochemical properties of high entropy alloys—a comparison with type-304 stainless steel, Corros. Sci. 47 (2005) 2257–2279. [13] Z.Q. Xu, Z.L. Ma, M. Wang, Y.W. Chen, Y.D. Tan, X.W. Cheng, Design of novel lowdensity refractory high entropy alloys for high-temperature applications, Mater. Sci. Eng. A 755 (2019) 318–322. [14] Z. Tang, T. Yuan, C.W. Tsai, J.W. Yeh, C.D. Lundin, P.K. Liaw, Fatigue behavior of a wrought Al0.5CoCrCuFeNi two-phase high-entropy alloy, Acta Mater. 99 (2015) 247–258. [15] C.Y. Hsu, C.C. Juan, W.R. Wang, T.S. Sheu, J.W. Yeh, S.K. Chen, On the superior hot hardness and softening resistance of AlCoCrxFeMo0.5Ni high-entropy alloys, Mater. Sci. Eng. A 528 (2011) 3581–3588. [16] Y. Lu, X. Gao, L. Jiang, Z. Chen, T. Wang, J. Jie, H. Kang, Y. Zhang, S. Guo, H. Ruan, Y. Zhao, Z. Cao, T. Li, Directly cast bulk eutectic and near-eutectic high entropy alloys with balanced strength and ductility in a wide temperature range, Acta Mater. 124 (2017) 143–150.

9

P. Cheng et al.

Materials Science & Engineering A xxx (xxxx) xxx

[44] H. Jiang, L. Jiang, D.X. Qiao, Y.P. Lu, T.M. Wang, Z.Q. Cao, T.J. Li, Effect of niobium on microstructure and properties of the CoCrFeNbxNi high entropy alloys, J. Mater. Sci. Technol. 33 (2017) 712–717. [45] C.M. Lin, H.L. Tsai, Evolution of microstructure, hardness, and corrosion properties of high-entropy Al0.5CoCrFeNi alloy, Intermetallics 19 (2011) 288–294. [46] J.M. Zhu, H.M. Fu, H.F. Zhang, A.M. Wang, H. Li, Z.Q. Hu, Synthesis and properties of multiprincipal component AlCoCrFeNiSix alloys, Mater. Sci. Eng. A 527 (2010) 7210–7214. [47] X. Liu, W. Lei, L. Ma, J. Liu, J. Liu, J. Cui, On the microstructures, phase assemblages and properties of Al0.5CoCrCuFeNiSix high-entropy alloys, J. Alloy. Comp. 630 (2015) 151–157. [48] A. Kumar, P. Dhekne, A. Kumar, M. Kumar, Analysis of Si addition on phase formation in AlCoCrCuFeNiSix high entropy alloys, Mater. Lett. 188 (2017) 73–76. [49] D.B. Cullity, S.R. Stock, Elements of X-Ray Diffraction, third ed., Prentice Hall, London, 2001. [50] K. Gong, Z.F. Zhou, P.W. Shum, H.L. Luo, Z.L. Tian, C.H. Li, Tribological evaluation on Ni3Al-based alloy and its composites under unlubricated wear condition, Wear 270 (2011) 195–203. [51] C. Huang, Y. Zhang, V. Rui, J. Shen, Dry sliding wear behavior of laser clad TiVCrAlSi high entropy alloy coatings on Ti-6Al-4V substrate, Mater. Des. 41 (2012) 338–343. [52] G.Y. Ouyang, X. Chen, Y.F. Liang, C. Macziewski, J. Cui, Review of Fe-6.5 wt%Si high silicon steel—a promising soft magnetic material for sub-kHz application, J. Magn. Magn. Mater. 481 (2019) 234–250. [53] T.T. Shun, Y.C. Du, Microstructure and tensile behaviors of FCC Al0.3CoCrFeNi high entropy alloy, J. Alloy. Comp. 479 (2009) 157–160. [54] F.J. Wang, Y. Zhang, G.L. Chen, Atomic packing efficiency and phase transition in a high entropy alloy, J. Alloy. Comp. 478 (2009) 321–324. [55] M. Victoria, N. Baluc, C. Bailat, Y. Dai, M.I. Luppo, R. Schaublin, B.N. Singh, The microstructure and associated tensile properties of irradiated fcc and bcc metals, J. Nucl. Mater. 276 (2000) 114–122. [56] Y. Zhang, T.T. Zuo, Y.Q. Cheng, P.K. Liaw, High-entropy alloys with high saturation magnetization, electrical resistivity, and malleability, Sci. Rep. 3 (2013) 1455. [57] S. Guo, C. Ng, J. Lu, C.T. Liu, Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys, J. Appl. Phys. 109 (2011) 103505. [58] J.Y. He, W.H. Liu, H. Wang, Y. Wu, X.J. Liu, T.G. Nieh, Z.P. Lu, Effects of Al addition on structural evolution and tensile properties of the FeCoNiCrMn highentropy alloy system, Acta Mater. 62 (2014) 105–113. [59] R. Kulkarni, B.S. Murty, V. Srinivas, Study of microstructure and magnetic properties of AlNiCo(CuFe) high entropy alloy, J. Alloy. Comp. 746 (2018) 194–199. [60] Y. Qiu, Y.J. Hu, A. Taylor, M.J. Styles, R.K.W. Marceau, A.V. Ceguerra, M. A. Gibson, Z.K. Liu, H.L. Fraser, N. Birbilis, A lightweight single-phase AlTiVCr compositionally complex alloy, Acta Mater. 123 (2017) 115–124. [61] Y.P. Wang, B.S. Li, M.X. Ren, C. Yang, H.Z. Fu, Microstructure and compressive properties of AlCrFeCoNi high entropy alloy, Mater. Sci. Eng. A 491 (2008) 154–158. [62] L.J. Santodonato, Y. Zhang, M. Feygenson, C.M. Parish, M.C. Gao, R.J. Weber, J. C. Neuefeind, Z. Tang, P.K. Liaw, Deviation from high-entropy configurations in the atomic distributions of a multi-principal-element alloy, Nat. Commun. 6 (2015) 5964. [63] A. Manzoni, H. Daoud, R. V€ olkl, U. Glatzel, N. Wanderka, Phase separation in equiatomic AlCoCrFeNi high-entropy alloy, Ultramicroscopy 132 (2013) 212–215. [64] V. Ferrari, W. Wolf, G. Zepon, F.G. Coury, M.J. Kaufman, C. Bolfarini, C. S. Kiminami, W.J. Botta, Effect of boron addition on the solidification sequence and microstructure of AlCoCrFeNi alloys, J. Alloy. Comp. 775 (2019) 1235–1243. [65] M. Doi, Elasticity effects on the microstructure of alloys containing coherent precipitates, Prog. Mater. Sci. 40 (1996) 79–180. [66] S.Y. Hu, L.Q. Chen, A phase-field model for evolving microstructures with strong elastic inhomogeneity, Acta Mater. 49 (2001) 1879–1890.

[67] J. Zhu, L.Q. Chen, J. Shen, Morphological evolution during phase separation and coarsening with strong inhomogeneous elasticity, Model. Simul. Mater. Sci. Eng. 9 (2001) 499–511. [68] C.J. Tong, Y.L. Chen, S.K. Chen, J.W. Yeh, T.T. Shun, C.H. Tsau, A.Y. Chang, Microstructural characterization of AlxCoCrCuFeNi high-entropy alloy system with multiprincipal elements, Metall. Mater. Trans. A 36 (2005) 881–893. [69] L. Guo, W. Wu, S. Ni, Z. Wang, M. Song, Effects of annealing on the microstructural evolution and phase transition in an AlCrCuFeNi2 high-entropy alloy, Micron 101 (2017) 69–77. [70] A. Takeuchi, A. Inoue, Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element, Mater. Trans. 46 (2005) 2817–2829. [71] Y.N. Sun, P. Chen, L.H. Liu, M. Yan, X.Y. Wu, C.Y. Yu, Z.Y. Liu, Local mechanical properties of AlxCoCrCuFeNi high entropy alloy characterized using nanoindentation, Intermetallics 93 (2018) 85–88. [72] Y. Chen, S. Zhu, X. Wang, B. Yang, G. Han, L. Qiu, Microstructure evolution and strengthening mechanism of Al0.4CoCu0.6NiSix (x¼0-0.2) high entropy alloys prepared by vacuum arc melting and copper injection fast solidification, Vacuum 150 (2018) 84–95. [73] W.H. Liu, Z.P. Lu, J.Y. He, J.H. Luan, Z.J. Wang, B. Liu, Y. Liu, M.W. Chen, C.T. Liu, Ductile CoCrFeNiMox high entropy alloys strengthened by hard intermetallic phases, Acta Mater. 116 (2016) 332–342. [74] R.L. Fleischer, Substitutional solution hardening, Acta Metall. 11 (1963) 203–209. [75] T.H. Courtney, Mechanical Behavior of Materials, McGraw-Hill, New York, 1990. [76] H.Y. Yasuda, K. Shigeno, T. Nagase, Dynamic strain aging of Al0.3CoCrFeNi high entropy alloy single crystals, Scr. Mater. 108 (2015) 80–83. [77] S.W. Tsai, Theory of Composites Design, Think Composites Press, Dayton, 1992. [78] S.H. Jiang, H. Wang, Y. Wu, X.J. Liu, H.H. Chen, M.J. Yao, B. Gault, D. Ponge, D. Raabe, A. Hirata, M.W. Chen, Y.D. Wang, Z.P. Lu, Ultrastrong steel via minimal lattice misfit and high-density nanoprecipitation, Nature 544 (2017) 460–464. [79] C. Li, Y. Ma, J. Hao, Y. Yan, Q. Wang, C. Dong, P.K. Liaw, Microstructures and mechanical properties of body-centered-cubic (Al,Ti)0.7(Ni,Co,Fe,Cr)5 high entropy alloys with coherent B2/L21 nanoprecipitation, Mater. Sci. Eng. A 737 (2018) 286–296. [80] J. Hao, Y. Ma, Q. Wang, C. Zhang, C. Li, C. Dong, Q. Song, P.K. Liaw, Formation of cuboidal B2 nanoprecipitates and microstructural evolution in the body-centeredcubic Al0.7NiCoFe1.5Cr1.5 high-entropy alloy, J. Alloy. Comp. 780 (2019) 408–421. [81] A.J. Ardell, Precipitation hardening, Metall. Trans. A 16 (1985) 2131–2165. [82] V. Gerold, H. Haberkorn, On the critical resolved shear stress of solid solutions containing coherent precipitates, Phys. Status Solidi B 16 (1966) 675–684. [83] B. Jansson, A. Melander, On the critical resolved shear stress from misfitting particles, Scr. Metall. 12 (1978) 497–498. [84] Y. Tong, D. Chen, B. Han, J. Wang, R. Feng, T. Yang, C. Zhao, Y.L. Zhao, W. Guo, Y. Shimizu, C.T. Liu, P.K. Liaw, K. Inoue, Y. Nagai, A. Hu, J.J. Kai, Outstanding tensile properties of a precipitation-strengthened FeCoNiCrTi0.2 high-entropy alloy at room and cryogenic temperatures, Acta Mater. 165 (2018) 228–240. [85] A. Melander, P.A. Persson, The strength of a precipitation hardened AlZnMg alloy, Acta Metall. 26 (1978) 267–278. [86] E. Nembach, Precipitation hardening caused by a difference in shear modulus between particle and matrix, Phys. Status Solidi A 78 (1983) 571–581. [87] W.F. Hosford, Mechanical Behavior of Materials, first ed., Cambridge University Press, New York, 2005. [88] R.J. Wasilewski, Elastic constants and young’s modulus of NiAl, Trans. Mct. Soc. AIME 236 (1996) 455. [89] ASM International Handbook committee, Properties and Selection: Irons, Steels and High Performance Alloys, second ed., vol. 1, ASM International, Ohio, 1993. [90] H. Wen, T.D. Topping, D. Isheim, D.N. Seidman, E.J. Lavernia, Strengthening mechanisms in a high-strength bulk nanostructured Cu-Zn-Al alloy processed via cryomilling and spark plasma sintering, Acta Mater. 61 (2013) 2769–2782. [91] K. Ma, H. Wen, T. Hu, T.D. Topping, D. Isheim, D.N. Seidman, E.J. Lavernia, J. M. Schoenung, Mechanical behavior and strengthening mechanisms in ultrafine grain precipitation-strengthened aluminum alloy, Acta Mater. 62 (2014) 141–155.

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