Materials Science & Engineering A 772 (2020) 138681
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Materials Science & Engineering A
journal homepage: http://www.elsevier.com/locate/msea
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: pengcheng.nuc@foxmail.com (P. Cheng), zhaoyuhong@nuc.edu.cn (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.
P. Cheng et al.
Materials Science & Engineering A 772 (2020) 138681
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
P. Cheng et al.
Materials Science & Engineering A 772 (2020) 138681
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
P. Cheng et al.
Materials Science & Engineering A 772 (2020) 138681
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
P. Cheng et al.
Materials Science & Engineering A 772 (2020) 138681
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
P. Cheng et al.
Materials Science & Engineering A 772 (2020) 138681
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)
P. Cheng et al.
Materials Science & Engineering A 772 (2020) 138681
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
P. Cheng et al.
Materials Science & Engineering A 772 (2020) 138681
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
Materials Science & Engineering A 772 (2020) 138681
P. Cheng et al.
coherent precipitation of BCC particles in the B2 matrix, while the
solid solution strengthening caused by Si is almost negligible.
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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.
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