Hot deformation of ultrafine-grained TiC-reinforced AlCrFeNbMoTiV refractory high entropy alloys

. In the present work, the hot deformation behavior of the AlCr 0.2 FeNbMoTiV 2 refractory high-entropy alloy was studied by means of its constitutive modeling. The samples were fabricated using mechanical alloying and spark plasma sintering, resulting in an ultrafine-grained microstructure consisting of a main bcc solid solution, Laves phase


Introduction
The current challenges of the aerospace industry require advanced materials that can overcome the performance of current materials in terms of high-temperature strength and oxidation resistance, among others. Among the potential candidates to fulfill these requirements, refractory highentropy alloys (RHEAs), first proposed in 2010 [1,2], have attracted the interest of the scientific community because of their outstanding performance in terms mechanical properties at elevated temperatures (even superior to that of commercial Ni-based superalloys) and elevated oxidation resistance [3]. As part of the high-entropy alloys (HEAs) family, these materials correspond to multicomponent alloys (typically over five) with contents between 5 and 35 at. pct., resulting in complex compositions far away from the boundaries of the traditional alloy design concept. RHEAs, particularly, are mainly constituted by refractory elements (like Mo, Nb, Ta, or W) that provide elevated hot softening resistance, alloyed with non-refractory elements (like Al, Si, or Fe) that reduce the density or enhance oxidation resistance properties. Even though RHEAs are commonly fabricated by casting techniques, the mechanical alloying (MA) followed by spark plasma sintering (SPS) route has proven to produce the strongest RHEAs because of the combination of fine or ultrafine grains and the formation of finely and homogeneously dispersed oxides and nitrides [4,5]. This particular microstructure results in superior properties at high temperatures and a superior balance of strength and ductility at room temperature [6,7].
The constitutive analysis of the high-temperature deformation of metallic materials can result not only in an accurate description of the effect of temperature and strain rate over the flow stress but it also provides insightful details about the deformation and softening mechanisms involved. Several expressions have been proposed for these purposes. One of them, the power law (Eq. 1), relates the Zenner-Hollomon (Z) parameter (defined as the temperature-compensated strain rate) with the stress, particularly in low-stress conditions (high temperatures and low strain rates) [8].
where Qapp corresponds to the apparent activation energy, ̇ to the strain rate, R to the gas constant, T to the temperature, and A' and n' are parameters of the model. To the authors' knowledge, this is the first work that addresses the constitutive modeling of a PMfabricated RHEA, resulting in an expression that accurately predicts the peak stress (σP) between 1000 -1100 ºC and 0.0005 -0.01 s -1 . Additionally, the physical meaning of n' and Qapp was discussed in order to contribute to the comprehension of the deformation mechanisms of RHEAs with typical microstructural features of powder metallurgy processing. Lastly, the effect of annealing on the alloy's microstructure and high-temperature mechanical properties was evaluated.

Materials and methodologies
The powder alloy (denominated R2) was produced mixing pure commercial powders of Al (< 45 µm, 99.5%), Cr (< 45 µm, 99%), Mo (3-7 µm, 99.95%), Nb (< 45 µm, 99.8%), Ti (< 45 µm, 99%), and V (<45 µm, 99.5%), employing hardened steel vials and balls which can act as a source of Fe. The milling process was conducted in a high-energy planetary ball mill Fritsch Pulverisette 5, for 50 h, using a ball-to-powder ratio (BPR) of 20:1 and 300 rpm of rotational speed under an Ar atmosphere. Additionally, 2.6 wt. pct. of ethylene bis-stereamide was added as a Process Control Agent (PCA), and on/off cycles of 30 min/30 min were utilized to avoid severe cold welding. Table  1 summarizes the composition of the 50 h-milled powder used in the sintering stage. The SPS was conducted in a Dr. Sinter SPS-1050-CE press, using 1150 ºC and 50 MPa of stress, with a dwell time of 10 min in vacuum. Disks of 30 mm in diameter and between 8 and 9 mm in height were sintered using graphite die and punches. As-sintered samples (R2AS) were subjected to an annealing treatment at 1350 ºC for 16 h under an Ar atmosphere (R2HT). X-ray diffraction (XRD) analysis was performed in a Bruker D8 Advance diffractometer, using Cukα1-radiation (λ = 0.15406 nm) equipped with a Ge monochromator. Besides, transmission electron microscopy (TEM) was performed employing a J2100F microscope equipped with energy-dispersive X-ray spectroscopy (EDS) detector. For these purposes, a lamella was prepared in a Focus Ion Beam (FIB)-SEM Neon40 Crossbeam™ workstation. A field-emission gun SEM JEOL JSM-7001F equipped with EDS and electron backscattered diffraction (EBSD) detectors was also used, utilizing the MTEX package to process the EBSD data. Lastly, 6 mm in diameter and 8 mm in height cylindrical samples were cut from the sintered samples for compression testing. Tests at different temperatures (950, 1000, 1050, and 1100 ºC) and different strain rates (0.0005, 0.001, 0.005, and 0.01 s -1 ) were performed in an Instron 4507 universal testing machine equipped with a load cell of 100 kN, using Ar flow to avoid oxidation of the samples, and a layer of mica and boron nitride to diminish the friction between the samples and the punches.

Results and discussion
According to the XRD analysis (Figure 1), both R2AS and R2HT samples are mainly constituted by a bcc phase with lattice parameters similar to that of V, TiC, and Laves phases (C14 and C36 polytypes observed in both samples, while minor C15 was observed in R2AS too). Additionally, in the case of the R2HT sample, Al2O3 peaks were observed.   strain rates at 950 ºC suggest that dynamic recrystallization (DRX) may have predominated instead. It is also important to highlight that a strain of 0.7 was achieved in most cases, except for those tests at 950 ºC using strain rates of 0.005 and 0.01 s -1 . In those samples, some cracks appeared during the elastic deformation region, indicating that the material was already brittle, which resulted in scarce ductility. Additionally, there is a considerable difference in the peak stresses (σP) obtained at 1000 ºC and 950 ºC at 0.001 and 0.0005 s -1 . All these findings suggest that the mechanical behavior changes in that temperature interval, either by dissolution/precipitation phenomena or a change in the controlling deformation mechanism. For the previous reasons, the constitutive analysis will be performed only considering the 1000-1100 ºC range.  .a illustrates the linear relationship between ln ε̇ and ln σP as described in Eq. 2. The slopes of the curves of each plot correspond to n', resulting in values of 2.60, 2.23, and 2.54, at 1100, 1050, and 1000 ºC, respectively, resulting in an average n' value of 2.46. The excellent R 2 values, as well as the similarity between the calculated n' values, confirm that there is no change in the deformation mechanism in the range of study. According to the literature, n' = 2 is associated with grain-boundary sliding (GBS) as the governing deformation mechanism. This is the typical deformation mechanism of ultrafine-grained materials, and it has been reported in several works contributing to the hot deformation of PM-fabricated RHEAs or in the recrystallized grains of coarse-grained RHEAs [9,10]. In the present analysis, the obtained n' value is slightly superior to the theoretical one of GBS. Nevertheless, it has been described that in multi-phase materials, the n' value obtained by means of the constitutive analysis is superior to the actual value; the load is actually distributed between two or more phases, and therefore, the stress actually exerted over the matrix phase is inferior to the experimental measured one [11]. Hence, the rest of the analysis considers n' = 2.  indicates. An average R 2 coefficient of 0.995 was obtained, evidencing that a single Qapp value can represent the experimental data (at least, at each strain rate). Considering n' = 2, an average Qapp value of 429.8 kJ·mol -1 was calculated. When GBS governs the deformation, Qapp corresponds either to the activation energy of grain boundary or of lattice diffusion (depending on which one of them controls it). Nevertheless, the evaluation of Qapp in the constitutive analysis of HEAs is still complex and unclear. Because of the compositional complexity of these alloys, there is usually no clear solute-solvent distinction, therefore is not easy to identify which elements play the main role in controlling the diffusion, indistinctly of the mechanism involved. In the present study, the obtained Qapp value is in the range of the self-diffusion activation energies of Mo or V [12]. Even though this would agree with the idea that lattice-controlled GBS is the governing deformation mechanism, an in-depth characterization of the microstructure and texture of the deformed samples is necessary to confirm it.
Lastly, Figure 5 illustrates the linear relationship between ln Z and ln σP. An elevated R 2 coefficient (0.993) was obtained, confirming the excellent agreement of the experimental data with the power law. Thus, a value of A' equals to 2.38·10 9 was calculated as the intercept of this curve. Therefore, the resulting relationship between Z and σP is represented in Eq. 4.  On the other hand, Figure 6 illustrates the compression curves of R2AS and R2HT at 1000, 1050, and 1100 ºC employing a strain rate of 0.001 s -1 . As can be observed, the R2HT samples presented a considerably superior σP than the R2AS samples. Since the only considerable difference between R2AS and R2HT microstructures is the grain size of the constituents, this was attributed as the responsible of this superior mechanical behavior. Despite the increase in strength, R2HT samples still presented elevated ductility. These findings suggest that adjusting the microstructural features of PM RHEAs can result in an improvement in their high-temperature mechanical performance. Regarding the controlling deformation mechanism, two possibilities are on the table. Firstly, the R2AS and R2HT samples presented different deformation mechanisms, which would be responsible for this considerable difference. Senkov et al. [13] found that the strength remarkably dropped when GBS governs deformation; this agrees with the lower strength of the R2AS, which deformation is controlled by GBS according to the constitutive analysis. The second option is that GBS is also the controlling deformation mechanism of R2HT samples. This is plausible since GBS is hindered by any condition that restricts the movement of grain boundaries, such as lower temperatures, higher strain rates, second phases in grain boundaries, and, as may be in the present case, coarser grain size; all these actions would produce an increase of the flow stress. Nevertheless, further microstructural analysis is required to determine the governing deformation mechanism. Figure 7 illustrates the specific yield strength (SYS) of PM RHEAs, casting RHEAs, and the alloys of the present study. As can be observed, the R2AS alloy presented a considerably inferior SYS than the R2HT samples, increasing from 33 to 98 MPa/g·cm -3 at 1000 ºC. On the other hand, the alloys of the present study presented a poorer performance compared to AlxCrNbMoV (x = 0, 0.1, 0.5, and 1) RHEAs produced by MA+SPS [4,5], which ranges between 155 and 188 MPa/g·cm -3 at 1000 ºC. Nevertheless, except for the AlCrNbMoV alloy, none of them achieved a strain of 0.3, revealing that this superior strength was obtained by sacrificing their ductility. Apart from that, the SYS of the R2HT samples exceeds most of that of RHEAs that present considerable ductility at 1000 ºC.  [4,5,14,15], R2AS, R2HT, and casting RHEAs at different temperatures (̇ = 0.001 s -1 ).

Conclusions
The high-temperature compression tests of the R2 RHEA fabricated by powder metallurgy were effectively performed. Hence, the main conclusions of this work are: i) A change in the mechanical behavior between 950 and 1000 ºC was observed that can be attributed to the precipitation of a phase, the dissolution of the Laves phase at high temperatures, or a change in the controlling deformation mechanism. Further studies are required to address this aspect.
ii) The expression ̇exp(429.8/ ) = 2.38 • 10 9 2 was obtained to model the σP in the studied temperature and strain rate range. An R 2 coefficient of 0.99 was obtained, evidencing the good agreement of the experimental data with the model. iii) n' and Qapp values of 2 and 429.8 kJ·mol -1 were obtained with the conventional constitutive analysis considering the load partitioning effect produced by the presence of second phases. Hence, it was assumed that grain boundary sliding controlled the hot deformation of the alloy, while Qapp is in the range of the activation energies of self-diffusion of Mo and V. iv) An increase of the grain size (from 0.35 to 1.2 µm in the case of the bcc phase) increased the strength while the ductility was not reduced. This can be attributed to a change in the controlling deformation mechanism, or well, that GBS is still the governing deformation mechanism but is hindered by the coarser grain size.