Tensile properties of the Cr–Fe–Ni–Mn non-equiatomic multicomponent alloys with different Cr contents

    Tensile properties of the Cr-Fe-Ni-Mn non-equiatomic multicomponent alloys with different Cr content N.D. Stepanov, D.G. Shaysultanov, M.A. Tikhonovsky, G.A. Salishchev PII: DOI: Reference:

S0264-1275(15)30257-4 doi: 10.1016/j.matdes.2015.08.007 JMADE 415

To appear in: Received date: Revised date: Accepted date:

18 June 2015 31 July 2015 1 August 2015

Please cite this article as: N.D. Stepanov, D.G. Shaysultanov, M.A. Tikhonovsky, G.A. Salishchev, Tensile properties of the Cr-Fe-Ni-Mn non-equiatomic multicomponent alloys with different Cr content, (2015), doi: 10.1016/j.matdes.2015.08.007

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Tensile properties of the Cr-Fe-Ni-Mn non-equiatomic multicomponent alloys with different Cr content N.D. Stepanov1,*, D.G. Shaysultanov1, M.A. Tikhonovsky2, G.A. Salishchev1

T

Laboratory of Bulk Nanostructured Materials, Belgorod State University, Belgorod 308015,

IP

1

2

SC R

Russia

National Science Center “Kharkov Institute of Physics and Technology” NAS of Ukraine,

*

NU

Kharkov, 61108, Ukraine

Corresponding author. Laboratory of Bulk Nanostructured Materials, Belgorod State

MA

University, Pobeda 85, Belgorod, 803015, Russia. Tel.: +7 4722 585416

AC

CE P

TE

D

E-mail address: [email protected], [email protected] (N.D. Stepanov)

1

ACCEPTED MANUSCRIPT Abstract A series of Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24 (at.%)) multicomponent alloys was prepared by vacuum arc melting. The Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys were

T

ductile single phase fcc solid solutions. The Fe40Mn28Ni8Cr24 alloy had intermetallic sigma phase

IP

matrix and was extremely brittle after homogenization. The tensile properties of the

SC R

Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 solid solution alloys were examined in recrystallized condition with average grain size of ~10 µm. The yield strength increased from

NU

210 MPa of the Fe40Mn28Ni28Cr4 alloy to 310 MPa of the Fe40Mn28Ni14Cr18 alloy. The elongation to fracture of the alloys decreased from 71% to 54%, respectively. Solid solution strengthening

MA

by the constitutive elements of the alloys was calculated using Labush approach. Strong solid solution strengthening by Cr was predicted. Gypen and Deruyttere approach was used to

D

estimate solid solution strengthening of the Fe40Mn28Ni32-xCrx alloys. Good correlation between

CE P

TE

predicted solid solution strengthening and the experimental yield strength values was found.

Keywords: High entropy alloy; Alloy design; Mechanical properties; Solid solution

AC

strengthening.

2

ACCEPTED MANUSCRIPT 1. Introduction The high entropy alloys (HEAs) [1] are multicomponent alloys composed of at least 5 principle elements with nearly equiatomic concentrations from 5 to 35 at.% according to original

T

definition [2]. The HEAs concept has been developed recently with intent on stabilization of

IP

complexly concentrated random solid solution phases by high mixing entropy. Later it was

SC R

revealed that many of HEAs can have complex multiphase structure and mixing entropy is not the principal factor governing phase formation in HEAs [3-5]. However, some of the equiatomic

NU

HEAs have been proved to have either fcc or bcc solid solution single phase structures. The single fcc phase CoCrFeNiMn alloy [6] has remarkable mechanical properties: good ductility at

MA

room and cryogenic temperatures [7] and exceptional fracture toughness at cryogenic temperature [8]. Similarity of mechanical behavior of the CoCrFeNiMn alloy with high-Mn

D

austenitic TWIP steels was pointed out [9]. Potential application of the alloy as energy-absorbing

TE

material was suggested [9]. But the CoCrFeNiMn alloy has rather low yield strength in

CE P

recrystallized condition [7]. The decrease of grain size [7] or cold working [10] can promote significant hardening, but at a cost of (drastic in case of cold working) reduce of ductility [7, 10]. Strength of the Co-Cr-Fe-Ni-Mn system alloys can be possibly increased by optimizing chemical

AC

composition. Complexly concentrated solid solutions are expected to benefit from strong solidsolution strengthening (SSS) caused by massive alloying [1]. Increased concentration of elements having strong SSS effect, i.e. development of non-equiatomic HEAs [11-13], can have positive effect on mechanical performance of the alloys. However, only limited effects have been made so far to qualify SSS effect in HEAs [14-16]. This limits the possibilities of tailoring composition of the alloys to maximize SSS effect. Analysis of mechanical properties of the various ternary and quaternary equiatomic alloys in the Co-Cr-Fe-Ni-Mn system suggests that Cr has the strongest strengthening effect among the constitutive elements of the alloys [17]. Therefore, in current study, we have examined mechanical properties of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24 (at.%)) alloys with different Cr and Ni content. The number and concentrations 3

ACCEPTED MANUSCRIPT of the constitutive elements in the Fe40Mn28Ni32-xCrx alloys don’t fit the HEAs definition, but the alloys are not based on single principal element and therefore are defined as multicomponent alloys. Co was excluded due to its high cost and potentially unfavorable effect on radiation

T

damage performance [18]. Two main aims were pursued: (i) to experimentally establish

IP

possibility of controlling mechanical properties of single phase multicomponent alloys by

SC R

appropriate alloying, (ii) to evaluate possibility of predicting SSS effect in multicomponent

NU

alloys.

2. Methods

MA

In this study, a series of Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24 (at.%)) alloys was studied. All the compositions given in the text are also in at.%. The alloys were produced by vacuum arc melting

D

of the high-purity (at least 99.9%) constitutive elements. The produced ingots had dimensions of

TE

≈8х12x40 mm3. Each ingot was remelted at least 5 times to ensure chemical homogeneity. The

CE P

produced ingots were homogenized at 1000°C for 24 hours in vacuum. SEM-EDX analysis showed that actual chemical composition of the alloys corresponded to nominal ones (Table 1). After homogenization, the alloys were cold rolled with ≈80% height reduction. However, the

AC

Fe40Mn28Ni8Cr24 alloy was found to be extremely brittle and fractured at the initial stages of rolling. Therefore the Fe40Mn28Ni8Cr24 alloy was excluded from further processing. The Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys were successfully rolled without any noticeable cracking. The cold rolled alloys were further annealed at 850°C for 30 min to produce recrystallized structure. Microstructure and phase composition of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24 (at.%)) alloys were studied using X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. The XRD analysis was performed using RIGAKU diffractometer and Cu Kα radiation. Samples for SEM observations were prepared by careful mechanical polishing. SEM

4

ACCEPTED MANUSCRIPT investigations were performed utilizing Quanta 200 3D microscope equipped with back-scattered electron (BSE) and energy-dispersive (EDS) detectors. Vickers microhardness of the homogenized Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24 (at.%)) alloys

T

was measured using a 250 g load applied for 15 s. 20 measurements were made for each alloy.

IP

Dog-bone specimens with gauge dimensions of 1.5×3×5 mm3 for tensile testing were cut using

SC R

electric discharge machine from the as-annealed Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys. Prior to testing, specimens were carefully mechanically polished.

NU

Testing to fracture was performed at constant crosshead speed of 1 mm/min in an Instron 5882 test machine. Elongation to fracture was determined by measurements of spacing between marks

MA

designating the gauge length before and after the test.

D

3. Results

TE

Fig. 1 and Fig. 2 demonstrate respectively XRD patterns and SEM-BSE images of the

CE P

Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) alloys. The results of the local EDX chemical analysis of the alloys are shown in Table 1. The XRD patterns of the Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys after rolling and subsequent annealing (Fig. 1) demonstrate presence of

AC

diffraction peaks from single fcc phase. The lattice parameter of fcc phase is not affected significantly by Cr and Ni content and is of 3.611-3.612 nm. The SEM images of the microstructure of the Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys (Fig. 2 ac) confirm single phase structure of the alloys. The average size of recrystallized grains is 12.9±3.2 µm, 8.9±2.2 µm and 8.1±2.5 µm respectively in the Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys. Numerous annealing twins are found inside the grains. The chemical composition of the grains is identical to the composition of the corresponding alloy. The XRD pattern of the homogenized Fe40Mn28Ni8Cr24 alloy (Fig. 1) reveals presence of two phases - tetragonal sigma phase and fcc phase. The lattice parameters of the tetragonal sigma 5

ACCEPTED MANUSCRIPT phase are а= 8.809 nm and c=4.582 nm. The lattice parameter of the fcc phase is 3.615 nm. The SEM-BSE image of the Fe40Mn28Ni8Cr24 alloy (Fig. 2d) confirms that the alloy has two-phase structure: inside matrix phase slightly elongated second phase particles appear. The volume

T

fraction of the particles can be roughly estimated as of 45%. Local chemical analysis (Table 1)

SC R

particles (point 2, Fig. 2d) contain only 17.8% of Cr.

IP

demonstrates that the matrix (point 1, Fig. 2d) is enriched with chromium (32.0%), whereas the

Microhardness measurements (Table 2) demonstrate that the Fe40Mn28Ni8Cr24 alloy is ≈3.5 times

NU

harder than other alloys after homogenization annealing – its microhardness is 410 HV, whereas the microhardness of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys is 111-126 HV. The

MA

microhardness of latter alloys also shows some dependence on Cr concentration – it increases from 111 HV of the Fe40Mn28Ni28Cr4 alloy to 126 HV of the Fe40Mn28Ni14Cr18 alloy.

D

The stress-strain curves obtained during tensile testing of the cold-rolled and annealed

TE

Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys are shown in Fig. 3. The resulting mechanical properties,

CE P

namely, yield strength (σ0.2), ultimate tensile strength (σUTS) elongation to fracture (δf) and uniform elongations (δu) are summarized in Table 3. The mechanical behavior of the tested alloys is similar: they demonstrate relatively low yield strength, but after yielding exhibit

AC

prolonged strain hardening stage which promotes high ductility. Chemical composition of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys has pronounced effect on their mechanical characteristics. For example, yield strength increases when Cr content increases: from 210 MPa of the Fe40Mn28Ni28Cr4 alloy to 310 MPa of the Fe40Mn28Ni14Cr18 alloy. In contrast, ductility is lower in alloys with higher Cr concentration. For example, the elongation to fracture and uniform elongation of the Fe40Mn28Ni28Cr4 alloy are 71% and 52% respectively, whereas corresponding values for the Fe40Mn28Ni14Cr18 alloy are 54% and 37%. The ultimate tensile strength of the alloys shows non-monotonic dependence on Cr content: the strength of the Fe40Mn28Ni28Cr4 alloy is 565 MPa, while the strength of the Fe40Mn28Ni20Cr12 alloy is slightly lower - 545 MPa. But σUTS of the Fe40Mn28Ni14Cr18 alloy is substantially higher – 605 MPa. 6

ACCEPTED MANUSCRIPT 4. Discussion In this study, structure and mechanical properties of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24)

T

alloys were examined. Among the examined alloys, the Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and

IP

Fe40Mn28Ni14Cr18 alloys are fcc solid solutions (Fig. 1). Their structure and mechanical behavior

SC R

are rather similar –cold rolling and annealing at 850°C produced recrystallized structure with grain size of ~10 µm (Fig. 2 a-c) in the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys. The recrystallized

NU

alloys demonstrate relatively low yield strength, but pronounced strain hardening capacity results in good ductility (Fig. 3). This type of mechanical behavior is typical for Co-Cr-Fe-Ni-Mn

MA

system fcc solid solution alloys [7-13, 17-18].

The mechanical properties of the solid solution Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys are clearly

D

dependent on Cr and Ni content: increase of Cr content and decrease of Ni content results in

TE

pronounced strengthening and decrease of ductility (Figure 3, Table 3). Although higher strength

CE P

of Cr-containing equitomic Co-Cr-Fe-Ni-Mn system alloys than their Cr-free counterparts has already been demonstrated [17], strengthening of complexly concentrated multicomponent alloys or HEAs by varying concentration of constitutive elements has never been reported. The

AC

examined alloys have single-phase structure and have not contained any precipitates. They also were examined in well-recrystallized condition. Therefore two mechanisms can be responsible for higher strength of higher Cr containing alloys: (i) grain boundary (Hall-Petch) strengthening and (ii) SSS. It is known that strong Hall-Petch dependence is often observed in the fcc Co-CrFe-Ni-Mn-system alloys [7, 19, 20]. The recrystallized grain size in the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys continuously decreases from 12.9 µm of the Fe40Mn28Ni28Cr4 alloy to 8.1 µm of the Fe40Mn28Ni14Cr18 alloy. Lower grain size could be attributed to presumably higher melting temperature of the alloys containing more Cr (melting temperature of 1907°C) instead of Ni (melting temperature of 1455°C). Thus the recrystallization annealing temperature (850°C) should correspond to lower homologous temperature for the alloys with higher Cr content. But 7

ACCEPTED MANUSCRIPT the grain sizes of the Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys are only ≈10% different (8.9 µm and 8.1 µm respectively), while the yield strength of the alloys demonstrates ≈25% difference (245 MPa and 310 MPa respectively). Thus higher strength observed in the Cr-rich

T

solid solution Fe40Mn28Ni32-xCrx alloys cannot be attributed to Hall-Petch effect and SSS has to

IP

be considered.

SC R

According to classical Labush approach [21] for concentrated solid solutions, already successfully applied to HEAs [14], the SSS caused by the atoms of i element can be described

NU

as: ∆σSSi = Z G fi4/3 Ci2/3

(1)

MA

Where G is the shear modulus of the alloy, Z is a fitting constant, Ci is the concentration of the i element, and fi is the mismatch parameter. The mismatch parameter, fi, can be calculated using

(2)

TE

fi = (δGi2 + α2 δri2)1/2

D

following formula:

where δGi=(1/G)dG/dCi and δri=(1/r)dr/dCi are the atomic modulus and atomic size mismatch

CE P

parameters, respectively, and α is a constant dependent on the type of the mobile dislocations. Generally, α is 2-4 for the screw dislocations and α≥16 for edge dislocations [22].

AC

The mismatch parameters δGi and δri can be estimated in accord to method proposed in [22, 23]. In fcc lattice every element has 12 nearest-neighbor atoms, thus forming a 13-atom cluster. If the local environment around the alloying element i is assumed to be equal to the average composition of the alloy, the i element has Nj=13cj of j-atom and Ni =13ci − 1of i -atom neighbors (j ≠ i). Then the atomic size, δri, and atomic modulus, δGi, mismatches in the vicinity of the element i are estimated as an average of the atomic size difference, δrij = 2(ri - rj)/(ri + rj), and shear modulus difference, δGij = 2(Gi - Gj)/(Gi + Gj), respectively, of this element with its neighbors: δri =

13  c jrij 12

(3)

8

ACCEPTED MANUSCRIPT δGi =

13  c jGij 12

(4)

The calculated values of δri and δGi for different constituent elements of the Fe40Mn28Ni32-xCrx

T

(x=4, 12, 18) alloys calculated using equations (3) and (4) are given in Table 4. Apparently,

IP

increase of the concentration of the i element will result in decrease of the mismatch parameters

SC R

for the i element as more neighbors of the i atoms will be of the same sort. In contrast, when the concentration of the i element decreases, the mismatch parameters for the i element will increase as more of the i atom neighbors will be of different sort. Partial replacement of Ni with Cr in the

NU

Fe40Mn28Ni32-xCrx alloys demonstrates such tendencies. The highest (absolute) atomic size

MA

mismatches, δri, in the Fe40Mn28Ni28Cr4 alloy are around Cr and Ni atoms - 0.0188 and -0.0156, respectively. Increase of Cr content and decrease of Ni content result in decrease of δrCr and

D

increase of δrNi to 0.0140 and -0.0204, respectively, in the Fe40Mn28Ni14Cr18 alloy. Similarly, the

TE

highest atomic modulus mismatches in the Fe40Mn28Ni28Cr4 alloy are around Cr and Ni atoms – 0.3743 and -0.0699, respectively. It should be noted that the absolute value of δGCr is more than

CE P

5 times higher than value of δGNi. In alloys with higher Cr content this difference decreases. For example, in the Fe40Mn28Ni14Cr18 alloy δGCr equals to 0.3124 and δGNi – to -0.1319.

AC

The dependence of mismatch parameter, fi, for constitutive elements of the Fe40Mn28Ni32-xCrx alloys on the Cr content (in range of 0-24%) is shown in Fig. 4a. The fi values were calculated using equation (2), and the α value of 2. Calculations were performed with assumption that all the Fe40Mn28Ni32-xCrx alloys are single solid solution phase with composition corresponding to nominal composition of the alloy. Obviously, the mismatch parameter for Cr is significantly higher than the mismatch parameters for other constitutive elements. However, increase of Cr content results in decrease of mismatch parameter for Cr and increase of mismatch parameter for other elements. For example, the fCr decreases from 0.394 to 0.287 when Cr content increases from 0% to 24%, whereas the fNi increases from 0.059 to 0.165. The mismatch parameters for Fe and Mn are lower than that for Ni, and reach maximum values of 0.078 and 0.090 at Cr content of 24%. 9

ACCEPTED MANUSCRIPT The dependence of ∆σSSi on Cr content in the Fe40Mn28Ni32-xCrx alloys is shown in Fig. 4b. The ∆σSSi were calculated using equation (1), Z value of 0.04 and G value of 80 GPa for the CoCrFeNiMn alloy [17]. Obviously, the ∆σSSCr shows strong dependence on Cr content,

T

increasing from 101 MPa to 217 MPa when Cr content increases from 4% to 18%. The ∆σSSCr is

IP

significantly higher than solid solution strengthening by other elements: the ∆σSSNi is 44.4-61.4

SC R

MPa at Cr concentrations of 4-18%, while the ∆σSSFe and ∆σSSMn are respectively 5.2-32.3 MPa and 7.8-35.2 MPa. It should be noted that, for example, at Cr concentration of 18%, the ∆σSSNi is

NU

only ≈28% of ∆σSSCr, whereas the ∆σSSFe and ∆σSSMn are respectively ≈15% and ≈16%. This analysis suggests that SSS by single element (Cr) with atomic fraction of 18% is about 1.5 times

MA

higher than strengthening by other elements. Thus the conclusion can be drawn that in complexly concentrated multicomponent alloys only certain elements can produce strong SSS effect, while

D

other constitutive elements only moderately strengthen solid solution.

TE

The SSS effect in multicomponent alloys can be calculated using Gypen and Deruyttere approach [24], already applied to HEAs [14]. According to this approach, solid solution

CE P

hardening of the alloy, ∆σSS, is calculated using the equation below by summarizing ∆σSSi of every component of the alloy: 3/2 2/3

]

AC

∆σSS =

(5)

The calculated values of the solid solution hardening, ∆σSS, of the Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys is plotted against the experimental yield strength values of the corresponding alloys in Fig. 5. In addition, data on several quaternary alloys of the Co-Cr-Fe-Ni-Mn system reported in literature [17, 18] with somewhat similar grain sizes of 15 µm [18] and 24-48 µm [17]. Good fit between the calculated values of ∆σSS and experimentally determined yield strength of the alloys is found. The correlation between predicted SSS and experimental yield strength illustrates two following facts: (i) the methodology developed for predicting SSS in conventional alloys, i.e. Labush approach and Gypen and Deruyttere approach, is adequate for multicomponent alloys or HEAs if contributions from each constitutive element 10

ACCEPTED MANUSCRIPT of the alloys are estimated and summarized; (ii) the differences in the yield strength of the solid solution Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys can be attributed to SSS. If the SSS is the main factor, governing mechanical properties of the solid solution Fe40Mn28Ni32alloys as it is suggested from Fig. 5, there is no surprise that the alloys with higher Cr

T

xCrx

IP

concentration demonstrate higher strength. Cr apparently produces much stronger hardening than

SC R

other constitutive elements of the alloys (Fig 4b) and increase of Cr concentration results in pronounced increase of yield strength. The experimentally observed decrease of ductility of the

NU

Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys (Table 3) due to higher SSS is also anticipated [25]. However, the σUTS of the solid solution Fe40Mn28Ni32-xCrx alloys shows non-monotonic

MA

dependence on Cr concentration, while the increased SSS is expected to result in increase of σUTS. Probably, the resulting values of the σUTS originate from two opposite tendencies: increase

D

of yield strength due to increase of Cr concentration and decrease of work hardening capacity,

TE

mirrored in lower values of uniform elongation. The strain hardening capacity could be

CE P

measured as the difference between σUTS and σ0.2 values [18]. The σUTS-σ0.2 values are 355 MPa, 300 MPa and 295 MPa for the Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys, respectively, i.e. they decrease with increase of Cr concentration. However thorough

AC

examination of strain hardening behavior of the Fe40Mn28Ni32-xCrx alloys is subject of further investigations.

The strong SSS caused by Cr in the Fe40Mn28Ni32-xCrx alloys suggests that Cr concentration has to be maximized to enhance strength of the alloys. But the Fe40Mn28Ni8Cr24 alloy has dual-phase structure, composed of intermetallic sigma phase and fcc solid solution (Fig. 1). Moreover, the results of chemical analysis (Table 1) suggest that Cr-rich matrix is sigma phase, and fcc phase particles are distributed in sigma phase. HEAs with matrix sigma phase have already been reported [23]. Sigma phase is known to be hard but extremely brittle [26]. Thus the drastic increase of hardness (Table 2) and loss of ductility (mirrored in fracture at initial stages of cold rolling) of the Fe40Mn28Ni8Cr24 alloy in comparison with the solid solution Fe40Mn28Ni28Cr4, 11

ACCEPTED MANUSCRIPT Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys is anticipated. Sigma phase formation in the high Cr containing Fe40Mn28Ni32-xCrx alloys is likely to be caused by high atomic size and modulus mismatches generated by Cr atoms in the fcc lattice (Table 4). High mismatches can result not

T

only in SSS, but also in destabilization of solid solution, like it was already demonstrated in the

IP

CoCrFeNiMnxVy alloys [23, 27].

SC R

Formation of sigma phase and related embrittlement of the Fe40Mn28Ni8Cr24 alloy demonstrates that there is a limit of Cr solubility in the fcc solid solution of the Co-Cr-Fe-Ni-Mn alloys. This

NU

result is in a good agreement with the previously obtained data. For example, while the equiatomic CoCrFeNiMn alloy is solid solution [7], sigma phase was observed in the

MA

Ni14Fe20Cr26Co20Mn20 alloy [9]. Similarly, the FeNiMnCr18 alloy is fcc solid solution [18], while the equiatomic FeNiMnCr alloy has multi-phase structure [28] and presumably contains sigma

D

phase. Using data of current investigation and other sources [7, 18, 27, 28], it can be suggested

TE

that 18-20% of Cr can be dissolved in the fcc lattice of the Co-Cr-Fe-Ni-Mn system

CE P

multicomponent alloys or HEAs, and when Cr concentration increases to 24-26% formation of sigma phase can be expected. But the equiatomic NiCoCrMn and FeNiCoCr alloys are fcc solid solution [28] despite the fact that Cr concentration in these alloys is 25%. From stainless steels

AC

experience it is known that other alloying elements including Co, Ni and Mn have complex effect on sigma phase formation [29]. Therefore additional experimental studies are required to establish mutual effect of the constitutive elements of the Co-Cr-Fe-Ni-Mn HEAs on sigma phase formation. In summary, the presented results clearly demonstrate that mechanical properties of the promising Co-Cr-Fe-Ni-Mn system HEAs can be tailored by varying concentration of constitutive elements to maximize SSS effect. Together with TWIP effect observed at room temperature in particular compositions of the Co-Cr-Fe-Ni-Mn-based alloys [13, 30], and possibility of easy microstructure control by cold or hot working and annealing treatment [9, 28, 31-35], this makes possible development of the single solid solution phase multicomponent 12

ACCEPTED MANUSCRIPT alloys based on Co-Cr-Fe-Ni-Mn system with desired combination of mechanical properties by optimizing their chemical composition and microstructure. Specific attention has to be paid to potential intermetallic phase formation, which may have negative effect on properties of the

IP

SC R

purpose promoting additional strengthening [5, 36-38].

T

alloys limiting their ductility. However, intermetallic or ordered phases can be introduced on

5. Conclusions

NU

In current study a series of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) non-equiatomic multicomponent alloys were produced and their structures and mechanical properties were

MA

examined. Following conclusions were made:

1) The Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys were ductile after

D

homogenization annealing and were successfully cold rolled and annealed to produce

TE

recrystallized single fcc solid solution phase structure with average grain size of ~10 µm.

CE P

2) The Fe40Mn28Ni8Cr24 alloy was extremely brittle after homogenization annealing. Brittleness of the alloy was associated with formation of intermetallic sigma phase matrix, while the fcc solid solution particles were distributed in the matrix.

AC

3) The tensile properties of the solid solution Fe40Mn28Ni28Cr4, Fe40Mn28Ni20Cr12 and Fe40Mn28Ni14Cr18 alloys were found to be largely dependent on Cr and Ni concentrations. The yield strength and ultimate tensile strength increased from 210 MPa and 310 MPa, respectively, of the Fe40Mn28Ni28Cr4 alloy, to 310 MPa and 605 MPa of the Fe40Mn28Ni14Cr18 alloy. In turn, uniform elongation and elongation to fracture decreased from 51% and 71%, respectively, to 37% and 54%. 4) The solid solution strengthening caused by different elements of the Fe40Mn28Ni32-xCrx alloys was calculated using Labush approach. It was demonstrated that Cr produces strongest solid solution strengthening among the constitutive elements of the alloys. The contributions from each element of the alloys were summarized in accordance with 13

ACCEPTED MANUSCRIPT Gypen and Deruyttere approach to estimate solid solution strengthening of the Fe40Mn28Ni32-xCrx alloys. Good correlation between experimental yield strength values

T

and predicted solid solution strengthening was observed.

IP

Acknowledgements

SC R

The authors acknowledge the financial support from the Russian Science Foundation Grant No. 14-19-01104. The authors are grateful to Mr. R. Chernichenko from Belgorod State University

AC

CE P

TE

D

MA

NU

for his assistance in experimental procedures.

14

ACCEPTED MANUSCRIPT References [1] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, et al., Prog. Mater. Sci. 61 (2014) 1-93. (doi:10.1016/j.pmatsci.2013.10.001)

IP

№8 (2004) 299-303. (doi:10.1002/adem.200300567)

T

[2] J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, et al., Adv. Eng. Mater. 6

SC R

[3] S. Singh, N. Wanderka, B.S. Murty, U. Glatzel, J. Banhart, Acta Mater. 59 (2011) 182-190. (doi:10.1016/j.actamat.2010.09.023)

NU

[4] D.G. Shaysultanov, N.D. Stepanov, A.V. Kuznetsov, G.A. Salishchev, O.N. Senkov, JOM 35 (2013)1815-1828. (doi:10.1007/s11837-013-0754-5)

MA

[5] O. N. Senkov, J. D. Miller, D. B. Miracle, C. Woodward, Nat. Commun. 6 (2015) 6529. (doi:10.1038/ncomms7529)

D

[6] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Mater. Sci. Eng. A 375-377 (2004) 213-

TE

8. (doi:10.1016/j.msea.2003.10.257)

CE P

[7] F. Otto, A. Dlouhy, C. Somsen, H. Bei, G. Eggeler, E.P. George, Acta Mater. 61 (2013) 5743-5755. (doi:10.1016/j.actamat.2013.06.018) [8] B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, Science

AC

345 (2014) 1153-8. (doi:10.1126/science.1254581) [9] A. J. Zaddach, A. J. Scattergood, A. J. Koch, Mater. Sci. Eng. A, 636 (2015) 373-8. (doi:10.1016/j.msea.2015.03.109) [10] N. Stepanov, M. Tikhonovsky, N. Yurchenko, D. Zyabkin, M. Klimova, S. Zherebtsov, et al., Intermetallics 59 (2015) 8-17. (doi:10.1016/j.intermet.2014.12.004) [11] M. J. Yao, K. G. Pradeep, C. C. Tasan, D. Raabe, Scripta Mater. 72 (2014) 5-8. (doi:10.1016/j.scriptamat.2013.09.030) [12] C. C. Tasan, Y. Deng, K. G. Pradeep, M. J. Yao, H. Springer, D. Raabe, JOM 66(10) (2014) 1993-2001. (doi:10.1007/s11837-014-1133-6)

15

ACCEPTED MANUSCRIPT [13] Y. Deng, C. C. Tasan, C. C. Pradeep, H. Springer, A. Kostka, D. Raabe, Acta Mater. 94 (2015) 124-133. (doi:10.1016/j.actamat.2015.04.014) [14] I. Toda-Caraballo, P. E. Rivera-Díaz-del-Castillo, Acta Mater. 85 (2015) 14-23.

T

(doi:10.1016/j.actamat.2014.11.014)

IP

[15] R. S. Mishra, N. Kumar, M. Komarasamy, Mater. Sci. Tech. 31(10) (2015) 1259-1263.

SC R

(doi:10.1179/1743284715Y.0000000050)

[16] Y. D. Wu, Y. H. Cai, X. H. Chen, T. Wang, J. J. Si, L. Wang, et al., Mater. Design 83

NU

(2015) 651-660. (doi:10.1016/j.matdes.2015.06.072)

[17] Z. Wu, H. Bei, G.M. Pharr, E.P. George, Acta Mater. 81 (2014) 428-441.

MA

(doi:10.1016/j.actamat.2014.08.026)

[18] Z. Wu, H. Bei, Mater. Sci. Eng. A 640 (2015) 217-224. (doi:10.1016/j.msea.2015.05.097)

D

[19] W.H. Liu, Y. Wu, J.Y. He, T.G. Nieh, Z.P. Lu, Scripta Mater. 68(7) (2013) 526-9.

TE

(doi:10.1016/j.scriptamat.2012.12.002)

CE P

[20] N. Kumar, M. Komarasamy, P. Nelaturu, Z. Tang, P. K. Liaw, R. S. Mishra, JOM 67(5) (2015) 1007-1013. (doi: 10.1007/s11837-015-1385-9) [21] R. Labusch, Phys. Status Solidi 41(2) (1970) 659-669. (doi: 10.1002/pssb.19700410221)

AC

[22] O. N. Senkov, J. M. Scott, S. V. Senkova, D. B. Miracle, C. F. Woodward, J. Alloys Compd. 509(20) (2011) 6043-8. (doi: doi:10.1016/j.jallcom.2011.02.171) [23] G.A. Salishchev, M.A. Tikhonovsky, D.G. Shaysultanov, N.D. Stepanov, A.V. Kuznetsov, I.V. Kolodiy, et al., J. Alloys Compd. 591 (2014) 11-21. (doi:10.1016/j.jallcom.2013.12.210) [24] L.A. Gypen, A. Deryuttere, J. Mater. Sci., 12 (1977) 1028-1033. (doi:10.1007/BF00540987) [25] W.D. Callister, Fundamentals of Materials Science and Engineering. 4th ed. John Wiley and Sons, Inc. 2001. [26]

E.O.

Hall,

S.H.

Algie,

Int.

Mater.

(doi:10.1179/mtlr.1966.11.1.61)

16

Review

11(1)

(1966)

61-88.

ACCEPTED MANUSCRIPT [27] N.D. Stepanov, D.G. Shaysultanov, G.A. Salishchev, M.A. Tikhonovsky, E.E. Oleynik, A.S. Tortika, et al., J. Alloys Compd. 628 (2015) 170-185. (doi:10.1016/j.jallcom.2014.12.157) [28] Z. Wu, H. Bei, F. Otto, G. M. Pharr, G. M. George, Intermetallics 46 (2014) 131-140.

T

(doi:10.1016/j.intermet.2013.10.024)

IP

[29] F.C. Hull, Weld. J. 52 (1973) 104-113.

SC R

[30] Z. Wu, C.M. Parich, H. Bei, J. Alloys Compd. 647 (2015) 815-822. (doi:10.1016/j.intermet.2013.10.024)

NU

[31] P.P. Bhattacharjee, G.D. Sathiaraj, M. Zaid, J.R. Gatti, C. Lee, C.W. Tsai, J.W. Yeh. J. Alloys Compd. 587 (2014) 544–552. (doi: 10.1016/j.jallcom.2013.10.237)

10.1016/j.jallcom.2015.02.184)

MA

[32] G. D. Sathiaraj, P. P. Bhattacharjee, J. Alloys Compd. 637 (2015) 267-276. (doi:

D

[33] G. D. Sathiaraj, P. P. Bhattacharjee, J. Alloys Compd. 647 (2015) 82-96. (doi:

TE

10.1016/j.jallcom.2015.06.009)

CE P

[34] F.Otto, N.L. Hanold, E.P. George. Intermetallics 54 (2014) 39-48. (doi:10.1016/j.intermet.2014.05.014) [35] N. D. Stepanov, D. G. Shaysultanov, N. Y. Yurchenko, S. V. Zherebtsov, A. N. Ladygin, G.

AC

A. Salishchev, et al., Mater. Sci. Eng. A 636 (2015) 188-195. (doi:10.1016/j.msea.2015.03.097) [36] D.B. Miracle, J.D. Miller, O.N. Senkov, C. Woodwart, M.D. Uchic, J. Tiley, Entropy 16(1) (2014) 494-525. (doi:10.3390/e16010494) [37] D.B. Miracle, Mater. Sci. Tech. 31(10) (2015) 1142-7. (10.1179/1743284714Y.0000000749) [38] Y. Lu, Y. Dong, S. Guo, L. Jiang, H. Kang, T. Wang, et al., Sci. Rep. 4 (2014) 6200. (doi:10.1038/srep06200)

17

ACCEPTED MANUSCRIPT Figure captions.

Fig. 1. The XRD patterns of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) alloys. The XRD patterns of

T

the Fe40Mn28Ni32-xCrx (x=4, 12, 18) were taken in cold-rolled and annealed state. The XRD

SC R

IP

pattern of the Fe40Mn28Ni8Cr24 alloy was taken in homogenized state.

Fig. 2. The SEM-BSE images of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) alloys: a – x=4; b –

NU

x=12; c – x=18; d – x=24. The images of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) were taken in coldrolled and annealed state. The image of the Fe40Mn28Ni8Cr24 alloy was taken in homogenized

MA

state. Chemical composition of numbered structural constituents is given in Table 1.

D

Fig. 3. Tensile stress-strain curves of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys after cold rolling

CE P

TE

and annealing at 850°C for 30 minutes.

Fig. 4. The dependencies of (a) mismatch parameter, fi, and (b) solid solution strengthening, ∆σSSi, for different constitutive elements of the hypothetical solid solution Fe40Mn28Ni32-xCrx

AC

alloys on Cr concentration.

Fig. 5. The dependence of yield strength, YS, on solid solution strengthening, ∆σSS, of the studied Fe40Mn28Ni32-xCrx alloys and some quaternary equiatomic alloys reported in literature [17, 18].

18

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

Fig. 1. The XRD patterns of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) alloys. The XRD patterns of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) were taken in cold-rolled and annealed state. The XRD pattern of the Fe40Mn28Ni8Cr24 alloy was taken in homogenized state.

19

SC R

IP

T

ACCEPTED MANUSCRIPT

b

TE

D

MA

NU

a

d

AC

CE P

c

Fig. 2. The SEM-BSE images of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) alloys: a – x=4; b – x=12; c – x=18; d – x=24. The images of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) were taken in coldrolled and annealed state. The image of the Fe40Mn28Ni8Cr24 alloy was taken in homogenized state. Chemical composition of numbered structural constituents is given in Table 1.

20

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

Fig. 3. Tensile stress-strain curves of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys after cold rolling and annealing at 850°C for 30 minutes.

21

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

Fig. 4. The dependencies of (a) mismatch parameter, fi, and (b) solid solution strengthening,

AC

CE P

TE

alloys on Cr concentration.

D

∆σSSi, for different constitutive elements of the hypothetical solid solution Fe40Mn28Ni32-xCrx

22

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

Fig. 5. The dependence of yield strength, YS, on solid solution strengthening, ∆σSS, of the

AC

studied Fe40Mn28Ni32-xCrx alloys and some quaternary equiatomic alloys reported in literature [17, 18].

23

ACCEPTED MANUSCRIPT Table 1. Chemical composition of different structural constituents of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) alloys as determined by SEM-based EDS-analysis. Typical regions of analysis are

IP

Cr

SC R

Ni

28.2±0.4 28.0±0.8

4.4±0.1 4.6±0.2

19.9±0.5 12.5±0.3 19.9±0.6 12.7±0.6 16.1±0.3 17.0±0.4 16.2±1.0 16.6±0.9 5.3±0.1 32.0±0.8 11.6±0.3 17.8±0.3 8.4±0.3 25.1±1.1

AC

CE P

TE

D

MA

NU

Element, at.% Fe Mn Constituent Fe40Mn28Ni28Cr4 № Designation Grains 40.8±0.5 26.6±0.3 Alloy composition 41.2±1.4 26.2±0.7 Fe40Mn28Ni20Cr12 Grains 40.6±0.6 27.0±0.4 Alloy composition 40.3±1.7 27.1±0.9 Fe40Mn28Ni14Cr18 Grains 39.8±0.4 27.1±0.5 Alloy composition 40.0±1.2 27.2±0.8 Fe40Mn28Ni8Cr24 1 Sigma phase 38.0±0.5 24.7±0.6 2 FCC particles 42.3±0.5 28.3±0.5 Alloy composition 40.4±1.5 26.1±0.9

T

shown on Fig. 2. For comparison actual chemical compositions of the alloys are also given.

24

ACCEPTED MANUSCRIPT Table 2. Microhardness of the Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24) alloys after homogenization annealing.

AC

CE P

TE

D

MA

NU

SC R

IP

T

Alloy Microhardness, HV Fe40Mn28Ni28Cr4 111±6 Fe40Mn28Ni20Cr12 115±4 Fe40Mn28Ni14Cr18 126±6 Fe40Mn28Ni8Cr24 410±19

25

ACCEPTED MANUSCRIPT

Table 3. Tensile properties of the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys after cold rolling and

AC

CE P

TE

D

MA

NU

SC R

IP

Alloy σ0.2, MPa σUTS, MPa δf, % δu, % 1 Fe40Mn28Ni28Cr4 210 565 71 51 2 Fe40Mn28Ni20Cr12 245 545 66 49 3 Fe40Mn28Ni14Cr18 310 605 54 37

T

annealing at 850°C for 30 minutes.

26

ACCEPTED MANUSCRIPT

Table 4. Calculated lattice, δri, and shear modulus, δGi, distortions near an individual constituent

Fe40Mn28Ni20Cr12

Ni -0.0156 -0.0699 -0.0183 -0.1053 -0.0204 -0.1319

Mn 0.0103 -0.0010 0.0076 -0.0366 0.0055 -0.0633

IP

Fe 0.0018 0.0122 -0.0010 -0.0234 -0.0030 -0.0501

AC

CE P

TE

D

MA

NU

Fe40Mn28Ni14Cr18

δri δGi δri δGi δri δGi

Cr 0.0188 0.3743 0.0161 0.3389 0.0140 0.3124

SC R

Alloy Fe40Mn28Ni28Cr4

27

T

element i in the Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys.

ACCEPTED MANUSCRIPT

AC

CE P

TE

D

MA

NU

SC R

IP

T

Graphical abstract

28

ACCEPTED MANUSCRIPT Highlights

CE P

TE

D

MA

NU

SC R

IP

T

A series of Fe40Mn28Ni32-xCrx (x=4, 12, 18, 24 (at.%)) alloys are examined. The Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys are ductile fcc solid solutions. Yield strength of Fe40Mn28Ni32-xCrx (x=4, 12, 18) alloys increases with Cr content. Increase of yield strength is attributed to solid solution strengthening. The Fe40Mn28Ni8Cr24 alloy has intermetallic sigma phase matrix and is brittle.

AC

• • • • •

29