Dynamic Mechanical Properties and Microstructure of an (Al0.5CoCrFeNi)0.95Mo0.025C0.025 High Entropy Alloy

The dynamic mechanical properties and microstructure of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 high entropy alloy (HEA) prepared by powder extrusion were investigated by a split Hopkinson pressure bar and electron probe microanalyzer and scanning electron microscope. The (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA has a uniform face-centered cubic plus body-centered cubic solid solution structure and a fine grain-sized microstructure with a size of about 2 microns. The HEA possesses an excellent strain hardening rate and high strain rate sensitivity at a high strain rate. The Johnson–Cook plastic model was used to describe the dynamic flow behavior. Hat-shaped specimens with different nominal strain levels were used to investigate forced shear localization. After dynamic deformation, a thin and short shear band was generated in the designed shear zone and then the specimen quickly fractured along the shear band.


Introduction
High entropy alloys (HEAs) contain at least five elements in equiatomic or near-equiatomic ratios and have excellent properties [1][2][3][4]. They tended to form a simple solid-solution phase when first proposed by Yeh et al. [5]. With the further study of HEAs, multiphase HEAs became more and more common. As a broad category of HEAs, the Al x CoCrFeNi HEAs have aroused huge interest from researchers since the appearance of HEAs. The crystal structure of the Al x CoCrFeNi alloys transforms from face-centered cubic (FCC) to body-centered cubic (BCC) with an increase in Al content [6][7][8]. Meanwhile, the properties of HEAs, such as hardness, electrical conductivity, and thermal conductivity, also change with the transformation of the structure [6,7]. Lin et al. [9] investigated the microstructure, hardness, and corrosion properties of the Al 0.5 CoCrFeNi alloys aged at different temperatures and found that an FCC + BCC solid solution structure with optimal hardness appeared when the alloys were aged at 350-800 • C. Niu et al. [10] studied the strengthening of nanoprecipitations in an annealed Al 0.5 CoCrFeNi HEA and found that the nano-sized BCC phase particles reinforced the Al 0.5 CoCrFeNi HEA. Wang et al. [11] discovered that the temperature of the FCC to BCC phase transformation in the Al 0.5 CoCrFeNi HEA was 1044 K, and the tensile strength increased after phase transformation. Therefore, previous works showed that the existence of the FCC + BCC solid solution structure is beneficial for improving the mechanical properties of the Al 0.5 CoCrFeNi alloy. Regarding the effects of the addition of Mo and C elements to HEAs, the addition of Mo could cause solution strengthening because of the large atomic size [12][13][14][15]. Additionally, Zhuang et al. [16] found that the addition of Mo into Al 0.5 CoCrFeNi HEA could enhance the formation of a (Cr, Mo)-rich σ phase and adjust the mechanical properties of the Al 0.5 CoCrFeNiMo x HEAs, including hardness, strength, and ductility. Jian et al. [17] suggested that the addition of C could promote the formation of carbides and induce precipitation strengthening. Jian et al. [17] also found that carbide precipitation could inhibit grain growth during recrystallization. The powder metallurgy method provides a promising way to prepare the Al 0.5 CoCrFeNi HEA reinforced by Mo and C elements.
Many materials researchers are paying more and more attention to the dynamic mechanical properties of HEAs for industry application. Kumar et al. [18] reached the conclusion that the deformation mechanism of the Al 0.1 CrFeCoNi HEA at a high strain rate is the same as that of low stacking fault energy materials. Dirras et al. [19] found that the yield strength in the Ti 20 Hf 20 Zr 20 Ta 20 Nb 20 HEA was much higher under dynamic loading conditions than under quasi-static conditions and observed a shear band in the dynamic regime. Wang et al. [20] investigated the serration behavior and microstructure of the CoCrFeMnNi HEA prepared by powder metallurgy at strain rates from 1 × 10 −4 s −1 to 1 × 10 −1 s −1 and from 1 × 10 3 s −1 to 3 × 10 3 s −1 . Additionally, the dynamic mechanical properties of the as-cast NiCrFeCoMn HEA were investigated by Wang et al. [21]. Ma et al. [22] studied the influence of the strain rate on the dynamic mechanical properties of the AlCrCuFeNi 2 HEA and found a linear relationship between the dynamic yield strength and strain rate. Shear localization, or shear band, is the main failure mechanism for the materials deformed under high velocity loading. Li et al. [23] studied the shear localization in the CrMnFeCoNi HEA and revealed that the deformation mechanism was rotational dynamic recrystallization. They also found that the Al 0.3 CoCrFeNi HEA was unable to form a shear band [24], and they attributed the remarkable resistance to shear failure to the excellent strain hardening ability. An et al. [25] found that the addition of Mo and C elements to the Al 0.5 CoCrFeNi HEA could significantly increase the tensile strength under quasi-static loading. However, the dynamic mechanical properties of Al 0.5 CoCrFeNi reinforced by Mo and C are not clear yet.
In this paper, we investigated the microstructure and mechanical behavior of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA prepared by powder extrusion and explored the forced shear localization of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA.

Materials and Methods
High purity Al, Co, Cr, Fe, Ni, Mo, and C powders of a nominal composition (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 (at.%) were melted in an induction heated vacuum furnace. Then, the melt was drop through a ceramic tube and atomized by high purity Ar with a pressure of 4 MPa. After cooling down the gas-atomized powder in the atomization chamber, a stainless can with dimensions of ϕ 60 mm × 150 mm, which was degassed for 12 h at a temperature of 500 • C and sealed in a vacuum, was used to fill the as-prepared HEA powder. The encapsulated powder was then pre-heated for 1 h at a temperature of 1150 • C and immediately hot extruded into bars with an extrusion ratio of 6. After hot extrusion, the bar was cooled in the air. The content of oxygen in the gas-atomized powder was 750 ppm, and the chemical compositions of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA are listed in Table 1. For an n-element multicomponent alloy at a random state, the configurational entropy ∆S mix can be calculated according to Boltzmann's hypothesis by the following equation [26]: where R is the gas constant and has a value of 8.314 JK −1 mol −1 , n is the number of total elements, and x i is the concentration of element i. By substituting the actual compositions of (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA, the configurational entropy ∆S mix can be calculated as 1.725R, which satisfies the definition of HEA [27].
To obtain the mechanical properties of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA, cylinder specimens were used for quasi-static compression tests and dynamic load tests. The cylinder specimens were cut from the as-received HEA bars along the extrusion direction (ED) with dimensions of ϕ 4 mm × 5.6 mm. The quasi-static compression tests were performed on INSTRON 8802 (Instron, the USA) with strain rates of 1 × 10 −1 , 1 × 10 −2 , and 1 × 10 −3 s −1 . The dynamic load tests were performed on a split Hopkinson pressure bar (SHPB, Beijing Xiaotu Technology Co., Ltd, China) with strain rates of 550, 1300, 2200, and 3000 s −1 . Hat-shaped specimens cut along the ED were used to induce forced shear localization, as shown in Figure 1. The shadow parts show the designed shear zones of the specimen. Measured sizes of the hat-shaped specimens of designed shear zones are shown in the Table 2. The nominal strain was γ nom. = 2 × (f before − f after )/(b before − a before ). After dynamic deformation, hat-shaped specimens were observed using a Quanta-200 scanning electron microscope (SEM, FEI, Netherlands). By substituting the actual compositions of (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA, the configurational entropy ΔSmix can be calculated as 1.725R, which satisfies the definition of HEA [27].
To obtain the mechanical properties of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA, cylinder specimens were used for quasi-static compression tests and dynamic load tests. The cylinder specimens were cut from the as-received HEA bars along the extrusion direction (ED) with dimensions of φ 4 mm × 5.6 mm. The quasi-static compression tests were performed on INSTRON 8802 (Instron, the US) with strain rates of 1 × 10 −1 , 1 × 10 −2 , and 1 × 10 −3 s −1 . The dynamic load tests were performed on a split Hopkinson pressure bar (SHPB, Beijing Xiaotu Technology Co., Ltd, China) with strain rates of 550, 1300, 2200, and 3000 s −1 . Hat-shaped specimens cut along the ED were used to induce forced shear localization, as shown in Figure 1. The shadow parts show the designed shear zones of the specimen. Measured sizes of the hat-shaped specimens of designed shear zones are shown in the Table 2. The nominal strain was γnom. = 2 × (fbefore − fafter)/(bbefore − abefore). After dynamic deformation, hat-shaped specimens were observed using a Quanta-200 scanning electron microscope (SEM, FEI, Netherlands).    Figure 2b shows the XRD pattern of the specimen. The phase composition of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA includes the FFC phase and the BCC phase. The chemical compositions of the phases were identified by an electron probe technique, as shown in Figure 3 and Table 3. It was found that the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA consists of a light gray FCC matrix phase (marked as point 1), a black (Al, Ni)-rich BCC phase (marked    Figure 2b shows the XRD pattern of the specimen. The phase composition of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA includes the FFC phase and the BCC phase. The chemical compositions of the phases were identified by an electron probe technique, as shown in Figure 3 and Table 3. It was found that the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA consists        Figure 5 shows the true stress-strain curves of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA deformed at strain rates of 550, 1300, 2200, and 3000 s −1 . The yield strengths of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA were 754, 878, 958, and 1057 MPa at strain rates of 550, 1300, 2200 and 3000 s −1 , respectively. The saw-like curves are much serious in dynamic compression strain-stress curves. As we observed from the optical micrograph and EPMA maps, the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA has small (Al,Ni)rich BCC phase particles and M23C6 phase particles. The saw-like curves could be attributed to the interaction between the dislocation and (Al,Ni)-rich BCC phase particles plus the M23C6 phase particles.  HEA were 754, 878, 958, and 1057 MPa at strain rates of 550, 1300, 2200 and 3000 s , respectively. The saw-like curves are much serious in dynamic compression strain-stress curves. As we observed from the optical micrograph and EPMA maps, the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA has small (Al,Ni)rich BCC phase particles and M23C6 phase particles. The saw-like curves could be attributed to the interaction between the dislocation and (Al,Ni)-rich BCC phase particles plus the M23C6 phase particles.  The trend of the yield strength of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA at quasi-static and dynamic loading tests is presented in Figure 6. The yield strength increased as a function of the strain rate, and the strain rate sensitivity m can be defined as follows:

Stress-Strain Curves of the High Entropy Alloy
where σ and . ε are the yield strength and strain rate, respectively. The trend of the yield strength of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA at quasi-static and dynamic loading tests is presented in Figure 6. The yield strength increased as a function of the strain rate, and the strain rate sensitivity m can be defined as follows: where σ and ε  are the yield strength and strain rate, respectively.
The value of strain rate sensitivity under quasi-static testing conditions was 4.29 × 10 −3 , and the value of strain rate sensitivity under dynamic loading conditions was 0.192, which shows a strong strain-rate dependence of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA at high strain rates. The Johnson-Cook model, which is considered to have a huge strain, high strain rate, and high temperature, was used in this work to describe the plastic deformation of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA. The equivalent flow stress σ can be expressed by the following equation: where A, B, and C are material constants, and ε and n are the equivalent plastic strain and the strain hardening exponent, respectively. * • ε is the normalized strain rate which can be expressed as The value of strain rate sensitivity under quasi-static testing conditions was 4.29 × 10 −3 , and the value of strain rate sensitivity under dynamic loading conditions was 0.192, which shows a strong strain-rate dependence of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA at high strain rates. The Johnson-Cook model, which is considered to have a huge strain, high strain rate, and high temperature, was used in this work to describe the plastic deformation of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA. The equivalent flow stress σ can be expressed by the following equation: where A, B, and C are material constants, and ε and n are the equivalent plastic strain and the strain hardening exponent, respectively.
. ε * is the normalized strain rate which can be expressed as ε is the strain rate and . ε 0 is a reference strain rate that is equal to 1 × 10 −3 s −1 . Using the Matlab program ( The strain hardening rate (dσ/dε) curve for the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA at the strain rate of 1 × 10 −3 s −1 along with the stress-strain curve is shown in Figure 8a. It can be seen that the value of the strain hardening rate was 1621 MPa at a strain level of 0.2, which is much higher than that of most engineering structural alloys, including AlxCoCrFeNi HEA, as shown in Figure 8b. Therefore, the addition of Mo and C elements can improve the strain hardening rate of AlxCoCrFeNi HEA.  Figure 9 shows the hat-shaped specimens with different nominal strain levels used to investigate The strain hardening rate (dσ/dε) curve for the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA at the strain rate of 1 × 10 −3 s −1 along with the stress-strain curve is shown in Figure 8a. It can be seen that the value of the strain hardening rate was 1621 MPa at a strain level of 0.2, which is much higher than that of most engineering structural alloys, including Al x CoCrFeNi HEA, as shown in Figure 8b. Therefore, the addition of Mo and C elements can improve the strain hardening rate of Al x CoCrFeNi HEA. The strain hardening rate (dσ/dε) curve for the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA at the strain rate of 1 × 10 −3 s −1 along with the stress-strain curve is shown in Figure 8a. It can be seen that the value of the strain hardening rate was 1621 MPa at a strain level of 0.2, which is much higher than that of most engineering structural alloys, including AlxCoCrFeNi HEA, as shown in Figure 8b. Therefore, the addition of Mo and C elements can improve the strain hardening rate of AlxCoCrFeNi HEA.  Figure 9 shows the hat-shaped specimens with different nominal strain levels used to investigate the forced shear localization of the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA. The hat-shaped specimen with a nominal strain of 2.53 was plastically deformed after dynamic deformation, and a small crack was generated at the upper part of the specimen, as shown in Figure 9a. When the designed nominal strain increased to 5.30, the designed shear zones in the hat-shaped specimen consisted of a predominant fracture zone and a small deformation zone, as shown in Figure 9b. Figure 9c is an enlarged view of the red rectangle in Figure 9b, and a short shear band with a width of about 10 microns can be observed. When the designed nominal strain increased to 9.83, the hat-shaped  Figure 9 shows the hat-shaped specimens with different nominal strain levels used to investigate the forced shear localization of the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA. The hat-shaped specimen with a nominal strain of 2.53 was plastically deformed after dynamic deformation, and a small crack was generated at the upper part of the specimen, as shown in Figure 9a. When the designed nominal strain increased to 5.30, the designed shear zones in the hat-shaped specimen consisted of a predominant fracture zone and a small deformation zone, as shown in Figure 9b. Figure 9c is an enlarged view of the red rectangle in Figure 9b, and a short shear band with a width of about 10 microns can be observed. When the designed nominal strain increased to 9.83, the hat-shaped specimen was fractured, as shown in Figure 9d. Some dimples and streamlines were observed along the shear direction, as shown in Figure 9e, which mean that shear bands were generated and then the specimen rapidly fractured along the shear band. predominant fracture zone and a small deformation zone, as shown in Figure 9b. Figure 9c is an enlarged view of the red rectangle in Figure 9b, and a short shear band with a width of about 10 microns can be observed. When the designed nominal strain increased to 9.83, the hat-shaped specimen was fractured, as shown in Figure 9d. Some dimples and streamlines were observed along the shear direction, as shown in Figure 9e, which mean that shear bands were generated and then the specimen rapidly fractured along the shear band. The formation of the shear band can be attributed to the instability of thermal viscoplastic behavior. The critical condition of the constitutive instability can be expressed as

Shear Localization of the High Entropy Alloy
where τ is the shear stress, γ is the shear strain, and is the shear strain rate.
The strain hardening ( ) and strain rate hardening ( • ) values are greater than 0, and the thermal softening ( ) value is less than 0. When the value of thermal softening is greater than the values of strain hardening and strain rate hardening, shear localization happens. Li et al. [24] investigated the shear localization of Al0.3CoCrFeNi HEA and found the value of strain hardening was greater than the value of thermal softening, which explains the failure of the Al0.3CoCrFeNi HEA to form a shear band. In our work, with the addition of the Mo and C elements, the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA had a much higher strain hardening rate than that of the Al0.3CoCrFeNi HEA. However, the shear band was generated in the (Al0.5CoCrFeNi)0.95Mo0.025C0.025 HEA. This was due to the dissolved Mo atoms in the matrix phase, which hinder the heat diffusion, thus decreasing the thermal conductivity. The decreasing of thermal conductivity can increase the value of thermal softening, therefore promoting the generation of shear bands. Because of the high strain hardening rate and low interfacial strength [25], the shear band is very short and easily fractured along the shear direction. The formation of the shear band can be attributed to the instability of thermal viscoplastic behavior. The critical condition of the constitutive instability can be expressed as where τ is the shear stress, γ is the shear strain, and .
γ is the shear strain rate. The strain hardening ( ∂τ ∂γ ) and strain rate hardening ( ∂τ ∂ . γ ) values are greater than 0, and the thermal softening ( ∂τ ∂T ) value is less than 0. When the value of thermal softening is greater than the values of strain hardening and strain rate hardening, shear localization happens. Li et al. [24] investigated the shear localization of Al 0.3 CoCrFeNi HEA and found the value of strain hardening was greater than the value of thermal softening, which explains the failure of the Al 0.3 CoCrFeNi HEA to form a shear band. In our work, with the addition of the Mo and C elements, the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA had a much higher strain hardening rate than that of the Al 0.3 CoCrFeNi HEA. However, the shear band was generated in the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA. This was due to the dissolved Mo atoms in the matrix phase, which hinder the heat diffusion, thus decreasing the thermal conductivity. The decreasing of thermal conductivity can increase the value of thermal softening, therefore promoting the generation of shear bands. Because of the high strain hardening rate and low interfacial strength [25], the shear band is very short and easily fractured along the shear direction. However, it shows that the shear band can coordinate deformation in the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA under high velocity loading.

Conclusions
The (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA prepared by powder extrusion has a uniform FCC + BCC solid solution structure and consists of the FCC matrix phase, the (Al, Ni)-rich BCC phase, and the (Cr, Mo, C)-rich M 23 C 6 carbide phase. The MoC phase can also be identified in the Mo-rich M 23 C 6 carbide phase. The (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA shows a strong strain rate sensitivity at high strain rates, and the yield strength of the HEA increases from 754 to 1057 MPa as the strain rate increases from 550 to 3000 s −1 . The Johnson-Cook model was used to describe the dynamic flow behavior. The addition of Mo and C elements can improve the strain hardening rate of the Al x CoCrFeNi HEA. A short shear band of about 10 microns in width was generated in the designed shear zone and then the specimen quickly fractured along the shear band, which indicates that the shear band can coordinate deformation in the (Al 0.5 CoCrFeNi) 0.95 Mo 0.025 C 0.025 HEA under high velocity loading.