Journal of Materials Science & Technology, 2020, 48(0): 146-155 DOI: 10.1016/j.jmst.2020.03.010

Research Article

The effect of Co and Cr substitutions for Ni on mechanical properties and plastic deformation mechanism of FeMnCoCrNi high entropy alloys

H.F. Zhanga, H.L. Yan,b,*, H. Yua,c,d, Z.W. Jie, Q.M. Hu,c,*, N. Jia,a,*

a Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), School of Material Science and Engineering, Northeastern University, Shenyang 110819, China

b State Key Lab Rolling & Automat, Northeastern University, Shenyang 110819, China

c Institute of Metal Research, Chinese Academy of Science, Shenyang 110016, China

d Shen Yang University of Technology, Shenyang 110870, China

e Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

Corresponding authors: * E-mail addresses:yanhaile@mail.neu.edu.cn(H.L. Yan);qmhu@imr.ac.cn(Q.M. Hu);jian@atm.neu.edu.cn(N. Jia).

Received: 2019-11-6   Accepted: 2020-01-27   Online: 2020-07-1

Abstract

The elastic constants, ideal tensile strength (ITS), stacking fault energy (SFE), lattice constant and magnetic moment of FeMnCoCrNi high entropy alloys with varying Co and Cr contents at 0 and 300 K were systematically investigated by first-principle calculations. For the alloys with Co substitution for Ni, at both temperatures the elastic stability of the face-centered cubic (fcc) phase, bulk elastic modulus (B), Young's modulus (E), shear modulus (G) and ITS increase monotonically with increasing Co content. However, the Cauchy pressure (CP), Pugh ratio (B/G), Poisson ratio (v), Zener anisotropy ratio (AZ) and elastic anisotropy ratio (AVR) decrease monotonically. The SFE also decreases with the increase of Co, resulting in the change of plastic deformation mechanism from dislocation slip to mechanical twinning, and then to hcp-martensitic transformation. This elucidates the underlying mechanism of the effect of Co addition on the strength and micromechanical behavior of FeMnCoCrNi alloys. Compared with Co, the Cr substitution for Ni leads to the more complex change of elastic constants and ITS. The increase of Cr shows the similar effect on SFE and deformation mechanism as that of Co. The variation of valence electron concentration and magnetism affect the SFE. The increase of either Co or Cr leads to the reduced magnetic moments of Fe and Mn. This could be responsible for the monotonic decrease of both lattice constant and SFE as the Co content increases. However, for the Cr addition case, multiple factors may affect the evolution of lattice constant and SFE. These findings shed light on the deformation mechanism of the alloys with different compositions.

Keywords: High entropy alloys ; First-principle calculations ; Elastic constants ; Ideal tensile strength ; Stacking fault energy

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H.F. Zhang, H.L. Yan, H. Yu, Z.W. Ji, Q.M. Hu, N. Jia. The effect of Co and Cr substitutions for Ni on mechanical properties and plastic deformation mechanism of FeMnCoCrNi high entropy alloys. Journal of Materials Science & Technology[J], 2020, 48(0): 146-155 DOI:10.1016/j.jmst.2020.03.010

1. Introduction

High entropy alloys (HEAs), also known as multi-principal element alloys (MPEAs) [1,2], have attracted great research interest owing to their excellent performances, such as high strength, superior ductility and good fracture resistance [3]. Based on mechanical performances, the existing HEAs have been classified into four categories [4], i.e., the soft HEAs solid solutions only including 3d-transition metal elements (e.g. Fe, Mn, Co, Cr and Ni), the alloys including transition metals and larger-atomic radius elements (e.g. Al and Ti), the alloys with refractory metals (e.g. W, Mo and Nb) and a few other alloying systems, such as CoFeReRu, MoPdRhRu and DyGdLuTbY.

As the classic example of 3d-transition-metal HEAs, the equiatomic FeMnCoCrNi HEA with the face-centered cubic (fcc) structure, also referred to as Cantor alloy [1,5], remains stable and exhibits excellent tensile ductility at both room temperature and cryogenic temperatures. Specifically, the alloy with an average grain size of ∼6 μm shows the yield strength of 370 MPa, ultimate tensile strength of 750 MPa and maximum elongation of 55% at 293 K. When the temperature drops to 77 K, the yield strength and ultimate tensile strength increase to 759 and 1280 MPa, respectively, while the maximum elongation reaches 71%. The simultaneously increased strength and ductility at cryogenic temperatures is attributed to the nano-scaled deformation twins [6]. Nevertheless, the yield strength of Cantor alloy at room temperature is much lower than that of the well-developed steels and superalloys, such as Fe-18Ni-3Al-4Mo-0.8Nb-0.08C-0.01B (wt%) [7], Fe-0.9C-1.7Mn-0.24Si (wt%) [8] and Ni-6.0Al-7.5Ta-6.0Co-6.0Cr-6.0Mo-4.0 W (wt%) [9]. Many researchers have tried to elevate the strength of the Cantor alloy by introducing interstitial atoms [10], grain refinement [11] and involving precipitates [12,13]. However, these approaches always lead to the reduced ductility even though the alloys are strengthened.

In recent years, the strategy of “metastable engineering” has been proven effective for overcoming the strength-ductility trade-off of the fcc structured HEAs. This is based on the tuning of stacking fault energy (SFE), as the SFE value determines the activation of different deformation mechanisms [14,15]. Li et al. [16,[16], [17], [18]] designed a FeMnCoCr HEA with high strain-hardening capacity at room temperature mainly contributed by the transformation induced plasticity (TRIP) effect. By adjusting the Mn content, a dual-phase microstructure consisting of austenite and hcp-martensite was produced during cooling from the high-temperature austenitic region. When deformed at room temperature, on the one hand, dislocations were blocked by the dense phase boundaries and thus the strength of the alloy was increased [19,20]. On the other hand, the transition from austenite to hcp-martensite occurred during deformation, contributing to the simultaneously enhanced strength and ductility [21]. Therefore, the excellent strength-ductility combination can be achieved by tuning the SFE and thus the micromechanical behavior of the material [22]. Based on this design concept, Wei et al. [23] and Liu et al. [24] successfully optimized mechanical properties of the Cantor alloy by adjusting the Co content. Both experiments and first-principles calculations show that the SFE of the alloy decreases with the substitution of Co for Ni. Accordingly, the deformation mode changes from dislocation slip of Fe20Co23Ni17Cr20Mn20 to deformation twinning of Fe20Co27Ni13Cr20Mn20, and then to austenite to hcp-martensitic transformation of Fe20Co30Ni10Cr20Mn20 [24]. This leads to the simultaneously improved strength and fracture elongation with the increased Co. Although the deformation mechanism of FeMnCoCrNi alloys with the varying Co contents has been investigated, in-depth understanding on the influence of the different elements on mechanical properties of the alloy system is still lacking. The remaining issues include: (1) The physical mechanism of the reduced SFE with the substitution of Co for Ni is unclear; (2) Compared with Co, the element Cr shows the larger difference of atomic radius between Cr and Ni. Thus, when Ni is substituted by Cr how the mechanical property and deformation mechanism change would be interesting but these are still unknown. (3) For HEAs, when dual-phase structures are obtained by modifying the compositions, the increased strength and ductility are usually attributed to the deformation-driven transformation from austenite to hcp-martensite. However, the effect of contents on the mechanical property of the fcc matrix remains ambiguous.

Numerous studies have shown that first-principles calculation is a powerful tool in screening chemical compositions and optimizing mechanical properties of alloys. To answer the questions as raised above in this work, elastic constants, ideal stress-strain curve and SFE of paramagnetic fcc alloys, i.e., Fe20Mn20CoxCryNi(60-x-y) with varying Co and Cr contents, are studied systematically by first-principles calculations. The experiments by Ref. [24] have shown that, when the Co content in the FeMnCoCrNi alloys increased from 27 to 30 at.%, a few thermally induced hcp-martensite laths with the volume fraction less than 2.0% formed within the austenitic matrix. Therefore, in order to study the mechanical properties of the alloys with a single fcc structure, we limit the atomic percentage of Co (x) in the calculation to be less than 30. On the other hand, our calculations show that when the content of Cr is larger than 35 at.% in the studied alloy system, the energy of the bcc structure is lower than that of the fcc structure, leading to the transition from fcc to bcc structures. To study the mechanical properties of single-phase austenite, the Cr content (y) is limited to be below 35 at.%. When the content of Co (or Cr) is changed, the contents of Fe, Mn and Cr (or Co) are fixed as 20 at.%, respectively. By revealing the effect of Co and Cr substitutions for Ni on mechanical properties and plastic deformation mechanism of the FeMnCoCrNi HEAs, the results will provide useful insights for the design and optimization of the Fe-Mn based HEAs with the high strength-ductility combination.

2. Calculation methods

In this study, the total energy was calculated with the exact muffin-tin orbitals (EMTO) method [25,26]. This is an improved screened Korringa-Koscreenedhn-Rostoker approach, and the full charge density method further elevates the accuracy for calculating the full potential total energy. An effective single atomic unit cell was used to model the chemical disorder within the coherent-potential approximation (CPA) [27,[27], [28], [29]]. By using this method the calculated elastic constants [30] and stacking fault energy [31] are more consistent with the experimental data compared with that by using the special quasi-random structures (SQS) method. For the self-consistent electronic density calculations we adopted the generalized gradient approximation (GGA) as the exchange-correlation density functional, while the total energy was obtained within the full Perdew-Burke-Ernzerhof (PBE) scheme [32]. The s, p, d, and f states were employed to treat the EMTO basis set. The Greens function was calculated for the 32 complex energy points around the valence states. The core states were treated in soft-core. All the studied alloys were described in the paramagnetic state. The disordered local moment (DLM) model was used to describe the random distribution of magnetic moment above the magnetic transition temperature [33,[32], [33], [34], [35], [36]]. Further details of the EMTO-CPA method can be found in Ref. [26]. The elastic constants were calculated from the strain derivative of the total energy. The polycrystal elastic modulus were obtained via the Voigt-Reuss-Hill averaging method [37]. For calculating the elastic constants, ideal tensile strength (ITS), SFE and magnetic moments at 300 K, only lattice expansion was considered in this work. The details for calculating SFE and ITS are included in the Supplemental materials 1 and 2, respectively.

3. Results and discussion

3.1. Elastic constants

The mechanical and physical properties of metallic materials in the ground-state are importantly theoretical basis used for optimizing the composition of alloys [30,38]. In order to systematically study the mechanical properties of paramagnetic fcc FeMnCrCoNi alloys with varying Co and Cr contents, the mechanical and physical parameters of the alloys in the ground-state were calculated. For assessing the accuracy of our calculations, the calculated elastic constants of the Cantor alloy were compared with other theoretical studies [30,38,39] (see details in the Supplementary Material 3).

Fig. 1 shows the obtained single-crystal elastic constants Cij and C' of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys at 0 K. The mechanical stability criteria of the materials with cubic lattice structures requires C11>0, C44>0, C'>0 and C11+ 2C12 >0 [40]. With increasing Co content, C11, C' and C44 approximately show the linear increasing tendency, while C12 is not significantly increased. This confirms that the addition of Co contributes to the elastic stability of the fcc phase [38,41]. As the Cr content increases, both C11 and C12 increase monotonously, while C44 and C' increase first and then decrease. When the Cr contents are 20 and 15 at.%, C44 and C' reach the maximum values, respectively. Therefore, compared with Co, the substitution of Cr for Ni shows the more complex effect on the elastic stability of the alloys. The single-crystal elastic constants at room temperature (300 K) are shown in Fig. 2. With increasing Co or Cr content, the variation trends of C11, C12, C44 and C' are consistent with that at 0 K. Compared with that at 0 K, the C' at 300 K is lower for each studied alloy, suggesting that temperature rise reduces the elastic stability of the alloys [38].

Fig. 1.

Fig. 1.   Theoretical single-crystal elastic constants of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys at 0 K.


Fig. 2.

Fig. 2.   Theoretical single-crystal elastic constants of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys at 300 K.


Fig. 3 shows the calculated polycrystalline elastic constants, i.e. bulk elastic modulus (B), Young's modulus (E), shear modulus (G), Cauchy pressure (CP), Pugh ratio (B/G), Poisson ratio (v), Zener anisotropy ratio (AZ) and elastic anisotropy ratio (AVR, AVR=$\frac{G_{ V } -G_{ R } }{ G_{ V } +G_{ R } }$), of the alloys at 0 K. With increasing Co content, B increases monotonically, suggesting the increasing resistance to volume change when the material is under an external pressure. In addition, E and G increase monotonically, suggesting the increasing resistance to tensile and shear deformation at the elastic deformation stage [41]. However, with the increase of Co, CP, B/G, ν, AZ and AVR show the linear decreasing tendency. The decrease of CP indicates that the covalency of chemical bonds increases with the Co substitution, leading to the increased brittleness of materials [42]. According to the Pugh guidelines, there exists B/G > 1.75 and ν > 0.26 in ductile materials. The reduced B/G and ν suggest an increased brittleness of materials [43], in good agreement with the analyses of CP. The AZ and AVR values are also important for evaluating the mechanical properties of materials. For isotropic alloys, AZ is equal to 1. With the increase of Co, AZ decreases from 4.8 to 3.9, suggesting the weakened anisotropy as well as the reduced probability of the occurrence of cross-slip pinning [41,44]. The anisotropy parameter AVR shows the similar evolution tendency as that of AZ, showing the reduced anisotropy of the alloys with the addition of Co.

Fig. 3.

Fig. 3.   Theoretical polycrystalline elastic parameters of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys at 0 K.


With the increase of Cr, only B shows a monotonous increasing tendency and the increase is larger than that with the increasing Co content. Both G and E first increase and then decrease, suggesting that the resistance to deformation changes accordingly at the elastic stage. The parameters CP, B/G, ν, AZ and AVR first decrease and then increase with increasing Cr, suggesting the first reduced and then elevated ductility as well as anisotropy of the alloys. Besides, when the Co or Cr contents are lower than 20 at.%, E and G are larger with the Cr addition than that with the equal addition of Co, whereas B, CP, B/G, v, AZ and AVR are smaller in the former case. That means the addition of Cr enhances the resistance to tensile and shear deformation in the elastic regime for the Fe20Mn20CoxCryNi(60-x-y) alloys. However, the influence of Cr on the resistance to volume change under external pressure, ductility and anisotropy are weaker. When the contents of Co or Cr are above 20 at.%, B, CP, B/G, v, AZ and AVR are bigger with the addition of Cr compared with the equal addition of Co, whereas E and G are smaller in the former case. Therefore, the addition of Cr is conductive to increase the resistance to volume change under external pressure, ductility and anisotropy of the alloys. However, the Cr addition reduces the resistance to tensile and shear deformation at the elastic stage.

Fig. 4 shows the variation of polycrystalline parameters, i.e. B, E, G, CP, B/G, ν, AZ and AVR, as a function of Co and Cr contents for the Fe20Mn20CoxCryNi(60-x-y) alloys at 300 K. As either Co or Cr increases, B, E, G, CP, B/G and ν show the same evolution trends as that at 0 K, respectively. Both AZ and AVR decrease as the Co content increases, while the parameters increase monotonically as the Cr content increases. However, compared with 0 K, the following features are obtained at 300 K: First, the values of B, E, and G are smaller. Therefore, the temperature rise corresponds to the reduction of the resistance to elastic deformation. Second, CP increases as the temperature increases, indicating that the metallicity of chemical bonds were enhanced in the alloys. In addition, both B/G and ν increase with increasing temperature, indicating the elevated ductility at 300 K. Last, both AZ and AVR increase at 300 K, indicating the elevated anisotropy of the alloys with increasing temperature.

Fig. 4.

Fig. 4.   Theoretical polycrystalline elastic parameters of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys at 300 K.


Fig. 5 presents the three-dimensional Young’s modulus anisotropy of the alloys as a function of Co and Cr contents at different temperatures. As shown in Fig. 5(a) and (b), with increasing Co and Cr contents anisotropy of the fcc structure are strong at both 0 and 300 K. One may also note that both the largest and the smallest Young’s modulus are distributed along the <111> and <100> directions, respectively, irrespective of how the Co and Cr contents change. This agrees with the first principles calculations for AlxCrMnFeCoNi, FeMnCoCrNi and CoCrFeNiMo alloys with the fcc structure [38,39,45]. Compared with 0 K, the thermal expansion effect at 300 K leads to the increase of lattice constant at the higher temperature [31], resulting in the changes of the elastic constants and anisotropy as presented above.

Fig. 5.

Fig. 5.   Three-dimensional surface plots of the single-crystal Young’s modulus for the (a) Fe20Mn20CoxCr20Ni(40-x) (x = 0, 30) and (b) Fe20Mn20Co20CryNi(40-y) (y = 0, 35) alloys, respectively. The calculated results at both 0 K and 300 K are presented.


3.2. Ideal tensile strength

Fig. 6(a) and (b) shows the ideal stress-strain curves of the Fe20Mn20CoxCr20Ni(40-x) alloys stretching along the [110] tension under 0 K and 300 K, respectively. To examine accuracy of the calculations, the ITS of the equiatomic FeMnCoCrNi alloy at 0 K is calculated first. At a strain of 6.5%, the ITS is ∼11 GPa. This is close to the previously theoretical investigation in Ref. [46]. At both 0 and 300 K, the ITS increases with increasing Co, consistent with the change of E. This is due to the fact that the chemical bonding strength within alloys increases as the Co content increases. The lattice constant decreases accordingly (to be discussed in detail later), leading to the increasing ITS. Besides, at 300 K the ITS of the alloys with the same Co contents is significantly lower than that at 0 K. This is caused by the weakened chemical bonding strength as the temperature rises. At the higher temperature, the expansion of lattice volume leads to the reduced ITS.

Fig. 6.

Fig. 6.   Ideal tensile strength of the Fe20Mn20CoxCr20Ni(40-x) (0≤x≤30) alloys at (a) 0 K and (b) 300 K as a function of the applied strain. The uniaxial tension axis is parallel to the [110] direction.


Fig. 7(a) and (b) presents the stress-strain curves of the Fe20Mn20Co20CryNi(40-y) alloys under the [110] tension at 0 K and 300 K, respectively. As the Cr content increases, ITS first increases and then decreases, reaching the maximum when the Cr content is ∼10 at.%. This variation trend is consistent with that of E. The ITS of the alloys with the same Cr contents at 300 K is significantly lower than that at 0 K, which also indicates that the temperature rise leads to the increasing lattice constant.

Fig. 7.

Fig. 7.   Ideal tensile strength of the Fe20Mn20Co20CryNi(40-y) (0≤y≤35) alloys at (a) 0 K and (b) 300 K as a function of the applied strain. The uniaxial tension axis is parallel to the [110] direction.


Experimental study has shown that for the Fe20Mn20CoxCr20Ni(40-x) alloys, as the Co content increased from 20 to 30 at.%, the yield strength increased by ∼40 MPa [24]. This was attributed to the thermally induced stacking faults and fine hcp-martensite laths in the microstructure as Co increases. The current calculations, on the other hand, reveal that the strength of the austenite increases continuously with the increasing Co content. This contributes to the elevated yield strength of the alloys. However, the addition of excessive Cr (y>10 at.%) does not lead to strengthening of the fcc phase. Therefore, it is possible to improve the strength of the austenite by increasing the Co content of the single-phase or dual-phase HEAs consisting of the fcc phase.

3.3. SFE and plastic deformation mechanism

For fcc structured materials, SFE is the key factor determining the activation sequence of different deformation modes [31,[47], [48], [49], [50]]. The theoretical study of the HEAs with an fcc structure has shown that the decreasing deformation temperature leads to the reduction of the SFE. Accordingly, the deformation-induced twinning or hcp-martensite transformation that cannot be triggered at room temperature become active at lower temperatures [47]. This has been recently confirmed by characterization of deformation microstructures of a cryogenically deformed FeMnCoCr HEA [51]. When the temperature decreases from 293 K to 77 K, the deformation mechanism changes from dislocation slip plus twinning to the deformation-driven hcp-martensite transformation plus minor slip and twinning. The variation of deformation modes contributes to the enhanced strain hardening capacity at cryogenic temperatures.

The accuracy of the calculated SFE for the Cantor alloy has been proven reliable by comparing with the results in Ref. [31] (Supplementary material 4). The difference of the calculated SFE between the usage of the LDA and GGA functionals were also discussed in the supplementary material. Fig. 8(a) and (b) presents the calculated variations of intrinsic stacking fault energy (γisf) and extrinsic stacking fault energy (γesf) as a function of the Co and Cr contents for the Fe20Mn20CoxCryNi(60-x-y) alloys, respectively. The results at both 0 K and 300 K are presented. With the increase of both Co and Cr contents, the SFE decreases monotonically. At 0 K, when the Co content increases from 0 to 30 at.%, γisf and γesf decrease by ∼110 mJ/m2. At 300 K, the both parameters decrease by ∼60 mJ/m2 as Co increases. Therefore, at the lower temperatures the influence of the Co content on the SFE becomes more significant. In other words, as the Co content increases the SFE are more dependent on temperatures. The decreasing tendency of the SFE with increasing Co content agrees well with the experimental data in Ref. [52]. For the Cr addition cases, at 0 K, when the Cr content increases from 0 to 35 at.%, γisf and γesf decrease by ∼180 and ∼200 mJ/m2, respectively. At 300 K, the both parameters decrease by ∼90 and 100 mJ/m2 as the Cr content increases. The influence of temperature on the SFE becomes more significant as the Cr content increases. On the other hand, at each temperature, the addition of Cr shows the more significant effect on SFE compared with that of Co addition. It is also noteworthy that at 300 K the SFE of all the studied alloys is higher than that at 0 K, which is attributed to the increased lattice constant as the temperature is elevated. The first-principles calculations by Ikeda et al. [53] reported that the addition of Co did not change the SFE significantly in the FeMnCoCrNi HEAs. Specifically, when the Co content increased from 0 to 30 at.% at 300 K, the SFE only decreased by ∼25 mJ/m2. The discrepancy between the current results and the literature data can be attributed to the different configurations and local compositions applied in the modelling. To be explicit, the Co content is increased in each layer of the supercell in our model, whereas only the Co content in the vicinity of stacking faults is changed in the literature. With the increase of Cr, the calculated variation of SFE agrees well with that reported by Ref. [53]. The calculated stacking fault energies of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys follow the universal scaling law (Supplementary material 5).

Fig. 8.

Fig. 8.   The intrinsic stacking fault energy (γisf) and extrinsic stacking fault energy (γesf) of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys as a function of (a) Co and (b) Cr contents. The calculated results at both 0 K and 300 K are presented.


The effective energy barriers (EEBs) of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys are also calculated in this work. The EEBs of the leading deformation modes, i.e., dislocation slip, twinning and stacking faults, are calculated as follows [47,48,54]:

${{\bar{\gamma }}_{SL}}=\frac{{{\gamma }_{usf}}-{{\gamma }_{isf}}}{\cos \left( {{60}^{o}}-\theta \right)}$
${{\bar{\gamma }}_{TW}}=\frac{{{\gamma }_{utw}}-{{\gamma }_{isf}}}{\cos \theta }$
${{\bar{\gamma }}_{SF}}=\frac{{\gamma }_{usf}}{\cos \theta }$

where θ reflects the effect of grain orientation relative to the resolved shear direction and varies between 0° and 60°; γisf is the intrinsic SFE; γusf is the unstable SFE and γutw is the unstable twin fault energy. Fig. 9 shows the EEBs curves of the Fe20Mn20CoxCr20Ni(40-x) (0≤x≤30) alloys with the change of θ at room temperature. When x<20, $\bar{\gamma}_{ TW }$ is less than $\bar{\gamma}_{ SF }$, indicating that twinning is more active than stacking faults. When x>20, however, $\bar{\gamma}_{ TW }$ is larger than $\bar{\gamma}_{ SF }$, indicating that as the Co content continuously increases stacking faults tend to be activated during deformation. As stacking faults act as nuclei for the formation of hcp-martensite [54], the extensive multiplication of these defects leads to the transformation from austenite to hcp-martensite. It should be mentioned that due to the randomness of grain orientation in the isotropic polycrystals, dislocation slip occurs in all the studied alloys with different Co contents. As θ increases, the EEBs of dislocation slip become smaller, contributing to the more activated slip systems. With the increase of Co, the angle range in which dislocation slip can be activated (i.e., $\bar{\gamma}_{ SL }$ < $\bar{\gamma}_{ TW }$ and $\bar{\gamma}_{ SL }$ < $\bar{\gamma}_{ SF }$) becomes narrower, suggesting that the tendency of slip is reduced as plastic deformation proceeds. As the Co content increases, the decreased SFE and the prohibited dislocation slip as derived here by calculations agrees with the experimental results [24]. Accordingly, the deformation-induced twinning and hcp-martensitic transformation are the dominant mechanisms and they jointly contribute to the work hardening of the alloys. Fig. 10 shows the EEBs curves of the Fe20Mn20Co20CryNi(40-y) (0≤y≤35) alloys with the change of θ at room temperature. The effect of Cr on the plastic deformation mechanism is consistent with that of Co. This is attributed to the fact that addition of the both elements leads to the reduction of the SFE.

Fig. 9.

Fig. 9.   Effective energy barriers of the Fe20Mn20CoxCr20Ni(40-x) (0≤x≤30) alloys with their corresponding lattice constants at 300 K as a function of θ.


Fig. 10.

Fig. 10.   Effective energy barriers of the Fe20Mn20Co20CryNi(40-y) (0≤y≤35) alloys with their corresponding lattice constants at 300 K as a function of θ.


3.4. Material parameters affecting the SFE

The composition-dependent SFE are mainly determined by valence electron concentration (VEC) and lattice constant [55]. The research on austenitic stainless steels [55,56] has shown that electronic and volume effects are responsible for the SFE. In this work, VEC and lattice constant are also found affecting the SFE of the studied Fe20Mn20CoxCryNi(60-x-y) alloys. Specifically, the valence electron numbers of Co and Cr are less than that of Ni, leading to the decreased VEC with increasing Co or Cr contents. In austenitic stainless steels, the VEC is increased (decreased) with the Ni (Cr) addition, leading to the destabilized (stabilized) hcp structure. The reason is that the density of states for the hcp phase presents the pronounced minima at energies slightly below Fermi level with the Ni (Cr) addition [55]. Thus the decreasing VEC promotes the stability of the hcp structure. In the studied HEAs with Co and Cr substitutions for Ni, the SFE is lowered. This agrees with the elevated phase stability of the hcp phase in austenitic steels as the Cr content increases [55]. The lattice constants of the studied alloys with different Co and Cr contents are shown in Fig. 11(a) and (b), respectively. With the increasing Co content (0≤x≤30), the lattice constant decreases monotonically, consistent with the evolution of the SFE. The reduced SFE with decreasing lattice constant is also found in the Cr addition (0≤y≤20) case. However, when the Cr content reaches 20 at.%, the SFE starts to increase with the further increased Cr. The nonlinear change of lattice constant with the increase of Cr has also been reported in a theoretical study of Co(1-x)Crx binary alloys [57].

Fig. 11.

Fig. 11.   Lattice constants and stacking fault energy of the Fe20Mn20CoxCryNi(60-x-y) (0≤x≤30, 0≤y≤35) alloys at 0 K with the variation of (a) Co and (b) Cr contents. Magnetic moments of the alloys at 0 K with the variation of Co and Cr contents are shown in (c) and (d), respectively.


For the FeMnCoCrNi alloys, the atomic radius of both Co and Cr are greater than that of Ni (RCo = 1.26 Å, RCr = 1.27 Å, and RNi = 1.24 Å). However, the lattice constant does not show a monotonic increase as either Co or Cr increases. Similar results were also found in a study of the Mn2NiGa shape memory alloy [58,59]. Therefore, the evolution of lattice constant with varying compositions cannot be simply ascribed to the change of atomic radius, and the other factors are expected to also play roles such as magnetism and chemical bonding [60]. We then focus on the variation of atomic magnetic moments of the constituent elements within the Fe20Mn20CoxCryNi(60-x-y) alloys. As shown in Fig. 11(c), with increasing Co, magnetic moments of the both Fe and Mn decrease. With increasing Cr, the magnetic moments changes of Fe and Mn are more significant (Fig. 11(d)). This agrees with the literature work on austenitic stainless steels that shows the decreased magnetic moment of Fe as Cr increases [55]. When the Cr content reaches 35 at.%, the magnetic moment of Mn is close to zero and that of Fe is reduced by a half compared with the alloy without the Cr addition. The magnetic moment of Co also decreases remarkably as the Cr content increases from 0 to 10 at.%. Compared with Co, the addition of Cr leads to the more significant reduction of magnetic moments for Fe and Mn. To this stage, it is deduced that the variation of lattice constant with the increase of Co content is consistent with that of the magnetic moments of Fe and Mn. Thus, the reduction of magnetic moments of Fe and Mn might be a factor leading to the decreased lattice constant and thus the reduced SFE. With the increase of Cr, the evolution tendency of lattice constant is different from that of magnetic moments of Fe and Mn. Therefore, we speculate that the decrease of the SFE originates from the decreased magnetic moments of those elements. When the Cr content is above ∼20 at.%, chemical bonding strength may also become a dominant factor leading to the change of lattice constant. However, this is not within the scope of the current paper as the CPA formulations implemented in the EMTO code are not perfect for predicting the metallic bonding in HEAs. In this work, the calculations clearly show that VEC and magnetism are the intrinsic parameters that lead to the reduced SFE with the increasing Co and Cr contents. As the interaction of multiple principal elements within HEAs is complex, the factors that influence the deformation mechanism may be diverse. To further explore the underlying correlation between material parameters and deformation behaviors of HEAs, more accurate models and advanced experimental approaches are required.

4. Conclusions

By employing first-principle calculations, elastic constant, ITS, SFE, lattice constant and magnetic moment of the PM fcc FeMnCoCrNi alloys with varying Co and Cr contents at both 0 K and 300 K were investigated systematically. The micromechanical properties and physical mechanism of plastic deformation of the fcc structure are discussed. The conclusions are:

(1)For the alloys with Co substitution for Ni, at both temperatures elastic stability of the fcc phase, B, E and G increase monotonically with increasing Co content, while CP, B/G, v, AZ and AVR decrease continuously. Nevertheless, the influences of Cr addition on the material parameters are more complex. Compared with 0 K, elastic stability, B, E and G are decreased whereas CP, B/G, v, AZ and AVR are increased at 300 K.

(2)For the alloys under uniaxial tension along the [110] direction, ITS increases as the Co content increases. With increasing Cr, ITS first increases and then decreases, showing the maximum when the Cr content is ∼10 at.%. For the both cases of Co and Cr addition, the ITS at 300 K is lower than that at 0 K.

(3)The additions of Co and Cr lead to the decreasing SFE. In addition, as either Co or Cr increases, SFE becomes more dependent on temperatures. The analysis of the EEBs at 300 K shows that as the Co content is below 20 at.%, the addition of Co promotes the activation of twinning during deformation whilst dislocation slip and stacking fault are prohibited. When the Co content is above 20 at.%, stacking fault and hcp-martensitic transformation become the dominant deformation mechanisms, while twinning and dislocation slip are prohibited. The addition of Cr shows the similar effect on SFE and deformation mechanism as that of Co.

(4)VEC and magnetism affect the composition-dependent SFE. With increasing Co (0≤x≤30) or Cr (0≤y≤20) contents, both VEC and lattice constant show the monotonic decreasing tendency. The addition of either Co or Cr leads to the decreased magnetic moments of Fe and Mn. This corresponds to the monotonically reduced lattice constant and SFE with increasing Co. For the Cr addition, except for atomic magnetic moment, chemical bonding strength may also play a role in the variation of lattice constant and SFE.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Nos. 51922026 and 51571057), the Fundamental Research Funds for the Central Universities (Nos. N2002005 and N2007011) and the Liaoning Natural Science Foundation (No. 20180510010). The authors thank Prof. L. Vitos and Dr. W. Li at KTH Royal Institute of Technology for providing the EMTO code and Dr. F.Y. Tian, S. Huang and S. Lu also at KTH for their helpful discussions.

Appendix A. Supplementary data

Supplementary material related to this article can be found, inthe online version, at doi:https://doi.org/10.1016/j.jmst.2020.03.010.

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