Nanoindentation characterised plastic deformation of a Al 0.5 CoCrFeNi high entropy alloy

Abstract

The plastic deformation of a high entropy alloy Al_0.5CoCrFeNi was investigated by instrumented nanoindentation over a broad range of strain rates at room temperature. Results show that the creep behaviour depends on the strain rate remarkably. In situ scanning images showed a significant pile up around the indents, demonstrating that a highly localised plastic deformation occurred in the process of nanoindentation. Under different strain rates, contact stiffness and elastic modulus basically remain unchanged. However, the hardness decreases as indentation depth increases due to indentation size effect. For the same maximum load, serrations became less prominent as the loading rate of indentation increased. Similar serrations have been observed in the current alloy upon quasi-static compression.

Keywords

High entropy alloy Plastic deformation Serrations Nanoindentation

Introduction

In the past decade, high entropy alloys (HEAs) have received increasing attention because of their unusual structural properties.^1–6 Traditionally, in designing an alloy, the major component is selected on the basis of a specific property requirement, and other alloying components are added in small amounts to achieve secondary properties without sacrificing the primary property. By contrast, HEAs are multiprincipal component alloys with at least five equiatomic or near equiatomic alloy elements.⁷ However, it is of particular interest to note that, despite containing a large number of components, HEAs actually exhibit a significant degree of mutual solubility and tend to form simple face centred cubic (FCC) and/or body centred cubic (BCC) solid solutions, instead of complex ordered intermetallics,⁸ which is often attributed to a high mixing entropy. As a result of the different atomic sizes and chemical bonds of the constituent elements, HEAs posses a highly distorted lattice structure,⁹ leading to an expected non-traditional plastic deformation in HEAs.

Investigations on the nanoscale mechanics have sprung up along with the development of nanoindentation instrument.¹⁰ The material hardness and modulus have been well evaluated at nanoindentation tests with the standard procedures,^11,12 and there has been considerable progress in the measurement of other mechanical parameters as well, including hardening exponent,¹³ creep parameter¹⁴ and residual stresses.¹⁵ Zhu et al.¹⁶ characterised the nature of incipient plasticity of a FeCoCrMnNi HEA with a single FCC structure and found that the maximum shear stress required to initiate plasticity was within 1/5 to 1/10 of the shear modulus and relatively insensitive to grain orientation. They observed that the plastic deformation was a thermally activation process. Wang et al.¹⁷ studied the temperature dependence of the hardness of Al_xCoCrFeNi and observed that the hardness decreased with temperature and the possible change of the deformation mechanism. Wang et al.¹⁸ found a crossover behaviour in the initial creep stage during nanoindentation with a constant load for a CoFeNi HEA and proposed that the initial creep behaviour is dominated by the strain hardening at the beginning and then transit into the dislocation migration induced viscous stage.

In the present study, the plastic deformation of Al_0.5CoCrFeNi HEA is investigated at room temperature through instrumental nanoindentation. The purpose of this paper is to report our preliminary results on the strain rate sensitivity of creep behaviour and serrated flow and indentation size effect (ISE) in nanohardness during nanoindentation of the HEA. Additionally, the serration behaviors were similar to those from quasi-static compression on the same HEA.

Experimental

Samples preparation

Ingots with a nominal composition of Al_0.5CoCrFeNi alloy was prepared by arc melting pure elements with a purity higher than 99.95 wt- under a high purity argon atmosphere on a water cooled Cu hearth. The alloy was remelted four times in order to obtain homogeneity. Cylindrical rods with a diameter of 3 mm were synthesised by copper mould suction casting. The microstructure was examined using scanning electron microscopy (SEM) equipped with energy dispersive spectrometer (EDS), and using transmission electron microscopy (TEM). Before nanoindentation, the alloy was mechanically polished to a mirror finish.

Nanoindentation tests

Nanoindentation experiments were performed on MTS Nano Indenter XP system using a Berkovich diamond tip at room temperature. Initial machine calibration was conducted on a fused silica standard to ensure the validity of testing data. In order to remove the thermal effect, thermal drift was maintained below 0.05 nm s^− 1 during each test. The load holding time was settled as 10 s to determine whether a creep behaviour occurred. The 20 μm interval was chosen to avoid any overlap of plastic zones created by neighbouring indentations. At least three indents at each loading rate were performed to verify the accuracy and scatter of the indentation data.

The tests were carried out over both strain rate control and loading rate control. Indentations for Al_0.5CoCrFeNi sample with various strain rates of 0.01, 0.2 and 0.5 s^− 1 under 600 and 2000 nm depth limitations were employed to study strain rate sensitivity and ISE in nanohardness. In addition, indentations were performed in load control mode to load as high as 200 mN using loading rates from 0.5 to 20 mN s^− 1, where the distinct pop in events could be easily detected to capture the characteristics of the serrated flow. After nanoindentation, the images around the indents were immediately examined using in situ scanning system. Finally, cylindrical samples of the alloy with an aspect ratio of 2:1 were prepared for quasi-static compression with a strain rate of 5 × 10^− 4 at room temperature.

Theory

A comprehensive method for determining the hardness and elastic modulus from depth sensing indentation using load–displacement data was developed by Oliver and Pharr.¹¹ For a perfect Berkovich diamond indenter, the projected contact area A_c can be linked to the contact indentation depth h_c by an area function where C₀, C₁, C₃ and C₄ are fitting coefficients. According to Oliver and Pharr,¹¹ the contact depth is determined by where h_max is the maximum indentation depth, P_max is the corresponding maximum load, S is the contact stiffness determined by the slope of the load–displacement curve at the initial stage of unloading curve and ϵ = 0.75 is a constant for the Berkovich indenter. The hardness of a material, defined as the mean pressure exerted by the indenter at maximum load, is calculated by

The reduced elastic modulus E_r can be extracted by¹¹ where β = 1.034 is the shape constant of Berkovich tip. Since the reduced elastic modulus is the combined response of the indenter tip and the sample, the elastic modulus of sample E can easily be obtained from the following relationship¹¹ where ν is the Poisson's ratio for the test material, and E_i and ν_i are the elastic modulus and Poisson's ratio respectively of the indenter. For the diamond indenter, the elastic constants E_i = 1141 GPa and ν_i = 0.07 are often used.^11,19

Results and discussion

Figure 1 shows the SEM image of the etched as cast sample. In the Al_0.5CoCrFeNi alloy, the interdendrite region clearly displays a periodic, fine scale structure consisting of alternating bright and dark interconnected phases. The alloy possesses a duplex FCC plus BCC structure.²⁰ Nominal composition of the alloy and chemical analysis of the different regions or phases were analysed using EDS, and the results are listed in Table 1.²⁰

Images (SEM) of etched as cast Al_0.5CoCrFeNi alloy

Table 1

Nominal composition of Al_0.5CoCrFeNi alloy and chemical analysis of different regions or phases by EDS/at-²⁰

			Chemical composition/at-
Nominal composition/at-	Phase	Crystal structure	Al	Co	Cr	Fe	Ni
Al_11.2Co_22.2Cr_22.2Fe_22.2Ni_22.2	DR	FCC	11.0 ± 0.4	22.3 ± 0.7	21.7 ± 1.9	22.5 ± 0.4	22.5 ± 0.9
	ID	BCC	17.5 ± 1.6	19.0 ± 0.8	24.0 ± 0.8	18.2 ± 0.4	21.3 ± 1.7
	B	BCC	27.4 ± 1.8	17.1 ± 0.7	13.1 ± 0.4	12.8 ± 1.0	29.6 ± 1.1

DR: dendrite, ID: interdendrite, B: boundary between DR and ID.

Figure 2a and b shows the load–displacement (P-h) curves of the alloy under different strain rates with a depth limit of 600 and 2000 nm respectively. Creep behaviour has been clearly observed at the higher strain rate of 0.5 s^− 1, although it gradually becomes weaker with decreasing strain rate. Under high strain rate, more viscous deformation related to the dislocation dynamics will be accumulated after loading,¹⁸ transforming into larger creep deformation during the holding stage. Figure 2c plots the creep displacement and corresponding logarithmic fit as a function of holding time under different strain rates with a depth limit of 2000 nm. It is interesting to note that the creep rate declines quickly at the initial holding stage and then decreases steadily, similar to the transient creep stage and steady state creep stage in the traditional uniaxial tensile test for creep respectively.²¹ However, nanoindentation creep does not involve the failure stage owing to the local indentation into the test specimen. Additionally, the indentation creep rate at the initial holding stage increases as the strain rate is increased. Creep depends on the material and normally diminishes to very low values within some seconds.²² It is noteworthy that the shape of creep curves for investigated alloy can be described with the well known logarithmic creep formula that was developed for metals²² where A and B are fitting parameters, and Δh and t are the displacement and time at the starting of holding time respectively. For metals, the parameters A and B depend among others on temperature, dislocation density, Burgers vector and yielding strengthening.²² The maximum difference between results and measured data is less than 1 nm, demonstrating that the creep behaviour of the Al_0.5CoCrFeNi alloy can be well described by the current logarithmic creep formula. In an attempt to elucidate the deformation morphologies for this alloy composition, typical in situ scanning images of the indent after nanoindentation at a strain rate of 0.01 s^− 1 with a depth limit of 2000 nm using a Berkovich tip are shown in Fig. 2d. The surface uplift due to the material pile up can be clearly observed around the indent, as indicated in the insets of Fig. 2d. The significant pile up of material around indenter suggests that a heavy and highly localised plastic deformation occurred in the process of nanoindentation.

Load–displacement (P-h) curves under different strain rates with depth limit of a 600 and b 2000 nm respectively. Creep displacement and corresponding logarithmic fit during the holding stage under different strain rates with depth limit of c 2000 nm. In situ scanning images after nanoindentation at strain rate of 0.01 s^− 1 with Berkovich indenter

According to the Oliver and Pharr method,^11,12 some important mechanical properties derived from the P-h curves of nanoindentations at different strain rates, including the maximum depth h_max, contact stiffness S, elastic modulus E and hardness H, are summarised in Table 2. Although the creep behaviour is strongly dependent on the strain rate, the mechanical properties obtained at different strain rates do not appear to be much different, indicating that the mechanical properties are less strain rate dependent. Figure 3a and b illustrates the average value and corresponding standard deviation of modulus and hardness of Al_0.5CoCrFeNi alloy as a function of indentation strain rate with a depth limit of 600 and 2000 nm respectively. It was revealed that the small change of elastic modulus can be attributed to nuance of contact stiffness under different strain rates resulted from the pile up during indentation process.²¹ However, the hardness decreases with increasing indentation depth, in which the underlying physical nature is elucidated based on ISE that reduction in the indent size leads to both increasing hardness and decreasing plasticity, which can be measured using the concept of geometrically necessary dislocations where the geometrically necessary dislocation density increases with decreasing indentation depth, resulting in the ISE of hardness for crystalline materials.²³

Table 2

Mechanical properties of Al_0.5CoCrFeNi alloy

Depth limit			600 nm			2000 nm
Strain rate/s^− 1	h_max/nm	S/μN nm^− 1	E/GPa	H/GPa	h_max/nm	S/μN nm^− 1	E/GPa	H/GPa
0.01	565.24	617.78	218.88	4.58	2001.77	1976.30	210.10	3.03
0.2	563.29	593.94	217.96	4.89	1978.55	1885.10	192.53	3.05
0.5	571.65	645.04	225.69	4.43	2014.76	1880.50	184.48	2.65
Average	566.73	618.92	220.84	4.64	1998.38	1914.00	195.70	2.91

Average value and corresponding standard deviation of modulus and hardness under different strain rates with depth limits of a 600 and b 2000 nm

In order to describe the dependence of nanohardness H on the depth of an indenter h_max, the power dependence is commonly used in the literature for the characterisation of the ISE²⁴ where A and i are constants.

In Fig. 4, the dependence of the average hardness H on the average maximum depth h_max under the depth limits of 600 and 2000 nm for Al_0.5CoCrFeNi alloy in logarithmic coordinates is shown. It follows from this figure that equation (7) is indeed satisfied and that i = − 0.3176, which agrees well with those varying from − 0.12 to − 0.32 for different materials.²⁴ It is evident that the computed value of the hardness coincides satisfactorily with experimental results obtained at constant loading rate of 0.5 mN s^− 1 with the maximum indentation load of 200 mN. Therefore, the use of the developed technique makes it possible to predict results of nanohardness under different maximum indentation depths.

Dependence of hardness H on maximum displacement h_max for Al_0.5CoCrFeNi alloy and experimental points obtained at constant loading rate of 0.5 mN s^− 1 with the maximum indentation load of 200 mN

Figure 5 shows the representative nanoindentation load–displacement curves during loading for Al_0.5CoCrFeNi alloy under different loading rates. The P-h curves for the alloy exhibit strong rate dependence. At low loading rates, the P-h curves are punctuated by a number of discrete bursts of displacement (or pop ins). Significant serrations can only be observed at a loading rate of 0.5 mN s^− 1. As the loading rates increased, the serrated displacement became less prominent, especially when the loading rate was higher than 10 mN s^− 1, the P-h curves became quite smooth. The serration behaviour of plastic flow can be explained by the displacement dependence of the strain rate, as plotted in Fig. 6. Here, the indentation strain rate is defined as ,²⁵ which is a non-linear function of time during nanoindentation with a constant loading rate. It can be seen from Fig. 6 that the strain rate during nanoindentation covers a broad range of values from low rates of below 10^− 2 s^− 1 to as high as 10^− 4 s^− 1. In addition, it is interesting to find that significant discontinuities could be only observed in P-h curves recorded during nanoindentation when the strain rate is lower than a critical values, i.e. ∼10^− 2 s^− 1 for the alloy, indicating that the serrated behaviour of the Al_0.5CoCrFeNi alloy is both loading rate and strain rate dependent, which is similar to serrated flow in metallic glasses.²⁶

Typical P-h curves measured on loading portion of nanoindentation experiments at different loading rates. Inset a and b are amplified images displaying serrated behaviors

Indentation strain rate plotted as function of indentation depth under different loading rates

The results in Figs. 5and 6 illustrate a strong rate dependence for serrated behaviour in the alloy studied. The serrations are thought to be correlated with the motion of individual dislocations, the carriers of plasticity in such alloys. The alloy exhibits serrated behaviour during nanoindentation, manifested as a stepped load–displacement curve punctuated by discrete bursts of plasticity. These discrete pop in events correspond to the activation of individual dislocation motions, and the character of serrations is strongly dependent on the indentation loading rate. Slower indentation rates promote more pronounced serrations, and rapid indentations arrest serrated behaviour. All of the present results suggest that the change in serrated behaviour from a low rate to a high rate is dominated by the accommodation between the slip band and the applied strain. If the indentation rate is low, a slip band would have sufficient time to adapt the applied strain, causing a distinct strain burst. Conversely, at high indentation rates, a single slip band cannot accommodate the imposed strain rapidly enough, and consequently, multiple slip bands must operate simultaneously, leading to the disappearance of serrated behavior.²⁶

Figure 7 displays the engineering stress–strain curve of the present Al_0.5CoCrFeNi alloy upon quasi-static compression with the strain rate of 5 × 10^− 4 s^− 1. It can be found that there exist serrations in the magnified region marked by the dashed box, indicating that the alloy responds in jerky way with sudden slips, likely related to the collective motion of dislocations, such as in the Portevin–Le Châtelier effect, or dynamic strain aging.^27,28 Similar to the serrated behaviour at sufficiently low indentation rate during nanoindentation, the Al_0.5CoCrFeNi alloy exhibits prominent serrations as well under compression at the slow strain rate. However, for serrated behaviour, the relationship of the deformation mechanisms upon nanoindentation and slow compression remains unclear. The serration behaviour of HEAs under slowly compression was studied and predicted by the serration statistics using a mean field model.²⁹ The fundamental deformation mechanism of serrated flow of HEAs under slow compression may include dislocation motion and deformation twinning.²⁹ Therefore, additional work is necessary to understand the deformation mechanics of serrated behaviour in HEAs.

Compression stress–strain curve of Al_0.5CoCrFeNi alloy at strain rate of 5 × 10^− 4 s^− 1. Inset shows magnified region marked by dashed box

Conclusions

Instrumented nanoindentation has been used to probe the plastic deformation of Al_0.5CoCrFeNi HEA. Creep behaviour of the alloy shows great strain rate sensitivity. A significant pile up around the indents suggests that a highly localised plastic deformation occurred under nanoindentation. The contact stiffness and elastic modulus under different strain rates are almost unchanged. Reduction in the indentation depth leads to increasing hardness, indicating ISE in nanohardness. Serrated behaviour is found to be strongly dependent on indentation rate, more rapid indentations suppress the serrations. However, slower indentations significantly promote such events. The transition from serrated to non-serrated behaviour is governed by the accommodation between the slip bands and the applied strain. It was revealed that similar serration behaviors were observed in present Al_0.5CoCrFeNi alloy under slow compression at a strain rate of 5 × 10^− 4 s^− 1.

Acknowledgements

J.W.Q. would like to acknowledge the financial support of National Natural Science Foundation of China (no. 51371122) and the Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi (2013). H.J.Y. would like to acknowledge the financial support from State Key Lab of Advanced Metals and Materials (no. 2013-Z03) and the Youth Science Foundation of Shanxi Province, China (no. 2014021017-3). Z.H.W. would like to acknowledge the financial support of the National Natural Science Foundation of China (no. 11390362), the Top Young Academic Leaders of Shanxi and the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi. The financial contributions are gratefully acknowledged.

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