Intermetallics 77 (2016) 23e33
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Intermetallics
journal homepage: www.elsevier.com/locate/intermet
Affordable FeCrNiMnCu high entropy alloys with excellent
comprehensive tensile properties
Z.Y. Rao, X. Wang, J. Zhu, X.H. Chen, L. Wang, J.J. Si, Y.D. Wu, X.D. Hui*
State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 21 March 2016
Received in revised form
20 June 2016
Accepted 21 June 2016
Available online 16 July 2016
Fe0.4Cr0.4NiMnxCu (0 x 1.4) high entropy alloys (HEAs) were prepared by copper-mold casting. The
phase selection, microstructure, tensile properties and fracture morphologies were investigated. The
microstructure with dual FCC phases was formed in the as-cast HEAs with x 1, and BCC phase was
crystallized from the central FCC dendrites of HEAs with x ¼ 1.2 and 1.4. In homogenized Fe0.4Cr0.4NiMnCu HEA, needle-like shaped BCC phase was formed resulting in a slight enhancement of yield
strength. Compositional heterogeneity was detected in both FCC and BCC dendrites. These HEAs exhibit
excellent comprehensive tensile properties, e.g. the yield strength, ultimate strength and elongation of
the HEA with x ¼ 1 reaches 439 MPa, 884 MPa and 23.4%, respectively. High density of dislocations in FCC
matrix was formed after tensile deformation. FCC type of fine polyhedra, which is mainly composed of Cr,
Mn and O, is formed in dendrites. In this work, the phase selection and strengthening mechanism were
evaluated based on atomic size factor. It was found that two criteria can be employed to predict the phase
regions of current alloys. The solid solution strengthening for this HEA system is the most important
among the four kinds of strengthening mechanisms.
© 2016 Elsevier Ltd. All rights reserved.
Keywords:
High entropy alloys
Mechanical properties
Microstructure
Solid solution strengthening
\
1. Introduction
For thousands of years, the conventional strategy of alloys
design is based on one or two principal elements and mediated
with other minor elements. This kind of design logos has brought
us a plenty of engineering alloy systems such as Fe-, Al-, Cu- and Nibased alloys, etc. Recently, a new kind of alloys, named high entropy
alloys (HEAs) has been developed by using a subversive design
strategy. In contrast to classical engineering alloys, HEAs contain
5e13 kinds of elements with equimolar or near equimolar compositions. The atomic fraction of each element is between 5 and
35 at.% [1,2]. According to traditional point of view, high concentration of alloying elements may cause the formation of intermetallic compounds, but not terminal solid solution phases (SS). This
rule has been cracked with the discovery of HEAs due to the formation of high configurational entropy [1e8]. Simple SS phases,
such as face centered cubic (FCC) or body centered cubic (BCC) etc,
have been formed in some HEAs. These HEAs have been found to
* Corresponding author. Tel.: þ86 10 62333066; fax: þ86 10 62333447.
E-mail address: [email protected] (X.D. Hui).
http://dx.doi.org/10.1016/j.intermet.2016.06.011
0966-9795/© 2016 Elsevier Ltd. All rights reserved.
possess unique mechanical, physical and chemical properties. For
example, FCC structured HEAs exhibit low strength and high plasticity, whereas BCC structured HEAs show the opposite trend in the
strength and plasticity [9].
Of all kinds of HEAs, FCC structured HEAs have been widely
researched to date. Most elements in FCC HEAs are transition
metals in the forth period in the periodic table of elements. For
instance, FCC structured FeCoCrNiMn HEA exhibits exceptional
mechanical properties with fracture strength and tensile elongation reaching to 496 MPa and 61.7%, respectively, at room temperature. With the addition of Al, the fracture strength of this kind
of HEAs is improved to 529 MPa and the elongation is reduced to
47.2%. Bernd Gludovatz et al. found that FeCoCrNiMn HEA has
much higher fracture toughness at cryogenic temperature due to
the strengthening mechanism similar to that of high Mn bearing
austenitic TWIP steels. He et al. proposed a further strengthening
method to improve the toughness of FeCoNiCr HEA by adding Al
and Ti to induce the precipitation of nano-size precipitates
[10e14]. Taking cost into account, however, these HEAs are comparable to some Ni-base superalloys, and much higher than most
of steels due to the addition of Co. The high cost has become one of
the problems to restrict the engineering application of Co-
24
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
containing HEAs [9].
Recently, Co-free (or low content of Co bearing) HEAs have
been investigated. Chen et al. substituted Co element by Mn in
AlCrCuFeCoNi HEA. They found that AlCrCuFeMnNi is composed
of both FCC and BCC phase, and the addition of Mn enhances the
formation of BCC phase, leading to an improvement of hardness
and decrease of plasticity [23]. Ren et al. designed CuCrFeNiMn
HEA alloy based on the concept of Ni- and Cr-equivalent. It is
shown that the HEAs with higher Nieq consist of a single FCC solid
solution phase, and those with higher Creq have FCC þ BCC
structure [24]. They prepared three kinds of Co-free HEAs with
single FCC phase. However, the tensile properties of these HEAs
have not been reported. Very recently, Chun Ng et al. [25] prepared Al0.5CrCuFeNi2 HEA with a fracture stress of 500 MPa and an
elongation of 16.1%, respectively. Ma et al. [26] performed cold
rolling and subsequent annealing for Al0.5CrCuFeNi2 HEA. It was
found that cold-rolled alloy demonstrates a large yielding
strength of 1132 MPa but a very limited tensile elongation of 1.6%.
All these Co-free HEAs are much cheaper, but show relatively
lower elongation, than FeCoNiCrX HEAs.
In this study, Co-free Fe0.4Cr0.4NiMnxCu HEAs with Mn content
changing from x ¼ 0 to x ¼ 1.4 are investigated. This alloy system is
designed as nonequiatomic HEAs in order to form FCC or FCC þ BCC
phase. The microstructure and tensile properties of these HEAs are
characterized at room temperature. And the phase selection and
strengthening mechanism were studied by TEM technology and
evaluated based on atomic size factor.
2. Experimental methods
In this work, Fe0.4Cr0.4NiMnxCu HEAs with x ¼ 0, 0.2, 0.4, 0.6, 0.8,
1, 1.2, and 1.4 (denoted as Mn0, Mn0.2, Mn0.4, Mn0.6, Mn0.8, Mn1,
Mn1.2 and Mn1.4, respectively, in the following context) were
designed. The alloy ingots were prepared by arc-melting elements
with the purity higher than 99 wt% in vacuum arc furnace in a
water-cooled copper hearth under a Ti-gettered argon atmosphere.
To ensure the chemical homogeneity, the alloys were remelted at
least four times. Then the specimens with the dimension of
10 10 60 mm3 were prepared by using a water-cooled cooper
mold cast. At last, the sample was homogenized at 1000 C for 24 h,
followed by water quenching.
The tensile properties were measured at room temperature by
CMT4105 universal electronic tensile testing machine with a
nominal strain rate of 1 103 s1. The tensile samples were
artificially machined to plate shaped specimens with gauge geometry of 1 mm 5 mm 10 mm. To ensure the facticity of tensile
properties, at least four samples were prepared for each nominal
composition of HEA.
The phase structure was characterized by X-ray diffraction
(XRD) using a PHILIPS APD-10 diffractometer (Philips, Amsterdam,
the Netherlands) with Cu Ka radiation. The XRD scanning angles
are ranged from 20 to 100 and the scanning rate is 5 per min. The
microstructure and fracture morphologies were investigated by
ZEISS SUPRA 55 scanning electron microscope (SEM) with energydispersive spectrometry (EDS). The proportion of dendrite region
and interdendrite region is computed by Adobe Photohop CS4 using at least three SEM micrographs for each alloy. The refined microstructures were studied by FEI G2F20 type of transmission
electron microscope (TEM). The TEM samples were primarily
punched to Ф3 mm of circular sheets and then ground to about
50 mm in thickness, followed by twin-jet electro-polishing using a
solution of HNO3:CH4O ¼ 1:4 with a voltage of 25 V and a current of
80 mA at the temperature of 230 K.
3. Results and discussion
3.1. Microstructural characterization
The phase compositions of as-cast Fe0.4Cr0.4NiMnxCu alloys with
different Mn concentrations can be differentiated by XRD patterns.
As shown in Fig. 1, there is only one set of FCC phase peaks in the
microstructure when the amount of Mn is 0 x 1.2. Actually,
there is some BCC phase in the HEA with x ¼ 1.2 when observed by
SEM (which will be discussed later). As the amount of Mn is
increased to x ¼ 1.4, a weak peak arises at the 2 theta of 55 ,
indicating that a new BCC phase appears. From Fig. 1(b), it is seen
that the peaks of FCC phase shift towards lower angle side with the
increase of Mn content because of the larger radius of Mn atom
than those of other four elements. In addition, the peaks of FCC
phase are broadened as Mn is added to this group of alloys. A
shoulder emerges on the original (111) peaks of the HEAS with Mn
content of x ¼ 0.2e1.2. According US patent 9150945 B2 [27], there
are actually two FCC phases with similar lattice parameters in
FeCoCrNiCu HEAs, although x-ray shows one sets of FCC peaks.
Therefore, the feature of broaden (111) peak together with a
shoulder means that Mn containing HEAs are composed of two
kinds of FCC phases. This deduction may be further verified by the
SEM observation and EDX measurement in the following section.
The SEM backscattering electron micrographs of Fe0.4Cr0.4NiMnxCu HEAs are shown in Fig. 2. Typical dendritic microstructures can be observed in all of the as-cast alloys. As the amount of
Mn is increased in these HEAs, dendrites become thinner and the
volume fraction of interdendrite region increases. When the fraction of Mn reaches x ¼ 1.2, a new kind of dendritic appears.
Combining the SEM image with XRD patterns, it can be inferred
that this new kind of dendrites has BCC type of structure. This result
is similar to that of Ref. [23]. As shown in Fig. 2 and the EDX results
listed in Table 1, there is compositional segregation in both the FCC
and BCC phases of as-cast samples. In FCC phase, Fe, Ni and Cr elements are enriched in dendrite and depleted in interdendrite region. On the contrary, Mn and Cu atoms were repelled into
interdendrite region. Especially, the atomic ratio of Cu element in
dendrite and interdendrite region reaches above 4, reflecting there
is indeed a severe heterogeneity in composition distribution in FCC
phase. Due to the compositional heterogeneity mentioned above, it
can be considered that there are two FCC phases in current alloys.
When further analyzing the composition of BCC phase, it is found
that the BCC phase is enriched with Fe and Cr but depleted with Ni,
Mn and Cu. The concentration of Cr in the BCC phase of Mn1.4 alloy
reaches 47.9%, which is about 5 times as the nominal composition.
It is also found that with the increase of Mn, the segregation of Fe
and Cr between dendrite and interdendrite region is aggravated,
whereas the partitioning of Ni is decreased. With the decrease of Ni
and increase of Cr and Fe in FCC dendrite, the FCC phase becomes
instable. From Fig. 2(g) and (h), it is shown that BCC phase is
crystallized in the dendrite of FCC phase but not in the interdendrite region. Therefore, it is reasonable to infer that the formation of
BCC phase is due to the redistribution of solutes in FCC dendrites
induced by the addition of Mn.
To further explore the structure of these HEAs, we performed
TEM investigation of deformed Mn1 HEA. From Fig. 3(a), it is found
that there is high density of dislocation lines in the FCC matrix,
indicating that strong work hardening has been produced. A
polyhedron phase with a side length of 0.5e1 mm can be observed
in Fig. 3(b). According to the selected area electron diffraction
(SAED) pattern, this polyhedron phase can be calibrated as FCC
structure with a lattice parameter of 0.415 nm. From the EDS
pattern (Fig. 3(c)), the polyhedron phase contains O, Cr and Mn.
This phase has been reported by Gludovatz and Zaddach et al.
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
25
Fig. 1. (a) XRD patterns of Fe0.4Cr0.4NiMnxCu HEAs, (b) Magnified peaks shown in (a).
[11,28], and was considered as the harmful phase to the mechanical
properties. In this work, there is high density of dislocation lines
around polyhedron phase, meaning that the particulates may cause
a block effect on the movement of dislocation lines so that the work
hardening effect may be further enhanced.
3.2. Tensile properties
So far as present, room temperature tensile properties are less
reported compared with the compressive properties for HEAs
[15e22]. Investigations on the tensile properties of Co-free FCC
structured HEAs are even much less. Fig. 4 shows the true stressstrain curves, ultimate tensile strength, yield strength and plastic
strain for Fe0.4Cr0.4NiMnxCu HEAs with different Mn contents. It is
seen that with the increase of Mn contents, the tensile strength and
elongation of these HEAs exhibit different changing trends. When
x 1, the tensile strength gradually increases with the addition of
Mn and reaches the maximal value at x ¼ 1. The elongation changes
very little for the HEAs ranging from Mn0 to Mn1, and maximal
elongation of 23.4% was obtained at x ¼ 1. When x > 1, both the
tensile strength and elongation decrease acutely with further
addition of Mn due to the formation of BCC phase. It is seen that
excellent comprehensive tensile properties were obtained for the
HEA with x ¼ 1. This HEA possesses the yield strength, ultimate
tensile strength and elongation of 439 MPa, 884 MPa and 23.4%,
respectively. From Fig. 4(a), it is also seen that Mn1 HEA exhibits
strong work hardening effect, which is responsible for the excellent
tensile strength and elongation.
The excellent tensile properties can be reflected by the fracture
morphology of these HEA alloys. As shown in Fig. 5, there are a
large amount of dimples and vein patterns on the fracture surfaces,
suggesting that high plastic deformation has taken place. It is also
found that the addition of Mn has some effect on the facture
morphologies. With the excessive addition of Mn, the veins in
patterns become coarse and inhomogenous. Especially, several
large dimples have been formed on the fracture surface of Mn1.4
alloy. It is noticed that except for Mn0 alloy, there are small particles
in some dimples, which take the shape of polyhedra. These particles should be the oxides of Cr and Mn as shown in Fig. 3(c), and
may act as preferred nucleation sites for microvoids [29]. On the
other hand, these polyhedra may be beneficial to the work
hardening by obstructing the movement of dislocation lines.
In order to discuss the phase selection, microstructure and
mechanical properties of homogenized HEAs, we prepared
Fe0.4Cr0.4NiMnCu HEA by aging this alloy at 900 C and 1000 C,
respectively, for 24 h. As shown in Fig. 6(a) and (b), the microstructure is mainly composed of homogeneous FCC matrix and a
little amount of remanent DR. A new kind of phase with needle-like
shape has been formed after homogenization. From the XRD
pattern (as shown in Fig. 6(c)) and EDS result, this new phase can be
identified as BCC phase abounding in Fe and Cr. Around the
remanent DR, needle-like BCC phase is depleted. As mentioned in
above section, Fe, Ni and Cr elements in FCC phase in the as-cast
microstructure are enriched in dendrite and depleted in interdendrite region. As a result, it is reasonable to consider that this kind of
BCC phase comes from DR region of as-cast alloy. Fig. 6(d) shows
the true stress-strain curves of as-cast and homogenized
Fe0.4Cr0.4NiMnCu HEAs. It is found that after homogenization, the
yield strength has been increased by about 40 MPa, while elongation has been decreased to 17% from 23.4%. Therefore, the precipitation of new BCC phase may slightly increase the strength with
some content of decrease in plasticity.
3.3. Phase selection for HEAs
Generally speaking, there are three kinds of phase regions
observed in HEAs: solid solutions (SS), solid solution plus intermetallics (SS þ IN), and metallic glasses (MG) [30]. To predict the
formability of these phases, phase selection has been discussed by
using several parameters based on the classical Hume-Rothery
rules [5,9,31e38]. According to these rules, all the atomic size differences, electronegativity, chemical valence, crystal structure,
valence electron concentration are essential to the phase selection
[39]. Among these parameters, the atomic size difference is of
special importance. For binary SS, the alloys will be unstable if the
atomic size difference exceeds 15%. However, the atomic size factor
defined by Hume-Rothery rules can’t be directly applied for HEAs
because there is not a clear identity of “solvent” or “solute” atoms in
HEAs [36]. Zhang [5] proposed a parameter representing the
standard deviation of atomic sizes, d, which is defined as:
26
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
Fig. 2. SEM backscattering electron micrographs of Fe0.4Cr0.4NiMnxCu HEAs.
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u n
n
X
uX r 2
d ¼ t Ci 1 i ; r ¼
Ci ri
r
i¼1
i¼1
(1)
where n is the number of the components in an alloy system, Ci is
the atomic percentage of the ith component, r is the average atomic
radius, and ri is the atomic radius which can be obtained in Ref. [40].
This definition has been widely used to describe the effect of the
atomic size difference on the structural instability. The criterion of
parameter d shows some inaccuracies, e.g. many intermetallic
phases have been detected as d ¼ 0.06, which is opposite to the
predication results of d criterion [38]. Moreover, the physical
meaning of d in determining the solubility is not well understood.
The mixing enthalpy, DHmix, was also proposed to predict the
chemical compatibility among the several principal components in
HEAs, which is defined as:
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
27
Table 1
Chemical composition in different region of Fe0.4Cr0.4NiMnxCu HEAs measured by EDS.
Regiona
Alloys
Mn0
Chemical compositions (at.%)
Nominal
DR
IR
Nominal
DR
IR
Nominal
DR
IR
Nominal
DR
IR
Nominal
DR
IR
Nominal
DR
IR
Nominal
DR (BCC)
DR (FCC)
IR
Nominal
DR (BCC)
DR (FCC)
IR
Mn0.2
Mn0.4
Mn0.6
Mn0.8
Mn1
Mn1.2
Mn1.4
Fe
Mn
Ni
Cr
Cu
14.29
19.31 ± 0.15
8.72 ± 0.08
13.33
18.62 ± 0.24
4.57 ± 0.12
12.5
18.89 ± 0.10
3.75 ± 0.06
11.76
20.42 ± 0.13
2.79 ± 0.05
11.11
21.47 ± 0.15
4.40 ± 0.06
10.53
19.66 ± 0.19
3.09 ± 0.11
10
25.06 ± 0.13
20.92 ± 0.11
1.55 ± 0.55
9.52
24.87 ± 0.16
16.55 ± 0.16
1.68 ± 0.09
0
0
0
6.67
4.11 ± 0.15
8.92 ± 0.15
12.5
8.89 ± 0.08
16.51 ± 0.11
17.65
12.17 ± 0.10
22.39 ± 0.12
22.22
17.02 ± 0.13
26.76 ± 0.13
26.32
20.31 ± 0.19
29.66 ± 0.24
30
13.30 ± 0.10
21.84 ± 0.11
34.71 ± 0.15
33.33
16.57 ± 0.14
30.16 ± 0.20
36.84 ± 0.25
35.71
42.74 ± 0.27
27.32 ± 0.16
33.33
40.61 ± 0.42
20.51 ± 0.28
31.25
37.52 ± 0.16
20.28 ± 0.14
29.41
36.84 ± 0.19
20.91 ± 0.13
27.78
31.07 ± 0.20
21.81 ± 0.13
26.32
28.64 ± 0.27
17.14 ± 0.24
25
11.84 ± 0.10
26.53 ± 0.13
17.65 ± 0.12
23.81
9.29 ± 0.11
27.37 ± 0.22
17.73 ± 0.21
14.29
19.82 ± 0.15
9.70 ± 0.08
13.33
20.11 ± 0.22
5.27 ± 0.11
12.5
20.38 ± 0.10
4.75 ± 0.06
11.76
18.42 ± 0.11
3.09 ± 0.05
11.11
19.85 ± 0.13
4.79 ± 0.06
10.53
19.96 ± 0.17
3.88 ± 0.10
10
47.82 ± 0.19
22.93 ± 0.13
2.42 ± 0.05
9.52
47.90 ± 0.22
14.37 ± 0.13
2.42 ± 0.08
35.71
18.13 ± 0.19
54.27 ± 0.24
33.33
16.56 ± 0.33
60.73 ± 0.51
31.25
14.32 ± 0.11
54.71 ± 0.24
29.41
12.15 ± 0.12
50.82 ± 0.21
27.78
10.59 ± 0.13
42.24 ± 0.19
26.32
11.43 ± 0.21
46.23 ± 0.42
25
1.99 ± 0.06
7.78 ± 0.08
43.67 ± 0.20
23.81
1.38 ± 0.07
11.55 ± 0.16
41.33 ± 0.33
a
Nominal: nominal composition, DR(FCC): FCC region in dendrite, DR(BCC): BCC region in dendrite, IR: interdendrite.
Fig. 3. (a) Typical TEM image of FCC matrix of Mn1 alloy, (b) Particulate distributed in the FCC matrix and its SADP, (c) EDS pattern of the particulate as shown in (b).
DHmix ¼
n
X
i¼1;isj
Uij Ci Cj ¼ 4
n
X
et al. [35], which reflects the stability by the packing states around
the largest and smallest atoms, and denoted as:
DHijmix Ci Cj
(2)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !
i¼1;isj
where Uij is the regular melt-interaction parameter between ith
and jth elements, and DHijmix is the mixing enthalpy of binary liquid
alloys obtained from Ref. [41]. Ci and Cj are the atomic percentage of
the ith and jth components, respectively. By combining parameters
d and DHmix, they proposed that the criteria for the formation of
random SS in HEAs are in the range of 15 < DHmix < 5 kJ/mol and
1% < d < 6.6%.
In general, the d parameter calculates the difference of the
atomic size among all elements in the alloy. Nevertheless, the SS
instability may be essentially determined by the largest and
smallest atoms in multicomponent alloy systems. Based on this
point of view, a new parameter, g, was recently, proposed by Wang
g¼
Ws
¼
Wl
1
2
ðrs þrÞ r
2
ðrs þrÞ
2
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !
1
2
ðrl þrÞ r
2
ðrs þrÞ
(3)
2
where rl and rs are the radii of the largest and smallest atoms, and r
is the average atomic radius. Ws and Wl are the solid angles around
the largest and smallest atoms in respect to the surrounding atoms.
In this formula, the atomic size difference of 15% in the HumeRothery rule for binary alloys corresponds to a critical value of
packing misfitting of g ¼ 1.167.
Wang et al. [37] also proposed another criterion to address the
28
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
Fig. 4. Tensile properties of Fe0.4Cr0.4NiMnxCu alloys: (a) the true stress-strain curves of HEAs, (b) yield strength, ultimate tensile strength and plastic strain as a function of Mn
concentration.
Fig. 5. SEM fracture morphology of Fe0.4MnxNiCr0.4Cu alloys: (a) Mn0, (b) Mn0.4, (c) Mn1, and (d) Mn1.4.
lattice distortion of crystalline lattice with a series of physical parameters: a1, a2, a3, a4, a5 …. The local lattice distortion is defined
by comparing a distorted lattice and its ideal counterpart lattice.
Then a1 is denoted as:
a2 ¼
n
X
Ci Cj
ri þ rj 2r j1
2r
(5)
based on the model, a series of parameters can be written as:
a1 ¼
n
X
i¼1
Ci
jri rj
r
(4)
But a1 is ineffective in differentiating the alloys with the
different phases containing solid solutions, a mixture of intermetallics and solid solutions, and metallic glasses because this
calculation overestimates the lattice distortion. Then another
parameter, a2, was defined to represent a local atomic distortion:
a3 ¼
n
X
kji
a4 ¼
n
X
kji
Ci Cj Ck
ri þ rj þ r 3r k
3r
Ci Cj Ck Cl
ri þ rj þ r þ r 4r k
l
4r
(6)
(7)
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
29
Fig. 6. (a) and (b) SEM backscattering electron micrographs of Fe0.4Cr0.4NiMnCu HEA homogenized at 900 C and 1000 C, respectively, for 24 h, (c) XRD pattern of Fe0.4Cr0.4NiMnCu
HEA homogenized at 1000 C for 24 h, and (d) true stress-strain curves of Fe0.4Cr0.4NiMnCu HEA at as-cast state and homogenized at 1000 C for 24 h.
n
X
a5 ¼
slkji
ri þ rj þ r þ r þ rs 5r k
l
Ci Cj Ck Cl Cs
5r
(8)
However, as the included component number is increased, the
parameters will be more average and lose their ability to describe
the lattice distortion. In summary, a2 is the best parameter to
describe the lattice distortion [37].
Based on the above proposed criteria, relevant parameters were
calculated and listed in Table 2 for this alloy system. The correlations of DHmixd, g-d, and a-d parameters are shown in Fig. 7. According to Zhang et al. [5], SS phases can form when 1% < d < 6.5%
and 15 < DHmix < 5. From Fig. 7(a), it is found that some HEAs fall
in, and others are close to this region. Therefore, this parameter is
not completely effective for predicting the formation of SS phase for
this alloy system. Wang et al. [37] proposed that single SS phase can
be formed in the region of g < 1.175. From the g-d plot as shown in
Table 2
Relevant parameters based on the proposed criteria for Fe0.4MnxNiCr0.4Cu alloys (d,
a1, a2, a3, a4 was amplified by 100 for clarity).
HEAs
d
DHmix (KJ/mol)
g
a1
a2
a3
a4
Mn0
Mn0.2
Mn0.4
Mn0.6
Mn0.8
Mn1
Mn1.2
Mn1.4
2.18
2.53
2.80
3.02
3.21
3.36
3.50
3.61
5.22
4.27
3.5
2.88
2.37
1.95
1.6
1.31
1.10
1.10
1.10
1.10
1.10
1.10
1.10
1.10
1.75
2.00
2.21
2.40
2.57
2.72
2.86
2.98
1.06
1.07
1.11
1.16
1.24
1.32
1.41
1.50
0.55
0.49
0.47
0.48
0.50
0.55
0.60
0.66
0.26
0.21
0.19
0.19
0.20
0.22
0.25
0.29
Fig. 7(b), it is seen that g parameter is more effective in predicting
the phase formation for this alloy system. All the alloys interested in
current work fall in the SS phase region.
The a-d graph is also plotted in Fig. 7(c). It is seen that a parameters are also effective for the prediction of phase selection for
current alloy system. In addition, as more component number
included, the value of a decreases, meaning that sensitivity to
describe the lattice distortion gradually decreases. Wang et al. [37]
considered that among a series of a parameters, a2 is the best
parameter to describe the lattice distortion. However, it is noticed
that for this alloy system, the changes of lattice distortion reflected
by a1 and a2 is not exactly same as those reflected by a3 and a4.
From Table 2, it is seen that with the increase of Mn content, a1 and
a2 increased monotonously, while a3 and a4 decrease at first and
reach a minimum value at 0.4, and then increase. If further
increasing the component numbers, all a5, a6, a7 … have a minimum value at x ¼ 0.4. Therefore, it seems that a2 is not the best
parameter in current work as it doesn’t exactly reflect the change of
lattice distortion.
3.4. Solid solution strengthening
In polycrystalline materials, the strengthening or hardening effect happens when the moving dislocations interact with crystalline defects or secondary phase. In general, there are mainly four
strengthening mechanisms including solid solution (SS), grain
boundary, dislocation, and precipitation strengthening. As a result
of these four kinds of strengthening effects, the strength of the
crystal, st, can be expressed as [30]:
30
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
generally accepted that solid solution strengthening (SSS) is the
main factor to the exceptional mechanical properties of HEAs. In
the following sections, we will mainly focus on the effect of SSS on
the mechanical properties of current HEA system, and then discuss
other strengthening manners.
In 1967, Fleisher et al. studied the effect of solute atoms in solid
solution [42]. They calculated the SSS effect of different elements in
FCC and BCC alloys. Based on this idea, Gypen and Deruyttere [43]
calculated the SSS effect in multicomponent alloys by assuming
that the interaction among solutes is so small that it can be ignored.
The SSS in multicomponent alloys is expressed as following:
X
Dsss ¼
!2
3
3
B2i Ci
(10)
i
where Bi is the strengthening parameter of the element i and Ci is
its content. SSS in HEAs caused by i element, Bi, can be expressed as
[44e47]:
4
Bi ¼ ZGfi3
(11)
where G is the shear modulus of the alloy, Z is a fitting constant, fi is
the mismatch parameter, which can be calculated using following
formula:
1
2
fi ¼ dG2i þ a2 dri2
(12)
where dGi and dri are shear modulus and atomic size mismatch
parameters, respectively. a is a constant dependent on the type of
the moving dislocations. Generally, a is 2e4 for the screw dislocations and a 16 for edge dislocations [44]. dGi and dri can be
calculated as:
dGi ¼
1 dG
G dXi
(13)
dri ¼
1 dr
r dXi
(14)
Kuznetsovand Hemphill et al. estimated the mismatch parameters based on dGi and dri [15,16]. Every element in this lattice has
12 nearest-neighbor atoms, thus forming a 13-atom cluster. The
local environment around an alloying element i can be roughly
estimated if the local composition is assumed to be equal to the
average composition of the alloy. As a result, element i has Nj ¼ 13Cj
of j-atom neighbors and Ni ¼ 13Ci1 of i-atom neighbors (j s i).
Then the lattice mismatch, dri , and shear modulus difference, dGi ,
in the vicinity of element i are estimated as an average of the atomic
size difference, drij ¼ 2 ðri rj Þ = ðri þrj Þ , and shear modulus
difference, dGij ¼ 2 ðGi Gj Þ = ðGi þGj Þ , respectively, of this
element with its neighbors:
dGi ¼
13 X
G dG
12 i j ij
(15)
dri ¼
13 X
rj drij
12
(16)
Fig. 7. (a) DHmix-d, (b) g-d, and (c) a-d graphs for Fe0.4 Cr0.4NiMnxCu alloys.
i
st ¼ sf þ sss þ Dssh þ Dspt þ Dsgb
(9)
where sf is the intrinsic or frictional strength of the crystal, Dsss,
Dssh, Dspt and Dsgb are strengthening effect caused by solid solution, dislocations, precipitates and grain boundary, respectively. It is
The calculated dGi , dri and Bi for different elements in the present alloys system are listed in Table 3. The parameters for the
constituent elements are from Ref. [48]. Here only the parameters
of as-cast Mn0-Mn1 HEAs which possess single solid solution phase
were calculated.
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
Table 3
Relevant parameters to evaluate the SSS effect near the constituent element, i, in
Fe0.4MnxNiCr0.4Cu HEAs.
HEAs
Parameters
Fe
Mn
Ni
Cr
Cu
Mn0
dri
dGi
Mn0.2
dri
dGi
0.0151
0.1799
135
0.0202
0.1688
126
0.0246
0.1591
119
0.0285
0.1505
114
0.0320
0.1429
110
0.0351
0.1361
106
e
e
e
0.0710
0.1559
163
0.0666
0.1461
150
0.0627
0.1375
138
0.0592
0.1299
128
0.0561
0.1231
119
0.0081
0.0998
61
0.0132
0.0862
53
0.0176
0.0787
50
0.0215
0.0700
46
0.0250
0.0623
45
0.0281
0.0554
44
0.0107
0.5279
555
0.0158
0.5178
542
0.0202
0.5089
530
0.0241
0.5011
521
0.0276
0.4941
512
0.0307
0.4879
505
0.0184
0.3829
364
0.0134
0.3943
377
0.0089
0.4043
389
0.0050
0.4131
400
0.0015
0.421
410
0.0016
0.4280
419
Bi (MPa)
Mn0.4
Mn0.6
Mn0.8
Mn1
Bi (MPa)
dri
dGi
Bi (MPa)
dri
dGi
Bi (MPa)
dri
dGi
Bi (MPa)
dri
dGi
Bi (MPa)
It can be seen that with the addition of Mn element, the atomic
size mismatch parameters of Mn and Cu decrease while those of Fe,
Ni and Cr increase. As for the shear modulus mismatch, dGi , it is
seen that the dGi of Cu increases with addition of Mn, while the dGi
of other four elements decrease. The highest atomic size mismatch
occurs around Mn element, and the highest shear modulus
mismatch is around Cr and Cu element. The SSS effect, Bi, induced
by each element in current alloy system is plotted in Fig. 8 by using
formula Eqs. (11) and (12). Referred to Ref. [44], the values of a and
Z G were taken to be 2, 1300 MPa (at.)(2/3) for FeCrNiMnCu alloy,
respectively. From Fig. 8, it can be seen that with the addition of Mn,
Fig. 8. SSH caused by different element atoms in Fe0.4Cr0.4NiMnxCu alloys.
31
only SSS induced by Cu element increases. Cr exhibits the largest
SSS effect as it also has the largest modulus mismatch. Therefore, it
can be concluded that the modulus mismatch plays the major role
in SSS, while the atomic size parameter has less effect on the SSS.
The calculated values to evaluate the solid solution strengthening by using Eq. (10) and the proportions of dendrite region and
interdendrite region computed by using Adobe Photohop CS4 are
listed in Table 4. It can be seen that the SSS effect of interdendrite
region enriched with Cu is higher than that of dendrite region.
Considering the proportion of dendrite and interdendrite region, u
and 1-u, in each alloy, the effect of solid solution strengthening,
DsSS, can be described as:
DsSS ¼ uDsSSDR þ ð1 uÞDsSSIR
(17)
The calculated values of DsSS are listed in Table 4 and plotted in
Fig. 9 with respect to the experimental yield strengths for current
alloy system. The calculated DsSSs are lower than experimental
yield strengths by about 49e188 MPa, indicating that SSS is the
most important among the four kinds of strengthening mechanisms for this HEA system. Nonetheless, the calculated DsSSs
decrease with the increase of Mn content, which doesn’t conform
to the tendency of experimentally measured data. This difference
may be due to grain boundary strengthening effect, Dsgb. The
smaller the grain size, the higher the volume fraction of grain
boundaries, which could impede the dislocation motion. Therefore,
grain refinement may further improve the strength of an alloy. In
current Mn0eMn1 HEAs, the dendrites are getting thinner with the
increase of Mn content, resulting in obvious strength enhancement.
Another effect we need to consider is the precipitation strengthening, Dspt. As discussed in Section 3.1, the polyhedron phase
containing O, Cr and Mn was found with the addition of Mn. It is
Fig. 9. Dependence of yield strength on the solid solution strengthening of
Fe0.4Cr0.4NiMnxCu HEAs.
Table 4
Relevant parameters of SSH effect in current alloys.
Alloys
DRa
IRa
DsssDR (MPa)
u(%)
DsssIR (MPa)
1-u
Dsss (MPa)
a
DR: dendrite, IR: interdendrite.
Mn0
Mn0.2
Mn0.4
Mn0.6
Mn0.8
Mn1
267
64.94
304
35.06
280
262
55.63
309
44.37
283
257
45.19
300
54.81
281
240
42.55
288
57.45
268
242
29.30
275
70.70
265
243
32.34
287
67.66
273
32
Z.Y. Rao et al. / Intermetallics 77 (2016) 23e33
known that the precipitation strengthening occurs either through a
dislocation by-pass mechanism (Orowan-type) or grain shearing
mechanism. Normally, the former happens when the radius of
grains exceeds a critical value or is incoherent with the matrix,
while the latter will dominate when precipitates are sufficiently
small and coherent. The precipitation strengthening may
contribute to the increase of experimental yield strength from Mn0
to Mn1.
4. Conclusion
(1) The microstructure with dual FCC phases are formed in HEAs
with the amount of Mn being x 1, and BCC phase is crystallized from the central FCC dendrites in Mn1.2 and Mn1.4
HEAs. Compositional segregations are detected in both the
FCC and BCC phases. In interdendrite FCC phase, Fe, Ni and Cr
elements are enriched, but Mn and Cu are depleted in
dendrite FCC phase. BCC phase is enriched with Fe and Cr but
depleted with Ni, Mn and Cu.
(2) High density of dislocations were observed in the FCC matrix.
FCC type of polyhedra phase, which is composed of O, Cr and
Mn and has a side length of 0.5e1 mm, is formed in the FCC
matrix.
(3) The HEAs with x 1 exhibit excellent comprehensive tensile
properties, e.g. Mn1 HEA possesses the yield strength, ultimate tensile strength and elongation of 439 MPa, 884 MPa
and 23.4%, respectively. Strong work strengthening effect
was produced during the deformation process in all of the
samples. Needle-like shape second BCC phase was formed
after homogenization, the yield strength of the Fe0.4Cr0.4NiMnCu HEA has been improved with some content of tradeoff in plasticity.
(4) The parameters, d, g and a, which are based on atomic size
factor were calculated to evaluate phase selection. It has been
found that g-d and a-d correlations can accurately predict the
phase regions of current alloys.
(5) Cu and Cr atoms produce the strongest strengthening effect
than other elements. The calculated DsSSs are lower than
experimental yield strengths by about 49e188 MPa, indicating that SSS mechanism is the most important among the
four kinds of strengthening mechanisms for this HEA system
Acknowledgments
The authors acknowledge the financial support of National
Natural Science Foundation of China (Nos. 51271018, 51571016 and
51531001), and the proprietary program of the State Key Laboratory
for Advanced Metalsand Materials, University of Science and
Technology Beijing (Nos. 2014-ZD04).
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