Minor solute addition effects—Al in FeCoNiCrMn HEA

Tsai et al.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} reported the impact of Al addition in a HEA matrix. Elevated-temperature creep measurements on Fe₂₀Co₂₀Ni₂₀Cr₂₀Mn₂₀ (FeCoNiCrMn) and Fe₁₈Co₁₈Ni₂₀Cr₁₈Mn₁₈Al₈ (FeCoNiCrMn-Al) HEAs using nanoindentation in the temperature range of 300–600°C were conducted. FeCoNiCoMn and FeCoNiCoMn-Al exhibit fcc structure and fcc + bcc structure, respectively. Figure 1a–b present the relationship between creep displacement (h) and creep holding time (t) of FeCoNiCrMn and FeCoNiCrMn-Al HEAs, respectively. The strain rate (${\rm{\dot{\varepsilon }}}$) as a function of creep time period, t, can be obtained based on ${\rm{\dot{\varepsilon }}} = {1 \over h}{{dh} \over {dt}}$, as shown in Figure 1c–d.

Figure 1.

Representative creep displacement–creep holding time (h–t) curves for (a) FeCoNiCrMn {111} grains and (b) face-centered-cubic (fcc) {111} grains in dual-phase FeCoNiCrMn-Al. Representative creep strain rate–creep time period (${\rm{\dot{\varepsilon }}}-$t) curve for (c) FeCoNiCrMn {111} grains and (d) fcc {111} grains in dual-phase FeCoNiCrMn-Al.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18}

The work of Li et al. illustrates how the creep stress exponent (n) is equal to the inverse of the strain-rate sensitivity (m).^{Reference Li, Henshall, Hooper and Easterling25} For FeCoNiCrMn, the average stress exponent n values of the fcc {111} planes are 3.8 (m ∼ 0.263) in the temperature range of 400–600°C.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} With decreasing temperature, n shows a dramatic jump to 14 at room temperature. Similarly, for the fcc {111} grains in FeCoNiCrMn-Al, the average n value over 400–600°C is approximately 4.3 (m ∼ 0.233) and increases to approximately 5.0 at 300°C and about 14 at room temperature.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} The creep strength of the Al-modified Cantor alloy, FeCoNiCrMn-Al, is comparable to that in the standard Cantor alloy, suggesting that the solid-solution effect (only ∼4 at.% Al remaining in the fcc grains and remaining Al present in the bcc grains) is insignificant for the fcc {111} grains at elevated temperatures.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} In the temperature range of 400–600°C, the stress exponent n is approximately 4 ± 1 (or m ∼ 0.25) for both of FeCoNiCrMn and FeCoNiCrMn-Al, suggesting possible climb-controlled dislocation creep.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} Creep is a thermally activated process, and the creep activation energy, Q _c, is linked to the activation energy for vacancy diffusion. The creep activation volume V _c for the fcc {111} grains in these two HEAs reaches approximately 140 ų at 600°C, which is larger than the typical activation volume of 50–100 ų for Ni-based alloys.^{Reference Li, Henshall, Hooper and Easterling25–Reference Knezevic, Schneider and Landier29}

In traditional dilute alloys, dislocation climb is controlled by vacancy diffusion, which involves a simple one-to-one atom–vacancy exchange. In HEAs, however, the lattice is distorted because of the different sizes as well as the chemistry of the constituent atoms. A vacancy is surrounded by various constituent elements, and vacancy–element exchange during diffusion is more complicated, involving the cooperative motion of several atoms in order to maintain compositional portioning.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} This collective atomic motion would certainly expand the activation volume to that larger than a single atom. Kim et al.^{Reference Kim, Jeong, Park, Park, Na and Choi30} reported that a solute drag effect occurs at low strain rates and at high temperatures, and the rate-controlling deformation mechanism is in relation to Al atoms. The estimated values of σ_break,^{Reference Friedel31} which represents the critical stresses for the breakaway of dislocations from the Al solute environment, are 25.5 and 14.5 MPa at 1023 and 1323 K, respectively.^{Reference Kim, Jeong, Park, Park, Na and Choi30} For equiatomic CoCrFeMnNi, Cr holds the largest size factor e _i (=(r _i-r _average)/r _average, where r _i and r _average represent the particular atom radius and the average radius), equal to 1.46 × 10^–2, among the five constituents.^{Reference Kim, Jeong, Park, Park, Na and Choi30} Thus, Cr is most likely to form the solute atmosphere around the dislocations. The σ_break of the Cr element is about 32× smaller than those of Al_0.5CoCrFeMnNi. Figure 2a–b

Figure 2.

Log Z-log (σ_0.6/E) plots at ε = 0.6 for (a) Al_0.5CoCrFeMnNi and (b) CoCrFeMnNi.^{Reference Kim, Jeong, Park, Park, Na and Choi30,Reference Jeong, Park, Park, Na and Kim32} Solute drag creep is dominant at very low strain rates in CoCrFeMnNi, but hardly contributes to hot deformation at the typical strain rate range for hot metal working, unlike Al_0.5CoCrFeMnNi. Note: σ_break, breakaway stress; Q _c, activation energy; Z, Zener–Hollomon parameter; σ_0.6, stress at a strain of 0.6; E, Young’s modulus; n, creep stress exponent.

^{Reference Kim, Jeong, Park, Park, Na and Choi30,Reference Jeong, Park, Park, Na and Kim32} show the solute drag creep becoming dominant at very low strain rates in CoCrFeMnNi, and hardly contributing to hot deformation in the typical strain rate range for hot metal working, unlike Al_0.5CoCrFeMnNi.^{Reference Kim, Jeong, Park, Park, Na and Choi30}

Structure effects

Ma et al.^{Reference Ma, Feng, Debela, Peng and Zhang24} studied the strain-rate sensitivity, m, and activation volume, V _c, of a CoCrFeNiCu (zero Al, namely, Al-0) HEA thin film with a fcc structure and CoCrFeNiCuAl_2.5 (2.5 at.% Al, namely, Al-2.5) HEA thin film with a bcc structure at room temperature. Figure 3a shows the creep displacement as a function of loading rate (log scale) from 0.05 mN/s to 2.5 mN/s. In the Al-0 film, the creep displacement almost doubled from 11.8 nm to 21.8 nm with increasing loading rate.^{Reference Ma, Feng, Debela, Peng and Zhang24} However, the Al-2.5 film maintained a stable creep displacement from 0.05 mN/s to 2.5 mN/s.^{Reference Ma, Feng, Debela, Peng and Zhang24} It can be concluded that the creep of Al-0 film had a strong correlation with the loading rate. The higher the loading rate, the greater disparity of creep displacements between Al-0 and Al-2.5.

Figure 3.

(a) Creep displacement as a function of the loading rate (log scale) for Al-0 and Al-2.5 high-entropy alloy ([HEA] CoCrFeNiCu) films. The creep for the Al-0 film strongly correlates with the loading rate. The higher the loading rate, the greater disparity of creep displacements between Al-0 and Al-2.5 (b) Nanoindentation hardness versus equivalent strain rates (log scale) of the HEA films for calculation of strain-rate sensitivities. These values are typical for face-centered-cubic (fcc) and body-centered-cubic (bcc) nanocrystalline metals and in agreement with previous experimental studies. Note: m, strain-rate sensitivity.^{Reference Ma, Feng, Debela, Peng and Zhang24}

Figure 3b shows the relationship between hardness and equivalent strain rate (log scale) for the Al-0 and Al-2.5 films. The value of m can be deduced from the slope of the linear regression lines, yielding m = 0.035 for the fcc Al-0 and m = 0.0048 for the bcc Al-2.5.^{Reference Ma, Feng, Debela, Peng and Zhang24} These results for the two HEAs are typical for fcc and bcc nanocrystalline metals according to previous experimental studies. A high value of m is obtained in ductile metals, in which plastic deformation is relatively more nonlocalized (preventing necking or shear banding in crystalline or amorphous alloys).^{Reference Bhattacharyya, Singh, Eswar Prasad, Narasimhan and Ramamurty33} The activation volume for dislocation nucleation in HEA films can be estimated based on the strain-rate sensitivity and shear stress.^{Reference Woo, Huang, Ngan and Yu34} The activation volume obtained is 0.08 nm³ for Al-0 and 0.51 nm³ for Al-2.5.^{Reference Ma, Feng, Debela, Peng and Zhang24} The significant enlargement of the activation volume thus predicts a reduction in strain-rate sensitivity with the structure transition from fcc to bcc. However, the underlying mechanism for the distinction of the activation volumes between nanocrystalline fcc and bcc HEAs remains unknown and was outside of the scope of that study.^{Reference Ma, Feng, Debela, Peng and Zhang24}

In addition to well-known factors such as the film structure, alloy system, and grain size, creep response also appears to be strongly dependent on the thermal history of sample preparation. For example, with the fast cooling rate in sputtering, the inner structure of the as-deposited HEA films remains in the nonequilibrium state with higher residual stress.^{Reference Ma, Peng, Wen and Zhang19} With the aid of annealing, flaws, lattice distortion, and residual stress would be reduced, yielding a stable structure for creep behavior.^{Reference Ma, Peng, Wen and Zhang19}

Grain-size effects

Recently, nanocrystalline HEAs have been widely investigated for their high-strength and high-temperature mechanical behavior. Zou et al. reported that the Nb₂₅Ta₂₅Mo₂₅W₂₅ refractory HEA exhibits an extraordinarily high yield strength of greater than 5 GPa at temperatures of up to 600°C, using micro-compression tests; this is 5× higher than that of its single-crystal equivalent.^{Reference Zou, Wheeler, Ma, Okle and Spolenak35}

Lee et al. also reported another significant result for nanocrystalline FeCoNiCrMn HEA creep behavior where nanoindentation analysis was performed with a constant loading rate of 0.5 mN/s and held for 1000 s at different maximum loads.^{Reference Lee, Seok, Zhao, Choi, He, Lu, Suh, Ramamurty, Kawasaki, Langdon and Jang20} With high-pressure torsion (HPT) processing, the grain size was reduced from ∼46 μm (coarse grains [cgs]) for the as-cast state to ∼33 nm (nanocrystalline [nc]) after HPT processing. It was found that the creep stress exponent, n, extracted from the nanoindentation creep test was ∼3 for coarse grains, while n was ∼1 for nanocrystalline material, as shown in Figure 4a.^{Reference Lee, Seok, Zhao, Choi, He, Lu, Suh, Ramamurty, Kawasaki, Langdon and Jang20}

Figure 4.

(a) Relationship between quasi-steady-state (QSS) creep strain rate and stress; the slope corresponds to the creep stress exponent, n. n is extracted from the nanoindentation creep test and was ∼3 for coarse grains (cgs) and was ∼1 for nanocrystalline (nc) material. (b) Logarithmic strain rate versus linear stress relation to estimate the activation volume (V*) for creep. The results indicate a transition from the dislocation-controlled mechanism in the coarse-grain state to the diffusion-controlled mechanism in the nanocrystalline state.^{Reference Lee, Seok, Zhao, Choi, He, Lu, Suh, Ramamurty, Kawasaki, Langdon and Jang20} Note: d, grain size; H, hardness; C, constant factor, typically ∼3 for metals; ε_i, indentation strain rate; b, Burgers vector; HEA, high-entropy alloy.

The activation volumes were also extracted, presenting a value of 4.6 b ^{Reference Stepanov, Shaysultanov, Salishchev and Tikhonovsky3} (b is Burgers vector) for the coarse-grained structure, while the value was 0.8 b ^{Reference Stepanov, Shaysultanov, Salishchev and Tikhonovsky3} for the nanocrystalline structure (Figure 4b).^{Reference Lee, Seok, Zhao, Choi, He, Lu, Suh, Ramamurty, Kawasaki, Langdon and Jang20} The results indicate the transition from the dislocation-controlled mechanism in the coarse-grain state to the diffusion-controlled mechanism in the nanocrystalline state. Elevated temperature creep tests from room temperature to 300°C using the nanoindentation system were carried out by the same group using strain-rate jump tests with three different strain rates (0.025, 0.008, and 0.0025 s^–1),^{Reference Lee, Choi, Yang, Lu, Kawasaki, Ramamurty, Schwaiger and Jang22} presenting the activation enthalpy for different temperatures. With temperatures lower than 473 K, the activation enthalpy was about 0.5 eV, indicating that the deformation is controlled by grain-boundary-mediated dislocation activity.^{Reference Lee, Seok, Zhao, Choi, He, Lu, Suh, Ramamurty, Kawasaki, Langdon and Jang20} A significant increase in activation enthalpy to about 1.8 eV for temperatures higher than 473 K was observed.^{Reference Lee, Seok, Zhao, Choi, He, Lu, Suh, Ramamurty, Kawasaki, Langdon and Jang20} This was attributed to the enhancement of grain-boundary diffusion.

Yu et al.^{Reference Yu, Cheng, Zhang, Zhang, Jing, Ma, Liaw, Li and Liu36} reported a similar trend in the Al_0.1CoCrFeNi alloy at room temperature with a 400 μN/s loading rate, up to 4000 μN maximum load and holding for 10 s. With decreasing grain size, the strain-rate sensitivity increased, leading to a decrease in activation volume (Figure 5).^{Reference Yu, Cheng, Zhang, Zhang, Jing, Ma, Liaw, Li and Liu36} It should be noted that the sample was processed by HPT as well, leading to coarser grains in the middle and finer grains at the edge (r represents the distance from the center). The results indicate that the dominant mechanism of creep changes from dislocation slip to grain-boundary sliding, resulting in lower creep resistance with decreasing grain size.^{Reference Yu, Cheng, Zhang, Zhang, Jing, Ma, Liaw, Li and Liu36} However, nanocrystalline alloys have never been used at elevated temperatures because of their poor high-temperature strength and stability. Therefore, the development of thermally stable nanocrystalline systems that can retain high strengths over a wide temperature range are highly desirable for both scientific study and engineering applications.

Figure 5.

Dependence of ln t versus lnH for the Al_0.1CoCrFeNi alloy after high-pressure torsion at 6 GPa for N = 2, at different positions from the sample center (r). Coarser grains were located in the middle of the sample and finer grains were located at the edge of the sample. With decreasing grain size (increasing r), the strain-rate sensitivity increased, leading to a decrease in activation volume. The dominant creep mechanism changes from dislocation slip to grain-boundary sliding, resulting in lower creep resistance.^{Reference Yu, Cheng, Zhang, Zhang, Jing, Ma, Liaw, Li and Liu36} Note: H, hardness; t, time ; N, number of torsion for 360°; m, strain-rate sensitivity.

Orientation effects

The anisotropic behavior in elevated-temperature creep deformation is another important mechanical characteristic. To exploit this for potential applications, it is necessary to develop a predictive system that can model effects of crystallographic anisotropy on high-temperature creep deformation of such materials. Ghosh^{Reference Ghosh37} reported the simulation of anisotropic behavior and creep resistance of single-crystal Ni-based superalloys. Wen et al.^{Reference Wen, Zhang, Li, Yue and Gao38} also reported high-temperature creep testing on notched samples.

To enhance the efficiency of creep testing, elevated-temperature creep via nanoindentation provides an efficient and precise method for research. The nanoindentation probe interacts with the samples at localized regions of the grains, which are much larger than the area indented by the indentation tip. This can be essentially treated as creep testing of a single crystal, which means the influence of the grain boundary can be neglected. Because of this, the single-crystal creep behavior can be extracted from a polycrystalline sample, reducing the difficulty of sample preparation.

Tsai et al.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} reported the elevated-temperature creep of fcc {100} and {111} FeCoNiCrMn HEAs. The elastic modulus of FeCoNiCrMn dropped from 190 ± 7 for {111} to 166 ± 5 for {100}; the corresponding hardness decreased from 2.9 ± 0.2 to 2.4 ± 0.2 GPa, respectively, when compared to the room-temperature elastic modulus and hardness of {111} and {100} grains. This result is similar to that observed for pure Ni,^{Reference Hu, Zheng, Hu, He and Yue39} Ni-based superalloys,^{Reference Wen, Zhang, Li, Yue and Gao38} and a fcc FeCoNiCr^{Reference Wu, Gao and Bei40} and FeCoNiCrMn^{Reference Kireeva, Chumlyakov, Pobedennaya, Kuksgausen and Karaman41} HEA single crystal, in which the strength along the 〈111〉 orientation is stronger than that along 〈100〉.

For elevated temperature creep behavior, fcc {111} grains are stronger than fcc {100} grains. At 550°C, the creep displacement was 75 nm for the {100} grains, but only 60 nm for the {111} grains. The activation volumes for {100} at elevated temperatures are also higher than those for {111}, suggesting that the creep resistance of the fcc {111} grains is higher than that of the fcc {100} grains.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} Despite this difference between {111} and {100} grains, the creep mechanism of these fcc {111} and {100} grains was shown to be the same, as deduced from the similar stress exponent and activation energy (Figure 6).^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} Few reports have focused on orientation effects, besides this work, and further exploration is clearly needed. These results showcase one of the benefits of using nanoindentation for creep characterization in polycrystalline materials. The individual creep response from each crystalline orientation would not be possible with traditional creep testing on bulk samples.

Figure 6.

The dependence of ln(strain rate) versus 1/T for (a) {111} grains and (b) {100} grains in Fe₂₀Co₂₀Ni₂₀Cr₂₀Mn₂₀. The creep mechanism of these face-centered-cubic (fcc) {111} and {100} grains are the same, as deduced from the similar stress exponent and activation energy values.^{Reference Tsai, Huang, Lin, Liu, Liao, Jang, Song and Nieh18} Note: Q _c, activation energy; ${\rm{\dot{\varepsilon }}}$, strain rate; T, temperature.