Introduction

One of the first and well-studied high-entropy alloys (HEAs) is the equiatomic CoCrFeNiMn alloy which has a significant potential for use in future industrial applications. This potential arises because of its extraordinary properties such as a high fracture toughness over a wide range of temperatures including cryogenic temperature, a high ductility, a high phase stability and an excellent resistance to hydrogen embrittlement [1–7]. This alloy shows superior ductility (up to 85% at room temperature and lower temperatures) due to its simple fcc phase and the activation of dislocation slip and twinning as the most important deformation mechanisms [7]. Basically, the CoCrFeNiMn alloy has a great potential for easy deformation by dislocation slip due to the large number of slip systems [8]. Nevertheless, the relatively low stacking fault energy (SFE) of the alloy, ~ 21 mJ m−2 [9–12], affects the deformation mechanism. It is well-established that deformation-induced twinning is a major deformation mechanism in fcc metals with SFE lower than ~ 25 mJ m−2 and, accordingly, it is expected that deformation-induced twinning will be activated along with dislocation slip as the controlling deformation mechanisms in the CoCrFeNiMn HEA [11, 13–16]. It was shown that deformation-induced twinning increases ductility by changing the strain hardening curve [17, 18]. In addition, it produces hardening due to a build-up of back-stress together with preventing the planar glide of dislocations which consequently can improve the strength and uniform elongation simultaneously. It is important to note that the latter is responsible for facilitating remarkable workability in the alloy.

Many attempts were conducted to improve the intrinsic low strength of the single fcc-phase CoCrFeNiMn HEA without producing any significant sacrifice of ductility [7, 8, 19–26] using grain refinement as one of the most effective procedures for improving strength based on the well-known Hall–Petch strengthening. It is important to note that deformation-induced twinning is responsible for significant grain refinement after imposing a sufficient strain during plastic deformation and this is known as the dynamic Hall–Petch effect which decreases the dislocation mean free path and should thereby increase the strength of the material [18]. The most important and effective procedure for introducing grain refinement is through the use of severe plastic deformation (SPD) followed by short-term annealing to tailor an ultrafine-grained microstructure which will improve the strength with no significant sacrifice of ductility in the CoCrFeNiMn alloy [27–29].

Basically, the grain size plays an active role to activate deformation-induced twinning during plastic deformation. The occurrence of deformation-induced twinning was confirmed in many investigations after deformation of the CoCrFeNiMn HEA alloy with different grain sizes, from several tens to a few micrometers, at both room and cryogenic temperatures [8, 10, 13, 30–32]. However, it was reported earlier that grain refinement, predominantly down to the specific grain size range of ultrafine-grained materials (< 1 µm), may increase the SFE and suppress deformation twinning [33]. It was also shown that there is a critical grain size in which no deformation twinning is observed during plastic deformation such that dislocation slip is the only mechanism accommodating the imposed strain [33–35]. This phenomenon may affect the mechanical aspects of the alloy including the strain hardening behaviour, strength, uniform elongation and workability. The present investigation was, therefore, initiated to provide a systematic demonstration of the role of grain size, especially in the range of a few microns to submicrons fabricated by SPD followed by short-term annealing, on the deformation mechanisms and mechanical properties of the CoCrFeNiMn HEA. The present investigation is focused on the grain growth kinetics to improve the understanding of grain size control during post-deformation annealing of the CoCrFeNiMn HEA. This research is important because the grain size, within the fine and ultrafine grain range, affects the deformation mechanism as an important parameter which determines the mechanical properties.

Materials and Methods

High purity elements of Co, Cr, Fe, Ni, and Mn were used to fabricate an equiatomic HEA by an arc melting method using a water-cooled copper crucible to make the alloy. The arc was formed in a high purity Ar atmosphere using a non-consumable tungsten electrode and the alloy was remelted several times to obtain the best chemical homogeneity. The as-cast alloy was homogenized at 1000 °C for 16 h under an Ar-controlled atmosphere and then disks of 10 mm in diameter and thicknesses of ~ 1 mm were prepared by electro-discharge machining. These disks were polished mechanically to final thicknesses of ~ 0.8 mm. The disks were processed by high-pressure torsion [36] under quasi-constrained conditions in which there is a small outflow of material around the periphery of the disk [37]. The HPT was conducted using an applied pressure of 6.0 GPa and processing through a total of five rotations. After HPT processing the specimens were subjected to annealing at different temperatures and times.

Foils for scanning transmission electron microscopy (STEM) were prepared after the HPT processing using a focused ion beam (FIB) Zeiss Nvision 40 FIB facility at 3 mm from the disk centers in the normal sections of the disks so that the normals of the images lay in the shear direction. The microstructures of the annealed specimens were studied using optical microscopy (OM) and scanning electron microscopy (SEM) after grinding through 800, 1200 and 4000 grit SiC papers, polishing using a 40 nm colloidal silica suspension and then etching with a solution of 50 mL H2O, 50 mL HCl and 10 g CuSO4. The electron channel contrast imaging (ECCI) technique was also used at a voltage of 15 kV, a probe current of 18 nA and with a working distance of 5 mm in a field emission SEM (FESEM 7900, JEOL, Japan). Grain size measurements were based on the standard intercept method (ASTM E112).

Hardness measurements were taken using a Vickers microhardness tester with a load of 500 gf and dwell times of 10 s where each reported value represents the average of seven separate hardness values. Tensile specimens with gauge dimensions of 1.1 × 1.0 × 0.6 mm3 were cut from symmetric off-centre positions near the edges of each disk using electro-discharge machining. Tensile tests were conducted on the samples using an initial strain rate of ~ 1.0 × 10–3 s−1 with a Zwick universal testing machine in which the tensile strengths were derived directly from the curves and the elongations were estimated by carefully measuring the gauge lengths before and after tensile testing using an optical microscope.

Results

Grain Size and the Grain Growth Behaviour During Post-deformation Annealing

Figure 1 shows the microstructure of the sample after SPD and post-deformation annealing at 800 and 900 °C. This set of microstructures reveals nano and fine equiaxed grains in the severely deformed and the annealed samples, respectively, with an absence of any secondary phases. It is important to note also that the microstructure before HPT processing (not shown) was typical of a fully annealed sample consisting of equiaxed grains with an average grain size of ~ 120 μm. Nano-deformation twins and annealing twins are shown by yellow arrows in the severely deformed and annealed samples, respectively. These images clearly reveal the very significant grain refinement after SPD and appropriate heat treatment.

Fig. 1
figure 1

Microstructure of CoCrFeNiMn HEA after a severe plastic deformation by HPT (STEM image), and b, c after post-deformation annealing (OM images)

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Detailed information is shown in Fig. 2 for the average grain sizes of samples after post-deformation annealing at different temperatures for 60 min together with the microhardness measurements. The results confirm there is no significant change in grain size up to 800 °C but thereafter at temperatures > 800 °C the grain size rapidly increases due to a coarsening effect. The trend of the hardness values shows an increase from 450 Hv (as a deformed condition) to 520 Hv after annealing at 500 °C followed by a rapid decrease with increasing annealing temperatures up to 1000 °C which then reaches a hardness value of ~ 130 Hv as in the initial condition before deformation. The significant grain refinement and the introduction of defects during SPD are responsible for this remarkable increment of hardness by a factor of ~ 3.5. These grain size and hardness changes are due to the formation of precipitates during annealing at < 800 °C and the subsequent dissolution of the precipitates at temperatures > 800 °C. The formation of Cr-rich precipitates at < 800 °C was reported earlier in this HEA [6, 7, 27, 29, 38–41] where the pinning effect of precipitates on the grain boundaries is the main obstacle to a coarsing phenomena at temperatures below ~ 800 °C. However, a dissolution of these precipitates and the associated high rate of diffusion at high temperatures are crucial factors in the occurrence of significant coarsening at temperatures greater than ~ 800 °C.

Fig. 2
figure 2

Hardness and grain size changes of CoCrFeNiMn HEA during post-deformation annealing at different temperatures for 60 min

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Based on the scope of this investigation, it was important to focus on the coarsening behavior at higher temperatures. Accordingly, Fig. 3a shows the grain size in terms of different holding times at temperatures of 800, 850, 900 and 950 °C. As expected, the grain size increases with increasing annealing time and this increment is larger at the higher temperatures. To study the grain growth behavior, a parabolic grain growth kinetics was considered in the present work based on Eq. 1 [42–44]:

$${D}^{n}-{{D}_{0}}^{n}=kt$$
(1)

where D, D0, n, k, and t are grain size, initial grain size (~ 0.05 µm), grain growth exponent, a temperature-dependent constant and the time (min), respectively. It is worth noting that D0 was ignored due to the very small value of D0 by comparison with D so that Eqs. 2 and 3 can be derived as:

$${D}^{n}=kt$$
(2)

and

Fig. 3
figure 3

a Effects of annealing temperature and holding time on grain size, b Plot of Lnt versus LnD, and c Plot of Lnk as a function of T−1 used for determining the activation energy for grain growth

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$$\mathrm{Ln} t=n\mathrm{Ln}D-\mathrm{Ln}k$$
(3)

A plot of Ln t versus Ln D then yields a straight line for each temperature from which the slope, n, and the intercept, Lnk, can be readily calculated as shown in Fig. 3b. According to these results, the n value increases with increasing temperature. The dependence of k on the grain growth activation energy and temperature is given by the following relationship:

$$k={k}_{0}\mathrm{exp}\left(-\frac{Q}{RT}\right)$$
(4)

where T is the temperature in degrees Kelvin, K0 is a constant, Q is the grain growth activation energy (kJ mol−1) and R is the gas constant (8.31 J mol−1 K−1). Thus,

$$\mathrm{Ln} k=\mathrm{Ln}{k}_{0}-\frac{Q}{RT}$$
(5)

According to the above equation and Fig. 3c, the grain growth activation energy, Q, was calculated as ~ 440 kJ mol−1.

Mechanical Properties

Figure 4a represents a set of true stress-true strain diagrams of the single-phase CoCrFeNiMn HEA with different grain sizes in the range of 0.05–120 µm which were obtained after SPD followed by post-deformation annealing. The results show a significant increase in strength of the nano-grain sample after SPD but with a corresponding decrease in the measured elongations to failure. The results demonstrate that the elongations to failure are restored and increase at the expense of a decrease in strength with increasing grain size after annealing. Figure 4b shows a summary of the mechanical properties of the CoCrFeNiMn HEA for different grain sizes. The results confirm that, with increasing grain size, the yield stress and the tensile strength decrease and the total elongation increases. The results show also that when the grain size reaches ~ 0.1 µm from ~ 120 µm the values of the tensile strength, yield stress and total elongation extend from ~ 1740 MPa, ~ 1270 MPa and ~ 0.04 to ~ 498 MPa, ~ 227 MPa and ~ 0.95, respectively. These values demonstrate that the total elongation decreases significantly at the critical grain size of ~ 2 µm (see Fig. 4b) where this is probably due to a change in the deformation mechanism. The flow curve in the region of uniform deformation is expressed by a power-law relation in which the exponent is known as the strain-hardening exponent. Representative plots of log true stress against log true strain are shown in Fig. 4c where the slopes of the curves give the strain hardening exponents. Thus, the small value of the strain hardening exponent at grain sizes less than ~ 0.1 µm indicates that the sample has very little uniform elongation. The results show this value increases by increasing the grain size. Furthermore, close inspection of these data demonstrates a significant change in the the strain hardening exponent by changing the grain size only from ~ 1.5 to ~ 2.5 µm in the annealed samples. This value then increases slightly after changing the grain size from ultrafine-grains to coarse grain samples of ~ 120 µm.

Fig. 4
figure 4

a True stress-true strain plot, b Plot of YS, UTS, and total elongation versus grain size, c Log true stress versus log true strain in which slope of each line represents the strain hardening exponent and d Strain hardening rate versus true strain for different grain sizes

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It is well-established that there is a correlation between the strain hardening exponent value and the deformation mechanism. Figure 4d represents the strain rate hardening against the true strain in which the strain rate hardening curves can be subdivided into three stages depending on the slope variation where there is a rapid decrease of strain rate hardening below a true strain of ~ 0.05 in Stage I, a plateau between a true strain of ~ 0.05 and ~ 0.45 in Stage II and a decrease above a true strain of ~ 0.45 in Stage III. All curves reveal similar behavior except for the curve representing the mechanical behavior of the sample with a grain size of ~ 1.5 µm in which the strain rate hardening curve shows a sharp decrease that is qualitatively similar to Stage I followed by a gradual decrease similar to Stage III that is not representative of the Stage II plateau.

Figure 5 shows ECCI images illustrating the microstructures of fine grain specimens after tensile testing including the presence of annealing and deformation twins as marked by AT and DT, respectively. These images show that the thickness of the DTs is less than the ATs and these values are in the nanoscale. Close inspection of the microstructures indicates the formation of deformation twins in grains having sizes above ~ 2 μm. Conversely, no deformation twins were detected in grains smaller than ~ 2 μm. The results clearly suggest the existence of a critical grain size for the formation of deformation twinning which affects the deformation mechanism.

Fig. 5
figure 5

a–f Set of ECCI images of fine-grained CoCrFeNiMn HEA samples (after post-deformation annealing) after tensile testing in different magnifications. Higher magnification of areas marked in c and e are presented in d and f, respectively. Annealing and deformation twins as marked by AT and DT, respectively

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Discussion

Significance of Grain Growth Resistance in Strengthening

The present results confirm the high recrystallization temperature (~ 700 °C) and the high grain growth resistance in this HEA. The high lattice distortion energy and sluggish diffusion, as well as the low SFE in the CoCrFeNiMn HEA, are responsible for this behavior [45–48]. In addition, the results confirm the significance of Cr-rich precipitates in postponing the coarsening by a Zener pinning mechanism in the nano and ultrafine-grained CoCrFeNiMn HEA which is consistent with earlier investigations [24, 49].

Table 1 shows the key parameters representing the grain growth phenomenon in some conventional alloys and the CoCrFeNiMn HEA processed by different procedures. These data reveal that the activation energy, the Q value, of the CoCrFENiMn HEA is very high compared to other conventional alloys. This suggests that the slow grain growth kinetics in HEAs is due to the sluggish diffusion and high lattice distortion. It is important to note also that the Q value for 316L stainless steel is very remarkable as a medium entropy alloy in which molybdenum significantly retards the grain growth towards higher temperatures and slower kinetics and effectively increases the grain growth activation energy due to the interaction energy between Mo and the grain boundaries [44]. Additionally, Table 1 summarizes the information extracted from the grain growth kinetics in the CoCrFeNiMn alloy under different processes. The values of n and the grain growth activation energy for the ball-milled sample are greater than for the other processes. This suggests that grain growth is faster in these conditions than in other conditions which may be due to the high energy that is stored in the ball milling process. The n value reported in this investigation is relatively low compared with the values reported earlier after rolling and milling followed by annealing of similar alloys. This is due to the lower temperature range selected for the post-deformation annealing in which decreasing the temperature leads to a slower grain growth and lower n value.

Table 1 Summary of key parameters representing grain growth phenomenon in some conventional alloys and CoCrFeNiMn HEA processed by different procedures
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It is well-known that an enhancement of the strength of the alloy can be obtained by grain refinement due to the introduction of a high-volume fraction of grain boundaries that retard the movement of dislocations [56]. The Hall–Petch equation describes the grain boundary strengthening as given by

$${\sigma }_{ys}=k{D}^{-0.5}+{\sigma }_{0}$$
(6)

where k, D, and \({\sigma }_{0}\) are the Hall–Petch strengthening coefficient, the average grain size, and the friction stress, respectively. Figure 6a represents the grain size dependency of the hardness in the form of Hall–Petch plots [57, 58] where the data can be fairly represented by a linear relationship of the form of Hv ≈ 235D−0.5 + 93, where Hv and D are expressed in Hv0.1 and µm, respectively. Additionally, the yield stress diagram is also shown in the form of the Hall–Petch relationship in Fig. 6a.

Fig. 6
figure 6

a Yield stress and hardness as a function of grain size in single-phase CoCrFENiMn HEA alloy, and b Yield stress as a function of grain size (Hall–Petch plot) to develop a general Hall–Petch relationship for the CoCrFeNiMn HEA alloy [8, 25, 26]

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There are several reports on grain boundary strengthening in the CoCrFeNiMn HEA. Nevertheless, they all develop different relationships in a different range of grain sizes. Figure 6b shows the Hall–Petch plot for the CoCrFeNiMn HEA in this study and various other studies [8, 25, 26] in which a general Hall–Petch relationship of YS = 508D−0.5 + 183 is developed for CoCrFeNiMn HEA in a wide range of grain sizes from ultrafine (< 1 μm) to coarse-grained (> 100 μm). It is important to note that the Hall–Petch strengthening coefficient of the CoCrFeNiMn HEA (~ 508 MPa μm0.5) is less than conventional materials such as 304L and 316L stainless steels (558 and 546 MPa μm0.5, respectively) where these are representative low and medium entropy alloys, respectively [59].

Effect of Grain Refinement on the Deformation Mechanism

The deformation mechanism is one of the most important features affecting the ductility of these alloys. The intrinsic characteristics of the material such as the crystal structure, the stacking fault energy and the grain size, together with the deformation temperature, the magnitude of the applied strain and the strain rate during plastic deformation, effectively determine the deformation mechanism in metals and alloys. Thus, it is well-established that dislocation slip, deformation-induced twinning and a deformation-induced martensitic phase transformation are three deformation mechanisms in fcc materials that are mainly based on the SFE and the deformation temperature [9]. Deformation-induced twinning is a major deformation mechanism in fcc metals when the SFE is lower than ~ 25 mJ m−2 [12]. In addition, decreasing the deformation temperature promotes the appearance of other plastic deformation mechanisms along with dislocation slip. Basically, deformation-induced twinning is a well-known deformation mechanism for improving uniform plastic deformation in alloys [10, 60] and the importance of this mechanism in HEAs (such as TWIP HEA) was considered very recently [12, 18].

Previous studies in HEAs and copper alloys also confirm the presence of mechanical twinning [31, 34, 35, 61]. Thus, the results of the present investigation, including the mechanical properties and microstructure investigations, suggest that deformation-induced twinning is an important deformation mechanism that improves the mechanical properties, particularly improving the uniform elongation, but it is fully suppressed in the CoCrFeNiMn HEA when the grain size is less than 2 µm. The reason behind the transition of the deformation mechanism from deformation-induced twinning to dislocation slip is probably the increase in twinning stress with grain refinement [10]. It was shown earlier that the SFE increases by grain refinement when the stacking faults have widths that are narrower than an equilibrium width in fine grains [62]. Accordingly, grain refinement is responsible for suppressing the deformation mechanisms such as deformation-induced twinning and the deformation-induced martensitic phase transformation.

The strain rate hardening plot (Fig. 4d) is a useful way to evaluate the deformation mechanism. As already noted, different behavior was detected in the CoCrFeNiMn in this investigation by decreasing the grain size below a critical value. The strain rate hardening behavior of the samples at Stage I (rapid decrease) can be attributed to the elastic–plastic transition [63, 64] and the strain rate hardening behavior of Stage III, which includes a gradual decrease, indicates a deformation mechanism due to dislocation slip [61, 65]. The strain rate hardening behavior of Stage II, which includes the plateau, indicates a deformation mechanism due to mechanical twinning.

It is important to note that a lower grain size is obtained after high straining by HPT followed by post-deformation annealing at lower temperatures. The strain hardening rate is high when the average grain size is higher due to the easier movement and generation of dislocations and also the formation of deformation twins which provides higher elongation during deformation. Basically, deformation twinning increases strain hardening and therefore increases the uniform deformation in which a lack of twinning formation during plastic deformation in very small grain size (< 2 µm) materials leads to a lower strain hardening.

Based on the results from this investigation, Fig. 7 schematically illustrates the deformation mechanism in different grain sizes for the CoCrFeNiMn HEA. The results show that the deformation mechanism at grain sizes below ~ 2 µm is based only on dislocation slip whereas at grain sizes larger than ~ 2 µm deformation-induced twinning is also effective in addition to dislocation slip.

Fig. 7
figure 7

Schematic diagram showing the microstructural evolution in CoCrFeNiMn HEA having different grain sizes during plastic deformation

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A Model to Optimize the Grain Size

The present results show clearly that deformation-induced twinning is suppressed at grain sizes less than a critical size of ~ 2 µm. It is important to note that twinning is responsible for the high ductility at low temperatures by providing an additional deformation mode [8]. In addition, the deformation-induced twinning is responsible for significant grain refinement after imposing sufficient strain during plastic deformation by the dynamic Hall–Petch effect which decreases the dislocation mean free path and thereby increases the strength of the material [18]. Accordingly, controlling the grain size by conducting an effective thermomechanical treatment, including plastic deformation followed by annealing, is important in order to tailor a fine-grained microstructure and improve the strength by activating deformation-induced twinning without any significant sacrifice of ductility. In the following, a model is derived to control the grain size immediately above the critical grain size of ~ 2 µm in the fine-grain range to benefit from the advantages of deformation-induced twining in the CoCrFeNiMn HEA.

According to Eqs. 3 and 5, the time and temperature of annealing can be obtained by imposing Dcritical, k0, Q, and R in Eq. 7 to derive Eq. 8:

$${\text{Ln}} t = n{\text{Ln}}D_{{{\text{critical}}}} - \left( {{\text{Ln}}k_{0} - \frac{Q}{RT}} \right)$$
(7)

and

$${\text{Ln}} t = n{\text{Ln}}2 - \left( {48 - \frac{53387}{T}} \right)$$
(8)

Figure 8a shows the grain growth exponent value, n, represented in Fig. 3b against the temperature (K) which gives a linear relationship in the form of n = 0.0056 T − 4.52, where T is expressed in K. Accordingly, Eq. 9 can be derived by putting the n value in Eq. 7 so that

Fig. 8
figure 8

a Grain growth exponent, n, against temperature. b Temperature against the time of annealing in order to deduce the optimum grain size

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$$\mathrm{Ln} t=\left(0.0056T-4.52\right)\mathrm{Ln}2-\left(48-\frac{53387}{T}\right)=0.0039T+\frac{53387}{T}-44.9$$
(9)

The above equation represents a guiding curve, as illustrated in Fig. 8b, for controlling the grain size with optimum mechanical properties. These data show that the temperature and time of post-deformation annealing must be in the upper region in order to activate the deformation-induced twinning in grains. Therefore, it can be considered as a model to tailor the microstructure by an appropriate thermomechanical treatment to achieve a good combination of strength and ductility in different HEAs.

Summary and Conclusions

  1. 1.

    Grain growth behavior was studied systematically during the annealing of a severely deformed CoCrFeNiMn HEA. The results revealed significant coarsening at temperatures > 800 °C due to the dissolution of precipitates together with a high rate of diffusion at high temperatures. The microstructure showed a wide range of grain sizes from ~ 0.05 to ~ 70 μm after SPD and after annealing at 1000 °C, respectively.

  2. 2.

    The results show that the value of the grain growth exponent, n, increased with increasing annealing temperature. In addition, the value of the grain growth activation energy, Q, is equal to ~ 440 kJ mol−1 which is a significant value by comparison with other conventional alloys. The results suggest a general Hall–Petch relationship of the form YS = 508D−0.5 + 183 for the CoCrFeNiMn HEA over a wide range of grain sizes from the ultrafine (< 1 μm) to coarse grained (> 100 μm).

  3. 3.

    The results suggest that there is a critical grain size of ~ 2 µm at which the total elongation decreases significantly due to a suppression of the activation of deformation-induced twinning as a useful deformation mechanism together with slip to improve the mechanical properties. A model is proposed to determine the optimum grain size by controlling the temperature and time of annealing in the range of fine grain sizes in order to benefit from the advantages of deformation-induced twining in the CoCrFeNiMn HEA.