Compressive creep behavior of an oxide-dispersion-strengthened CoCrFeMnNi high-entropy alloy

Author’s Accepted Manuscript Compressive creep behavior of an oxidedispersion-strengthened CoCrFeMnNi high-entropy alloy Ferdinand Dobeš, Hynek Hadraba, Zdeněk Chlup, Antonín Dlouhý, Monika Vilémová, Jiří Matějíček www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(18)30915-8 https://doi.org/10.1016/j.msea.2018.06.108 MSA36663

To appear in: Materials Science & Engineering A Received date: 19 April 2018 Revised date: 28 June 2018 Accepted date: 29 June 2018 Cite this article as: Ferdinand Dobeš, Hynek Hadraba, Zdeněk Chlup, Antonín Dlouhý, Monika Vilémová and Jiří Matějíček, Compressive creep behavior of an oxide-dispersion-strengthened CoCrFeMnNi high-entropy alloy, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2018.06.108 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Compressive creep behavior of an oxide-dispersion-strengthened CoCrFeMnNi high-entropy alloy Ferdinand Dobeš1*, Hynek Hadraba1*, Zdeněk Chlup1, Antonín Dlouhý1, Monika Vilémová2, Jiří Matějíček2 1

Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Žižkova 22,

616 62 Brno, Czech Republic 2

Institute of Plasma Physics, Academy of Sciences of the Czech Republic, Za Slovankou

1782/3, 182 00 Praha, Czech Republic *Corresponding author. E-mail address: [email protected]

Abstract Creep tests of two equiatomic CoCrFeMnNi alloys were conducted in the temperature range from 973 K to 1073 K. The alloys were prepared by milling blends of powders of pure elements in a planetary ball mill and compacting by the spark plasma technique. Two variants of the alloys were prepared: (i) without and (ii) with the dispersion of oxides. Creep resistance was substantially improved by the presence of oxides. Diffusion creep controlled by lattice diffusion was suggested as a possible mechanism at low stresses. The effective diffusion coefficient calculated for Nabarro-Herring creep was comparable to the lattice diffusion coefficient of Ni in the same high-entropy alloy. At high stresses, the creep behavior was characterized by the presence of a threshold stress invoked by oxide particles.

Keywords high-entropy alloy; oxide dispersion strengthened alloy; creep; mechanical alloying; powder metallurgy; spark plasma sintering

1. Introduction High configurational entropy solid solutions based on a mixture of multiple principal elements in roughly equal proportions have acquired considerable attention since the publication of seminal articles that anticipated their attractive properties [1, 2]. Thanks to their excellent mechanical properties, high entropy alloys (HEAs) represent a promising alternative structural material for a number of applications, e.g., vacuum vessels and the plasma-facing components of future fusion reactors [3]. The restricted diffusion because of local distortions in the crystal lattice may foster applications at elevated temperatures. The CoCrFeMnNi equiatomic quinary alloy is probably the only HEA with well-characterized diffusion of all the constituting elements [4]. On the other hand, the creep of this alloy was studied only to a limited extent: the behavior of nanocrystalline and coarse-grained CoCrFeMnNi HEAs was investigated in nanoindentation creep experiments at room temperature [5]. Excellent ductility in tensile testing at 873–1073 K (including superplastic elongations >600 %) was observed in a CoCrFeMnNi alloy processed by high-pressure torsion [6]. Tensile testing at 1023 K over strain rates from 10−4 to 10−1 s−1 indicated superplasticity associated with grain boundary sliding [7]. Two deformation regions were suggested on the basis of relatively quick tensile tests at temperatures ranging from 1023 to 1123 K [8]. In the high strain rate region, a dislocation-climb mechanism controlled by the diffusion of Ni was suggested. In the low strain rate region, the viscous glide of dislocations was proposed. Microstructural examinations revealed that various Mn and Cr-enriched precipitates were formed, especially in samples subjected to prolonged thermal exposure [8]. In the present work, we report results of creep tests at lower strain rates substantially below the strain rates applied in the above papers. At the same time, we would like to examine a capability of increasing the creep-resistance of a single-phase CoCrFeMnNi alloy by yttrium-rich nano-sized oxide particles.

2. Experimental The preparation of single-phase equiatomic CoCrFeMnNi alloy (designated as HEA-SP in what follows) was described in detail in a previous paper [9]. The preparation consisted of mechanical alloying by milling blends of powders of pure elements using a planetary ball mill. The fully homogenous powder was obtained after 24 h of milling. The oxide-dispersionstrengthened variant of the same alloy (hereafter, HEA-ODS) was prepared by adding O2 gas, Y and Ti to the blend during mechanical alloying. The amount of added Y, Ti and O2 was fixed to form approximately 0.3 wt. % of oxides in the alloyed powder. The milled powders

were compacted using the spark plasma technique at a temperature of 1423 K and pressure of 50 MPa with a dwell time of 5 min and a heating/cooling rate of 100 K/min. The composition of the studied alloys is given in Table I. Table I. Composition of the Alloys (at. %) Element

Co

Cr

Fe

Mn

Ni

Y

Ti

O

HEA-SP

19.24

19.82

22.25

19.59

18.89

0

0.03

0

HEA-ODS

19.05

19.57

22.46

19.41

18.39

0.12

0.40

0.42

The creep tests were performed in uniaxial compression mode on samples with a gauge length of 12 mm and a diameter of 5 mm. The samples were prepared by traveling wire electro-discharge machining and fine grinding of contact surfaces. The tests were performed under a constant load in a protective atmosphere of dry purified argon at temperatures of 973 K, 1023 K and 1073 K. The test temperature was held constant within ±1 K for each individual test. Changes in specimen length were measured using a linear variable displacement transducer. The samples were subjected to stepwise loading, where the load was changed after a steady creep rate was established for a given load. A significant amount of strain was allowed before a constant creep rate was registered after each loading step. Figure 1 shows two examples which document how the creep rate evolves with time after one loading increment. The instantaneous creep rate was obtained by a simple differentiation of two consecutively recorded strain points. The terminal values of the true stress and the creep rate, i.e., the true compressive strain rate, were evaluated for each step. The terminal value of the creep rate was found by linear fitting of the creep strain vs. time curve in the steady rate section.

-8

CREEP RATE (1/s)

3*10

1023 K HEA-SP, 13.3 MPa

-8

2*10

HEA-ODS, 29.5 MPa

-8

1*10

0 0

100

200

300

400

500

600

700

TIME (h) Fig. 1. Time dependence of the instantaneous creep rate at 1023 K for both studied alloys.

A transmission electron microscope (TEM) JEM-2100F (JEOL, Japan) was used for microstructural analyses. TEM samples were prepared from slices (~1 mm thick) cut from the creep specimens with a precision saw equipped with a SiC cutting blade. The slices were ground on both sides to a thickness of ~300 μm using SiC paper with a grit size of P500 and then by finer SiC paper (grit size P1000) to obtain foils of thickness ~120 μm. Round discs with a diameter of 3 mm were punched out of these foils and electropolished in a double jet polishing system using an electrolyte consisting of 95% acetic acid and 5% perchloric acid at a temperature of 12 °C and an applied voltage of 30 V. The TEM was operated at the accelerating voltage of 200 kV in scanning mode, and the diffraction contrast images were acquired by bright-field (BF) and high angular annual dark-field (HAADF) detectors.

3. Results The microstructure of as-received alloy HEA-SP was characterized by rather non-uniform equiaxial grains of size d = 0.8 μm (the median value was used for the characterization of the grain size) [9], see Fig. 2. This is substantially finer than the coarse dendritic microstructure obtained by other authors using an arc melting technique [1, 10]. Additionally, no preferable orientation was observed. A significantly finer microstructure (see Fig. 3) was found in the HEA-ODS, where uniform grains of mean size d = 0.4 μm resulted probably due to the grain boundary pinning effect of oxide nanoparticles. Energy-dispersive X-ray spectra and their

quantitative analyses confirmed the nearly equiatomic composition of the matrix containing Y2O3 precipitates enriched by Ti and other elements from the matrix [9].

Fig. 2. The grain structure of HEA-SP in the as-received state (up) and after creep at 1023 K for 767.5 h (down) visualized by EBSD SEM.

Fig. 3. The grain structure of HEA-ODS in the as-received state (up) and after creep at 1023 K for 1173 h (down) visualized by EBSD SEM.

Fig. 4. Dependence of the creep rate of the HEA-SP alloy on applied stress.

Fig. 5. Dependence of the creep rate of the HEA-ODS alloy on applied stress. The dependence of the creep rate,  , of the HEA-SP and HEA-ODS alloys on the applied stress,  , at the various temperatures is shown in Figs. 4 and 5, respectively, on a double logarithmic scale. The data were analyzed using the following empirical relation of the Arrhenius-type:  Q  ,  RT 

  An n exp  

(1)

where An is a material constant, n is the stress exponent, Q is the apparent activation energy for creep, R is the gas constant and T is the absolute temperature. The values of n and Q were determined from eq. (1) by multiple linear regression and by assuming that the stress exponent n is independent of the temperature. In the alloy without oxides, n is equal to

approximately 6.3, and the activation energies are 246 kJ/mol at temperatures between 973 K and 1023 K and 704 kJ/mol at temperatures between 1023 K and 1073 K. In the alloy with oxides, it is apparent that the data shown in Fig. 5 exhibit two distinct regions: In the low stress region, the stress exponent value is approximately 1.8, and the activation energy Q is 210 kJ/mol. In the high stress region, the stress exponent is 13.2, and the activation energy Q = 580 kJ/mol. A comparison of creep resistance of the alloy without and with oxides is given in Fig. 6 in terms of the ratio of stresses resulting in a given creep rate. The stress applied in the creep tests of the alloy with the oxides was divided by the corresponding stress for the alloy without oxides found by fitting the experimental data. The ratio increases with the decreasing creep rate. At low creep rates, i.e., in the range of interest from the viewpoint of application at elevated temperatures, the creep resistance is substantially improved by the presence of oxides. For creep rates below 10-8 s-1 the ratio decreases with the decreasing creep rate. This effect is probably connected with a difference in the grain size between the alloys, as will be discussed below. 4

STRESS RATIO HEA-ODS/HEA-SP

973 K 1023 K 1073 K

3

2

1

0 -10 10

10

-9

10

-8

10

-7

10

CREEP RATE (1/s)

-6

10

-5

10

-4

Fig. 6. Ratio of stress for producing a given creep rate in the HEA-ODS alloy to the analogous stress in the HEA-SP alloy.

4. Discussion

To characterize more closely the microstructural processes that may give rise to the observed macroscopic creep parameters n and Q, an attempt was made to evaluate an activation volume, V*, of the irreversible deformation events. The activation volume can be estimated as

  ln   V *  3kT   ,   T

(2)

where k is Boltzmann's constant. The above Fig. 4 can be redrawn in semilogarithmic coordinates, and the data subjected to a linear fit (see Fig. 7). The values of V* estimated in the HEA-SP alloy are displayed in Fig. 8 in terms of multiples of b 3 , where b is the Burgers vector length, b  2.55  1010 m. The values ranging from ~300 b 3 to ~800 b 3 are typical for a dislocation motion [11, 12]. For comparison, the activation volumes reported previously for the indentation creep of a high-entropy alloy of similar composition having two different grain sizes at room temperature are included in the figure. The combination of results from completely different experiments presents a quite consistent view of possible deformation mechanisms.

10

MINIMUM CREEP RATE (1/s)

10

10

10

10

-4

-5

-6

-7

-8

HEA-SP 973 K

10

1023 K

-9

1073 K

10

-10

0

20

40

60

80

100

APPLIED STRESS (MPa) Fig. 7. Dependence of the creep rate of the HEA-SP alloy on the applied stress in semilogarithmic coordinates.

1000

1073 K

3

ACTIVATION VOLUME (b )

1023 K 973 K

100

10

298 K, 46 m

1

298 K, 49 nm

This work Ref. [5]

10

100

1000

APPLIED STRESS (MPa) Fig. 8. Applied stress dependence of the estimated activation volume in the HEA-SP alloy. For comparison, the volumes found in the HEA alloy of the same composition at room temperature are given [5]. The dependence of the steady-state creep rate,  , of solids on the applied stress,  , is generally expressed by a relationship of the form [13]

ADGb  b         , kT  d   G  p

 

n

(3)

where D is the appropriate diffusion coefficient, G is the shear modulus, d is the grain size, p is the exponent of the inverse grain size, and A is a dimensionless constant. The value of the stress exponent observed in the HEA-ODS alloy at low applied stresses is close to the value n = 2 anticipated by Langdon [14] for grain boundary sliding in superplasticity. This mechanism was evidenced in the same-type of single-phased HEA alloy tested by tension at 873-1073 K [6]. Contrary to the present material, the alloy studied by Shahmir et al. was prepared by high-pressure torsion resulting in a grain size of ~ 10 nm. The grain size of the

present material of (~ 400 nm [9]) is substantially larger, and the potential strain rate of this mechanism (p = 2) is 1600 times slower. The elongation of the present material in the tensile test at 1073 K is rather moderate, ~ 9.3 % [9]. It seems, therefore, more likely that the origin of the low value of the exponent (n = 1.75) results from a superposition of the exponent observed at larger applied stresses and the exponent n = 1. This idea is tested in Fig. 9 by plotting creep rate vs. applied stress on linear axes. Two creep mechanisms are characterized by a linear dependence of their strain rate on the applied stress: diffusion creep and Harper-Dorn creep. Diffusion creep occurs either by diffusion through the crystalline lattice (Nabarro–Herring creep [15, 16]) or along the grain boundaries (Coble creep [17]). If both lattice and grain boundary diffusions are combined, the rate of diffusion creep is described by the following equation [18, 19]

 

28b 3 Deff , kTd 2

(4)

where Deff is the effective diffusion coefficient,

 66.8b DGB   2.4b DGB    DL 1  , Deff  DL 1  28d DL  d DL   

(5)

and DL and DGB are the diffusion coefficients in the lattice and along the grain boundaries, respectively. Using eq. (4), the effective diffusion coefficient can be calculated. The calculated values are compared with the measured values of the lattice diffusion coefficient [4] in Fig. 10. Though the respective temperature ranges do not overlap, the agreement between measured and calculated values is satisfactory. The lower slope of the fitted line, i.e., a lower activation energy, suggests that the grain boundary diffusion contributes to the effective diffusion coefficient in creep. The other mechanism characterized by a linear stress dependence of the strain rate is Harper-Dorn creep [20]. The rate of this mechanism should be independent of the grain size. In the HEA-SP alloy without oxide dispersion, a transition to the linear stress dependence (or generally speaking, to a region with a reduced stress exponent) was not unequivocally documented in the available stress range. It can, therefore, be concluded that the absence of this transition is due to the increased grain size of the alloy without oxide (d = 800 nm). The activity of the Harper-Dorn creep thus does not seem to be very probable.

The activation energies for lattice diffusion of individual elements in the CoCrFeMnNi alloy range from 288.4 kJ/mol (Mn) to 317.5 kJ/mol (Ni) [4]. These values are substantially lower than the activation energy of creep estimated in the temperature range from 1023 to 1073 K (704 kJ/mol). It should be emphasized that the measured activation energy of creep represents an apparent value only: a real value can be obtained if the phase composition is the same over the whole considered temperature range. As was shown recently, a single-phase solid solution of the equiatomic CoCrFeMnNi alloy remains unchanged after long-term annealing at 1173 K, but it is unstable after annealing at 973 K [21]. Relatively large blocky precipitates of a chromium-rich sigma phase were observed after such annealing. The present creep results suggest the appearance of the above instability even at a temperature of 1023 K. The high value of the apparent activation energy of creep in the temperature range from 1023 to 1073 K can then be ascribed to a relatively quick creep process in the single-phase lattice at 1073 K, which is in contrast to the more difficult deformation of a particle-strengthened matrix at 1023 K. This explanation is consistent with the schematic time–temperature– transformation diagram proposed in Ref. [21].

10*10

-9

HEA-ODS 973 K

MINIMUM CREEP RATE (1/s)

8*10

-9

1023 K 1073 K

6*10

4*10

2*10

-9

-9

-9

0 0

20

40

APPLIED STRESS (MPa)

60

Fig. 9. Applied stress dependence of the creep rate of the HEA-ODS alloy at low stresses in linear coordinates.

2

DIFFUSION COEFFICIENT D (m /s)

10

-15

Diffusion of Ni in CoCrFeMnNi [4]

10

10

10

-16

-17

-18

calculated from creep data

10

-19

0.0007

0.0008

0.0009

0.0010

0.0011

1/T (1/K) Fig. 10. Comparison of the diffusion coefficient of Ni in the CoCrFeMnNi with the diffusion coefficients estimated from the present data.

In more complex materials, particles of a second phase embedded in a matrix obstruct dislocation glide. In these materials, the stress controlling the dislocation velocity is reduced to an effective value obtained by subtracting the stress necessary for overcoming particles from the applied stress. Equation (3) is then replaced by [22]

ADGb  b      0   ,    kT  d   G  p

 

n

(6)

where  0 is the threshold stress induced by the particles. The analysis in the following section makes use of the above equations. It was shown in the previous paper [9] that the effect of the

added oxide dispersion on the shear modulus, G, was not significant (G = 133 GPa at 1073 K). It can also be supposed that the matrix diffusion coefficients in a material without and with oxide dispersion are the same. From the viewpoint of equations (3) and (6), the only difference between the studied materials consists of different grain sizes ( dSP = 0.8 m and

d ODS = 0.4 m in the alloy without oxide dispersion and with oxide dispersion, respectively). We can, therefore, simplify the above equations for the studied materials at a given temperature as follows:

SP  A n ,

(7)

p

ODS

 d  n  A SP     0  ,  dODS 

(8)

where A is a function of temperature. The value of the exponent p is dependent on the ratecontrolling mechanism, e.g., p = 0 in Harper-Dorn creep, p = 1 in grain boundary sliding in creep, p = 2 in Nabarro-Herring creep and p = 3 in Coble creep. Note that it is supposed that the parameters A and n have the same value in both the material without and with the oxide dispersion. From the viewpoint of this approach, the power n estimated in the alloy without oxides (and in the absence of the threshold stress) is the true stress exponent. The power determined in the alloy with oxides in the high stress region (i.e. 13.2, cf. Section 3) is the apparent stress exponent, nap . These stress exponents are related as

nap 

n    0 

(9)

The observed value of the activation energy in the alloy with oxides (580 kJ/mol) can be interpreted in the same way as an apparent value [22]  n  1T G   ln   nT  0   Qap     Q*  RT 1   G T    0  T    1 / RT   

(10)

where Q* is the true activation energy for the deformation process. The value of the threshold stress,  0 , is usually determined by the linear extrapolation method. In this procedure, the experimental data are plotted on linear axes, as 1/ n vs.  [23], and extrapolated to zero strain rate. With respect to the above equations (7) and (8), the procedure is modified as follows: The creep rate is normalized by the parameter A (found by

regression of the HEA-SP alloy at a given temperature) and by the relevant grain sizes and p    d   ODS ODS    plotted as   A  d SP  

1/ n

vs. the applied stress. An example of the procedure for p = 2 is

given in Fig. 11. To eliminate the contribution from the diffusional creep at lower stresses, only the results at applied stresses greater than approximately 60 MPa were included into the analysis. The resulting values of the threshold stress are slightly sensitive to the choice of the exponent p, see Fig. 12, and the standard deviations seem to prefer greater values of p. At low temperatures, the particle threshold stress may be identified with the Orowan stress. At high temperatures, dislocations can bypass particles by climbing. The existing models for this situation are based either on local or general climb [24]. An identification of the most realistic model corresponding to the estimated values of the threshold stress requires a detailed analysis of the microstructure, and this work is in progress. 80

p=2 973 K

60

1023 K 1073 K

40

20

0 0

40

80

120

APPLIED STRESS (MPa) Fig. 11. Example of the linearization of creep rate vs. applied stress dependence to obtain the threshold stress.

50

THRESHOLD STRESS (MPa)

40

30

20

10

0 0

1

2

3

EXPONENT p Fig. 12. Estimated values of the threshold stress as a function of the inverse grain size exponent p.

SEM backscatter electron images of studied alloys after creep are shown in Figs. 2 and 3. Grains size in both alloys remains essentially the same as that observed in as received alloys: grains of about 0.8 μm in diameter are observed in HEA-SP alloy while HEA-ODS alloy has a much finer grain size, on the order of 0.4 μm. The HAADF image in Fig. 13 shows a representative microstructure of the HEA-ODS alloy observed after 9 % of creep strain accumulated at 1073 K and 67 MPa. The three arrows in the STEM micrograph highlight typical locations in which oxide particles interact with a high-angle grain boundary (GB, location A), a low-angle dislocation boundary (LADB, location B) and individual dislocations (location C). All the three interaction types slow down the corresponding deformation kinetics, and thus, improve the creep resistance of the alloy. In particular, Zener pinning (location A) hinders GB migration and recrystallization [25], interactions with LADBs (location B) result in temperature-dependent threshold stresses [26],

and similarly, the pinning of dislocations on the departure side of the oxide particles (location C) contributes to high values of the stress exponent n [27].

Figure 13: STEM HAADF image of the microstructure formed during creep at 1073 K and 67 MPa, for an accumulated strain of 9 %. The arrows highlight three locations in which oxide particles interact with a GB (location A), a LADB (location B) and an individual dislocation (location C).

5. Conclusions

The creep of two equiatomic CoCrFeMnNi alloys was studied in the temperature range from 973 K to 1073 K. The alloys were prepared by a powder metallurgical route consisting of milling blends of powders of pure elements using a planetary ball mill and compacting by the spark plasma technique. Two variants of the alloy were prepared (i) without the dispersion of oxides and (ii) with the dispersion of oxides. The following conclusions regarding the creep resistance of both alloys can be drawn: 

The creep mechanism in the single-phase alloy without dispersion of oxides can be

characterized by the activation volume ranging from 300 to 800 b3. Such a range of values is typical for dislocation motion. 

In the alloy with oxides, two different stress exponents were observed: At low stresses,

the value is approximately 1.8, whereas at the high stress region, the stress exponent is 13.2. Diffusion creep controlled by lattice diffusion is suggested as a possible mechanism at low stresses. The effective diffusion coefficient calculated for Nabarro-Herring creep is

comparable with the measured values of the lattice diffusion coefficient of Ni in the same high-entropy alloy. 

At high stresses, the creep data of the alloy with the dispersion of oxides can be

rationalized by introducing an effective stress given as the difference of the applied stress and the threshold stress invoked by the presence of oxide particles. The value of the threshold stress  0 was determined by a modification of the linear extrapolation method that also included data obtained for the HEA-SP alloy without oxides.

Acknowledgements This work was financially supported by Czech Science Foundation project No. 17-23964S.

References

[1] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 375–377 (2004) 213–218. [2] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes, Adv. Eng. Mater. 6 (2004) 299–303. [3] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122 (2017) 448-511. [4] K.-Y. Tsai, M.-H. Tsai, J.-W. Yeh, Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys, Acta Mater. 61 (2013) 4887–4897. [5] D.-H. Lee, M.-Y. Seok, Y. Zhao, I.-Ch. Choi, J. He, Z. Lu, J.-Y. Suh, U. Ramamurty, M. Kawasaki, T. G. Langdon, J.-i. Jang, Spherical nanoindentation creep behavior of nanocrystalline and coarse-grained CoCrFeMnNi high-entropy alloys, Acta Mater. 109 (2016) 314-322. [6] H. Shahmir, J. He, Z. Lu, M. Kawasaki, T.G. Langdon, Evidence for superplasticity in a CoCrFeNiMn high-entropy alloy processed by high-pressure torsion, Mater. Sci. Eng. A 685 (2017) 342–348. [7] S.R. Reddy, S. Bapari, P.P. Bhattacharjee, A.H. Chokshi, Superplastic-like flow in a finegrained equiatomic CoCrFeMnNi high-entropy alloy, Materials Research Letters 5 (2017) 408-414.

[8] J.Y. He, C. Zhu, D.Q. Zhou, W.H. Liu, T.G. Nieh, Z.P. Lu, Steady state flow of the FeCoNiCrMn high entropy alloy at elevated temperatures, Intermetallics 55 (2014) 9-14. [9] H. Hadraba, Z. Chlup, A. Dlouhy, F. Dobes, P. Roupcova, M. Vilemova, J. Matejicek, Oxide dispersion strengthened CoCrFeNiMn high-entropy alloy, Mater. Sci. Eng. A 689 (2017) 252–256. [10] F. Otto, A. Dlouhý, C. Somsen, H. Bei, G. Eggeler, E.P. George, The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high entropy alloy, Acta Mater. 61 (2013) 5743–5755. [11] J.C.M. Li: Kinetics and dynamics in dislocation plasticity. In: A.R. Rosenfield, G.T. Hahn, A.L. Bement, Jr., R.I. Jaffee: Dislocation Dynamics, McGraw-Hill, 1968, p. 87-116. [12] N. Balasubramanian, J.C.M. Li: The Activation Areas for Creep Deformation. J. Mater. Sci. 5 (1970) 434-444. [13] T.G. Langdon, Dependence of creep rate on porosity, J. Amer. Ceram. Soc. 55 (1972) 630–631. [14] T.G. Langdon, A unified approach to grain boundary sliding in creep and superplasticity, Acta Metall. Mater. 42 (1994) 2437–2443. [15] F.R.N. Nabarro, Report of a Conference on Strength of Solids. The Physical Society, London, (1948) 75-90. [16] C. Herring, Diffusional viscosity of a polycrystalline solid, J. Appl. Phys. 21 (1950) 437. [17] R.L. Coble, A Model for Boundary Diffusion Controlled Creep in Polycrystalline Materials, J. Appl. Phys. 34 (1963) 1679-1682. [18] T.G. Langdon, F.A. Mohamed, A simple method of constructing an Ashby-type deformation mechanism map. J. Mater. Sci. 13 (1978) 1282-1290. [19] H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps, The Plasticity and Creep of Metals and Ceramics. Pergamon Press, Oxford, United Kingdom, 1982. [20] J. Harper, J.E. Dorn, Viscous creep of aluminum near its melting temperature, Acta Metall. 5 (1957) 654-665. [21] F. Otto, A. Dlouhý, K.G. Pradeep, M. Kubenova, D. Raabe, G. Eggeler, E.P. George, Decomposition of the single-phase high-entropy alloy CrMnFeCoNi after prolonged anneals at intermediate temperatures, Acta Mater. 112 (2016) 40-52. [22] Y. Li, T.G. Langdon, High strain rate superplasticity in metal matrix composites: The role of load transfer, Acta Mater. 46 (1998) 3937-3948. [23] R. Lagneborg, B. Bergman, The stress/creep rate behaviour of precipitation-hardened alloys, Metal Sci. 10 (1976) 20-28.

[24] M. Heilmaier, B. Reppich: Particle Threshold Stresses in High Temperature Yielding and Creep: A Critical Review. Creep Behavior of Advanced Materials for the 2lst Century. Edited by Rajiv S. Mishra, Amiya K. Mukhejee, and K. Linga Murty. The Minerals, Metals & Materials Society (1999) 267-281. [25] C.S. Smith, Grains, phases, and interphases: an interpretation of microstructure, Trans. Metall. Soc. AIME 175 (1948) 15-51. [26] T. Záležák, J. Svoboda, A. Dlouhý, High temperature dislocation processes in precipitation hardened crystals investigated by a 3D discrete dislocation dynamics, International Journal of Plasticity 97 (2017) 1-23. [27] J. Rösler, E. Arzt, A new model-based creep equation for dispersion strengthened materials, Acta Metall. Mater. 38 (1990) 671-683.