Revisiting the role of prestrain history in the mechanical properties of ultrafine-grained CoCrFeMnNi high-entropy alloy

Abstract

The yield strength of face-centered cubic (FCC) alloy is always insufficient for applications. In this work, different prestrain histories were imposed to improve the yield strength and strain-hardening capability of an ultrafine-grained (UFG) CoCrFeMnNi high-entropy alloy (HEA). In contrast to the specimens prestrained at 293 K, the specimens prestrained at 77 K possess higher yield strength, elongation, and strain-hardening capability, which were intensely related to the formation of deformation twins. The cryogenic strengthening magnitude is found to be strongly associated with the grain size, but slightly affected by dislocations. By modulating the prestrain history, an ultrahigh yield strength of 1.84 GPa and a considerable uniform elongation of 13% were achieved at 77 K in the CoCrFeMnNi HEA. Hence, imposing prestrain on HEAs at 77 K could be an efficient strategy to harmonize the mechanical properties of the FCC HEAs, which would enrich the application of HEAs in cryogenic fields.

Full text

Materials Science and Engineering A 801 (2021) 140398, https://doi.org/10.1016/j.msea.2020.140398
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Revisiting the role of prestrain history in the mechanical properties of
ultrafine-grained CoCrFeMnNi high-entropy alloy
S.J. Sun a, b, Y.Z. Tian c, d,*, H.R. Lin a, b, Z.J. Wang e, Z.F. Zhang a, b **
a Shi-changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
b School of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China
c Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), School of Materials Science and Engineering, Northeastern
University, Shenyang 110819, China
d Research Center for Metal Wires, Northeastern University, Shenyang 110819, China
e State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China
Abstract
The yield strength of face-centered cubic (FCC) alloy is always insufficient for applications. In this work, different
prestrain histories were imposed to improve the yield strength and strain-hardening capability of an ultrafine-grained
(UFG) CoCrFeMnNi high-entropy alloy (HEA). In contrast to the specimens prestrained at 293 K, the specimens
prestrained at 77 K possess higher yield strength, elongation, and strain-hardening capability, which were intensely
related to the formation of deformation twins. The cryogenic strengthening magnitude is found to be strongly associated
with the grain size, but slightly affected by dislocations. By modulating the prestrain history, an ultrahigh yield strength
of 1.84 GPa and a considerable uniform elongation of 13% were achieved at 77 K in the CoCrFeMnNi HEA. Hence,
imposing prestrain on HEAs at 77 K could be an efficient strategy to harmonize the mechanical properties of the FCC
HEAs, which would enrich the application of HEAs in cryogenic fields.
Keywords: High-entropy alloy; Prestrain; Deformation twins; Cryogenic strengthening; Yield strength
* Corresponding authors
E-mail addresses: tianyanzhong@mail.neu.edu.cn (Y.Z. Tian), zhfzhang@imr.ac.cn (Z.F. Zhang).
1. Introduction
In contrast to the conventional alloys with a principal element, high-entropy alloys (HEAs), also known as multi-
principal-element alloys (MPEAs) or complex concentrated alloys (CCAs), usually contain multiple principal elements
[1-6]. The equiatomic or near-equiatomic compositions in HEAs maximize the configuration entropy, which generally
results in the formation of single-phase microstructure [7-10]. Among these HEAs, single-phase HEAs with face-
centered cubic (FCC) structure were widely investigated because of their outstanding properties, such as the irradiation
resistance, corrosion resistance and mechanical performance especially at cryogenic temperature [11-15]. In particular,
there is no ductile-to-brittle (DTB) transition during the deformation process of HEAs and medium-entropy alloys
(MEAs) at cryogenic temperature, which usually occurs in ferritic, martensitic and duplex stainless steels [14, 16-23].
The superior cryogenic mechanical properties of the HEAs or MEAs are mainly due to the deformation twins, which
introduce new interfaces and decrease the mean free path of dislocations, as referred as the dynamic Hall-Petch effect
[16]. However, deformation twins are difficult to occur at room temperature due to the insufficient flow stress to
approach the critical twinning stress [16, 24, 25]. In contrast, when the deformation temperature decreases to the liquid
nitrogen temperature, the flow stress increases dramatically to activate deformation twins, and multiple deformation
mechanisms including dislocations, stacking faults and deformation twins were activated during the deformation process,
resulting in the simultaneous improvement of strength and ductility [24]. Jo et al. designed a HEA with partially
recrystallized microstructures containing retained deformation twins, which exhibited ultra-high strength at liquid
nitrogen temperature [23]. Furthermore, in CoCrNi MEA with lower stacking fault energy (SFE) relative to
CoCrFeMnNi HEA, the twinning stress could be reached at lower strains, which results in an extended strain-hardening
range, leading to much more excellent mechanical properties compared to CoCrFeMnNi HEA [26]. Albeit the dramatic

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temperature dependence of mechanical properties of HEAs, the intrinsic mechanisms for enhanced yield strength (σYS)
and strain-hardening behavior at cryogenic temperature is unclear.
Besides the deformation temperature, grain size can also influence the deformation mechanisms especially the
twinning capability. Our previous study on the ultrafine-grained (UFG) CoCrFeMnNi HEA indicates that deformation
twins and dislocations could be activated at liquid nitrogen temperature, while only dislocations could be captured at
room temperature during tensile tests [24]. In this case, an UFG CoCrFeMnNi HEA was chosen as model material and
different prestrains at 293 K and 77 K were applied to introduce distinct defects. Then the roles of dislocations and
deformation twins in the cryogenic strengthening effect were clarified by comparing tensile properties at 293 K and 77
K. We aimed to unveil the roles of prestored dislocations and twins in the yield strength and subsequent strain-hardening
capability, and achieve a superior balance of strength and ductility to extend the cryogenic applications of HEAs.
2. Experimental method
2.1. Starting material
A bulk CoCrFeMnNi HEA ingot with 110 mm in diameter and 90 mm in height was fabricated using magnetic
levitation melting technique with the starting elemental metals (>99.7% wt%). The bulk ingot was homogenized at 1373
K for 2 h. Then the ingot was hot forged at 1273 K and cold rolled to sheets with 1 mm in thickness at room temperature.
Details about the casting and manufacture procedures can be found in the earlier work [27]. The original specimens
(defined as ORI) were obtained by annealing the cold-rolling sheets for 5 minutes at 998 K.
2.2. Mechanical testing
Tensile specimens with rectangular dog-bone shape (gauge dimensions, 10×2×1 mm) were cut from the recrystallized
sheets, and the tensile loading direction was parallel to the rolling direction. The specimens were mechanically ground
using 400-2000 grid sized fine sandpapers before the tensile tests. One group of specimens were firstly stretched to
specific plastic strains (10% and 20%) at room temperature, then unloaded. The other group of specimens were stretched
to specific plastic strains (10%, 20% and 30%) at liquid nitrogen temperature, then unloaded. All prestrain tests were
conducted on an Instron 5982 testing machine with a strain rate of 10-3 s-1. The sample code and the corresponding
processing states were also listed in Table 1. After the prestrained tests, all the specimens were ground afresh using the
SiC paper. At room temperature, the strains could be measured with an extensometer attached to the tensile specimens.
At liquid nitrogen temperature, the extensometer could not be used, so strains had to be determined from the crosshead
displacement. However, the displacement of the crosshead is typically larger than the real strains. In this work, we
calculated the difference between the extensometer and crosshead displacements at room temperature and assumed the
same difference at liquid nitrogen temperature. The strains at both temperatures were corrected by the difference.
Furthermore, the elongations of specimens after fracture were calculated using the change in spacing of the indents with
10 mm initial interval, and they showed good agreement with the above corrected strains. The tensile tests were
conducted on the testing machine with a strain rate of 10-3 s-1 at 293 K and 77 K until fracture. During the cryogenic
tests, the specimens were firstly immersed in the liquid nitrogen for about 5 minutes and the tests were performed on
the specimens immersed in the liquid nitrogen. Several tests for each condition were conducted to ensure the
reproducibility of the experiments.
Table 1. Sample code and processing states.
Sample code
Processing states
ORI
Fully recrystallized UFG specimens
PL1
ORI prestrained to strain of 10% and unloaded at 77 K
PL2
ORI prestrained to strain of 20% and unloaded at 77 K
PL3
ORI prestrained to strain of 30% and unloaded at 77 K
PR1
ORI prestrained to strain of 10% and unloaded at 293 K
PR2
ORI prestrained to strain of 20% and unloaded at 293 K
2.3. Microstructure characterization

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The prestrained specimens were characterized by electron backscattering diffraction (EBSD), electron channeling
contrast imaging (ECCI) and transmission electron microscopy (TEM). The microstructural and crystallographic
information were obtained by an EBSD system equipped on a field emission scanning electron microscope (FE-SEM,
JSM 7100F). An accelerated voltage of 20 kV, a working distance of ~15 mm and a step size of 40 nm were used to
acquire the EBSD data. The TSL OIM Analysis 7 software was used to analyze the ESBD data. The microstructures of
the specimens were characterized by the ECCI technique conducted on a LEO Supra 35 FE-SEM, and a working distance
of ~6 mm was used to acquire the ECCI images. TEM analyses were conducted on an FEI Tecnai F20 with an accelerated
voltage of 200 kV. The specimens for EBSD and ECCI characterization were prepared by electropolishing at 30 V using
an electrolyte consisting of 90 vol% ethanol and 10 vol% perchloric acid at room temperature. Thin foils for TEM
characterization were prepared by twin-jet electropolishing method in the above-mentioned solution at 253 K under a
working voltage of 20 V.
3. Results and discussions
3.1. Original microstructure of the UFG specimen
Fig. 1 shows the typical microstructure of the ORI specimen. The observation plane is the rolling direction-normal
direction plane (RD-ND). The ECCI image and grain orientation map show that the equiaxed grains containing
annealing twins distribute homogeneously, and the inverse pole figure (IPF) inset shows the maximum pole density
value is 2.1, which indicates that the crystallographic orientation is nearly random and the texture is weak. The average
grain size determined by the linear intercept method is about 0.65 μm by counting high-angle grain boundaries including
twin boundaries.
Fig.1. Typical microstructure of the ORI CoCrFeMnNi HEA. (a) ECCI image, (b) grain orientation map. The color code used for grain orientation
map is IPF coloring-Z inserted in the upper right corner in Fig.1 (b).
3.2. Mechanical behavior of prestrained HEAs
Various prestrain levels (strain of 10%, 20% and 30%) were applied to ORI HEA specimens at 293 K (simplified as
PR1 and PR2) and 77 K (PL1, PL2 and PL3), respectively, as given in Fig. 2(a), which also exhibited promising
experimental reproducibility. Figs. 2(b) and (c) show the uniaxial tensile engineering stress-strain curves of the ORI and
prestrained HEAs at 293 K and 77 K, respectively. It is found that the yield point phenomenon occurred at both
temperatures, as shown in Fig. 1(a). The recrystallized UFG grains are clean inside and contain nearly no dislocations.
In that case, high stress is required to activate dislocations, then a lower stress is enough to glide these activated
dislocations, exhibiting the yield point phenomenon. [28, 29]. The yield strength (σYS) and uniform elongation (εUE) are
summarized in Fig.3. Compared to the ORI specimen, the prestrain has led to significant increases in σYS of the HEAs,
but slight decreases in εUE, as shown in Fig. 2 and Fig. 3. With the increase of applied prestrain level, the σYS increases
and the εUE decreases at both temperatures. Furthermore, for the PR specimens, the σYS increases slowly with the increase
of prestrain levels, which shows weak sensitivity to the prestrain levels. For the PL specimens, the σYS increases sharply
with the increase of prestrain levels, which shows strong sensitivity to the prestrain levels. When the deformation
temperature decreases from 293 K to 77 K, the strength, ductility, as well as the strain-hardening ability increase
remarkably. It is found that the PL specimens exhibit higher strength and ductility relative to the PR specimens with the
same prestrain level, as discussed in the previous work [28]. The PL3 specimen exhibits striking properties with an

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ultrahigh σYS of 1.84 GPa and a εUE of 13% at 77 K, which are even better than the partially recrystallized CoCrFeMnNi
HEA [30]. For the engineering structural materials, the σYS is a critical value that limits the utmost stress that can be
loaded on a material without bringing about the plastic deformation. It can be seen easily that σYS could be enhanced
efficiently through managing prestrain on the HEAs. Hence, modifying the prestrain history and building advanced
defect architecture could be an efficient way to design high strength HEAs used as cryogenic components.
Fig. 2. (a) Tensile stress-strain curves of the ORI HEA prestrained to various amounts of strain at 293 K (named as PR1 and PR2) and 77 K (named
as PL1, PL2 and PL3), (b) tensile stress-strain curves of the ORI, PR and PL specimens at 293 K, (c) tensile stress-strain curves of the ORI, PR
and PL specimens at 77 K.
Fig. 4 shows the cryogenic strengthening magnitude of the ORI and prestrained specimens, which was calculated by
the following equation:
     (1)
where σYS,77 K and σYS,293 K are the yield strengths of specimens at 77 K and 293 K, respectively. For the PR specimens,
ΔσYS increases slightly after imposing higher prestrain, indicating that the strength enhancement due to temperature
effect is insensitive to the imposed prestrain at 293 K. In contrast, ΔσYS increases dramatically after imposing prestrain
at 77 K. These results indicate that the prestrain history can be crucial for the cryogenic strengthening effect. In fact,
this cryogenic strengthening phenomenon has been frequently detected in HEAs, twinning-induced plasticity (TWIP)
steels and Cu-Al alloys [20, 31-33], but the intrinsic mechanism for the cryogenic strengthening magnitude is still
unclear. It is thus desired to characterize the microstructures of the prestrained specimens to explore evidences that
induce different cryogenic strengthening effects.
Fig. 3. Plots of yield strength (σYS) and uniform elongation (εUE) of ORI and prestrained HEAs: (a) σYS for ORI and PR specimens, (b) σYS for ORI
and PL specimens, (c) εUE for ORI and PR specimens and (d) εUE for ORI and PL specimens.

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Fig. 4. The cryogenic strengthening magnitude ΔσYS for PR and PL specimens with different prestrain histories.
3.3. Microstructures of the HEAs with different prestrain histories
It is particularly found that the variations in dislocations and deformation twins in the prestrained specimens interfere
the ΔσYS, and examining the density of dislocations and deformation twins are insightful to understand the mechanism
of the cryogenic strengthening in the prestrained CoCrFeMnNi HEA. Plastic deformation involves many dislocations
in the microstructures of polycrystalline materials, and the dislocations usually consist of geometrically-necessary
dislocations (GNDs) and statistically-stored dislocations (SSDs) [34-36]. Generally, the density of SSDs with a net-zero
Burgers vector is irrelevant to the characteristics of the microstructures, while the density of GNDs with a non-zero
accumulated Burgers vector is dependent on the microstructural characteristics, such as grain size, texture and phase
[35, 37]. Therefore, the variations of the dislocations in the ORI and prestrained specimens could be regarded as the
variations of the GNDs. The density of the GNDs could be estimated through the EBSD misorientation calculated by
the following equation [38, 39]:
 
 (2)
where β is a constant determined by the type of dislocation boundaries, θ is the average misorientation within a certain
distance Δx, and b is the Burgers vector.
Fig. 5. EBSD results of kernel average misorientation (KAM) maps of the prestrained HEAs: (a) PL1, (b) PL2, (c) PL3, (d) PR1 and (e) PR2; (f)
KAM value distributions of the prestrained HEAs, and the enlarged misorientation curve of the prestrained HEAs are displayed in the inset.
The average misorientation θ in the above Eq. (2) is usually referred as the kernel average misorientation (KAM),
which quantifies the average misorientation around a kernel point with respect to the next-nearest neighbors. The KAM
maps and corresponding peak values of the prestrained HEAs are shown in Fig. 5. With increasing the prestrain level,
the KAM values increase obviously, and the density of the GNDs would be enhanced, as calculated by Eq. (2). It is also
found that the KAM values in PL specimens are slightly higher relative to the PR specimens at the same prestrain level.
High KAM values were observed near the grain boundaries, which indicates that more GNDs were accumulated near
the grain boundaries during the plastic deformation. The average KAM values and the GNDs densities of the prestrained

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specimens were obtained through analyzing the EBSD data, as shown in Fig. 6. For the prestrained specimens, with the
increase of the prestrain level, the density of the GNDs raises evidently. It is worth noting that the density of GNDs in
PR specimens is only slightly lower than that in the PL specimens with the same prestrain level. This could be resulted
from the low SFE of CoCrFeMnNi HEA, which inhibits dislocation recovery even at 293 K. Hence, coupling with the
fact that the significant cryogenic strengthening in PL HEAs relative to the PR HEAs, while they had roughly the same
density of GNDs, we deduced that the density of GNDs did not contribute notably to the ΔσYS. Therefore, other factors
including deformation twins may contribute significantly to ΔσYS in the PL specimens.
Fig. 6. EBSD results of (a) average KAM value and (b) geometrically necessary dislocations (GND) density of the prestrained HEAs.
Fig. 7. Typical microstructures of the PR HEAs: (a), (b) ECCI and TEM images of the PR1 HEA. (c), (d) ECCI and TEM images of the PR2 HEA.
Fig. 8. Typical microstructures of the PL HEAs: (a), (b) ECCI and TEM images of the PL1 HEA. (c), (d) ECCI and TEM images of the PL2 HEA.
(e), (f) ECCI and TEM images of the PL3 HEA.

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Fig. 7 and Fig. 8 present microstructures in the PR and PL specimens, respectively. The interactions of the dislocations
were captured in the PR HEAs, but no deformation twins were detected, as shown in Fig. 7. It is also found that the
quantity of the dislocations accumulated in grains and annealing twins raises evidently with the increase of the prestrain
level, which is consistent with the above-mentioned density of GNDs. The absence of deformation twins can be related
to the constrained twinning capability with grain refinement [25]. These results substantiate that the dislocations are the
main deformation modes in the UFG HEA, which is consistent with the reported work [24]. In contrast, the ECCI and
TEM images in Fig. 8 reveal that deformation twins were activated in the PL specimens, as indicated by the arrows, and
the fraction of deformation twins raises with the increase of the prestrain level. The interaction between dislocations and
deformation twins were captured, and more twinning systems were activated with increasing prestrain level, as shown
in Fig. 8b, c and d. The volume fraction (f) of the deformation twins was calculated through measuring the average twin
width (t) and mean twin spacing (λ) in the TEM images using the method [17, 40]:
  



 (3)
The calculated volume fraction is shown in Fig. 9. Furthermore, the volume fraction was also evaluated by counting
the area fraction of deformation twins in the ECCI images as reported by Luo and Huang [41], which is consistent with
the calculated values. With increasing the prestrain level, both the average twin width and the fraction increase, and the
mean twin spacing decreases, as shown in Fig. 9. In addition, with the increase of prestrain level, more twinning systems
from one system in PL1 HEA to three systems in PL3 HEA were activated, as shown in the high-resolution TEM in Fig.
10. The fine twins could become obstacles for hindering dislocation slip, which is similar to the effect of grain
boundaries that lead to the Hall-Petch strengthening effect [42]. Hence, the σYS increases sharply with the increase of
prestrain levels in PL specimens, which shows sensitive to the prestrain levels. In contrast, the σYS increases slowly with
the increase of prestrain levels in PR specimens because only dislocations were introduced in the microstructures of
specimens prestrained at room temperature.
Fig. 9. (a) Average twin width and mean twin spacing of the deformation twins, (b) the volume fraction of deformation twins in the PL
specimens.
Fig. 10. High-revolution TEM images for the PL specimens: (a) PL1 HEA, twinning occurring in one system, (b) PL2 HEA, twinning occurring
in two systems, (c) PL3 HEA, twinning occurring in three systems.

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3.4. Cryogenic strengthening magnitude
Fig. 11. Plots of the cryogenic strengthening magnitude against grain size for various FCC alloys [16, 19, 21-23, 26, 43, 49-52].
Considering the significant difference of ΔσYS of the PR and PL specimens, as shown in Fig. 4, the roles of dislocations
and deformation twins were considered and discussed as follows. For the ORI specimen without dislocations and
deformation twins, the yield strength could be calculated by the following empirical equation [43]:
     (4)
where d is grain size in micrometer, T is the temperature in Kelvin. Therefore, the ΔσYS for ORI specimens resulted from
the grain boundaries (σg) and friction stress (σ0) is about 370 MPa, which is determined directly by experimental results.
In the prestrained HEAs with dislocations and deformation twins, the σYS could be written as:
      (5)
where σ0, σg, σρ and σT are the contribution of friction stress, grain boundaries, prestored dislocations and deformation
twins, respectively. Here the contribution of dislocations can be expressed by the classical Taylor relation [44]:
  (6)
where M is the Taylor factor, α is a geometric constant, G is shear modulus, b is Burgers vector and ρ is dislocation
density. Usually, the contribution of the deformation twins to the strength could be calculated as following equation [24,
45]:
 (7)
where f is the fraction of deformation twins, λ is the mean spacing of the deformation twins, and K is the Hall-Petch
constant for twinning, which is several times of the Hall-Petch constant for slip (K=CkS, where C is a constant) [46].
For the PR specimens with only dislocations, the grain boundaries and dislocations contribute to σYS, and ΔσYS can
be written as below:
      (8)
With decreasing the temperature from 293 K to 77 K, b changes very slightly and can be supposed to be a constant.
Thus, a combined equation for ΔσYS in PR specimens through the Eqs. (6) and (8) gives
     (9)
Here the shear modulus G of CoCrFeMnNi HEA increases slightly as the temperature decreases from 293 K to 77 K
[47, 48]. Hence, the enhanced ΔσYS in PR specimens with increasing the prestrain level results from the increasingly
stored dislocations. But the limited magnitude is induced by the weak dependence of G on temperature.
For the PL specimens with dislocations and deformation twins, combining Eqs. (5), (6) and (7), the ΔσYS can be
expressed as below:
         (10)

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The first two items on the right-hand side of the above equation approximately equal to the two items on the right-
hand side of Eq. (9) due to the roughly same density of dislocations. The Hall-Petch constant for twinning (K=CkS) in
the last item has a strong temperature dependence [43], so it would amplify the strengthening effect caused by
deformation twins in the PL specimens. In summary, introducing more boundaries in the microstructures would lead to
the superior cryogenic strengthening magnitude. In this connection, we plot the difference in the normalized yield
strength (σYS/G) between two temperatures as a function of grain size, as shown in Fig. 11. Data of typical FCC metals,
i.e. copper and aluminum, were also included. Datum points of the CoCrFeMnNi HEA were schematically fitted for
clarification. It is found that ΔσYS increases remarkably with grain refinement.
3.5. Strain-hardening capability of the prestrained HEAs
Fig. 12 shows true stress-strain and strain-hardening curves for the typical PL2 and PR2 HEAs after tensile tests at
293 K and 77 K. It is well known that materials would be necking when strain-hardening rate Θ is equal to true stress
σ, which is described as the Considère’s criterion [53, 54]. The true stress-strain curves and strain-hardening curves
before necking points for each state are shown in Fig. 12. At the same deformation temperature, the strain-hardening
rate of the PL2 is higher than that of PR2 HEAs. At 293 K, PR2 HEA suffers early necking while PL2 HEA possesses
promising ductility, indicating that the prestrain history can be critical for the optimization of strength and ductility [28].
At 77 K, both PR2 and PL2 exhibit ultrahigh σYS of ~1.5GPa along with high εUE of ~0.2, as shown in Fig. 12(a). For
the strain-hardening behavior, it is found that the strain-hardening rate of PL2 HEA is higher than PR2 HEA at 293 K
and 77 K, indicating that imposing prestrain at 77 K is benefinical for the mechanical property optimization. It is noted
that the strain-hardening rate at 77 K is apparently higher than 293 K, as shown in Fig. 12(b). Such a high strain-
hardening ability at 77 K is largely related to the deforamtion twins activated at cryogenic temperature. It is reported
that the twins are very effective in enhancing strain-hardening rate of alloys, such as Mg alloys and TWIP steels, which
results in the hump in strain-hardening curve [32, 55, 56]. Furthermore, lowering the temperature would facilitate the
suppression of dynamic recovery and promote the dislocation storage, which could enhance the work hardening ability
[55, 57]. During the plastic deformation process, the dislocations could be dissociated when interacting with twin
boundaries, which could avoid excessive stress concentration due to piling-up of dislocation, allowing the materials to
deform with retaining ductility [58].
Fig. 12. (a) Typical true stress-strain and (b) strain-hardening curves for PL2 and PR2 HEAs at 293 K and 77 K. The necking points for each
state were indicated in (a).
Generally, the dislocation evolution resulted from the plastic strain could be calculated by the Orowan equation [53]:
 
 (11)
where ρgen is the density of dislocations, γp is the shear strain, k is a correction parameter, b is the Burger vector, and l is
an average distance that dislocations travel, as referred as the mean free path. When grain and twin boundaries are
considered as the main barriers for dislocation slip, l could be calculated by the following equation [59]:



 (12)
where d is the grain size and λ is the twin spacing.

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Substituting Eq. (12) into Eq. (11) gives
 
 

 (13)
Eq. (12) indicates that the mean free path would be reduced with introducing deformation twins in the grains. As a
result, ρgen increases as calculated by Eq. (13), which would improve the strength. Furthermore, the interactions of
dislocations and deformation twins afford room for storing dislocations efficiently, which would facilitate pronounced
strain-hardening capability [60].
A comparison of the σYS and εUE of the prestrained HEAs with those of reported HEAs is shown in Fig. 13. Although
FCC HEAs are soft, σYS could be enhanced by introducing various defects, i.e. dislocations and deformation twins
through prestrain. It is clear that modulating prestrain history brings a superior balance of σYS and εUE in CoCrFeMnNi
HEA. To our knowledge, the cryogenic σYS of 1.84 GPa and εUE of 13% in PL3 HEA are particularly noteworthy, and
such high cryogenic σYS surpassed those of the existing CoCrFeMnNi HEAs, as shown in Fig. 13(b). Furthermore, the
strength and ductility balance also shows superiority in contrast to other HEAs and MEAs. These results indicate that
the strength and ductility of HEAs can be harmonized by modulating the prestrain history, providing a simple but
efficient strategy to process HEAs for potential applications in cryogenic fields.
Fig. 13. Plot of σYS and εUE for CoCrFeMnNi HEAs at (a) 293 K and (b) 77 K in this work. Data of other HEAs and MEAs as reported in the
previous work [14, 16-18, 20-23, 26, 30, 31, 43, 61-64].
4. Conclusions
Fully recrystallized UFG HEA (ORI) with an average grain size of 0.65 μm was obtained by cold rolling and annealing
treatment. ORI specimens were tensioned to specified strains at 293 K and 77 K and unloaded to obtain PR and PL
specimens. ORI, PR and PL specimens were further tensioned at 293 K and 77 K to investigate the mechanical behavior.
The following conclusions were drawn:
(1) Dislocation features were captured in the PR specimens. In the PL specimens, both dislocations and deformation
twins were stored.
(2) The dependence of cryogenic strengthening magnitude (ΔσYS=σYS,77K-σYS,293K) on prestrain level shows distinct
features in the PR and PL specimens. ΔσYS rose slightly with increasing the prestrain level in the PR specimens,
which was induced by the weak dependence of G on temperature in the dislocation strengthening effect. ΔσYS rose
dramatically with increasing the prestrain level in the PL specimens, which was attributed to the twin boundary
strengthening effect via the remarkable change of Hall-Petch slope with temperature.
(3) Cryogenic strengthening magnitude (ΔσYS=σYS,77K-σYS,293K) is found to be negatively correlated with the grain size
in various FCC alloys.
(4) In contrast to the PR specimens, the PL specimens exhibit superior mechanical properties at 293 K and 77 K due to
the introduction of deformation twins, which reduce the mean free path of dislocations and contribute significantly
to the strength and strain-hardening capability.
(5) Modulating the microstructures by applying prestrain can lead to an ultrahigh σYS of 1.84 GPa and a considerable
εUE of 13% at 77 K in PL3 specimen.

Materials Science and Engineering A 801 (2021) 140398, https://doi.org/10.1016/j.msea.2020.140398
11
Acknowledgements
This work was financially supported by the Fundamental Research Funds for the Central Universities (No. N180204015), the fund
of the State Key Laboratory of Solidification Processing in NPU (No. SKLSP201922) and LiaoNing Revitalization Talents Program
(No. XLYC1808027). S.J. Sun, Y.Z. Tian and Z.F. Zhang acknowledge the support of the Chinese Academy of Sciences (CAS) and
Japan Society for the Promotion of Science (JSPS) through the Bilateral Program (No. GJHZ1774). The authors also thank Prof. N.
Tsuji for valuable discussions.
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