2.1. Carbon Doping—CoCrFeMnNi

Two studies have determined the critical resolved shear stress (CRSS) of single crystals of equiatomic, single-phase f.c.c. CoCrFeMnNi. Patriarca et al. ^[1] determined the CRSS at 77 and 273 K to be 175 MPa and 70 MPa, respectively, from compression tests on (591)-oriented single crystals. Later, Abuzaid and Sehitoglu ^[2] determined the CRSS for several crystal orientations under tension at 77 and 293 K to be 145–172 MPa and 53–60 MPa, respectively. Thus far, there have been no studies on similar HEAs containing interstitials.

There have been a number of studies looking at grain-size strengthening in cast, cold-rolled, and recrystallized polycrystalline equiatomic CoCrFeMnNi. Otto et al. ^[3] determined σ_y as a function of grain size for equiatomic single-phase f.c.c. CoCrFeMnNi at temperatures from 77 to 1073 K, see Table 1 and Table 2. Note that only three grain sizes were tested (4.4, 50, 155 µm) at each temperature with the reported results being the average of two tensile tests performed at each condition. k was found to decrease gradually from 538 MPa·µm^−1/2 at 77 K to 425 MPa·µm^−1/2 at 473 K, was independent of temperature from 473 K to 873 K, and then decreased rapidly to 127 MPa·µm^−1/2 at 1073 K, see Figure 1. In contrast, σ₀ decreased rapidly from 310 MPa at 77 K to 125 MPa at 293 K, but then decreased more slowly to 43 MPa at 873 K, see Figure 2.

Figure 1. Graph of Hall–Petch parameter, k, versus temperature for undoped equiatomic CoCrFeMnNi, data from ^[3][4][5]; and for 1 at. % C-doped CoCrFeMnNi from Stepanov et al. ^[6].

Interestingly, Otto et al. ^[3] reported a higher σ₀ value of 69 MPa at 1073 K than at 673 K or 873 K. This does not indicate an error in measurements; σ_y for the largest grain-sized material always decreased with increasing temperature, and was 93 MPa, 79 MPa and 74 MPa at 673, 873 and 1073 K, respectively. In fact, the higher value of σ₀ at 1073 K compared to 673 K and 873 K simply reflects the lower value of k at that temperature.

WHR showed a similar dependence on temperature. At 77 K, the WHR was independent of grain size at ~1725 MPa. The WHR decreased continuously with increasing temperature. At room temperature the two largest grain-sized (50 µm, 155 µm) HEA showed a slightly higher WHR than the finest grain-sized (4.4 µm) material, i.e., ~1260 MPa versus ~1100 MPa. The finest grained HEA showed no work-hardening at 1073 K.

ε_f decreased continuously with increasing temperature for large-grained (155 µm) CoCrFeMnNi from 84% at 77 K to 20% at 1073 K, whereas the finest-grained (4.4 µm) material showed a decrease from 72% at 77 K to 32% at 673 K after which it increased up to 51% at 1073 K. ε_f appeared to be lowest for the finest grain size from 77 to 873 K, whereas fine-grained material showed double the ε_f (~50%) at 1073 K compared to the two coarser-grained materials. Room temperature specimens showed average ε_f values of 59% for the largest grain sizes (50 µm, 155 µm), and 51% for the finest-grained (4.4 µm) material. Deformation occurred by planar dislocation glide at low strains, but that (nano)twinning occurred at higher strains, leading to the high WHR and large observed ε_f values ^[3][10]. Deformation nanotwinning occurs at lower strains as the temperature is decreased ^10] (~7.4% at 77 K and ~25% at 293 K) since the critical stress for nanotwinning is reached at a lower strain ^[11].

Sun et al. ^[4] also determined the Hall–Petch behavior of equiatomic single-phase f.c.c. CoCrFeMnNi from 77 to 873 K. The cast material was hot-forged and either annealed (to produce coarse-grained material) or cold-rolled and recrystallized (to produce fine-grained material). As with Otto et al. ^[3], only three grain sizes were tested (0.65, 2.1 and 105 µm) at each temperature, but with only one test appearing to have been performed for each grain size. They found that k decreased roughly linearly from 645 MPa·µm^−1/2 at 77 K to 306 MPa·µm^−1/2 at 873 K, see Table 1 and Table 2, and Figure 1. It is worth noting that their k values were greater than those determined by Otto et al. ^[3] at all temperatures up to 673 K, but less at 873 K—they did not observe the plateau in k values from 473 to 873 K reported by Otto et al. ^[3]. One should be somewhat wary of ascribing too much significance to these differences in k between the two groups since, as noted earlier, changes in texture due to differences in processing conditions and small changes in interstitial content (even in these undoped HEA) can each have large effects on its value.

Similar to the results of Otto et al. ^[3], Sun et al. ^[4] found that σ₀ decreased rapidly from 436 MPa at 77 K to 188 MPa at 293 K, but then decreased more slowly to 119 MPa at 873 K. Their σ₀ values were always significantly greater than those determined by Otto et al.  ^[3] at all temperatures, see Table 1 and Table 2, and Figure 2.

At 77 K, the WHR was significantly lower for the finest grain-sized (0.65 µm) HEA at 854 MPa compared to the two larger grain-sized (2.1 µm, 105 µm) HEAs at 1644 MPa and 1465 MPa, respectively. This grain size dependence of the WHR is even greater at 293 K, i.e., 287, 1115 and 1168 MPa. The value for the largest grain size at 293 K is similar to that calculated from Otto et al. ^[3]. Interestingly, the two finest grain sized (0.65 µm, 2.1 µm) materials showed no work-hardening at 873 K.

Sun et al. ^[4] found that ε_f decreased with increasing temperature for the two finer grain sizes e.g., from 41% at 77 K to 2% at 873 K for the 0.65 µm material, but for the coarsest-grained (105 µm) material ε_f decreased from 82% at 77 K to ~60% at 203 K after which it was constant up to 293–873 K. The coarser the grain size the greater the ε_f value at all temperatures, e.g., at room temperature ε_f was 27%, 33% and 60% for grain sizes of 0.65 µm, 2.1 µm and 105 µm, respectively.

Sun et al. ^[4] confirmed the earlier observations ^[3][10] that deformation occurs by a combination of dislocation motion and twinning at 77 K and 293 K. Twinning did not occur at higher temperatures, but dynamic recrystallization was observed at 873 K.

Recently, Liu et al. ^[5] determined the Hall–Petch behavior of equiatomic single-phase f.c.c. CoCrFeMnNi at room temperature only. The cast material was subsequently cold-rolled and recrystallized. They obtained values for σ₀ and k of 214 MPa and 394 MPa·μm^−1/2, respectively, see Table 1 and Figure 1 and Figure 2. We should note that in this study four different grain sizes were tested but they spanned less than an order of magnitude (3.9 µm, 10.8 µm, 20.5 mm and 30.1 µm) and only one test appears to have been performed for each grain size. Their room temperature value of σ₀ is almost identical to that obtained by Sun et al. ^[4], but their k value is less than that of both Sun et al. ^[4] and Otto et al. ^[3].

The WHR calculated from data in Figure 6 in Liu et al. ^[5] showed that the room temperature WHR was independent of grain size at 1100–1166 MPa.

ε_f also showed little grain size dependence but the finest grain size (3.9 µm) showed the lowest ε_f of 51% while the largest grain size (30.1 µm) showed the largest ε_f of 55%, with the intermediate grain-sized specimens (10.8 mm, 20.5 µm) showing an intermediate ε_f of 53%. The tensile specimens were produced from cold-rolled and annealed, recrystallized material. They showed that the HEA had considerable segregation both before and after the recrystallization anneals. Since the different grain sizes were produced by anneals at different temperatures (1073–1273 K), presumably the segregation varied for different grain sizes.

Earlier, Liu et al. ^[12] demonstrated a Hall–Petch relationship between the Vickers hardness and the grain size for equiatomic CoCrFeMnNi at 293 K and obtained a k value of 677 MPa·μm^−1/2, which is higher than the values obtained by Liu et al. ^[5] of 394 MPa·μm^−1/2, Otto et al. ^[3] of 494 MPa·μm^−1/2 and Sun et al. ^[4] of 586 MPa·μm^−1/2. The higher value may reflect that the Vickers hardness represents the flow stress at 8–10% strain rather than σ_y.

Stepanov et al. ^[5] determined σ_y as a function of grain size at 293 K for as-cast equiatomic CoCrFeMnNi containing (measured) 0.97 at. % C that was given a homogenization anneal, 80% cold-rolled and annealed at temperatures from 873 to 1373 K. Specimens annealed at temperatures ≥973 K were fully recrystallized and occasionally contained a very small volume fraction (≤0.2%) of M₂₃C₆ particles within grains that would likely have had a negligible effect on the mechanical properties. They compared their Hall–Petch plot to that of Otto et al. ^[3] at the same temperature for C-free CoCrFeMnNi. They performed three tensile tests on each of four grain sizes, i.e., 1.4, 4.9, 12 and 69.7 µm. We should note that the finest-grained material (1.4 µm), which was annealed at 700 °C, had a very inhomogeneous grain structure consisting of regions of very fine grains and regions of much coarser grains (Figure 5b in their paper). This resulted in the σ_y values for this material showing a very large scatter, i.e., the average σ_y was 1070 MPa, but the individual values were 1010, 1050 and 1150 MPa ^[13].

The carbon addition increased the room temperature value of k, from 394 to 586 MPa·μm^−1/2 (measured by ^[3][4][5]) to 935 MPa·μm^−1/2. Thus, carbon has a strong effect on the Hall–Petch slope, see Figure 1. The carbon addition more than doubled the room temperature σ₀ from the 125 MPa determined by Otto et al. ^[3] to 288 MPa, a strengthening effect due to carbon of 168 MPa/at. % C. If, however, we compare the σ₀ value from Stepanov et al. ^[6] with the lattice friction value from Sun et al. ^[4] of 218 MPa, the strengthening effect due to carbon is only 72 MPa/at. % C, see Figure 2. It is worth noting that although there were a few particles present in the carbon-doped CoCrFeMnNi, Stepanov et al. ^[6] noted that their wide separation meant that they contributed little to the strength.

The WHR calculated from Table 1 in Stepanov et al. ^[6] suggests a grain size dependence, i.e., 1131, 1170 and 1408 MPa for 4.9, 12 and 69.7 µm grain-sized HEAs. The large scatter of σ_y values for the fine-grained (1.4 µm) material makes calculating the WHR problematic for this grain size, see above.

Stepanov et al. ^[6] found a very large grain-size dependence for ε_f with it increasing from 14% for 1.4 µm grains to 37% for 4.9 µm grains, to 48% for 12 µm grains, to 66% for 69.7 µm grains, a trend similar to that noted by Sun et al. ^[4]. The lowest ε_f value was less than any value recorded by Sun et al. ^[4], Otto et al. ^[3] or Liu et al. ^[5]—a feature that may be related to the inhomogeneous microstructure of the finest grained material noted above—but the largest ε_f had been observed by some of these other workers. The carbon appears to result in a greater dislocation density and fewer twins than in the undoped alloys, a feature that the authors ascribed to an increase in the stacking fault energy (SFE): ab initio quantum-mechanical calculations indeed indicate that carbon increases the SFE of CoCrFeMnNi ^[14].

There have been a number of studies where carbon has been added to large-grained equiatomic CoCrFeMnNi to assess its strengthening effect. Wu et al. ^[7] examined the effect of adding 0.5 at. % C on the strength at both 77 K and 293 K of large-grained (115 µm) CoCrFeMnNi that was given a homogenization anneal, cold-rolled and recrystallized and compared their results to those of Otto et al. ^[3]. The 0.5 at. % C increased σ_y from 165 to 225 MPa at 293 K and from 350 to 510 MPa at 77 K, that is a strengthening effect due to C of 120 MPa/at. % C at 293 K and a much larger value at 320 MPa/at. % C at 77 K, see Table 2. The carbon addition decreased the ε_f at both temperatures from ~85% to 69 % at 77 K, and from ~60 % to 38 % at 293 K.

The WHR, calculated from data in Table 1 in Wu et al. ^[7], showed that carbon increased the WHR substantially (compared to data in Otto et al.^[3]) at both 77 K and 293 K to 1868 MPa (33% increase) and 1842 MPa (57% increase), respectively. The authors suggested that the increased WHR was due to the earlier onset of deformation twinning than in the undoped HEA, as suggested by electron backscattered diffraction images. This is in sharp contrast to the transmission electron microscope observations of Stepanov et al., who reported the opposite effect of carbon ^[6].

Chen et al. ^[8] found the (measured) 1.1 at. % C that they added to as-cast large-grained (110 µm—the authors did not state the grain size, thus, this value was obtained using the linear intercept method to estimate the grain size from Figure 10a of their paper) CoCrFeMnNi increased σ_y from 250 to 310 MPa, while also slightly increasing ε_f from 52% to 60%, see Table 2. Interestingly, the WHR did not show any effect of carbon with a value of 908–919 MPa, which is slightly lower than the values reported for large-grained undoped CoCrFeMnNi reported above. Note that the strength of their undoped CoCrFeMnNi was comparable to those reported by Otto et al. ^[3], Sun et al. ^[4] and Liu et al. ^[5], for coarser-grained materials. Chen et al.’s ^[8] carbon-doped CoCrFeMnNi had significant segregation of the carbon to interdendritic regions in the columnar grain structure—note that most other researchers gave cast material a homogenization anneal, and sometimes cold-rolling followed by a recrystallization anneal. The observed strengthening due to carbon was only 55 MPa/at. % C. This lower value than those observed by Stepanov et al. ^[6] and Wu et al. ^[7] may be because of differences in grain size between Chen et al.’s ^[8] undoped and C-doped material. Similar to Wu et al. ^[7], Chen et al. ^[8] found that the carbon addition led to a greater extent of deformation twinning.

Li ^[9] looked at the effects of different carbon contents (0.25, 0.53, 0.9 at. %, measured by wet chemical analysis after casting) on the room-temperature mechanical properties of equiatomic CoCrFeMnNi at 293 K, which were found to be large elongated 200 µm-wide single-phase f.c.c. grains upon casting. After hot-rolling and a homogenization anneal at 1473 K, 200 µm equi-axed grains were also present. The elemental distribution after the latter treatment was homogeneous whereas it was inhomogeneous upon casting. They tested three specimens for each condition. Surprisingly, σ_y of both the as-cast and thermo-mechanically-treated CoCrFeMnNi was ~200 MPa irrespective of carbon content, i.e., there appeared to be no solid solution strengthening from the carbon, or heat treatment, see Table 2.

In contrast, increasing the carbon content appeared to slightly increase the WHR for both the as-cast and thermo-mechanically-treated CoCrFeMnNi ( ^[9]) from 829 MPa for 0.25 at. % C to 878 MPa for 0.53 at. % C to 1022 MPa for 0.9 at. % C for the as-cast HEA, and from 1108 MPa for 0.25 at. % C to 1103 MPa for 0.53 at. % C to 1284 MPa for 0.9 at. % C for the thermo-mechanically treated HEA. Note that the thermo-mechanically-treated CoCrFeMnNi had a higher WHR than the as-cast HEA for the same carbon content. However, it is worth noting that these values are all low compared to those reported by other researchers.

The carbon content and heat treatment also had little effect on ε_f (44–51%); as noted by others, deformation at low strains was due to dislocation slip whereas twinning occurred at higher strains; the twinning density decreased as the carbon content increased, an effect ascribed to an increase in the SFE. These HEAs were also subjected to cold-rolling and annealing after which they had higher σ_y values with reduced ε_f for the larger carbon contents. It is not possible to assess the effects of interstitial carbon in the latter specimens since nanocarbides were present, and either the grain size was substantially reduced (4.5 µm) for the 0.2 at. % HEA, or they were not fully recrystallized for the larger carbon contents.

Li ^[9] noted that deformation occurred initially by dislocation motion but that at larger strains deformation twinning occurred. He noted that for the same strain, the deformation nano-twin density decreased with increasing carbon content due to the increase in stacking fault energy, the same observation as Stepanov et al. ^[7].

It is worth noting that when equiatomic CoCrFeMnNi with high carbon contents (0.5–2 at. %) are subject to cold-rolling followed by recrystallization, large volume fractions of carbides are often present as well as changes in grain size. The carbide’s effect on the mechanical properties in addition to the reduction in solute strengthening from the reduction in carbon in solution ^{[15][16][17][18][19]} make it infeasible to determine the solid-solution strengthening effect of the carbon. CoCrFeMnNi with very high carbon contents (2.2–8.9 at. %) show large volume fractions of carbides even upon casting ^[8]^[20], but can still show very good ε_f values.

Cheng et al. ^[21] added both titanium and carbon simultaneously to equiatomic CoCrFeMnNi making it impossible to determine the individual elemental contributions to the strength. Similarly, Klimova et al. ^[22] added both aluminum and carbon simultaneously to equiatomic CoCrFeMnNi, again making it impossible to determine the individual elemental contributions to the strength.

Klimova et al. ^[23] examined the effect of three different (measured) carbon levels (0.53, 0.95 and 2.11 at. %) on the strength of as-cast, large-grained (150–200 µm) non-equiatomic CoCrFeMnNi, i.e., CoCr_0.25FeMnNi, at both 77 K and 293 K: only the highest carbon level was reported to contain particles (<1 vol. %). Note that the undoped HEA tested for comparison contains a small amount of carbon (0.03 at. %). At least three specimens were tested for each composition. The carbon addition led to a linear increase in lattice parameter measured at room temperature from 0.3590 nm with no carbon to 0.3613 nm with 2.11 at. % C, a lattice parameter increase of 1.1 pm/at. % C or a lattice strain (= Δa/(Δc × a), were a is the lattice parameter and Δc is amount of interstitial) of 0.30 per at. % C. A linear increase in σ_y due to the carbon was found at both temperatures from 315 MPa with no carbon to 605 MPa with 2.11 at. % C at 77 K, and from 185 MPa with no carbon to 320 MPa with 2.11 at. % C at 293 K, see Figure 3a. These represent strengthening effects of 137 MPa/at. % C at 77 K and 64 MPa/at. % C at 293 K. It is worth noting that σ_y for CoCr_0.25FeMnNi ^[23] is similar to the values reported at both 77 K and 293 K for equiatomic CoCrFeMnNi ^[7][8][9].

Figure 3. (a) Yield stress (σ_y) and work-hardening rate (WHR) for CoCr_0.25FeMnNi at 77 K and 293 K. (b) Elongation to failure (ε_f) for CoCr_0.25FeMnNi at 77 K and 293 K. Data from Klimova et al. ^[23].

The carbon addition produced a higher WHR (calculated from data in Table 2 ^[23]) at both temperatures, i.e., from 1376 to 1394 MPa for 0 and 0.53 at. % C to 1521 MPa for 0.95 at. % C at 77 K; and from 912 MPa for the undoped HEA, to 1105 MPa for 0.53 at. % C to 1255 MPa for 0.95 at. % C at 293 K, see Figure 3a. The values of WHR for CoCr_0.25FeMnNi are comparable to those for equiatomic CoCrFeMnNi noted above. Unlike the equiatomic CoCrFeMnNi, CoCr_0.25FeMnNi did not exhibit any signs of deformation twinning even at 77 K, but greater planarity of slip was observed at 77 K.

ε_f decreased slightly with increasing carbon content at both temperatures, e.g., at 293 K from 64% with no carbon to 53% for 2.11 at. % carbon, see Figure 3b.

2.8. Hydrogen Doping

Using an electrolytic technique, Luo et al. ^[44] introduced 8.01 wt. p.p.m. hydrogen into equiatomic CoCrFeMnNi that was cast, hot-rolled, given a homogenization anneal, cold rolled and recrystallized. Energy dispersive spectroscopy in a scanning electron microscope showed no large-scale segregation of elements. Interestingly, the hydrogen produced no change in σ_y, and very modest increases in both ε_f and the ultimate tensile strength. The hydrogen was reported to increase deformation nano-twinning density.