2024 Volume 65 Issue 9 Pages 1015-1024
In this study, we focused on the effects of various deformation amounts and subsequent heat treatment on σ-phase precipitation in CoCrFeMnNi high entropy alloy, known as Cantor alloy. Homogenized specimens with an initial FCC single-phase structure were deformed to various shear strains (1.1–25.8) using high-pressure torsion (HPT). This process resulted in a variety of deformation microstructures, with low to medium shear strains leading to the formation of twin-matrix lamellae intersected by shear bands, while high shear strains resulted in nanocrystalline structures. After deformation, the specimens were heat-treated at 700°C for up to 5 h, which led to recrystallization of the FCC matrix accompanied by precipitation of σ phase. The kinetics of recrystallization and precipitation and their interactions during the heat treatment were greatly different among the specimens with different degrees of pre-deformation. Notably, the precipitation of σ phase was accelerated in the specimens subjected to higher shear strains, particularly in those with nanocrystalline structures. The increased rate of precipitation was beneficial for grain refinement since the presence of numerous precipitates within the recrystallized microstructures inhibited their grain growth. Tensile testing of the heat-treated specimens displayed various combinations of strength and ductility, with specimens subjected to higher pre-deformation exhibiting enhanced strength due to finer recrystallized grain sizes and larger fractions of precipitates. Our findings offer valuable insights into fabrication processing of HEAs, aiming to optimize microstructure and mechanical properties for potential engineering applications.
High entropy alloys (HEAs), also known as multi-principal element alloys (MPEAs), have attracted significant attention since being introduced in 2004 [1, 2]. HEAs are defined as alloys consisting of at least five major elements, each with a concentration range of 5–35 at% [3]. Following their introduction, HEAs have been studied from various viewpoints, such as phase stability and mechanical properties [4].
The equiatomic CoCrFeMnNi alloy, so-called Cantor alloy, is one of the most studied HEAs due to its excellent mechanical properties. Cantor alloy has been reported to have a single-phase FCC solid solution after homogenization at high temperatures above 1000°C [2, 5–7]. However, second phases such as NiMn-rich L10 phase, Cr-rich BCC phase, FeCo-rich B2 phase, and Cr-rich σ phase form following heat treatments of the FCC matrix at relatively low temperatures below 800°C [8–13].
Among these second phases, σ phase requires careful attention because it may strongly affect the mechanical properties of Cantor alloy. σ phase is an intermetallic compound that belongs to a tetragonal space group of P42/mnm [9, 14]. It often forms in various types of stainless steels [15–17] and Ni-base superalloys [18] having Cr contents above a certain level. The σ-phase precipitation in these conventional alloys is undesirable because it results in embrittlement [15–17]. Nonetheless, some studies have utilized σ phase to improve strength and other mechanical properties of alloys without causing severe embrittlement [19–23]. Jo et al. [20], for example, reported that fine precipitates of σ phase within the FCC matrix of a VCrFeNi HEA helped to refine the grain size by pinning the grain boundaries during thermo-mechanical processes. Therefore, these fine precipitates contributed to material’s strengthening through both grain refinement and precipitation strengthening. In such a strategy, controlling the fraction and distribution of σ phase is essential for achieving a good balance between strength and ductility.
The kinetics of σ-phase precipitation in Cantor alloy is notably slow, which makes it difficult to effectively utilize the precipitation as a strengthening factor in Cantor alloy. Pickering et al. [8] annealed a coarse-grained Cantor alloy at 700°C, and σ phase was observed only after extended heat treatment for 500 h. However, the σ-phase precipitation can be greatly accelerated by applying severe plastic deformation prior to heat treatment. It was reported that in Cantor alloy, processed by high-pressure torsion (HPT) to five revolutions, σ phase precipitated quickly during a short, 1-hour annealing at 700°C [10, 12, 24]. Despite these studies on Cantor alloy, there is a lack of comprehensive understanding about the precipitation behavior of σ phase, especially when the amounts of plastic deformation prior to heat treatment change systematically.
Therefore, the present study focuses on the effects of pre-deformation on the σ-phase precipitation during subsequent heat treatment. We applied various degrees of deformation on Cantor alloy using HPT, and subsequently heat-treated the specimens at 700°C. Microstructure evolution after HPT and heat treatment, along with the related phenomena such as precipitation and recrystallization are discussed. Moreover, tensile properties of the thermo-mechanically processed specimens were measured, and the effects of σ phase on mechanical properties were evaluated.
An equiatomic CoCrFeMnNi alloy was prepared by vacuum induction melting. The alloy was cast into a cylindrical ingot with a diameter of 100 mm and height of 230 mm. Subsequently, the ingot was hot-forged at 1000°C down to a thickness of 50 mm and homogenized at 1200°C for 2 h. The thickness of the ingot was further reduced to 19 mm by hot-rolling at 1000°C. A rectangular specimen with a dimension of 100 mm (length) × 10 mm (width) × 10 mm (thickness) was cut from the rolled material using a wire-cut electrical discharge machine. The specimen was homogenized at 1200°C for 24 h under Ar atmosphere. To eliminate the coarse-grained structure after the prolonged homogenization, the specimen was cold-rolled to 90% reduction in thickness and annealed at 1000°C for 1 h under a vacuum condition (≈5 × 10−3 Pa). The latter process led to a fully recrystallized microstructure having an average grain size of 30 µm, where twin boundaries were considered. This specimen was used as a starting material.
Disc-shaped specimens with a diameter of 10 mm and a thickness of 0.8 mm were cut from the starting material using the wire-cutting machine. The discs were deformed by HPT at room temperature with a rotational speed of 0.2 rotation per minute under a pressure of 6 GPa. The applied shear strain, γ, is calculated as follows:
| \begin{equation} \gamma = \frac{2\pi rN}{t} \end{equation} | (1) |
where r, N, and t are the radial distance from the center of the disc, the number of rotations of the anvil, and the actual thickness of the disc after compression (0.73 mm), respectively. In this study, N = 1/24, 1/8 and 1 were selected to apply various amounts of shear strain to the specimen. After HPT, the specimens were heat-treated at 700°C for up to 5 h in a salt bath, and then water quenched. Regions at a radial distance of 3 mm from the center of the discs were used for microstructural observations. The amounts of shear strains at r = 3 mm were equal to γ = 1.1, 3.2, and 25.8 for N = 1/24, 1/8, and 1.
The surface normal to the axial direction of the discs was mechanically polished using SiC papers with grit sizes of 400–4000, and then electropolished with 10 vol% perchloric acid-90 vol% acetic acid solution at 20 V at room temperature. Afterwards, X-ray diffraction (XRD) measurements were performed in X’Pert PRO Alpha-1 (Malvern PANalytical) system, employing Cu-Kα radiation (wavelength λ = 0.154 nm) over diffraction angles, 2θ, ranging from 30° to 100° with a scanning step of 0.017° at a tube voltage of 45 kV and a tube current of 40 mA.
Microstructural characterizations were carried out using field emission scanning electron microscope (FE-SEM), transmission electron microscope (TEM), and scanning transmission electron microscope (STEM). Cross-section of the HPT discs was prepared for microstructure observation. For the SEM observation, the cross-section was polished with the same method used for the XRD measurements. The polished surface was investigated with FE-SEM (JEOL, JSM-7800F) equipped with a backscattered electron (BSE) detector. The accelerating voltage and working distance were 25.0 kV and 3–5 mm, respectively. TEM samples were prepared from thin slices cut from the cross-section of the discs. The slices were mechanically polished to a thickness of ≈70 µm using SiC paper. Finally, they were electropolished with a twin-jet polishing system (Struers, Tenupol-5) in 70 vol% methanol-30 vol% glycerin solution at a temperature of −20°C and a voltage of 20 V. Microstructural observations were carried out using TEM (JEOL, JEM-2010 and JEM-2100F) and STEM (JEOL, JEM-2100F) at an accelerating voltage of 200 kV.
The area fraction, size, and number density of σ phase were measured from the SEM-BSE images using the image analysis software ImageJ. As a necessary first step, the σ-phase particles in the images were manually filled in black to enable ImageJ to precisely distinguish the σ-phase particles from the FCC matrix based on their different grayscale values. Binarization was then performed based on certain threshold values, converting the grayscale images into binary ones, where pixels representing the σ-phase particles were set to black, and pixels representing the FCC matrix were set to white. These binary images were then analyzed by ImageJ for quantitative measurements of the σ-phase particles. Additionally, the recrystallized grain size of the FCC phase was measured using the linear intercept method.
Tensile tests were performed using a universal tensile test machine (Shimadzu AG-X Plus) at a strain rate of 8.3 × 10−4 s−1. Sub-size tensile specimens with a gauge length of 2 mm and a gauge cross-section of 1 mm × 0.5 mm were cut from the discs in a way that the gauge part was 3 mm away from the center of the discs. The strain in the gauge section was precisely measured with the digital image correlation (DIC) method using Vic-2D software [25]. In our previous studies (Ref. [26] for example), it was established that the stress-strain curves obtained by applying the DIC method to miniature tensile specimens closely matched those obtained from large standard-size specimens of the same material using a strain gauge.
Deformation microstructures after HPT are shown in Fig. 1. With a shear strain of γ = 1.1 (Fig. 1(a)), a high density of deformation twins appeared, which led to the formation of twin-matrix (T-M) lamellar structures. Additionally, shear bands penetrating the T-M lamellae were found. With larger deformation up to γ = 3.2 (Fig. 1(b)), a nanocrystalline structure emerged and gradually replaced the T-M lamellar structure. When the shear strain reached γ = 25.8 (Fig. 1(c), (d)), the deformed microstructure evolved into a homogeneous nanocrystalline structure with an average grain size of less than 50 nm. The selected area diffraction (SAD) pattern obtained by TEM confirmed that the nanocrystalline specimen maintained the single-phase FCC structure after HPT, consistent with the findings of a previous study by Schuh et al. (Ref. [10]).
SEM-BSE images (a)–(c) and TEM image (d) representing deformation microstructures of specimens after HPT. The applied shear strains were as follows: (a) γ = 1.1, (b) γ = 3.2, and (c), (d) γ = 25.8. The inset in (d) represents the selected area diffraction (SAD) pattern from the nanocrystalline structure, with the ring pattern labeled by the Miller indices of the diffracting planes of an FCC structure. “GB” in (a) and “T-M lamellae” in (b) mean “grain boundary” and “twin-matrix lamellae”, respectively.
Following HPT, the specimens were subjected to isothermal heat treatments at 700°C for different periods of time. Microstructures of the heat-treated specimens having different pre-strains are shown in Fig. 2. In the specimen deformed by a pre-strain of γ = 1.1, recrystallization began within 1 min of heat treatment (Fig. 2(a)). The recrystallized grains were preferentially formed along initial grain boundaries (GBs) and within shear bands, whereas no recrystallized grains were found within T-M lamellar structures. After heat treatment for 3 min (Fig. 2(b)), some of the recrystallized grains grew into the T-M lamellae. Moreover, a fraction of precipitates was found on the recrystallized GBs, as pointed out by a white arrow in the inset in Fig. 2(b). After heat treatment for 5 h (Fig. 2(c)), recrystallization was complete. There emerged a heterogeneous structure composed of the areas with larger grains and fewer precipitates, and the areas with smaller grains and a higher density of precipitates.
SEM-BSE images of specimens subjected to HPT ((a)–(c) γ = 1.1, (d), (e) γ = 3.2, (f), (g) γ = 25.8) and subsequent heat treatments at 700°C for (a) 1 min, (b), (d), (f) 3 min, (c), (e), (g) 5 h, respectively. An unrecrystallized area is enclosed by a white dashed line in (d). White arrows in (b)–(g) indicate precipitates. SD, SPND, and RD indicate the shear direction, shear-plane normal direction, and radial direction, respectively.
In the specimen having a pre-strain of γ = 3.2, recrystallization was nearly complete after heat treatment for 3 min (Fig. 2(d)). The nanocrystalline structure quickly underwent recrystallization and disappeared, while remnants of the T-M lamellar structure could still be found in unrecrystallized regions. Precipitates were frequently observed on the recrystallized GBs. Following heat treatment for 5 h (Fig. 2(e)), recrystallization was complete, with both recrystallized grains and precipitates growing larger compared to those observed after the 3-min heat treatment (Fig. 2(d)).
In the specimen having a pre-strain of γ = 25.8, heat treatment for 3 min resulted in complete recrystallization (Fig. 2(f)). An ultrafine-grained (UFG) structure with an average grain size of D = 0.37 µm was formed. There were many precipitates on the recrystallized GBs and triple junctions. The recrystallized UFG structure had a uniform grain distribution with evenly distributed precipitates, in contrast to the heterogeneous microstructure seen in the annealed specimen with the smaller pre-strain of γ = 1.1 (Fig. 2(c)). Both recrystallized grains and precipitates exhibited growth after 5 h of heat treatment (Fig. 2(g)). However, the grains were still refined even after prolonged heat treatment. The slow grain growth can be attributed to the pinning of GBs by the precipitates [12].
XRD measurements were conducted to identify the phases in the deformed and heat-treated specimens. Figure 3 represents XRD profiles of the specimens after HPT by one rotation and after the subsequent heat treatment at 700°C for 5 h. Following HPT, there were only peaks of the FCC structure with a lattice constant of a = 0.36 nm. This value is consistent with that previously reported for Cantor alloy [12]. Additional peaks resulting from the precipitate formation appeared after the heat treatment for 5 h. The new peaks, marked by squares in the enlarged profile in Fig. 3(b), belong to a tetragonal space group with lattice constants of a = b = 0.878 nm and c = 0.455 nm. These features match those of σ phase in Cantor alloy [8, 11, 12, 24]. Therefore, the second-phase precipitates observed in Fig. 2 were identified as σ phase.
(a) XRD profiles of the specimens after HPT by 1 rotation and after a subsequent heat treatment at 700°C for 5 h. The circles and squares indicate peaks associated with the FCC phase and σ phase, respectively. (b) Enlarged XRD profile of the heat-treated specimen, representing the peaks of σ phase in the range of 2θ = 38°–52°.
Precipitation and recrystallization happened simultaneously during the heat treatment. It was unclear whether the second phases formed before the onset of recrystallization or afterwards. To clarify this, partially recrystallized specimens obtained after short heat treatments were examined by TEM and STEM. Figure 4(a), (b) show representative microstructures in the specimen subjected to the pre-strain of γ = 1.1 and subsequent heat treatment for 3 min. The unrecrystallized area consisted of T-M lamellae and micro bands (Fig. 4(a)), with no clear evidence of the σ-phase precipitation in this region. In the recrystallized area, however, there were σ phases on the recrystallized GBs, as pointed out by white arrows in Fig. 4(b). It seemed that these σ phases precipitated after recrystallization. Figure 4(c) represents a microstructure in the specimen subjected to the pre-strain of γ = 3.2 and subsequent heat treatment for 15 s. Certain areas of the nanocrystalline structure formed by HPT remained unrecrystallized within 15 s. White arrows in Fig. 4(c) indicate precipitates that (1) formed in the nanocrystalline region before it underwent recrystallization, and (2) appeared along the recrystallized GB. The precipitates had elliptical shapes with an average size less than 200 nm.
(a), (b) Representative microstructures of the specimen after HPT (γ = 1.1) and subsequent heat treatment at 700°C for 3 min. (a) STEM bright-field image of an unrecrystallized area. (b) TEM bright-field image of recrystallized grains and precipitates located along grain boundaries. The white arrows indicate precipitates. (c) TEM microstructure (bright field) of the specimen after HPT (γ = 3.2) and subsequent heat treatment at 700°C for 15 s. The white arrows in (c) point out precipitates that formed (1) inside an unrecrystallized area, and (2) along a recrystallized grain boundary.
The area fraction and number density of σ phase, along with the size of recrystallized FCC grains were measured from the SEM images. Figure 5 represents the area fraction of σ phase. In the specimen with pre-strains of γ = 1.1 and 3.2, small amounts of σ phase below 1% precipitated following heat treatment for 3 min. The area fractions of σ phase in these specimens gradually increased with increasing the time. The precipitation kinetics was slightly faster for γ = 3.2 than for γ = 1.1. After heat treatment for 5 h, the area fractions of σ phase finally reached 1.3% and 3.9% for γ = 1.1 and γ = 3.2, respectively. For γ = 25.8, the amount of σ phase was already 5.4% after just 3 min of heat treatment, and the fraction reached 7.5% after 5 h. The precipitation kinetics was analyzed using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation, which is represented as follows:
| \begin{equation} f = \frac{A_{\sigma}}{A_{\textit{eq}}} = 1 - \exp (-kt^{n}) \end{equation} | (2) |
where 0 < f < 1 is the fraction of σ phase transformed at a given time of t, Aσ is the area fraction of σ phase measured at t, Aeq is the maximum area fraction of σ that can be achieved at an equilibrium condition, and k and n are constants. Aeq was estimated to be around 8.1% for the equiatomic CoCrFeMnNi HEA at 700°C based on a previous work by Laplanche et al. [27]. The values of n were determined by plotting ln(ln(1/(1 − f))) versus ln(t) and calculating the slope of the linear fit. The n values were 0.44, 0.42, and 0.17 for γ = 1.1, 3.2, and 25.8, respectively. Using these values, fitting curves for the data points in Fig. 5 were drawn.
Area fraction of σ phase as a function of heat-treatment time. The dashed lines represent fitting curves based on Johnson-Mehl-Avrami-Kolmogorov equation.
As previously shown in Fig. 2, σ phase tended to precipitate at higher number densities in specimens with larger pre-strains. This tendency is clearly shown in Fig. 6, where the number density of σ phase is plotted as a function of the heat-treatment time. The trend was drastically different for γ ≤ 3.2 compared to γ = 25.8. For the pre-strains of γ = 1.1 and 3.2, the number density remained in low levels below 0.21 µm−2 throughout the heat treatment for up to 5 h. In contrast, the specimen with the pre-strain of γ = 25.8 had a much higher density of σ phase, estimated around 1.9 µm−2 just after 3 min of heat treatment. The density gradually decreased over 1 h, but largely dropped to 0.58 µm−2 after 5 h.
Number density of σ phase precipitates (counted within recrystallized regions) as a function of heat-treatment time.
Recrystallization took place concurrently with precipitation during the heat treatments. Figure 7 shows the recrystallized grain sizes measured by the linear intercept method in which GBs excluding annealing twin boundaries were counted. The data points shown by empty and solid symbols belong to the specimens having partially and fully recrystallized microstructures, respectively. In the specimen subjected to the small pre-strain of γ = 1.1, recrystallization took a longer time to finish, allowing the recrystallized grains grew larger during heat treatment. The slow recrystallization was mainly attributed to the presence of the T-M lamellar structures which did not serve as potential nucleation spots for recrystallization. In the specimens with larger pre-strains, recrystallization completed faster, and the recrystallized grains were smaller. Moreover, grain growth during heat treatment was slower due to the higher densities of precipitates that could pin GBs in those specimens. As a result, the specimen with the pre-strain of γ = 25.8 exhibited a UFG structure with a grain size of 0.82 µm after 5 h of heat treatment.
Recrystallized grain size as a function of heat-treatment time. Annealing twin boundaries are not counted as grain boundaries. The data points shown by empty and solid symbols belong to the specimens having partially and fully recrystallized microstructures, respectively.
Tensile tests were carried out on specimens processed by different pre-strains followed by heat treatment for 5 h. The nominal stress-strain curves are shown in Fig. 8. The total elongation (TE), yield strength (YS), and tensile strength (TS) of these specimens are summarized in Table 1, along with the grain size considering twin boundaries, D′, and the area fraction of σ phase, Aσ. For the estimation of grain size, we counted twin boundaries for better comparison with the literature, which is discussed later in section 4.3. TE, YS, and TS of the specimen with the pre-strain of γ = 1.1 were measured as 47%, 395 MPa, and 678 MPa, respectively. As the applied shear strain increased, leading to decreased grain sizes and increased fractions of σ precipitates, the total elongation decreased, while the yield and tensile strength increased. The specimen with the pre-deformation of γ = 25.8 exhibited a TE of 7.6%, YS of 895 MPa, and TS of 954 MPa. This specimen showed discontinuous yielding which often happens in recrystallized UFG materials.
Tensile stress-strain curves of CoCrFeMnNi HEA after HPT and subsequent heat treatment at 700°C for 5 h. The variable γ refers to the applied shear strain by HPT.
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The fracture surfaces after tensile testing are shown in Fig. 9. All fractured specimens showed dimple patterns, a typical feature of ductile fracture. The size of the dimples was different among specimens processed by different shear strains. The specimen with γ = 1.1, which exhibited a heterogeneous microstructure after heat treatment (Fig. 2(c)), had uneven dimple sizes. Large dimples had diameters above 5 µm, while the small ones were around 2 µm in diameter. Regardless of their sizes, most of dimples contained small particles within them. Given their shape, size, and density, these particles are likely to be σ phase. The fracture surfaces of the specimens with γ = 3.2 and 25.8 also displayed dimples with small σ particles inside. However, the dimples were more uniform in size and smaller than those in the specimen with γ = 1.1.
SEM images representing the fracture surfaces of the tensile specimens. The specimens were processed by HPT to different shear strains of (a) γ = 1.1, (b) γ = 3.2, and (c) γ = 25.8, and subsequently heat-treated at 700°C for 5 h.
Previous studies have reported that the FCC phase in Cantor alloy decomposes into second phases, including σ phase, during heat treatments below 800°C [8, 9]. In addition, Schuh et al. [10] and other researchers [11, 12, 24] have shown that large deformation before heat treatments accelerates the precipitation. However, no efforts have been made to clarify how different amounts of pre-deformation affect the precipitation behavior of σ phase. In the present study, we applied a wide range of shear strains to Cantor alloy by HPT and studied the microstructure evolution during subsequent heat treatments at 700°C for various time lengths.
Figure 10 provides a schematic illustration to describe the microstructure evolution during heat treatment. For convenient discussion, deformation microstructures before heat treatment are categorized into type I: T-M lamellar structure (Fig. 10(a)) and type II: nanocrystalline structure (Fig. 10(d)), which respectively form after applying small and large amounts of strains. To keep the illustration simple, the deformation microstructure at medium strains, which is a mixture of T-M lamellae and nanocrystalline structures, is not considered in Fig. 10. For the T-M lamellar structure, recrystallization initiates at initial GBs or shear bands shortly after the heat treatment starts (Fig. 10(b)). The newly formed GBs can act as easy diffusion paths for solute atoms and nucleation sites for precipitates, thus promoting GB precipitation in the partially recrystallized regions. No recrystallized grains appear within the T-M lamellar regions. These regions containing a high density of twin boundaries can be thermally stable [28] during the early stage of heat treatment. This suggests that unlike high-angle GBs, twin boundaries, which typically have coherent interfaces, do not provide favorable pathways for the nucleation of σ phases. After long-term heat treatment, some recrystallized grains in the vicinity of the T-M lamellae can expand into these precipitate-free regions until the growing grains impinge upon each other (Fig. 10(c)). In some recrystallized regions, in which the precipitation occurs soon after the recrystallization, the precipitates can pin the GBs and delay the grain growth. As a result, a heterogenous microstructure made of precipitate-free coarse-grained regions and precipitate-rich fine-grained regions forms. Note that the fraction of precipitates in this heterogenous structure (<2%) cannot reach its equilibrium value (≈8.1%) even after the prolonged heat treatment. This observation can be rationalized by the substantial reduction in the number of GBs due to the grain coarsening after several hours of heat treatment (Fig. 7), requiring solute atoms to diffuse longer distances through the bulk (lattice) to reach the nearby GBs. The latter process can be extremely slow. In fact, Otto et al. [9] reported that around 500 days of heat treatment were needed to achieve the phase equilibrium in a coarse-grained Cantor alloy.
Schematic illustrations of microstructure evolution after HPT ((a) γ ≈ 1, (d) γ > 20) and subsequent heat treatment at 700°C for (b) less than 5 min, (c) more than 1 h, (e) less than 30 s, and (f) more than 1 h.
Compared to the T-M lamellae, the nanocrystalline structure having large stored energy (Fig. 10(d)) is highly unstable during the heat treatment. Following the heat treatment, both recrystallization and precipitation take place almost immediately (Fig. 10(e)). Fine recrystallized grains and precipitates form throughout the matrix in less than half a minute. Precipitates appear on the recrystallized GBs as well as within the nanocrystalline regions before these regions undergo the recrystallization. The latter is because the nanocrystalline structure made by HPT and other severe plastic deformation processes contains abundant GBs, dislocations, and lattice defects. Diffusion along these short-circuit paths is fast and it greatly promotes the precipitation kinetics. As a result, the incubation period for precipitation is so brief that it cannot be experimentally realized (see Fig. 5). The high density of precipitates can effectively pin the GBs [13] and prevent significant grain growth. The slow grain coarsening during the prolonged heat treatment results in the formation of a homogeneous UFG structure (Fig. 10(f)). A large fraction of GBs still remains in the UFG structure, continuously feeding Cr atoms to the GB precipitates. Therefore, the fraction of σ phase can increase steadily until it almost reaches the equilibrium value. Additionally, precipitate coarsening occurs, especially in the later stage of heat treatment (Fig. 2(g)). The coarsening involves the dissolution of smaller particles and the re-deposition of the dissolved atoms (Cr) on larger particles. This phenomenon, also known as Ostwald ripening, leads to a decrease in the number of σ phase, as previously pointed out in Fig. 6.
4.2 Precipitation kinetics of σ phaseIt was confirmed that the precipitation kinetics of σ phase was accelerated by increasing the amount of pre-deformation (Fig. 5). The exponent n in the JMAK equation was estimated as 0.44, 0.42, and 0.17 for shear strains of γ = 1.1, 3.2, and 25.8, respectively. For comparison, reported n values for the σ-phase precipitation in an off-equiatomic Co20Cr26Fe20Mn20Ni14 [27], AISI 310 steel (≈24%Cr) [29], and AISI 316 steel (≈17%Cr) [29] were 0.64, 0.72, and 1.1, respectively, all associated with the heat treatment at 700°C. The n values in our study were smaller partly due to the difference in microstructures, as we used pre-deformed microstructures before the heat treatment while other studies used coarse-grained microstructures. It is known that precipitation behaviors in deformed materials, especially those having nanograined structures, are completely different from those in coarse-grained materials [30–32]. In addition, the n values in our study decreased with increasing the amount of deformation. Great care must be taken in interpreting the n values, especially that associated with the higher strain of γ = 25.8. In the heavily deformed specimen, the precipitation kinetics was so fast that a part of experimental data corresponding to the early stage of precipitation was missing in our analysis (Fig. 5), potentially affecting the estimation of the n value. Another experimental difficulty is that deformed microstructures are replaced when recrystallization and grain growth take place during the heat treatment. Under such a circumstance, the exact interpretation of n is complicated and still an open question at present. Aside from these challenges, the n parameter is dependent on factors such as nucleation and growth rates of precipitates [33]. We discussed that both nucleation and growth of σ phase took place differently in the specimens with different pre-strains (Figs. 2, 4–6, 10), which is the main reason for realizing various n values in our study.
4.3 Effects of σ phase on mechanical propertiesIt is known that Cantor alloy having a single-phase FCC structure displays excellent ductility as well as good strength owing to its solid-solution strengthening. Nevertheless, the strength of the material does not significantly surpass that of traditional alloys. Additional strengthening mechanisms are required to further strengthen the FCC matrix in Cantor alloy. In the present study, we used deformation and subsequent heat treatment to promote the precipitation of σ phase in Cantor alloy. It is revealed that increasing the amount of pre-strain (γ = 1.1, 3.2, 25.8) is an effective way to increase the σ fraction (Fig. 5) and simultaneously refine the grain size (Fig. 7). Accordingly, the yield strength and tensile strength increased (Fig. 8) due to the strengthening by grain-refinement, commonly described by the Hall-Petch relationship, as well as additional reinforcement of the matrix by the precipitates. Nevertheless, an increase in the strength was accompanied by a reduction in the ductility. It is unclear whether the primary cause of the ductility loss is precipitation or grain refinement. Sun et al. [34] measured the tensile properties of Cantor alloy having various grain sizes. No second phases were reported in their Cantor alloy, or the amount seemed to be negligible. Compared to their results, the specimens having the same grain sizes with the σ fraction up to 4% (the specimens pre-deformed by γ = 1.1 and 3.2) showed comparable tensile elongation. This suggests that the fine σ precipitates up to a certain fraction have a negligible impact on the ductility. It is interesting that even in the specimen having the highest fraction of σ phase (7.5%) and the smallest grain size (0.43 µm), i.e., the specimen pre-deformed by γ = 25.8, minimum elongation of 7.6% could still be realized. Also, the fracture surface in this specimen showed no indication of severe embrittlement (Fig. 9(c)). It is suggested that the interface between σ phase and FCC matrix can be the source of crack/micro-void initiation, and then the coalescence of cracks/micro-voids leads to the final fracture of specimens. Nevertheless, we hypothesize that the high-entropy matrix in Cantor alloy has an excellent ability to resist the propagation of cracks/micro-voids once they initiate at the interfaces of precipitates/matrix. Therefore, Cantor alloy exhibits reasonable ductility, even in the presence of σ-phase precipitates in the matrix. Aligned with our speculation, Zhang et al. [35] reported exceptional damage tolerance in Cantor alloy during tensile loading. They discussed that the activation of multiple deformation mechanisms, including the formation of nanoscale twins, effectively delays fracture.
In the present study on Cantor alloy, we revealed that various amounts of deformation and the resulting deformation microstructures play a substantial role in the recrystallization behavior and σ-phase precipitation during subsequent heat treatments. We used this strategy to control microstructures and mechanical properties in Cantor alloy. It is worth mentioning that σ phase in Cantor alloy may be somewhat different in terms of chemical compositions, morphologies, and mechanical properties from those commonly found in conventional alloys such as stainless steels. The characteristics of σ phase in Cantor alloy can be an interesting topic for future investigations.
We systematically investigated the effects of various deformation degrees and subsequent heat treatment on the σ-phase precipitation in Cantor alloy. Additionally, tensile tests were carried out to evaluate the effects of σ phase on mechanical properties. We reached the following conclusions.
This work was financially supported by the Grant-in-Aid for Scientific Research on Innovative Area “High Entropy Alloys” (No. JP18H05455), the JST CONCERT (JPMJSC21C6), the Grant-in-Aid for Scientific Research (A) (No. JP23H00234), the Grant-in-Aid for Scientific Research on International Leading Research (No. JP23K20037), the Grant-in-Aid for Early-Career Scientists (No. JP22K14501), the Grant-in-Aid for Research Activity Start-up (No. JP21K20487), and the Grant-in-Aid for JSPS Research Fellow (No. JP18J20766), all through the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. The financial supports are gratefully appreciated.
