Introduction

Due to the equiatomic concentration of each component and high mixing entropy, the high entropy alloys have varied effects compared with conventional alloys and attract great attention for their unique compositions, excellent properties, and huge scientific importance (Ref 1, 2). Different techniques have been explored to synthesize high entropy alloys, such as arc-melting (Ref 3), laser cladding (Ref 4), mechanical alloying, and spark plasma sintering (Ref 5, 6), etc. Among these methods, the arc melt casting process is widely used in preparing high entropy alloys. However, shape and size of the final products prepared by this method are limited. The composition segregation is also inevitable in as-cast ingots. By contrast, the spark plasma sintering technique, which can consolidate elemental powder to high density rapidly by pressure and passing electric pulse current (Ref 5), is a preferable route for synthesizing advanced materials. The products prepared by the spark plasma sintering technique have a bigger size and more homogeneous components. Therefore, it is a convenient and economical way to prepare the high entropy alloys.

Among the high entropy alloy systems, the equiatomic CoCrFeMnNi high entropy alloy is generally recognized as a “model” high entropy alloy with a simple FCC structure, and exhibits both remarkable ductility and fracture toughness properties. Recent literature reports indicated that the strength of the alloy is relatively low, only around 200 MPa in the as-cast state (Ref 7). Large quantities of the published data are obtained from tensile (Ref 8) or compressive tests (Ref 9) at low strain rate, especially in quasi-static state. In addition, the influence of composition (Ref 10) or grain size (Ref 11) on microstructure and mechanical properties of the high entropy alloy are investigated. Also, the effects of dislocation and element addition on microstructural evolution at different strain rate levels are investigated (Ref 12, 13). Serration behavior of the high entropy alloys can be defined as a saw-like appearance in the strain-stress curves (Ref 3). They are often exhibited at a medium strain rate of 1 × 10−3 s−1 or at low temperatures (Ref 3). However, the microstructural evolution and related serration behavior of the equiatomic CoCrFeMnNi high entropy alloy under high strain rate deformation are also seldom reported.

In the present paper, we focus on the dynamic mechanical behavior of the equiatomic CoCrFeMnNi high entropy alloy prepared by spark plasma sintering. The aims of this paper are: (1) to report the mechanical properties and the microstructure of the CoCrFeMnNi high entropy alloy under high strain rate deformation; (2) to obtain the Zerilli-Armstrong plastic model of the alloy; (3) to discuss the microstructural mechanism for serration behavior of the alloy deformed at high strain rate.

Experimental and Procedures

High purity Co, Cr, Fe, Mn, and Ni powders of an equiatomic ratio were melted in an induction-heated vacuum furnace (Ref 12). The melt was dropped through a ceramic tube and atomized by high purity Ar with the atomization pressure of 4 MPa. The ceramic tube is made of Al2O3 materials and does not interact chemically or physically with the melt. The liquid droplet was filled in the atomization chamber, cooled down, and solidified to powder. Then, the powder was collected and sieved. The average size of the gas-atomized powder is less than 20 μ, as shown in Fig. 1.

Fig. 1
figure 1

Scanning electron micrograph of the gas-atomized powder

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The gas-atomized powder was put into a graphite die with a diameter of 40 mm. Spark plasma sintering was conducted in a HP D 25/3 SPS equipment with a vacuum pressure of 1 × 10−3 Pa (Ref 12). The powders were heated to 1000 °C, and held for 480 s at a pressure of 30 MPa. After the sintering, the CoCrFeMnNi high entropy alloy was cooled down to ambient temperature in the furnace. The final size of the sintered specimens is a height of 15 mm and diameter of 40 mm. The chemical composition is given in Table 1.

Table 1 Chemical composition of the CoCrFeMnNi high entropy alloy
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Cylindrical specimens with diameters of 4 or 6 mm were machined from the sintered specimens with the impact axes parallel to the longitudinal direction. To ensure uniaxial deformation conditions, the end faces of the specimens were lubricated. The impact tests were performed at varying strain rates ranging from 1 × 103 to 3 × 103 s−1 and ambient temperature, using a split-Hopkinson pressure bar system.

When the cylindrical specimens were loaded by a split-Hopkinson pressure bar, the force applied to the deformation region was calculated from data collected by the strain gages on the incident and transmitted bars. The strain rate, true strain, and true stress can be obtained by the following equations.

$$\dot{\varepsilon } = - \frac{{2C_{0} }}{{L_{\text{s}} }}\varepsilon_{\text{r}} (t)$$
(1)
$$\varepsilon = - \frac{{2C_{0} }}{{L_{\text{s}} }}\int_{0}^{t} {\varepsilon_{\text{r}} (t)} dt$$
(2)
$$\sigma = \frac{{A_{0} }}{{A_{\text{s}} }}E_{0} \varepsilon_{\text{t}} (t),$$
(3)

where E 0 and C 0 are elastic modulus and elastic wave speed in the split-Hopkinson pressure bar; A 0 is the cross-sectional area of the bar; A s and L s are the cross-sectional area and the length of the cylindrical specimens; ε r(t) and ε t(t) are the experimentally measured strain of incident and transmitted stress pulse on the split-Hopkinson pressure bars, respectively.

The average strain rate of the specimens during dynamic deformation can be calculated using Eq 1. Thus, the specimens (A-H) are loaded at strain rates of 1200, 1260, 1400, 1600, 2500, 2700, 2710, and 2800 s−1, respectively.

The specimens for investigation were cut from the cylindrical specimens by electrical discharge machining. The etchant for the CoCrFeMnNi high entropy alloy was 10 mL hydrochloric acid + 10 mL hydrofluoric acid + 10 mL nitric acid + 10 mL water. Optical microscopy was performed with POLYVAR-MET. Crystallographic structures of the alloy were identified by x-ray diffraction (Rigaku D/ MAX-2500 x-ray diffractometer), using a Cu target at an operating voltage of 40 kV and current 250 mA. The differential scanning calorimetry (DSC) experiment was carried out using a simultaneous thermal analyzer (NETZSCH STA 449F3), and the heating rate was fixed at 10 K/min from room temperature to 1400 °C. Scanning electron microscopy (SEM) observations were carried out with a FEI Quanta—250 scanning electron microscope operated at 20 kV.

Results and Discussion

Microstructure of the CoCrFeMnNi High Entropy Alloy

Figure 2 shows the optical micrograph of the sintered specimen. It can be seen that the gas-atomized powder is sintered, and the grains are polygonal. The x-ray diffraction analytical results show that the CoCrFeMnNi high entropy alloy consists of a simple FCC structure, as shown in Fig. 3. The plane scanning of elements Co, Cr, Fe, Mn, and Ni is taken across the transverse section of the specimen, as shown in Fig. 4. The element contents of Co, Cr, Fe, Mn, and Ni are 19.8, 19.94, 20.6, 19.34, and 20.32 atomic percent (at.%), respectively. The distribution of these elements in the sintered specimen is extremely homogeneous. Therefore, the CoCrFeMnNi high entropy alloy is successfully prepared by the spark plasma sintering technique.

Fig. 2
figure 2

Optical micrograph of the CoCrFeMnNi high entropy alloy and cylinder specimen

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Fig. 3
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The XRD pattern of the CoCrFeMnNi high entropy alloy

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Fig. 4
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Elemental planar scan of the CoCrFeMnNi high entropy alloy

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Mechanical Responses of the CoCrFeMnNi High Entropy Alloy

The relation of the true flow stress and true strain in the deformation region can be obtained using Eq 2 and 3, as shown in Fig. 5. These stress-strain curves demonstrate the deformation process of the CoCrFeMnNi high entropy alloy. A certain strain hardening and strain rate hardening can be found in these stress-strain curves. The dynamic yield strength, which distributes from 500 to 700 MPa, presents a positive relationship with strain rate, as shown in Fig. 6. Beyond the dynamic yield strength, serration behavior can also be observed in these stress-strain curves.

Fig. 5
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Compressive true stress-strain curves of the CoCrFeMnNi high entropy alloy at high strain rate

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Fig. 6
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Dynamic yield strength-strain rate curve of the CoCrFeMnNi high entropy alloy. The black line is the linear fit of the experimental data

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The Constitutive Equation of the CoCrFeMnNi High Entropy Alloy

Zerilli-Armstrong (Z-A) plastic model is one of the common physically based constitutive models (Ref 14). It is derived based on the dislocation mechanisms which play an essential role in the plastic deformation of metallic materials under various deformation conditions. The Zerilli-Armstrong plastic model has a relatively simple expression compared to other dislocation-based constitutive models. The main characteristic of the model is that each material structure type has a different expression due to the different strain rate controlling mechanism for the particular structure.

In the present work, the Zerilli-Armstrong plastic model which is used for predicting the strain rate flow behavior of the CoCrFeMnNi high entropy alloy with face-centered cubic (FCC) structure can be represented as follows (Ref 14):

$$\sigma = (C_{1} + C_{2} \times \varepsilon^{P} )e^{{T \times [C_{3} \times \ln (\dot{\varepsilon }) - C_{4} ]}},$$
(4)

where C 1, C 2, C 3, C 4, and P are material constants. Note that T is 298.15 K. Furthermore, σ is the flow stress, ε is the equivalent plastic strain, \(\dot{\varepsilon }\) is the equivalent plastic strain rate (Ref 15).

The values of constants C 1, C 2, C 3, C 4, and P in Eq (4) are determined using a least-squares regression analysis technique. The stress-strain curves of specimens A and G are nearly the same as specimens B and H, respectively. Thus, the stress-strain curves of specimens A, C, D, E, F, and H, are chosen from Fig. 5, as shown in Fig. 7. The constants in the Zerilli-Armstrong plastic model are found to be as follows: C 1 = 600 MPa; C 2 = 491.85 MPa; C 3 = 4.679 × 10−4; C 4 = 3.822×10−3; T = 298.15 K; and P = 0.764.

Fig. 7
figure 7

Comparison between the experimental and predicted stress by the Zerilli-Armstrong plastic model. The strain rate for A, C, D, E, F, and H are 1200, 1400, 1600, 2500, 2700, and 2800 s−1, respectively

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Therefore, the constitutive equation based on the Zerilli-Armstrong plastic model can be obtained as follows:

$$\upsigma = \left( {600 + 491.85 \times \varepsilon^{0.764} } \right) \times e^{{298.15\; \times \;\left[ {4.679 \times 10^{ - 4} \; \times \;\ln (\dot{\varepsilon })\; - \;3.822\; \times \;10^{ - 3} } \right]}}$$
(5)

As shown in Fig. 7, the theoretical results obtained from Eq 4 for the stress-strain response of the present CoCrFeMnNi high entropy alloy specimens are in good agreement with the experimental measurements.

Microstructure of the Deformed Alloy

Figure 8 shows the optical micrograph of the deformed specimen H deformed at the strain rate of 2800 s−1. The grains in the specimen are squashed after plastic deformation. The deformation band marked by an arrow is also observed.

Fig. 8
figure 8

Optical micrograph of the deformed CoCrFeMnNi high entropy alloy

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The serrations on the corresponding stress-strain curve in Fig. 9 are invisible. Figures 10, 11, 12, and 13 show the scanning electron micrographs of the specimens A, B, G, and H at strain rates 1200, 1260, 2710, and 2800 s−1, respectively. Nearly no deformation can be observed in the specimen A, as shown in Fig. 10. However, numerous cracks and microvoids emerge in the boundaries of the grains in the specimen B which has the same deformation level as the specimen A, as shown in Fig. 11. The serrations on the corresponding stress-strain curve are visible, as shown in Fig. 9. With increasing of the strain rate, the serration behavior is also visible in the stress-strain curves of the specimens G and H. The shear bands with about 2 μ in width are generated in the specimen G, as shown in Fig. 12. The cracks along the shear bands are induced by the coalescence of microvoids, as shown in Fig. 13. Therefore, the serration behavior of the CoCrFeMnNi high entropy alloy at high strain rate is sensitive to the change of the strain rate.

Fig. 9
figure 9

Compressive true strain curves of the CoCrFeMnNi high entropy alloy at high strain rate. The strain rate for A, B, G, and H are 1200, 1260, 2710, and 2800 s−1, respectively

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Fig. 10
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Scanning electron micrograph of the CoCrFeMnNi high entropy alloy deformed at the strain rate of 1200 s−1

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Fig. 11
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Scanning electron micrographs of the microvoids formed on the boundaries of the grains. (b) Has a higher magnification than (a)

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Fig. 12
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Scanning electron micrographs of the shear bands in the CoCrFeMnNi high entropy alloy

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Fig. 13
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Scanning electron micrographs of the cracks in the specimen. (a) The cracks along the shear bands. (b) The cracks induced by the coalescence of microvoids

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Calculation of Temperature in the Deformation Zone

At high strain rates (>1 × 103 s−1), the deformation process is extremely fast and can be considered as an adiabatic process. Temperature rise in the adiabatic deformation band associated with the deformation plays a significant role in the study of microstructure mechanism and is calculated by the following equation (Ref 16, 17):

$$\Delta T = T - T_{0} = \frac{\eta }{{\rho C_{\text{V}} }}\int_{{\varepsilon_{\text{s}} }}^{{\varepsilon_{\text{e}} }} {\sigma d\varepsilon },$$
(6)

where T 0 is the ambient temperature, ρ is the mass density, C V is the heat capacity, ε is the strain, σ is the stress, and η is the fraction of plastic energy converted to heat (Ref 16). The ρ and C V for CoCrFeMnNi high entropy alloy are 8042 kg/m3 and 430 J/kg K (Ref 12), respectively. T 0 = 298 K, and η = 0.9 (Ref 16).

Substituting Eq 5 into Eq 6, the calculated general temperature in the deformed specimen G is about 1300 K. The melting point of the CoCrFeMnNi high entropy alloy is about 1600 K, as shown in Fig. 14. In the deformed specimens, the distribution of stress is also fairly inhomogeneous and always concentrates in the severe deformation zone, such as the shear band. The local hotspots in the specimen weaken the bonding of the grains. The cracks and microvoids can be easy to emerge in the severe deformation zone, as shown in Fig. 12 and 13. Therefore, the local hotspots and thermal softening caused by high strain rate deformation are important reasons causing the collapse of the grains and the serration behavior of the CoCrFeMnNi high entropy alloy at high strain rate.

Fig. 14
figure 14

DSC curve of the CoCrFeMnNi high entropy alloy (the heating rate of DSC is 10 K/min)

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Mechanism of Dynamic Serration Behavior

The above analysis on the microstructure and the thermodynamic calculation results of the CoCrFeMnNi high entropy alloy specimens deformed at high strain rates suggest that the collapse of the grains in the deformation zone and the thermal softening are the essential reasons for the related serration behavior of the CoCrFeMnNi high entropy alloy at high strain rate.

As shown in Fig. 15, the microstructural mechanism for the serration behavior of the CoCrFeMnNi high entropy alloy at high strain rate is described as follows. (a) At the beginning of the dynamic deformation, the dislocations in the deformation region are immediately accumulated. (b) The grains are elongated at an angle about 45° to the horizontal. Numerous dislocations are accumulated in the boundaries of the elongated grains. (c) As the deformation continues, the width of elongated grains becomes narrow. The local hotspots weaken the bonding of the grains. The boundaries of the elongated grains collapse gradually when the bonding of the grains become weak, and the concentrated stress is much larger than the bonding strength of the grains. Numerous microvoids form on the boundaries of the grains. The shear bands are also generated in the specimen. In this stage, the serration behavior of the CoCrFeMnNi high entropy alloy appears. (d) As soon as the boundaries of microvoids reach the neighbor, the cracks are formed by the coalescence of microvoids.

Fig. 15
figure 15

Schematic illustration of microstructural evolution during dynamic plastic compressive deformation: (a) homogeneous distribution of dislocations, (b) formation of elongated grains, (c) collapse of boundaries, and emergence of microvoids and shear bands, and (d) coalescence of microvoids, and formation of cracks

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Conclusion

The equiatomic CoCrFeMnNi high entropy alloy prepared by the spark plasma sintering technique consists of a simple FCC structure. Serration behavior is observed in the stress-strain curves. The dynamic yield strength, which distributes from 500 to 700 MPa, presents a positive relationship with strain rate. The Zerilli-Armstrong plastic model of the CoCrFeMnNi high entropy is obtained as follows:

$$\sigma = \left( {600 + 491.85 \times \varepsilon^{0.764} } \right) \times e^{{298.15\; \times \;\left[ {4.679 \times 10^{ - 4} \; \times \;\ln (\dot{\varepsilon }) - 3.822\; \times \;10^{ - 3} } \right]}}$$
(7)

The serration behavior of the CoCrFeMnNi high entropy alloy at high strain rate is sensitive to the strain rate. Microvoids form on the boundaries of the grains in the specimen deformed at high strain rate. With increasing of the strain rate, the shear bands with the width about 2 μ are found in the specimens. The cracks along the shear bands and the cracks induced by the coalescent microvoids are also observed. The collapse of the grains in the deformation zone and the thermal softening are the essential reasons for the related serration behavior of the CoCrFeMnNi high entropy alloy under high strain rate deformation.