The Temperature Dependences of Mechanical Properties, Deformation Hardening, and Fracture of FeMnNiCoCr Heterophase Alloy

It is established that the temperature dependence of the mechanical properties and deformation behavior of a heterophase multicomponent Cantor alloy (FeMnNiCoCr) and the mechanisms of its fracture under uniaxial static tension in the temperature range 77–300 K are determined by the mechanism of formation and distribution of dispersed phases in it. The heterogeneous formation of chromium-enriched σ‑phases and phases with an fcc crystal lattice,mainly at grain boundaries in the course of annealing of homogenized samples (when particles are inhomogeneously distributed over the structure) and at deformation defects in the course of annealing of preliminarily strained samples (when particles are distributed uniformly over the structure), takes place in the Cantor alloy as a result of annealing. It is found that the grain-boundary phases slightly affect the temperature dependence of yield stress σ0.2, the deformation behavior of the heterophase alloy and its mechanism, but contribute to a decrease in the plasticity and to the formation of brittle secondary cracks on fracture surfaces under low-temperature deformation. The complex effect of the dispersion and the grain boundary hardenings in samples with a uniform distribution of particles that are formed in the course of aging of pre-strained samples leads to a substantial increase in the strength properties of the Cantor alloy in the entire temperature range while maintaining high plasticity and a strong temperature dependence of σ0.2.


INTRODUCTION
A large-scale study of high-entropy alloys (HEAs) began in 2004 after the studies of Cantor and Yeh [1,2]. The idea of creating an HEA was based on the fact that the high entropy of mixing in alloys comprised of five or more chemical elements can provide the formation of a disordered single-phase structure with a simple crystal lattice. Over the past almost 20 years, many theoretical and experimental studies devoted to HEAs have been published [1][2][3][4][5][6][7][8]. It quickly became clear that high configurational entropy is not a sufficient condition for structure stabilization. Otto et al. studied the quinary Cantor's alloy CoCrFeMnNi and replaced the main elements in it with transition metals that are similar in their properties (such as electronegativity, atomic size, and lattice type at room temperature) [3]. Despite having the same values of the configurational entropy, the modified alloys had a heterophase structure; only Cantor's alloy could be considered a true HEA [3]. Rogachev correctly noted in his review [4] that the criterion for high entropy of a system depends not only on the number of components, but also on the magni-tude of the enthalpy change upon ordering and with an increase in the temperature, i.e., it is unreasonable to exclude the possibility of ordering and formation of new phases in the HEA. Gorban' et al. [8] described the relationship between phase formation and the average electron density C sd (el./at., i.e., the number of electrons per atom) in equiatomic HEAs. In accordance with the criteria they developed, the value of C sd = 8 el./at. in the Cantor alloy provides the formation of an fcc structure [8]. This C sd value is above the upper limit corresponding to the formation of 100% intermetallic σ-phases; however, the alloy contains pairs of elements that form such phases (Cr-Mn, Cr-Fe, and Cr-Co) and a small amount of them can be formed according to the electronic structure of the alloy.
At low temperatures, the Cantor alloy has an austenitic structure that is stable to supercooling and deformation and is characterized by enhanced mechanical properties [5][6][7][9][10][11]. However, its structure is unstable under high-temperature deformation [12], long-term annealing [13][14][15], and short-term postdeformation annealing [16,17]. In a homogenized STRENGTH AND PLASTICITY alloy, heterogeneous nucleation and growth of secondary phases occur in the temperature range of 723-973 K (500 h) [13]. The L1 0 -NiMn and B2-FeCo phases, and a chromium-enriched bcc phase are formed at a temperature of 773 K, and a chromiumenriched σ-phase is formed at T = 973 K. The latter has the same crystal structure as the binary Fe-Cr σ phase in stainless steels [8,13,18]. In addition to the grain-boundary σ-phase, an fcc phase with a lattice parameter of about 10.6 Å was observed and identified as M 23 C 6 carbide after long-term aging of the homogenized Cantor alloy (up to 1000 h) at T = 973 K in [14,15]. After plastic deformation, the rate of nucleation and growth of secondary phases in the Cantor alloy is faster. The authors of [16,17] observed σ-phase particles in the alloy structure after deformation (rolling [16] and high-pressure twisting [17]) and 1-h annealing treatments in the temperature range of 873-1073 K, and a bcc phase enriched in chromium is formed at temperatures of 773-973 K [16]. The plastic strain contributed to the homogeneous growth of particles in the body of the grains and provided the formation of fine and ultrafine grains.
Thus, there is already an overal picture of phase transformations in the Cantor alloy; the temperature ranges of phase formation and their structure have already been determined. In the studies described above, the fraction of identified secondary phases was a few percent, i.e., the changes that occur in the course of annealing are not significant from the point of view of the macroscopic structure. At the same time, it is not clear how the formed phases affect the deformation behavior and mechanical properties of the Cantor alloy at low temperatures, at which it demonstrates the best mechanical properties owing to being in a singlephase state. The aim of this study was to establish the influence of the mechanism of formation of dispersed phases (their distribution) in the course of annealing at T = 973 K on the structure, mechanical properties, deformation behavior, and fracture mechanisms of the Cantor alloy in the temperature range of 77-300 K.

MATERIALS AND METHODS
The equiatomic Cantor alloy (19.9 at % Fe, 19.9at % Mn, 20.0 at % Cr, 20.0 at % Ni, and 20.2 at % Co) obtained by induction melting in vacuum was chosen as a material for the study. To homogenize the composition, cast billets were subjected to hot forging at T = 1503 K and then to annealing for 2 h at T = 1473 K with subsequent quenching into water at room temperature. A part of the billets was annealed at T = 973 K for 1 h, and the other part was rolled at 300 K to a reduction of 75% and annealed with the same regime. Heat treatments were carried out in an SUOL 0.16/11 electric furnace in the atmosphere of an inert gas (helium). The annealing temperature was chosen based on the published data [16] to form the largest fraction of the σ phase. Samples in the shape of double blades with working part dimensions of 1.3 × 2.5 × 18 mm 3 were cut from billets. After mechanical grinding, they were electrolytically polished in a supersaturated solution of CrO 3 in phosphoric acid. Uniaxial static tension of the samples was conducted with an initial strain rate of 5 × 10 -4 s -1 in the temperature range from 77 to 300 K (Instron 1185).
An X-ray diffraction study of the samples was performed on a Dron-7 diffractometer with a CoKα radiation source. For metallographic studies, an Altami MET 1C microscope was used. Foils for electron microscopic studies were thinned by jet polishing (110 Twin Jet Electropolisher, Fischione). The microstructure was studied using a JEOL JEM-2100 transmission electron microscope (TEM). The micromechanisms of alloy fracture were revealed using scanning electron microscopy (SEM) on an LEO EVO 50 microscope (Zeiss).

RESULTS AND DISCUSSION
After homogenization, Cantor alloy samples had a coarse-grained austenite structure with a grain size of 200 ± 110 μm (Fig. 1a). The X-ray diffraction patterns for the homogenized alloy contain only the reflections of the austenite phase with the lattice parameter a = 3.601 ± 0.004 Å. Annealing of homogenized and rolled samples at T = 973 K does not change the appearance of the X-ray diffraction patterns and no additional reflections are observed. In this case, the lattice parameter of austenite slightly decreases to a = 3.594 ± 0.003 Å. Since no secondary phases were revealed by the X-ray diffraction method, their volume fraction after annealing does not exceed 5%, which correlates with the published data [16,17].
The annealing treatment of the homogenized alloy does not affect the size of the austenite grain (Fig. 1b). The increased etchability of the grain boundary regions after annealing indicates that they have a composition different from that of the grain body. Transmission electron microscopy of the samples revealed the formation of thin interlayers of the chromiumenriched σ-phase along the grain boundaries (Fig. 1c). The most commonly observed plates were 76 ± 22 nm in thickness, with wet grain boundaries and particles located directly at the boundaries (Fig. 1c). Part of the grain boundary phase had an fcc crystal lattice (with lattice parameter a = 10-11 Å) that was completely coherent with the austenitic matrix and was enriched in chromium relative to the base composition of the alloy (Figs. 1c and 1d). As was previously shown in [14,15], its lattice parameters are close to those of carbide of the M 23 C 6 type; however, the energy dispersive analysis of particles does not confirm an increased carbon concentration in such particles. It is difficult to completely exclude nonmetallic elements from the alloy composition; after melting, it contains less than 0.011 wt % carbon and 0.006 wt % nitrogen. These concentrations are not sufficient for the formation of a noticeable amount of carbides or carbonitrides. The issue of the possibility of formation of the σ phase in HEAs through an intermediate ordered fcc phase or the formation of chromium carbides or carbonitrides will be addressed in a separate publication. It is important to comprehend that a negligible carbon content, which is inevitably present in the industrial production of the alloy, can lead to the formation of carbides when heated.
In the course of annealing of a preliminarily deformed alloy, the growth of particles of the σ-phase (the phase with the fcc structure also grows) in the body of austenite grains and the formation and growth of recrystallization nuclei occur simultaneously. Typical TEM images of the alloy microstructure prior to and after annealing are shown in Fig. 2. The fine grained structure formed in the course of annealing has an average grain size of 4.5 ± 3.0 μm and contains spherical particles of the σ-phase (the average particle size is 76 ± 22 nm, and the volume fraction is 1.1%). The particle sizes are close to the thickness of the plates of the grain-boundary phase formed in the samples aged without preliminary deformation, i.e., the plastic deformation has no effect on the type of phases formed in the course of annealing, and their growth is determined by the coefficient of bulk diffusion of elements to the nucleus [19]. Since, the formation of recrystallization nuclei occurs in the alloy structure along with the phase transformation upon annealing, the grain growth in the course of annealing is restrained by the Zener force [20].
In both cases described above, heterogeneous nucleation and growth of particles of secondary phases occur. However, the phases are formed preferentially at the crystal structure defects and sub-boundaries (in the body of grains) in contrast to the annealing of rolled samples of a homogenized alloy, in the course of which the formation of secondary phase occurs predominantly near the grain boundaries. This is due to the fact that the plastic deformation prior to annealing creates a large number of sites for the formation of nuclei of secondary phases and new grains, such as dislocations, stacking defects, and sub-boundaries [19]. Thus, the operation of different mechanisms for the formation of dispersed phases leads to the formation of the two types of Cantor alloy samples: coarsegrained samples with nanosized interlayers of secondary phases along the grain boundaries and fine-grained samples with dispersed phases uniformly distributed over the structure. Tensile diagrams obtained for such samples in the temperature range of 77-300 K are shown in Figs. 3a and 3b (the dotted lines in the fig-   The tensile diagrams and mechanical properties for the annealed homogenized alloy, in which the mechanism of phase formation is associated with heterogeneous nucleation at grain boundaries and with nonuniform distributions of dispersed phases over the structure and particles along grain boundaries, are close to those for the homogenized alloy that does not contain secondary phases (Figs. 3a and 3c). The stepwise behavior of flow curves, the deforming stresses, and the strain hardening in them are the same. Noticeable differences are observed only in the values of elongation to failure (δ) (Fig. 3d). The single-phase Cantor alloy is characterized by an almost linear increase in the elongation to failure with a decrease in the test temperature, and two characteristic temperature ranges with different slopes in the δ(T) dependences can be distinguished for the annealed samples. At temperatures of T > 225 K, the Δδ/ΔT slope is the same as in the single-phase Cantor alloy. At T < 225 K, the slope of the δ(T) dependence for the annealed samples changes sign, i.e., the elongation to failure decreases with a decrease in the temperature (Fig. 3d). An analysis of the data given in Fig. 3d indicates that the formation of interlayers of the grain-boundary phase negatively affects the plasticity of coarse-grained samples in the temperature range of T < 225 K, but simultaneously leads to an increase in the plasticity at T > 225 K.
The strong temperature dependence of σ 0.2 is typical of the Cantor alloy. It exceeds the σ 0.2 (T) dependences for pure metals and binary substitutional solid solutions [11,[21][22][23]. The temperature dependences of the conditional yield stress (σ 0.2 ) for the singlephase alloy and the alloy with particles along the boundaries coincide (Fig. 3c). Since the critical temperature of the transition from a thermally activated flow to athermal one in HEAs (473-673 K) is higher than in binary substitutional solid solutions [21,23],

Phases in grain bodies
V, MPa the temperature interval considered in this study belongs to the region of thermally activated deformation processes. Therefore, the σ 0.2 (T) dependences do not show a stress plateau characteristic of the region of athermal deformation.
In the early stages of plastic flow, a homogenized alloy is characterized by the development of a planar dislocation structure, which rather quickly transforms into a network structure and then into a uniform structure with a high density of dislocations. Moreover, mechanical twinning develops after substantial shear deformation and contributes to deformation hardening and an increase in the plasticity of the alloy (especially at low temperatures, at which the twinning activity is high and the structure is more planar than at room temperature) [11,21]. In the annealed samples, the phases formed along the boundaries have a small effect on the composition of the material inside the grains (except for the near-boundary regions) and do not change the grain size. The dislocation structures in the homogenized and annealed alloys are the same and represent flat dislocation clusters (Figs. 4a and 4b). Since the deformation mechanism (dislocation glide), the type of dislocation glide (planar), and the free paths of dislocations in the early stages of plastic flow do not change in the course of annealing, the flow stresses at the yield point are similar in the homogenized and annealed alloys (Fig. 3c).
Despite common hardening mechanisms and deformation behavior, the annealed alloy is characterized by a slight increase in plasticity at T > 225 K. The reason may be atomic ordering caused by the exposure of samples to T = 973 K. The formation of a shortrange order in the nonequiatomic Fe 50 Mn 30 Co 10 Cr 10 alloy was proved in [24] and it was suggested that this effect can be observed to some extent in equiatomic HEAs. A slight decrease in the lattice parameter of the austenitic phase after annealing correlates with this assumption [20]. The degree of ordering in this case is probably insufficient to cause hardening and a visible increase in the planarity of the dislocation structure, which are characteristic of this effect [20,25]; however, it is sufficient for a slight increase in the plasticity of the alloy at T > 225 K (Fig. 3d).
Figures 5a-5c show fracture surfaces of specimens deformed at temperatures of 300 and 77 K. At room temperature, specimens of an annealed homogenized alloy (particles along grain boundaries) crack in a transcrystalline ductile manner with the formation of a pronounced neck at the last stage of plastic flow. The destruction proceeds through a pitting micromechanism (Fig. 5a) similar to that observed for the singlephase Cantor alloy, which undergoes ductile fracture up to cryogenic deformation temperatures [9,23]. That is, grain-boundary phases do not affect the fracture mechanism of the alloy at T > 225 K. At low temperatures, ductile transcrystalline fracture also predominates; however, secondary brittle cracks are visible on the fracture surfaces (Figs. 5b and 5c). They are formed due to the brittle fracture of the material along the grain boundaries, which obviously leads to a decrease in the degree of elongation of the annealed alloy in the region of deformation temperatures T < 225 K.    Figure 3b shows the tensile diagrams for the Cantor alloy samples, in which dispersed particles were formed in the course of aging in the body of grains (heterogeneous nucleation of phases on defects in the crystal structure, uniform distribution of particles over the volume of the material, and fine austenite grains). The change in the mechanism of formation of dispersed phases associated with plastic deformation prior to annealing and, as a result, dispersion hardening and the formation of a fine grained structure has an effect on the deformation behavior and strength properties of the alloy (Figs. 3b and 3c). Moreover, the degree of elongation remains sufficiently high and increases with a decrease in the temperature, just as in the single-phase Cantor alloy (Fig. 3d).
The shape of the flow curves changes and becomes close to a parabolic shape characteristic of dispersion hardened alloys with large incoherent inclusions [19,20,25]. The presence of particles in the alloy structure causes a change in the type of dislocation structure compared to a single-phase alloy, and dispersed phases stimulate wavy glide. As can be seen from the electron microscopic images, large planar pileups in fine austenite grains are not formed in the early stages of deformation, as occurred in a coarse grained single-phase alloy (Figs. 4c-4e). The particles are not deformed or hinder the motion of dislocations and are enveloped by dislocation tangles with an increase in the degree of deformation (Fig. 4d). As a result, the accumulation of dislocations due to the barrier effect from particles and grain boundaries provokes strong deformation hardening and causes a change in the tensile diagrams in comparison with the diagrams of the single-phase coarse grained Cantor alloy and the annealed alloy, in which a different dispersion hardening mechanism occurred, namely, heterogeneous nucleation and growth of particles along the grain boundaries.
The temperature dependence of the conditional yield strength in samples with fine grains and a homogeneous distribution of dispersed particles remains as high as in the other two states. This occurs despite the change in the mechanism of formation of phases and their distribution in the structure, which contribute to the depletion of substitution atoms in the solid solution in austenite grains. The Δσ 0.2 /ΔT slope is similar for all the studied states (Fig. 3c). The persistence of a strong dependence of σ 0.2 on the temperature despite the decrease in the concentration of substitutional elements in the austenite solid solution during annealing is compensated for by the strong temperature dependence of grain boundary hardening, which is confirmed in the literature for the Cantor alloy [9,23]. In particular, the experimentally determined K y coefficient in the Hall-Petch relationship, Δσ HP = K y d -1/2 [19,20,25] equals K y = 494 MPa/μm 1/2 at T = 293 K and K y = 538 MPa/μm 1/2 at T = 77 K [11]. According to calculations with use of the Hall-Petch relationship, annealing-induced grain refinement causes an increase in the yield strength by 200 MPa at room temperature and by 230 MPa at 77 K. These calculated values are lower than the experimentally observed differences between the yield strengths of a fine grained heterophasic alloy and a single-phase coarse grained alloy, which were 250 MPa at 300 K and 290 MPa at 77 K (Fig. 3c). Given that the electron microscope data indicate that the particles of phase grains formed in the body are not coherent with the austenitic matrix, Orowan's relationship [26] Δσ DH = (0.85MGbΦ/2πλ)ln(λ/2b) (where M = 3.06 is the Taylor factor; G = 80(85) GPa is the shear modulus at 300 K (77 K) [27]; b = 2.54 Å is the Burgers vector for the shear dislocation; Φ = 1.18 (1.17) is the coefficient characterizing the type of dislocations interacting with particles at T = 300 K (77 K); λ = 524 nm is the average distance between particles with an average size of 76 nm and a volume fraction of 1.1%) can be used to estimate dispersion hardening in the annealed alloy [26]). The contribution calculated from this relation for the hardening from dispersed particles is less, but of the same order of magnitude as the contribution from grain boundary hardening, i.e., 130 MPa at 300 K and 140 MPa at 77 K. The total contributions of the dispersion and the grain boundary hardening are overstated with respect to the experimentally measured values, but correctly describe the increase in the yield strength and its temperature dependence on the whole. The above calculations show that both hardening mechanisms play an important role in the formation of the mechanical properties of the Cantor alloy subjected to rolling and annealing, and a change in the dispersion hardening mechanism (particle distribution) causes a substantial increase in the yield strength of the Cantor alloy while maintaining a strong σ 0.2 (T) temperature dependence.
The study of the temperature dependence of the fracture mechanism of an alloy with dispersed particles in the body of grains showed that the samples crack in a transcrystalline ductile manner in the studied temperature range with the formation of numerous fracture pits on the fracture surfaces (Figs. 5d-5f). The depth of pits in fine grained samples with particles in the body of grains is less than in the single-phase alloy, which becomes more pronounced with a decrease in the test temperature. This indicates a lower degree of local plastic deformation upon fracture and correlates with the macroscopic mechanical properties of the alloys.
Thus, it can be concluded based on the obtained experimental data and estimates of the main mechanisms of hardening of the Cantor alloy in the course of annealing that a change in the mechanism of formation of secondary phases makes it possible to substantially vary the strength properties, deformation behavior, and fracture micromechanisms of the Cantor alloy. The heterogeneous nucleation and growth of particles at grain boundaries has a small effect on the strength properties and deformation behavior of a multicomponent alloy under uniaxial tension. The heterogeneous formation of phases in the body of grains on defects of deformation origin contributes not only to the uniform distribution of particles of secondary phases throughout the structure, which causes the effect of dispersion hardening, but also prevents the migration of grain boundaries due to recrystallization in the course of annealing of deformed samples. The combined effect of dispersion and grain boundary hardening leads to a substantial increase in the strength properties of the Cantor alloy, affects the deformation hardening, and suppresses the formation of brittle secondary cracks upon fracture of a specimen.

CONCLUSIONS
The influence of the mechanism of formation and distribution of dispersed phases formed after annealing the Cantor alloy (FeMnNiCoCr) at T = 973 K for 1 h on the mechanical properties, deformation behavior, deformation mechanisms, and fracture micromechanisms under uniaxial static tension in the temperature range of 77-300 K has been analyzed.
It is experimentally established that nanosized grain-boundary phases (heterogeneous formation at grain boundaries), i.e., chromium-enriched σ-phases and phases with an fcc crystal lattice with a = 10-11 Å, are formed in homogenized coarse grained alloy samples in the course of annealing. The grain-boundary phases have small effects on the temperature dependence of the yield strength, the multistep behavior of plastic flow, the deformation hardening, and the mechanisms of alloy deformation, but contribute to a decrease in the plasticity and the formation of brittle secondary cracks on the fracture surfaces under lowtemperature deformation (T < 225 K).
It is shown that the plastic deformation preceding the annealing procedure provides the formation of a fine grained austenitic structure with a uniform distribution of particles in the heterophase alloy under study (heterogeneous nucleation and growth of phases on deformation defects). The yield strength of the alloy doubles due to the grain boundary and dispersion hardening mechanisms while maintaining a strong temperature dependence typical of the single-phase Cantor alloy. Although the elongation to fracture decreases after annealing, it remains quite high (50-70%), and the specimens undergo fracture in a transcrystalline ductile manner over the entire temperature range under study. FUNDING This study was supported by the Russian Science Foundation within project no. 20-19-00261. The measurements were carried out using the equipment of Center for Collective Use Nanotech at the Institute of Physics and Mathematics, Siberian Branch, Russian Academy of Sciences.

CONFLICT OF INTEREST
The authors declare that they have no conflicts of interest.

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