Affordable FeCrNiMnCu high entropy alloys with excellent comprehensive tensile properties

Intermetallics 77 (2016) 23e33

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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

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-

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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.

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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:

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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:

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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

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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]:

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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

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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). References [1] 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) 299e303. [2] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 375e377 (2004) 213e218. [3] J.W. Yeh, Recent progress in high-entropy alloys, Ann. Chim. Sci. Mat. 31 (6) (2006) 633e648. [4] F. Otto, Y. Yang, H. Bei, E.P. George, Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys, Acta Mater. 61 (2013) 2628e2638. [5] Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Solid-solution phase formation rules for multi-component alloys, Adv. Eng. Mater. 10 (2008) 534e538. [6] S. Guo, C.T. Liu, Phase stability in high entropy alloys: formation of solidsolution phase or amorphous phase, Prog. Nat. Sci. 21 (2011) 433e446. [7] X. Yang, Y. Zhang, Prediction of high-entropy stabilized solid-solution in multi-component alloys, Mater. Chem. Phys. 132 (2012) 233e238.

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