Severe Plastic Deformation of High-Entropy Alloys

Abstract

An overview of the severe plastic deformation (SPD) of high entropy alloys (HEAs) is given with a focus on microstructure and texture evolution, phase transformation, strength and ductility, superplasticity, and thermal stability. It combines the now well-established research area of SPD with that of a recently discovered new class of advanced materials. The peculiarities of HEAs in relation to SPD are shown, such as phase decomposition and reduced grain growth. This offers the possibility of producing ultra-hard HEA materials by SPD processes or by post-annealing and enables extremely high superplasticity at high strain rates. The effect of SPD on changing properties is demonstrated mainly for the prototypes fcc Cantor and bcc Senkov HEA, but few examples of more complex HEAs indicate the high research potential of these advanced materials in the field of nanoSPD.

Anomaly of room temperature microhardness of CrMnFeCoNi high-entropy alloy processed by high pressure torsion at room and liquid nitrogen temperature (open and filled symbols, respectively)

1. Introduction

The recently developed high-entropy alloys (HEAs) represent a new generation of single-phase multi-element (≥5) solid solution alloys with concentrations between 5 and 35 atomic percent of the individual elements.^1,2) The HEA design concept shifts the focus away from the corners of phase diagrams toward the middle, enabling compositions that go beyond the scope of traditional alloys and offer unprecedented properties, challenges, and opportunities for a variety of structural and functional applications. In some cases, due to the large number of constituent elements, the contribution of configurational entropy to the Gibbs free energy is high enough to suppress compound formation and phase separation. Among the wide variety of reported HEAs with simple crystal structures, such as face-centered cubic (fcc), body-centered cubic (bcc) and hexagonal close-packed (hcp), the most thoroughly investigated alloy is the quinary equiatomic fcc HEA CrMnFeCoNi,³⁾ often referred to as Cantor alloy. This alloy is stable as a fcc single-phase solid solution at high temperatures above about 1073 K, but decomposes into several different metallic and intermetallic phases during annealing at intermediate temperatures.^4–8) Application of hydrostatic pressure at room temperature (RT) transforms it to the hcp structure, see review.⁹⁾

In the fcc solid-solution state, HEAs exhibit certain noteworthy mechanical properties, including simultaneous strength and ductility increase with decreasing temperature leading to outstanding fracture toughness at cryogenic temperatures, e.g. see review.¹⁰⁾ At RT and below, above a certain stress (equivalently strain) in addition to dislocation slip mechanical twinning contributes to deformation due to a medium/low stacking fault energy (SFE).^11–13) Twinning is more pronounced at cryogenic temperatures and enhances ductility. Crystallographic texture is formed during deformation, but its intensity is quite low. The brass-type textures observed for different deformation modes are typical of medium/low SFE metals and alloys, see review.¹⁴⁾

Since the spurt in research activities pertaining to nano-technology, much interest has arisen in processes involving severe plastic deformation (SPD), e.g. see review.¹⁵⁾ This process has drawn considerable attention due to its potential to produce ultra-fine grained (ufg) or in some cases nanocrystalline (nc) materials in bulk form. It is well known by now that materials with such small grain sizes have extraordinary properties, such as simultaneous high strength and moderate ductility as well as the capability of superplastic forming. Therefore, they have a high potential for technical applications. As a result, it was tempting to also apply SPD to the advanced new alloys to further enhance their properties.

Therefore, the aim of the present work is to provide an overview on SPD of HEAs, with a focus on microstructure (sect. 2) and texture evolution (4), phase transformation (3), strength and ductility (5.1), superplasticity (5.2), and thermal stability (6). According to the available publications, sections 2–4, 5.1 cover RT and below, while sections 5.2 and 6 of cause cover higher temperatures, but again microstructure is addressed in terms of grain size. A current compilation of the publications covering SPD of HEAs is given by Edalati et al.¹⁶⁾ The compilation shows that most of the work relates to fcc HEAs, mainly the Cantor alloy, a small part to bcc and dual phase fcc + bcc, but not to hcp HEAs. The main SPD process applied is high pressure torsion (HPT). To present an overall picture of SPD of HEAs, here the extensive results reported for the Cantor HEA prototype are illustrated. Results for other HEAs are mentioned in context.

2. Microstructure Development

The development of the microstructure during SPD of the Cantor alloy is shown in Fig. 1 for HPT at RT and a nominal pressure of 7.8 GPa. With increasing shear strain, the initially coarse-grained (cg) structure refines and finally reaches a nc state. In addition to the main dislocation activity, deformation twinning also contributes to strain.⁵⁾ To investigate the microstructure of nc materials quantitatively, X-ray line profile (XRLP) analysis is the method of choice.^17,18) The results of the convolutional multiple whole profile (CMWP) procedure show that during HPT of the Cantor alloy a very fast refinement of the fcc microstructure takes place.^19,20) The crystallite size (⟨x⟩_area) at RT and liquid nitrogen temperature (LNT, 77 K) reaches a very low steady-state value of 24 nm after a shear strain of about 20 (Fig. 2(a)). Simultaneously, the dislocation density saturates at a high value of 3 × 10¹⁶ m⁻² (Fig. 2(b)). Surprisingly, it is lower at 77 K (10¹⁶ m⁻²). The dislocation character q at RT changes from near edge-type (q_edge = 1.4) to near screw-type (q_screw = 2.4) and then slightly decreases to 2, which is the saturation value at 77 K (Fig. 2(c)). The dipole character of the dislocation arrangement given by the parameter M is quite weak (M > 1) and at RT saturates at about 6 (Fig. 2(d)). It is even weaker at 77 K, M about twice as large. The twin density at RT reaches a maximum value of 2% at γ ≈ 20 (Fig. 2(e)) leading to a mean twin separation distance d_Tw smaller than the crystallite size ⟨x⟩_area for 10 < γ < 60 (Fig. 2(f)). As a result, twins are rarely seen by TEM in the steady-state nanostructure (Fig. 3(a)).⁵⁾ During HPT at 77 K instead of mechanical twinning a deformation-induced phase transformation from fcc to hcp is observed (Fig. 3(b)).²⁰⁾ There are clear diffraction peaks of the hcp phase ((100) and (101)) found in the TEM diffraction pattern. Unfortunately, the hcp diffraction spots cannot be selected separately to locally identify the hcp phase by dark-field imaging. However, in comparison with high resolution TEM images of cg CrCoNi and CrFeCoNi medium-entropy alloys (MEAs)^21,22) tensile tested at cryogenic temperatures showing hcp nano lamellae, the lamellar features observed in Fig. 3(b) may be reasonably attributed to the hcp phase. Further information on the fcc to hcp phase transformation during HPT of the Cantor alloy, particularly on the effect of hydrostatic pressure, can be found in sect. 3. The spotty TEM diffraction pattern for HPT at LNT in comparison to that at RT indicates that with decreasing temperature deformation becomes more heterogeneous. Qualitatively similar results for the microstructural development of the HPT deformed Cantor alloy have been reported by Heczel et al.²³⁾ (RT, 3 GPa) and Podolskiy et al.²⁴⁾ (RT and LNT, 6 GPa).

Fig. 1

Evolution of the microstructure with shear strain γ in the Cantor alloy during RT HPT (7.8 GPa) using backscatter electron imaging contrast. (a) Schematic diagram showing the viewing direction. (b) Undeformed cg initial structure of the cast alloy. (c) Deformation structure of the HPT disc for shear strains γ ≤ 2 with the dashed circle showing the center of the disc. (d) Deformation structure with multiple twinning systems after γ ≈ 2.4. (e) Fragmentation of the twinned structure at higher strains, γ ≈ 2.4. (f) Final saturation microstructure for γ ≈ 50.⁵⁾

Fig. 2

(a) Grain size ⟨x_area⟩, (b) dislocation density ρ, (c) dislocation character q, (d) dislocation arrangement parameter M, (e) twin density β and (f) average distance between adjacent twin boundaries d_Tw of the Cantor alloy versus shear strain γ for HPT at 7.8 GPa. Open and filled symbols refer to RT and 77 K, respectively.²⁰⁾

Fig. 3

Bright-field TEM images and corresponding diffraction patterns representing the microstructure in the steady state regime of the Cantor alloy after HPT at RT⁵⁾ (a) and LNT²⁰⁾ (b). At LNT 100 and 101 spots in inner and outer Debye-Scherrer ring belong to the hcp phase.

The drastic grain refinement in the Cantor alloy is correlated to the high mechanical twinning activity in the medium/low SFE (≈30 mJm^{−2 11–13)}) alloy. Based on TEM investigations a mechanism of fast grain refinement via primary and secondary twinning has been proposed by Wang et al.²⁵⁾ for brass. Primary twins by accumulation of a high density of dislocations evolve into curved high angle grain boundaries from which secondary twins are emitted. The emission of secondary twins further refines the grains and transforms the elongated grains into equiaxed nanograins. At a certain shear strain twinning ceases (Fig. 2(e)), may be because grain boundary sliding (GBS) takes over as the deformation mechanism. A supporting indication of GBS is texture weakening.^19,20) In addition to twinning, in CrFeCoNi MEA Wu et al.²⁶⁾ observed nanobands and attributed the significant grain refinement to concurrent nanoband subdivision and deformation twinning. Instead of mechanical twinning, during HPT at LNT a strain-induced phase transformation takes place. Nano hcp lamellae seem to have a similar effect on grain refinement as twin lamellae. Surprisingly, despite phase transformation and in particular the 220 K lower HPT temperature, the steady-state crystallite size in the fcc phase within the accuracy of measurement is not smaller and the dislocation density is not higher than after HPT at RT. Reasons for this finding may be: (i) recovery and grain growth, and/or (ii) back-transformation of part of the hcp phase to fcc during pressure release, heating up to RT, and storage at this temperature. All these processes depend on purity of the material, SFE, temperature and degree of deformation. Evidence for process (i) has been provided for pure metals HPT-deformed at cryogenic temperature (100 K),²⁷⁾ but also for Cr₂₆Mn₂₀Fe₂₀Co₂₀Ni₁₄ HPT deformed at LNT.²⁸⁾ This HEA has a low SFE (3.5 mJm⁻²) and a moderate melting temperature T_m = 1557 K. Thus, HPT at LNT (homologous temperature T/T_m = 0.05) leads to an increased stored energy of deformation promoting “self-annealing” at RT (T/T_m = 0.19).

It is surprising that the dislocation density after HPT at LNT is lower than that after HPT at RT. A plausible reason would be recovery during “self-annealing”, as was found for Cr₂₆Mn₂₀Fe₂₀Co₂₀Ni₁₄²⁸⁾ in combination with a lowering of the microhardness. However, the same effect has not been observed for the Cantor alloy.²⁴⁾ Therefore, it has been suggested, that the shear produced by the deformation-induced hcp phase formation leads to a reduction in strain due to dislocation slip and, thus, to a reduction in dislocation density in the fcc phase.

The medium/low SFE of the Cantor alloy leads to widely dissociated dislocations (screws: ≅4 nm, edges: ≅6 nm).¹²⁾ After relatively low compressive strains at LNT, dislocations with long screw segments and large kinks having mixed character are seen on the {111} planes suggesting that the mobilities of edge and screw dislocations are not significantly different.¹²⁾ Here, it is found that during HPT at RT and LNT with increasing shear strain the dislocation character q tends to become more screw-like, taking a value of q ≈ 2 at large shear strain. It is somewhat surprising that the steady-state dipole character of the dislocation arrangement given by the parameter M is weak at RT and becomes even weaker at LNT (RT: M ≈ 5; 77 K: M ≈ 12). This may be caused by the wide dislocation dissociation suppressing thermally activated edge dislocation climb and screw dislocation cross slip.

Refractory metal HEAs with near equiatomic concentrations crystallize in the bcc structure. In the cg state they are characterized by high strength at elevated temperatures.²⁹⁾ Compared to the very ductile cg fcc HEAs, only some of the cg bcc HEAs have a good RT ductility, in particular the HfNbTaTiZr HEA,³⁰⁾ often referred to as Senkov alloy. Juan et al.³¹⁾ reported a simultaneous increase of strength and ductility with decreasing grain size down to a few microns. To further increase the strength, this alloy was successfully processed by HPT at RT into a nc structure with a steady-state grain size below 100 nm, which is reached at a shear strain of about 40.^32,33) At small shear strains dislocation substructures and deformation twins ({332}⟨113⟩) are formed. Additionally, the deformation starts to localize into bands, in which the microstructure is significantly more refined than in the surrounding material. With increasing shear strain, the number of deformation bands increases until a homogeneous equiaxed nc grain structure is reached in the steady-state.

Recently, Raturi et al.³⁴⁾ deformed the non-equiatomic refractory HEA Mo₅Nb₃₅Ta₁₅V₁₀W₃₅ by HPT at RT and 7 GPa to a maximum shear strain of 50. The development of the microstructure was studied by electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and XRLP analysis. For shear strains up to 11 the microstructure is quite inhomogeneous consisting of slip and kink bands in soft and hard oriented grains, respectively. The slip bands are developed by slip activity on the {110}$\langle 1\bar{1}1\rangle $ slip system, while the kink bands are formed due to slip-induced lattice rotation about the ⟨110⟩ axis with activation of {112}$\langle 11\bar{1}\rangle $. At higher shear strains, continuous dynamic recrystallization leads to a homogeneous nc grain structure through conversion of low to high angle grain boundaries.

To investigate the effect of SPD by HPT on phase transformation and microstructural evolution of a dual-phase HEA, AlFeCoNiCu with 52 vol% of Al-rich bcc phase and 48 vol% of Cu-rich fcc phase was investigated by Mohammadi et al.³⁵⁾ Both phases show grain refinement to 31 nm by severe shear straining and exhibit diverse structural and microstructural features. The fcc phase transforms to an expanded form and accumulates numerous nanotwins and stacking faults, but the bcc phase transforms to a denser form and accumulates dislocations. None of the phases exhibit major phase transformations during plastic straining.

3. Phase Transformation

Severe plastic deformation induces phase transformations in HEAs, see review.³⁶⁾ These transformations include the decomposition of a single-phase solid solution to form second-phase nanoparticles, the formation of high-pressure phases, spinodal decomposition, disordering of ordered phases and amorphization.

In the Cantor alloy, a phase transformation from fcc to hcp under HPT was observed at RT and LNT, with the onset pressure decreasing with decreasing temperature.³⁷⁾ A lamellar structure is formed upon transformation along the {111} planes of the fcc parent phase. The orientation relationship (OR) found by EBSD is: (111)_fcc || (0001)_hcp and [101]_fcc || $[11\bar{2}0]_{\text{hcp}}$ (Shoji-Nishiyama OR). This martensitic transformation is quite heterogeneous yielding an inhomogeneous microstructure that eventually forms a grain-refined two-phase nanostructure. Only a small shear strain is necessary to transform the material to a high amount. In general, further straining only slightly increases the volume fraction.

Figures 4(a) and (b) depict the diffractograms for samples subjected to HPT under different pressures at RT and LNT, respectively, at a shear strain γ ≈ 100. As can be seen, at LNT the phase transformation occurs at all pressures applied, while at RT it is only present at the highest pressure of 10 GPa. The minor (100)_hcp reflection of the samples HPT-deformed at RT and 6 and 7.8 GPa stems from stacking faults in the fcc structure resulting from the dissociation of 1/2⟨110⟩ dislocations into 1/6⟨112⟩ partials. These stacking faults represent hcp layers of atomic thickness. The thin layers lead to the absence of the (101)_hcp peak due to the infinite broadening of peaks with (00l)_hcp components. The volume fraction of the hcp phase increases with pressure with the onset pressure decreasing with decreasing temperature from about 8 GPa at RT to about 3 GPa at LNT (Fig. 5(a)). It should be mentioned that even at LNT and a pressure of 7.8 GPa additional shearing is needed to promote the martensitic transformation.³⁷⁾

Fig. 4

X-ray diffractograms of the Cantor alloy after HPT under different pressures at RT (a) and LNT (b).³⁷⁾

Fig. 5

(a) Volume fraction of the martensitic phase in the Cantor alloy versus pressure at a shear strain γ ≈ 100. The symbols represent different series of HPT samples, for which the phase composition was measured after the number of months indicated. (b) Reverse phase transformation of hcp to fcc during RT storage at ambient conditions for samples HPT-deformed at LNT.³⁷⁾

Interestingly, storage of the LNT HPT-deformed Cantor alloy at ambient conditions leads to a reverse transformation of hcp to fcc.³⁷⁾ This has been demonstrated independently for two samples deformed at LNT and 10 GPa to a shear strain γ ≈ 100 (Fig. 5(b)). The reverse transformation is very sluggish over time. The Rietveld analysis indicates about 85% of hcp phase immediately after the HPT process and about 64% after three years of storage, i.e. a reduction by 25%, and then remains unchanged.

Hydrostatic pressure applied to the Cantor alloy stabilizes the hcp structure.⁹⁾ In order to transform the fcc phase to hcp, a certain onset pressure is required depending on hydrostaticity and grain size. On the one hand, the use of different media for pressurization reduces the onset pressure at RT from 22.1 GPa (helium) to 6.9 (silicone oil) and (2.2–6.6) GPa (amorphous boron), i.e., with decreasing hydrostaticity.^38,39) The effect of stress state on the onset pressure of phase transformations has been discussed by Levitas.⁴⁰⁾ On the other hand, for a given medium (silicone oil), decreasing the grain size from 5 µm to about 0.01 µm increases the onset pressure from 6.9 GPa to 12.3 GPa.³⁹⁾ However, the origin of this effect is not well understood. The fcc to hcp martensitic transformation occurs through slip of 1/6⟨112⟩ Shockley partial dislocations on every second {111}_fcc plane,⁴¹⁾ giving the Shoji-Nishiyama OR. The nucleation of the phase transformation by tearing apart of dissociated 1/2⟨110⟩ dislocations is easier the lower the SFE. After nucleation the phase transformation under decreasing load continues at almost the speed of sound. The participating partial dislocations possess such a large kinetic energy, such that in a pole mechanism they are able to pass each other dynamically at closer range than would be possible under quasi-static conditions.⁴²⁾ Thus, shear stresses support the nucleation process as well as the motion of partial dislocations along (111)_fcc/(0001)_hcp interphase boundaries. HPT at RT did not lead to the transformation below about 8 GPa. The reasons for this may be an insufficient difference in the Gibbs free energy of the phases or the fast grain refinement of both phases during SPD into a globular nc structure suppressing the transformation similar to deformation twinning.⁴³⁾ However, lowering the HPT temperature to 77 K, i.e., lowering the SFE,^11,44) favours the transformation at the pressures applied.

According to finite-temperature ab initio calculations in the Cantor alloy the hcp structure is energetically favored at low temperatures.^11,44,45) However, in situ X-ray diffraction during cooling down to 3 K did not reveal any phase transformation from fcc to hcp.⁴⁶⁾ The hcp phase was also absent after large tensile deformation (true strain of 35%) at 4 K as was proven by highly sensitive X-ray diffraction with high-energy synchrotron radiation at RT (own results, unpublished). On the other hand, the hcp phase produced by hydrostatic compression at RT is quite stable during decompression and heating up above RT,³⁸⁾ but nevertheless partly transforms back to fcc. Similarly, there is a reverse transformation of the hcp phase produced by HPT at LNT during long-term storage under ambient conditions. These results strongly suggest that the fcc structure is the thermodynamically stable structure at low temperatures, contrary to theory. The reason for that may be the experimentally determined stacking fault energy which is larger than that computed by ab initio calculations. However, the hcp structure becomes stable under hydrostatic pressure. The sluggishness of the forward and reverse transformation may be due to the difficult movement of partial dislocations in the concentrated alloy producing the displacive transformation. For further discussion of the discrepancy between the experiment and theory on phase stability the reader is referred to Refs. 47, 48).

Shahmir et al.⁴⁹⁾ show evidence of fcc to hcp and bcc martensitic transformations in the Cantor alloy by SPD. The fcc to hcp transformation is not a subject of any concern, however, the fcc to bcc transition leaves some room for controversy since the authors show diffraction patterns including (220)_bcc reflection but do not see a much stronger (110)_bcc peak. This reflection has to appear independently of crystallographic texture. The volume fractions of the bcc phase calculated by Shahmir et al. based on the same X-ray results (with Kurdjumov-Sachs OR: (111)_fcc || (011)_bcc and $[\bar{1}01]$_fcc || $[\bar{1}\bar{1}1]$_bcc) are approximately 7% and 15% for 10 GPa HPT processing through 5 turns at RT and LNT, respectively. However, no bcc phase was observed by Chulist et al.³⁷⁾ under the same HPT conditions (Fig. 5). A phase transformation to bcc was also reported by Asgharirad et al.⁵⁰⁾ after HPT cold-consolidation of CrMnFeCoNi HEA gas-atomized powder. The authors speculated that the formation of bcc-martensite might be due to the segregation of Mn in interdendritic regions of the powders that alters the local phase stability.³⁾

Heczel et al.⁵¹⁾ deformed the Ti-rich bcc Ti₃₅Zr_27.5Hf_27.5Nb₅Ta₅ refractory HEA by HPT at RT. X-ray diffraction revealed a deformation-induced lamellar hcp martensitic phase. The change in structure and properties under the influence of HPT at RT was studied for the equiatomic alloy AlCrFeCoNiNb.⁵²⁾ This alloy in the cast state consists of two phases, namely a bcc and a hcp Laves phase (volume ratio about 40:60). It is interesting that in the cast and homogenized state, the bcc phase forms continuous intermediate layers along the grain boundaries of the Laves phase due to wetting. This structure is partially retained after HPT, but the bcc phase shows a spinodal decomposition characterized by Cr-enriched and Cr-depleted regions. The size of these regions is small, it is about 80 nm.

The AlTiFeCoNi HEA with the addition of 0.45% C has been studied by Edalati et al.⁵³⁾ As-cast, this alloy contains large grains of an iron-rich ordered L2₁ phase (ca. 77%) surrounded by interlayers of an iron-poor disordered bcc phase (ca. 23%), with discrete carbide inclusions of fcc structure. After HPT at RT, such a structure of grain boundary wetting, when the interlayers of the bcc phase separate the grains of the L2₁ phase from each other, almost did not change. At the same time, a phase transformation of the L2₁ ordered phase into a second disordered bcc phase takes place.

Severe plastic deformation of the Cantor alloy under extreme conditions leads to amorphization.⁵⁴⁾ The cold-swaged starting material (strain about 0.8) was deformed at RT in quasi-static uniaxial compression (strain rate 10⁻³ s⁻¹, strain 0.8), dynamic uniaxial compression (strain rate 1.7 × 10³ s⁻¹, strain 0.15) and in dynamic shear (local strain rate of 6 × 10⁵ s⁻¹, strain 2.2). Under quasi-static deformation conditions, a very high defect density is observed by TEM, especially with planar features (twin and hcp nanolamellae). Amorphous islands form at the intersection of these lamellae. Under dynamic loading, the deformed microstructure near macroscopic shear bands provides an ideal location for multiple, well-developed and amorphous bands. At both low and high strain rates, the amorphous regions comprise nanosized islands, roughly 10 nm in size or nanobands embedded in regions of concentrated deformation involving dislocations, stacking faults, twins and hcp lamellae. A hierarchal deformation mechanism paradigm for the CrCoNi-based HEAs with increasing deformation energy (defect density) is proposed. Amorphization of the Cantor alloy was also observed during in situ TEM tensile straining near the crack tip and in nanobridges in the crack wake in regions of high dislocation density.⁵⁵⁾ The amorphization process dissipates strain energy and therefore provides an effective toughening mechanism for HEAs.

4. Texture Development

Texture formation during deformation and recrystallization of HEAs is generally observed.¹⁴⁾ Reliable texture measurements on the HPT-deformed Cantor alloy have been made with synchrotron radiation using a high-resolution 2D detector.³⁷⁾ The textures are represented by sections of the orientation distribution function (ODF) and pole figures (PFs), intensities are given in multiples of a random orientation distribution (mrd), details on texture measurement, analysis and representation are given in Ref. 37). The weak texture of the fcc phase developing during HPT at RT is a typical shear texture of fcc metals with medium/low SFE. The dominant texture components are B resp. $\overline{B }$ and $A_{1}^{*}$ resp. $A_{2}^{*}$; minor components are A resp. $\overline{A }$ (Fig. 6 left). For key figure and designation of the fcc shear texture components, see Fig. 10(a). With increasing volume fraction of secondary phase (hcp) the texture strength decreases and the relative contributions of the texture components change (Fig. 6 right). This is a general trend that appears in two-phase materials. For HPT at LNT the randomization is even stronger (Fig. 7). Reasons for the weak texture development are phase transformation, twinning and grain refinement, the latter leading to possible GBS.^19,20) Evidently, grain/interphase boundary sliding is more pronounced in the two-phase HEA.

Fig. 6

Texture of the fcc parent phase in the Cantor alloy after HPT at RT and pressures of 7.8 GPa (no hcp phase) and 10 GPa (43 vol% hcp phase) at a shear strain γ ≈ 100. (SPN = shear plane normal, SD = shear direction; intensities are given in multiples of a random orientation distribution; for key figure and designation of the fcc shear texture components see Fig. 10(a)).³⁷⁾

Fig. 7

Texture of the fcc and hcp phase in the Cantor alloy after HPT at LNT at 7.8 GPa pressure and a shear strain γ = 98. The hcp volume fraction is 29%. (PFs of the hcp phase are also given in Miller notation; for key figure and designation of the fcc and hcp shear texture components see Figs. 10(a) and (b), respectively).³⁷⁾

The texture of the hcp phase is strongly influenced by the volume fraction transformed during HPT. Samples with volume fractions lower than about 50% exhibit a texture that is associated with the texture of the parent fcc phase, i.e. with the c-axis fiber parallel to the A-fiber (Fig. 7), (0001)_hcp || (111)_fcc. This relation can be easily recognized by comparing the (002)_hcp = (0001) and (100)_hcp = $(10\bar{1}0) $ or (110)_hcp = $(11\bar{2}0)$ with (111)_fcc and (110)_fcc PFs, respectively. For larger volume fractions (>50%) the hcp phase prevails the deformation. In this case, a typical shear texture with the c-axis fiber rotated anticlockwise about the transverse direction (TD) by about 30° with respect to the shear plane normal (SPN) is observed (Fig. 8). For key figure and designation of the hcp shear texture components see Fig. 10(b). As the c/a ratio of the hcp phase produced by a displacive transformation is ideal (c/a = 0.4142/0.2544 = 1.633 ≈ (c/a)_id = 1.633⁵⁶⁾), basal and prismatic slip systems should have the same critical resolved shear stresses and therefore should contribute equally to deformation. It should be noted that the texture of HPT processed samples is relatively weak. It can be estimated by the low mrd factor for (002)_hcp PFs of the hcp phase that does not exceed 8. Strong textures of hcp metals exhibit even up to 100 mrd.

Fig. 8

Texture of the fcc and hcp phase in the Cantor alloy after HPT at LNT at 10 GPa pressure and a shear strain γ = 106 after 1 month storage at RT. The hcp volume fraction is 85%. (PFs of the hcp phase are also given in Miller notation; for key figure and designation of the fcc and hcp shear texture components see Figs. 10(a) and (b), respectively).³⁷⁾

The reverse transformation seems to be related to the self-annealing process since after long-term storage at RT a new component of the fcc phase occurs. After being stored over two years at ambient conditions from the initially almost random texture (after one month of storage) a strong 45° TD-rotated cube component is formed (Fig. 9 left). In the hcp phase in the φ₂ = 0° ODF section, two new components A and B appear at Euler angles (0, 45, 0) and (60, 70, 0), respectively. Their basal planes are related to the {111} planes of the fcc oblique cube component, compare A and B in the (111)_fcc and (002)_hcp PFs of Fig. 9. This indicates that during the recrystallization of the hcp phase, the two components A and B are formed which, through reverse transformation (and eventual grain growth), yield the new fcc grains with rotated cube orientation. Apparently, such a mechanism leads to the orientation relationship mentioned above yielding low-energy interphase boundaries.

Fig. 9

Texture of the fcc and hcp phase in the Cantor alloy after HPT at LNT at 10 GPa pressure and a shear strain γ = 94 after 2 years storage at ambient conditions. The remaining hcp volume fraction is 67%. The two hcp recrystallization and/or grain growth components are marked A and B in the ODF and the (002)_hcp PF. The related components in the fcc phase are also marked in the (111)_fcc PF. (PFs of the hcp phase are also given in Miller notation; for key figure and designation of the fcc and hcp shear texture components see Figs. 10(a) and (b), respectively).³⁷⁾

Fig. 10

Key figure of shear texture components of HPT deformed fcc (a) and hcp phase (b) and their crystallographic description {hkl}⟨uvw⟩ with regard to shear plane and shear direction.³⁷⁾

Recently, texture measurements have been also done on the fcc Al₆Co_23.5Fe_23.5Mn_23.5Ni_23.5 HEA (medium SFE of 40–45 mJm⁻²) severely deformed at RT by high-pressure compressive shearing.⁵⁷⁾ The shear texture developed compares well with that of the HPT-deformed Cantor alloy. The best agreement between the experimental and simulated textures is obtained when the initial grain fragmentation simulation up to a shear strain of 6.9 is followed by grain boundary shearing (generally called sliding) simulation. The slip systems used are {111}$\langle \bar{1}10\rangle $ for perfect and {111}$\langle \bar{1}\bar{1}2\rangle $ for partial dislocation slip with a reference strength ratio of 1.25. The contribution of mechanical nanotwinning to texture development is found to be marginal. The simulations show that 35% of the total deformation is produced by grain boundary shearing.

Electron backscatter diffraction of the Senkov alloy HPT-deformed at RT shows a preferred alignment of {112} and {110} lattice planes parallel to the shear plane.³³⁾ This indicates $\{ 11\bar{2}\} $⟨111⟩ (D₁), $\{ \bar{1}\bar{1}2\} $⟨111⟩ (D₂), {110}$\langle 1\bar{1}1\rangle $ (E), {110}$\langle 1\bar{1}2\rangle $ (J) and $\{ \bar{1}\bar{1}0\} $$\langle \bar{1}1\bar{2}\rangle $ ($\bar{J}$) texture components typical for shearing of bcc metals and alloys.⁵⁸⁾ These components are favorable for slip on the main slip systems in the bcc structure, i.e. {110} and {112} slip planes with ⟨111⟩ slip direction. Recent texture studies on bcc Mo₅Nb₃₅Ta₁₅V₁₀W₃₅ refractory alloy HPT-deformed at 473 K and 7 GPa for a shear strain of 26 also report a shear texture with dominant D₁ and weak D₂, E, {110}⟨001⟩ (F), J and $\bar{J}$ components, as well as a weak 45° TD-rotated cube component.⁵⁹⁾

5. Mechanical Properties

5.1 Strength and ductility

High-entropy materials processed by SPD contain a high density of defects such as vacancies, dislocations, stacking faults, grain boundaries, and often second-phase particles.⁶⁰⁾ These defects represent obstacles for dislocation glide, leading to extreme hardening. On the other hand, the low work-hardening rate of high-strained materials leads to fast necking in tension, i.e. to a limited ductility. The situation is even worse for nc materials containing second-phase particles. Therefore, there is an urgent need to find a compromise of these properties for structural applications.¹⁵⁾ In this context, the Cantor alloy is characterized by several interesting mechanical properties.¹⁰⁾ For example, it shows a weak temperature dependence of strength at elevated temperatures. On the other hand, below 473 K a much stronger temperature dependence is observed. In addition, the work hardening rate increases with decreasing temperature. One of the remarkable properties of the Cantor alloy is its high toughness at very low temperatures, making it suitable for cryogenic applications. This property is mainly due to continuous steady strain hardening resulting from high dislocation and nano-twinning activity.

Figures 11(a) and (b) show the Vickers hardness as a function of shear strain measured at RT for HPT Cantor samples deformed at RT and LNT, respectively.³⁷⁾ The RT microhardness increases with shear strain and saturates at a certain strain level depending on pressure and HPT temperature. While the saturation microhardness slightly increases with pressure up to 7.8 GPa, it decreases at 10 GPa because of the phase transformation. In addition, the microhardness values show a larger scatter. Similarly, in the case of HPT at LNT, there is a large scatter in microhardness. The scatter is more pronounced at low shear strains and becomes smaller with increasing pressure. Despite the large scatter, it is evident that a kind of microhardness saturation takes place at much higher strains with the transition strain decreasing with pressure. Moreover, there is a clear microhardness anomaly: (490–520) HV for RT HPT, in contrast to (420–480) HV for LNT HPT (Fig. 12). There does not appear to be any correlation between microhardness and amount of hcp phase, only with pressure. The values for RT and LNT HPT-deformed samples seem to approach each other for pressures higher than 10 GPa.

Fig. 11

Microhardness of the Cantor alloy measured at RT of samples HPT-deformed at RT (a) and LNT (b) versus shear strain γ. The disc diameters used were 6 mm and 8 mm.³⁷⁾

Fig. 12

Microhardness of the Cantor alloy measured at RT versus pressure (a) and volume fraction of hcp phase (b) of samples HPT-deformed at RT and LNT (γ ≈ 100). The disc diameters used were 6 mm and 8 mm. The numbers indicate volume fractions of hcp phase (a) and months after HPT of microhardness measurements (b).³⁷⁾

From the maximum microhardness of 510 HV at RT and a pressure of 7.8 GPa a maximum stress σ_max ≈ 10 HV/3 = 1.7 GPa can be estimated, which represents about the maximum strength achievable at RT in the polycrystalline Cantor alloy. This value is about 1/20 of the theoretical strength σ_th ≈ M_TG/2π, with the shear modulus G = 79 GPa¹²⁾ and M_T = 3.07 the Taylor factor for a random orientation distribution. In the case of nc Pd–10 at%Au a slightly higher value 1/15 was measured.⁶¹⁾ The strength determined here from microhardness compares well with that measured in tension (1.95 GPa^5,62)) and compression (2.0 GPa,^63,64) Fig. 13). For the material deformed by HPT at LNT, the steady-state strength at RT (1.5 GPa) is approximately 15% lower.

Fig. 13

Temperature dependence of the yield stress in compression of coarse- and nano-grained Cantor HEA.^63,64)

In the PtRu alloy (5 and 10 at% Ru), the RT microhardness of the LNT HPT-deformed sample is higher than that of the sample HPT-deformed at RT.⁶⁵⁾ Therefore, the strength anomaly (softening) of the Cantor alloy is related to the martensitic phase transformation. Assuming that during pressure release and/or temperature increase as well as during RT indentation the hcp phase becomes unstable, then a reverse transformation is very likely. This process leads to a reduction of internal stresses and the formation of dislocation-free new grains of fcc phase. Consequently, because of this process, the overall dislocation density of the fcc phase and the hardness of the polyphase aggregate are lowered. Moreover, the microstructure and microhardness become quite inhomogeneous, too. The decrease in microhardness of the specimens deformed at RT and 10 GPa and the large scatter of the data can also be explained in the same way.

The hardness anomaly of the HEA resembles that of austenitic steel.⁶⁶⁾ Assuming that the nano grain size falls into the inverse Hall-Petch⁶⁷⁾ regime, the increase in RT hardness with increase of HPT temperature may also be controlled by grain/interphase boundary sliding. This assumption is reinforced by the fact that the amount of hcp phase affects hardness only slightly.

The temperature dependence of the yield stress in compression of the nc Cantor alloy processed by HPT at RT and LNT is shown in Fig. 13.^63,64) The nc materials, which also show the strength anomaly at cryogenic temperatures, are much stronger than the cg counterpart. The yield stress of the nc material HPT-deformed at RT is 1/13 of the theoretical strength at 4 K. Moreover, the temperature sensitivity of the yield stress of the nc materials is much stronger. Thermal activation analysis of the cg material has shown that the yield stress is most likely controlled by the thermally activated motion of dislocations in the grain interior, either by overcoming local barriers (local fluctuations of solute concentrations⁶⁸⁾) or the Peierls barrier.⁶³⁾ In contrast, the much higher critical stress for non-thermally activated motion of dislocations (yield stress at 0 K) and the much lower activation volume suggest that in the nc material yielding is determined by the emission of dislocations from grain boundaries. Such a process has been confirmed by computer simulations of nc materials.⁶⁹⁾ From RT down to 77 K, the microhardness shows the same temperature dependence as the yield stress, with the values of the samples HPT deformed at 77 K being about 10% lower than those of samples deformed at RT.⁷⁰⁾ A strong temperature dependence of the microhardness was also reported for HPT-deformed Co_25−xCr₂₅Fe₂₅Ni₂₅C_x alloys.⁷¹⁾

In contrast to the hardness anomaly reported by Chulist et al.³⁷⁾ for the Cantor alloy HPT deformed at 10 GPa, the results of Shahmir et al.⁴⁹⁾ show a normal hardening of the sample HPT deformed at RT and even a stronger hardening for the sample HPT deformed at LNT. The reason could be the deformation-induced bcc phase existing in their samples, due to microsegregation of Mn in interdendritic regions.⁵⁰⁾ Obviously, small differences in chemical composition can greatly alter phase stability, leading to significant hardness changes. In this context, SPD of carbon alloyed, strongly Cr-reduced CrMnFeCoNi HEA has to be mentioned.⁷²⁾ Dissolution of the Cr-carbides in the cg material during SPD leads to interstitially distributed carbon and carbon segregation at grain boundaries or in areas with high density of dislocations. With increasing carbon content, more grain refinement and dislocation storage is observed, resulting in pronounced strengthening but a decrease in ductility. No appreciable carbon segregation was observed after HPT at LNT,⁷³⁾ suggesting that SPD does not lead to carbide dissolution at this temperature, but rather to refinement of carbide particles. In this case, the strengthening effect is lower.

HEAs are considered as new hydrogen compatible materials, but enhancing their yield strength without deteriorating their hydrogen embrittlement resistance is challenging. To achieve this goal, Mohammadi et al.^62,74) deformed fcc CrMnFeCoNi and Al_0.1CrFeCoNi by HPT and studied the correlations between applied strain, microstructural features, strength, and hydrogen embrittlement. The unstrained cg alloy shows elongations over 80% under hydrogen, but its yield strength is only 220 MPa. Twinning is a major deformation mechanism at the early stages of straining (Fig. 1), resulting in over 1 GPa yield strength and 9% elongation in the presence of hydrogen. With a further increase in strain, dislocation-based defects including Lomer-Cottrell locks and Frank partial dislocations with low mobility are formed, enhancing the strength further. At large strains, a nc structure is generated, resulting in a yield strength of about 1.9 GPa but with poor hydrogen embrittlement resistance due to large hydrogen diffusion and hydrogen-enhanced decohesion. These results suggest that twins and defects with low mobility such as Lomer-Cottrell locks and Frank partial dislocations are effective to achieve a combination of high yield strength and good hydrogen embrittlement resistance by suppressing the hydrogen-enhanced localized plasticity in HEAs.

The steady-state microhardness of the Senkov alloy after HPT of cast material at RT is ≈420 HV for 50 < γ < 150,³²⁾ ≈480 HV for 50 < γ < 350 increasing to ≈510 HV for 350 < γ < 1000,³³⁾ while that produced by mechanical alloying via HPT at RT is ≈565 HV for 1000 < γ < 2500.⁷⁵⁾ The higher hardness according to ultra-SPD combined with a reduced ductility indicates the formation of nc precipitates (see sect. 6) and/or the change of grain boundary structure favoring segregation of individual elements from the bulk solid solution.³⁶⁾ Evidence of this is given by an increase in the lattice constant.⁷⁶⁾ Similar conclusions were drawn for the Cantor alloy produced by HPT mechanical alloying.^36,77) It should be noted that the combination of high hardness of the HPT-processed Senkov alloy and moderate elastic modulus compared with conventional Ti-based alloys shows the potential of this nc HEA for biomedical applications.⁷⁵⁾ The powder-HPT route can be easily used for reinforcement of HEAs with nanoparticles.⁷⁸⁾

To further increase hardness, two-phase HEAs that decompose and/or undergo phase transformations during HPT must be chosen.¹⁶⁾ Two such HEAs have already been discussed in sect. 3: AlTiFeCoNiNb (bcc + hcp) with 1030 HV⁵²⁾ and C-doped AlTiFeCoNi (L2₁ + bcc) with 950 HV.⁵³⁾ In the first case, interfaces and spinodal decomposition are responsible for the extra hardness. In the second case the main hardening increase comes from carbide fragmentation and transformation of L2₁ into disordered bcc phase.

5.2 Superplasticity

Normally, cg fcc HEAs exhibit high ductility at RT and cryogenic temperatures.⁹⁾ However, for industrial forming of intricate parts with fine details, much higher ductilities are required. Accordingly, superplastic forming is a viable approach. Superplasticity is the ability of materials to undergo unusually large, homogeneous tensile elongations to failure (typically > 400%⁷⁹⁾) at elevated temperatures when deformed within a characteristic range of strain rates.⁸⁰⁾ During superplastic deformation, GBS accommodated by slip within the grains is the main operating deformation mechanism. Therefore, small grain sizes are required, typically <10 µm. Consequently, grain refinement during SPD facilitates superplasticity. The contribution of SPD to research on the superplasticity of conventional alloys has been reviewed by Kawaski and Langdon.⁸¹⁾ It is shown that specimens with grain sizes in the submicron or nanometer range exhibit superplastic strains at fast strain rates and therefore offer a potential for achieving superplastic forming operations in short times. In some alloys SPD enables RT superplasticity.⁸²⁾

Superplastic deformation of HEAs has been reported by Shahmir et al.,^83–86) a recent review is given by Motabelli et al.⁸⁷⁾ Figure 14(a) shows the stress - elongation curves of the HPT-deformed Cantor alloy. The high elongations above 873 K (T/T_m = 0.54, T_m = 1612 K¹²⁾) are demonstrated for different strain rates in Fig. 14(b).

Fig. 14

(a) Engineering stress - elongation curves for Cantor HEA samples processed by HPT (6 GPa, 5 turns, 1 rpm) at different temperatures at an initial strain rate of 10⁻³ s⁻¹.⁸⁴⁾ (b) Examples of superplasticity after processing by HPT and then testing at different strain rates in tension at 973 K.⁸⁵⁾

According to Langdon⁸⁸⁾ superplasticity can be quite well described by the power law equation relating the strain rate $\dot{\varepsilon }$ to the stress σ of the form   

\begin{equation} \dot{\varepsilon} = A\frac{D_{gb}Gb}{kT}\left(\frac{b}{d}\right)^{2} \left(\frac{\sigma}{G}\right)^{2}, \end{equation} (1)

  

\begin{equation} \text{with}\quad D_{gb} = D_{0}\exp \left(-\frac{Q_{gb}}{kT} \right), \end{equation} (2)

where D_gb is the diffusion coefficient and Q_gb is the activation energy for grain boundary diffusion, T is the absolute temperature, k is Boltzmann’s constant, G is the shear modulus, d is the grain size, b is magnitude of the Burgers vector, and A and D₀ are constants. Plotting the maximum flow stress of Fig. 15(a) as a function of strain rate yields a strain rate sensitivity m = 0.31, which is smaller than 0.5, which is typically observed for superplasticity (the stress exponent in eq. (1) is n = 1/m = 2). The lower value suggests control by an intragranular dislocation glide mechanism, but samples deforming by dislocation glide are not capable of achieving elongations up to 500%. Accordingly, Shahmir et al.^83–86) interpreted the data in a different way by noting that an anomalously low strain rate sensitivity may be attained due to the occurrence of massive grain growth during tensile testing, where the nanograins grew to about 1 µm after tensile testing at 973 K (see also sect. 6). The strain rate at constant stress of 200 MPa as a function of inverse temperature (Fig. 15(b)) yields Q_gb = 113 kJ/mol. This value agrees with the activation energy of 115 kJ/mol reported for grain boundary diffusion in pure Ni.⁸⁹⁾ Ni is also the slowest diffusing species in the Cantor alloy.⁹⁰⁾

Fig. 15

Flow stress versus strain rate of the Cantor HEA to determine the strain rate sensitivity m = 0.31. (b) Strain rates at 200 MPa (dashed line in (a)) versus reciprocal temperature to determine the apparent activation energy.⁸⁴⁾

Overall, the plot of the experimental data from each set of results available for HEAs up to the year 2017 in the form of the temperature and grain size compensated strain rate against the normalized stress (Fig. 16) shows that the data are in fair agreement with the theoretical prediction of eq. (1) for A ≈ 10 and this is consistent with conventional alloys processed by SPD with A of ≈1 (Al alloys) and ≈10 (Mg alloys).⁸¹⁾ The HEAs in Fig. 16 prior to tensile testing were severely deformed in different ways: (i) multidirectional forging (AlCoCrCuFeNi),^91–93) (ii) HPT (CrMnFeCoNi⁸⁴⁾ and CrMnFeCoNiTi_0.1⁸⁶⁾) and (iii) warm-rolling plus annealing (CrMnFeCoNi).⁹⁴⁾ The wrought AlCoCrCuFeNi HEA has a complex microstructure consisting of four different ordered and disordered phases with volume fractions from 7% to 46% with fine grain/particle size of about 2 µm. During superplastic deformation, variations in the volume fractions of the phases, changes in their chemical composition, and phase transformations occur while the grain size stays almost constant. In contrast, the CrMnFeCoNi-based HEAs stay single-phase during superplastic deformation, except for possible nanoprecipitate formation, see sect. 6. However, there is massive grain growth in the HPT starting material from the 10 nm to the µm range. In the warm-rolled and annealed material the initial grain size of 1.4 µm for the high strain rate (10⁻¹ s⁻¹) slightly decreases to 1.0 µm implying dynamic recrystallization, while for the low strain rate (10⁻⁴ s⁻¹) it increases to 4.4 µm. In the latter case, the strain rate sensitivity is 0.59, the elongation to failure is 325%, and the texture randomizes. These features are characteristic of superplasticity. In all cases, the grain size in the tensile test remains in the range typical for superplastic flow. The reduced grain growth in single-phase HEAs is due to sluggish diffusion⁹⁰⁾ and/or to nanosize precipitates often forming at elevated temperatures,^86,95) see sect. 6. A stronger effect on grain growth is observed for multiphase HEAs that exhibit extreme high superplasticity (elongation to fracture >1000%) at high strain rates (≥10⁻² s⁻¹).^{91–93,96,97)}

Fig. 16

Temperature and grain size compensated strain rate versus normalized stress of different HEAs. (Multidirectional forging: white^91,92) and red⁹³⁾ data, HPT at RT: blue⁸⁴⁾ and yellow⁸⁶⁾ data, warm rolling at 473 K: green⁹⁴⁾ data).⁸³⁾

6. Thermal Stability

Materials processed by SPD contain a high density of defects. Therefore, they are prone to changes of microstructure and phase decomposition during annealing. The thermal stability of the HPT deformed Cantor alloy and its effect on the mechanical properties was carried out by Schuh et al.,^5,98) Shahmir et al.,^99,100) Lee et al.,¹⁰¹⁾ Maier-Kiener et al.¹⁰²⁾ and Keil et al.¹⁰³⁾ They showed that with increasing annealing temperature and annealing time there is a pronounced hardness increase (Fig. 17). Similar observations were also made by Shahmir et al.¹⁰⁴⁾ when tempering the Cantor alloy after equal channel angular pressing (ECAP), whereby the increase in hardness in the ECAP ufg material is lower due to a lower degree of deformation. The hardness increases up to an annealing temperature of about 773 K and steeply drops down to a value close to that of the homogenized cg starting material before SPD.

Fig. 17

Microhardness of isochronally (1 h) (a) and isothermally (723 K) (b) annealed Cantor HEA samples.⁵⁾

During HPT at RT the Cantor alloy does not decompose as proven by three-dimensional atom probe tomography (3D-APT).⁵⁾ However, TEM and 3D-APT reveal that during annealing at elevated temperatures the Cantor alloy is not stable and decomposes in various nanosized precipitates, such as (MnNi)-rich L₁₀, Cr-rich A2 and tetragonal σ phase as well as for long annealing times a (FeCo)-rich B2 phase (Fig. 18).^{5,98–101,104)} The precipitated volume culminates at about 773 K, at 1173 K all the precipitates are dissolved and the Cantor alloy is single-phase again.^99,100) The phase formation is reflected in thermodynamic calculations.¹⁰⁵⁾ The SPD microstructure facilitates phase decomposition due to the high density of defects that enhance diffusivity¹⁰⁶⁾ and serve as nucleation sites of new phases. In the cg undeformed material the phase decomposition is much slower.⁶⁾ Moreover, at 773 K massive grain growth sets in, with the grain size reaching several microns at 1173 K.¹⁰³⁾ The onset temperature of grain growth in SPD HEAs is about 150 K lower than the recrystallization temperature of swaged and rolled HEAs.^107,108) Both effects (precipitation and dissolution, and grain coarsening) are clearly correlated with the hardening and softening observed.

Fig. 18

Bright-field TEM microstructures (a), (d), (g) and their representative diffraction patterns (b), (e), (h) of Cantor HEA samples annealed at 723 K for different times ((a), (b), (c): 5 min; (d), (e), (f): 1 h; (g), (h), (i): 15 h). The three dimensional atom probe tomographic images (c), (f), (i) show the decomposition of the alloy. Isoconcentration surfaces represent regions of >70 at% (Ni + Mn) (green), >50 at% Cr (purple) and >35 at% Co (blue).⁵⁾

The SPD state shows remarkably high strength accompanied by moderate ductility. Annealing at the peak hardness temperature leads to a further increase in strength but also loss of ductility, which becomes even more pronounced for longer annealing times. This effect is due to the precipitation of brittle second phases mainly on the grain boundaries.⁵⁾ Subjecting the material to higher annealing temperature regains ductility, and for anneals at 1073 K pronounced work-hardening is restored, which is typical for this alloy in the cg state.¹⁰⁾ The combination of strength and ductility can be optimized for certain applications by annealing, see also Ref. 8).

Similar to the Cantor alloy, the Senkov alloy HPT-deformed at RT shows a continuous increase in microhardness up to 773 K during isochronous annealing.³²⁾ Thereafter, with increasing annealing temperature, it decreases to the value of the starting material before HPT and reaches this at 1073 K. In contrast to the Cantor alloy, with increasing annealing time at peak temperature, the microhardness goes beyond a maximum at 1 h. Diffraction of synchrotron radiation of the HPT-deformed sample annealed at 573 K does not show decomposition of the parent bcc phase. However, at 773 K it decomposes into a NbTa-rich bcc and a HfZr-rich hcp phase. The phase fractions do not change too much with annealing time, but the microhardness decreases drastically. At higher temperatures (1073 K) an additional HfZr-rich bcc phase is formed at the cost of the hcp phase. At 1173 K only two bcc phases exist, which change to the original bcc phase at 1373 K. The diffraction of synchrotron radiation shows that the composition of the phases changes with the annealing temperature. The experimental findings on decomposition are reflected by CALPHAD modeling. Annealing at 573 K gives just some recovery. The nc multiphase structure developed at 773 K slightly coarsens up to 1073 K. At 1173 K, abnormal grain growth starts in the dual phase bcc alloy with coarse grains in the 10 µm range. At 1273 K a homogeneous grain structure exists with 25 µm grains. Increasing the annealing temperature to 1373 K further growth to 50 µm takes place in the single-phase structure. It is interesting that the hard SPD material, with an elongation at fracture of approximately 10%, has almost the same ductility as the soft, cg starting material. The ductility decreases with the amount of HfZr-rich hcp phase leading to brittleness through intercrystalline fracture at 773 K. So, unlike the Cantor alloy, annealing does not improve ductility.

It should be noted that the isochronous anneal hardening is the same in the Cantor and Senkov alloy up to 873 K, although the phase decomposition is different. However, there is a distinct difference in isothermal annealing. In the case of the Senkov alloy, anneal hardening decreases after 1 h of tempering, the decrease being related to the change in the chemical composition of the two constituent phases. Anneal hardening was also observed for HPT-deformed pure metals (i) Al,¹⁰⁹⁾ (ii) (Cu, Ni)¹¹⁰⁾ and alloys (iii) (Pt–Ru)⁶⁵⁾ without phase decomposition. In case (i), it was suggested that the phenomenon might arise from rapid dislocation annihilation at the abundance of grain boundaries found in nc materials. This leaves the grain interior largely depleted of dislocation sources, and hence subsequent deformation requires dislocations to be emitted from grain boundaries. These are often in a relaxed state after annealing and dislocation emission can be more difficult, leading to the observed increase in hardness.^111–113) In case (ii), the small effect was attributed to obstacles created by the agglomeration of vacancies caused by deformation.^110,114) The same explanation was also given to anneal hardening of two biodegradable Mg–Zn–Ca alloys, in which precipitation and segregation of alloying elements at grain boundaries¹¹⁵⁾ was estimated to have a minor effect.¹¹⁶⁾ In case (iii), anneal hardening decreasing with increasing grain size after HPT at increasing temperature (77 K, RT, 473 K) was explained by annihilation of lattice dislocations and grain boundary defects during annealing, which makes it difficult for dislocation absorption at grain boundaries after heat treatment.⁶⁵⁾ To what extent these effects contribute to the pronounced anneal hardening of HEAs, especially at long annealing times, is not clear. For a further discussion of this complex problem the reader is referred to Refs. 32, 98, 117, 118).

The softening for high annealing temperatures can be explained by the onset of grain growth and by the fact that the single-phase character of the alloys is restored for very high annealing temperatures. It should be mentioned that deformation of the anneal-hardened Cantor alloy produces strain softening.¹⁰¹⁾ This effect was attributed to the deformation-induced dissolution of the nanosized precipitates produced during annealing. The dissolution mechanism was explained by the destabilization of precipitates during plastic deformation due to the increase in interface energy, which in turn can be explained by dislocation accumulation and friction at the matrix/precipitate interfaces.

7. Conclusions

Within the research done on SPD of HEAs during the last decade based on the results presented in this overview the following conclusions can be drawn:

Similar to traditional metallic alloys, SPD of HEAs leads to nc microstructures, high dislocation densities and weak textures. This is associated with a high strengthening effect and a loss of ductility. However, due to the multi-element solid solution, HEAs in the high-energy SPD state become quite unstable with respect to phase transformations, grain boundary segregation, and phase decomposition. Due to a defect-enhanced diffusivity, the kinetics of the decomposition is increased. This offers the possibility of producing ultra-hard materials by SPD processes or by post-annealing. Reduced grain growth, either caused by sluggish diffusion, segregation or nanoprecipitation, enables extremely high superplasticity at high strain rates. The effect of SPD on changing properties has been demonstrated mainly for the HEA prototypes fcc Cantor and bcc Senkov, but few examples of more complex HEAs indicate the high research potential of this new class of advanced materials in the field of nanoSPD.

Acknowledgement

The authors are grateful to the many coworkers mentioned in their publications that greatly helped to enlighten the complex problem of SPD of HEAs. R.C. acknowledges Project No. 2020/37/B/ST5/03267 of the National Science Centre of Poland.

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