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High strain rate compression behaviour of single phase CoCuFeMnNi high entropy alloy
Journal Pre-proof High strain rate compression behaviour of single phase CoCuFeMnNi high entropy alloy Reshma Sonkusare, Roopam Jain, Krishanu Biswas, Venkitanarayanan Parameswaran, N.P. Gurao PII:
S0925-8388(20)30126-2
DOI:
https://doi.org/10.1016/j.jallcom.2020.153763
Reference:
JALCOM 153763
To appear in:
Journal of Alloys and Compounds
Received Date: 31 August 2019 Revised Date:
1 January 2020
Accepted Date: 8 January 2020
Please cite this article as: R. Sonkusare, R. Jain, K. Biswas, V. Parameswaran, N.P. Gurao, High strain rate compression behaviour of single phase CoCuFeMnNi high entropy alloy, Journal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/j.jallcom.2020.153763. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Credit Author statement Reshma Sonkusare and Roopam Jain performed all the experiments, carried out data analysis and prepared the first draft of the manuscript. Krishanu Biswas, Venkitanarayanan Parameswaran and N. P. Gurao conceptualised and supervised the project as well as edited the final manuscript.
High Strain Rate Compression Behaviour of Single Phase CoCuFeMnNi High Entropy Alloy Reshma Sonkusare1, Roopam Jain1, Krishanu Biswas1, Venkitanarayanan Parameswaran2, N. P. Gurao1* 1
Department of Materials Science and Engineering, Indian Institute of Technology Kanpur, Kanpur208016, India 2
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur-208016, India
*corresponding author (email ID : [email protected] ) Abstract Deformation behaviour of FCC CoCuFeMnNi single phase high entropy alloy (HEA) was studied under quasistatic and dynamic loading conditions in compression at strain rate of 0.001 s-1 and 3000 s-1 using screw driven universal testing machine and Split Hopkinson Pressure Bar respectively. A detailed microstructural characterization was carried out using electron back scatter diffraction (EBSD) while bulk texture measurement was carried out using X-ray diffraction. The high strain rate deformed sample shows high strain rate hardening as well as higher strain hardening that is attributed to operation of deformation twinning as observed from EBSD. The operation of deformation twinning and multiple slip systems leads to grain fragmentation and weakening of characteristic <101> compression texture in sample subjected to high strain rate. Constitutive behaviour of the CoCuFeMnNi HEA explained using the Johnson-Cook phenomenological model further justifies better strain rate and strain hardening response of the alloy compared to individual elements.
Keywords: metals and alloys, mechanical properties, microstructure, dislocations and disclinations, scanning electron microscopy 1
1. Introduction High entropy alloys (HEAs) are a new class of materials with minimum five principal elements having concentration varying from 5 to 35 atomic percentage that show many interesting mechanical and functional properties. The high configurational entropy of mixing (∆
≥ 1.5R, where R is the universal gas constant) stabilizes the solid solution phases
over brittle intermetallic phases [1–4]. HEAs exhibit exceptional mechanical properties and therefore, they have been a subject of tremendous research in the last few years [5–8]. Various investigations have probed the mechanical properties of HEAs across wide strain, strain rate and temperature regimes and have indicated excellent mechanical properties. Tensile behaviour of single phase FCC CoCrFeMnNi HEA shows a very strong dependence on temperature indicating that the thermal component of stress is very important in FCC HEAs unlike conventional pure FCC metals but similar to conventional substitutional solid solution alloys [9,10]. It is therefore, imperative to study the effect of strain rate on deformation behaviour of HEAs [11] to fully understand the fundamentals of deformation processes in HEAs vis a vis traditional alloy. Of particular importance is the dynamic deformation (strain rate > 103 s-1) behaviour of HEAs as additional mechanisms like twinning, shear banding and phase transformation have been reported to occur in conventional metals and alloys at high strain rate deformation [12]. The high strain rate (HSR) behaviour of very few HEAs have been studied so far with major focus on the very first high entropy alloy developed by Cantor et al. [13] due to its unique mechanical properties. Recently, Tsai et al. [14] showed that high strain rate deformation of the Cantor alloy leads to significant rise in yield stress, strain hardening rate and strain rate sensitivity due to extensive nano-twinning and stacking fault hardening. High strain rate behaviour of other HEAs also indicate the higher strain rate sensitivity and excellent work hardening [15– 17] in the dynamic deformation regime. Kumar et al. [15] reported that HSR deformation of
2
Al0.1CrFeCoNi HEA was similar to low stacking fault energy (SFE) materials. Multiple deformation mechanism like thermal softening, dislocation drag, solid solution strengthening, nano twinning, forest dislocation strengthening have been reported to be operative in the dynamic regime for metallic materials [18–21]. Efforts have been made to model the constitutive response using phenomenological and physics based constitutive models [16, 17]. Wang et al. [17] have shown the utility of the physics based Zerilli–Armstrong model [22] which corresponds well with the experimental results. However, a detailed investigation combining mechanical testing with detailed microstructural and textural characterization of single phase high entropy alloy is still missing. The present investigations aims to study the evolution of microstructure and mechanical properties in newly developed equiatomic FCC CoCuFeMnNi HEA with copper-rich nanoclusters (~2.5) [23] for quasistatic and dynamic deformation
in
compression
using state of the art
characterization
tools
and
phenomenological modelling. 2. Materials and methods High purity Co, Cu, Fe, Mn and Ni nuggets were used to prepare the alloy using vacuum arc melting technique with water-cooled copper hearth and non-consumable tungsten electrode. The alloy was homogenized at 1273 K for 24 hours to achieve chemical homogeneity and then water quenched to retain the single phase microstructure. Cylindrical samples with 6 mm diameter and 9 mm height and 6 mm diameter and 6 mm height were machined for quasistatic and dynamic tests respectively using electric discharge machining. Both quasistatic and dynamic tests were conducted at room temperature. Strain rate of 10-3 s-1 and 3000 s-1 were chosen to compare the stress strain response of the two regimes. High strain rate tests were performed using the compression split Hopkinson bar setup which is a widely accepted instrument for intermediate regime of strain rate (102 – 104 s-1). Compression samples were subjected to stress pulse by varying the striker velocity to obtain a strain rate of 3
3000 s-1. Incident, reflected and transmitted pulses were recorded using strain gauges attached on incident and transmitter using which the stress strain relationship was derived [12]. Compression samples were sandwiched between incident (3 m) and transmitted (2 m) bars made of maraging steel of 20 mm diameter. A 300 mm long striker bar was propelled using a gas gun at 6 kg/cm2 pressure to achieve strain rate close to 3000 s-1. For high strain rate experiments stress, strain and strain rate can be calculated from the following equations. = −
(i) = −
(ii) =
(iii) Here,
is longitudional wave velocity in the bars,
is length of the specimen,
and
are respectively the experimentally measured reflected and transmitted strain histories, is the cross-sectional area of the specimen, transmission bars and,
is the cross-sectional area of the incident and
is the elastic modulus of the incident as well as transmission bars.
Three tests were performed at the two strain rates to obtain statistically significant data. The deformed samples were machined along the compression axis from the centre using diamond saw and one half was metallographically prepared by polishing with emery paper followed by alumina cloth polishing and finally with colloidal silica polishing (Vibromet) for electron back scatter diffraction (EBSD). The microstructural examination was carried out in field emission scanning electron microscope Nano Nova SEM 450 FE-SEM operating at 20 kV. EBSD measurement was carried out using EDAX TSL-OIM setup with step size of 0.15 μ".
4
Data analysis was carried out using TSL-OIM version 8 data analysis software. Bulk texture measurements were carried out using Rigaku Ultima diffractometer with Cu Kα radiation, in reflection mode. Three incomplete pole figures 111, 200 and 220 were measured and Resmat software was used to calculate orientation distribution function (ODF) as well as compression direction inverse pole figure (IPF) for all the deformed samples. 3. Results & Discussion 3.1 Initial sample Fig. 1. (a) shows the crystal orientation or inverse pole figure (IPF) map of annealed sample of CoCuFeMnNi HEA with a grain size of 96 µm and is characterized by presence of few annealing twins. Earlier investigations have shown that this HEA is characterized by the presence of CoCuFeMnNi FCC matrix and copper rich nanoclusters with size of 2.5 nm from atom probe tomography results [23]. The presence of few annealing twins in the sample is similar to that of medium stacking fault energy copper and has been reported in previous investigations by the authors [10, 24]. 3.2 Mechanical behaviour True stress - true strain curves at the strain rate of 10-3 s-1 and 3000 s-1 are shown in Fig. 1. (b) for comparing the mechanical behaviour of CoCuFeMnNi HEA. A noticeable strain rate hardening is observed in dynamically deformed sample. In order to obtain better insight of the strain hardening behaviour at different strain rates, Kocks-Mecking plots that provide the evolution of strain hardening rate with plastic stress were determined and are represented in Fig. 1 (b). The Kocks-Mecking plot for the sample tested at low strain rate shows gradual decrease in strain hardening rate with increase in stress indicating delayed dynamic recovery. Earlier investigation by the authors on rolling of CoCuFeMnNi alloy attributed the evolution of Goss-Brass type texture to the operation of planar partial slip in addition to conventional 5
octahedral slip [24]. Thus, the delayed onset of recovery can be attributed to operation of octahedral and partial slip at low strain rate. The strain hardening response of the sample tested at high strain rate is characterized by initial decrease in strain hardening rate followed by a plateau. The plateau in strain hardening curve indicates additional strain hardening from operation of twinning or phase transformation in FCC materials [12]. The Kocks-Mecking plot clearly indicates that there is significant increase in strain hardening with increase in strain rate and more importantly characteristic difference in the nature of the curves indicates operation of different micro-mechanism at high strain rate. In order to decipher the operative micro-mechanism of deformation, detailed microstructural characterization was carried out using electron back scatter diffraction and is discussed in the next section. 3.3 Microstructural evolution In order to isolate the effect of strain rate, CoCuFeMnNi HEA samples were subjected to similar amount of strain in quasistatic and dynamic loading. The crystal orientation or inverse pole figure map along the compression direction on the longitudinal plane of the two samples deformed at quasistatic and dynamic strain rates is shown in Fig. 2. (a, b). Inverse pole figure maps for both the samples are characterized by large colour gradient within the grains with the sample deformed at high strain rate showing lower grain size compared to sample deformed at low strain rate. The colour gradient within the grains corresponds to the orientation gradient and indicates intense slip activity. In order to obtain more insight about the evolution of microstructure, composite map comprising of image quality and grain boundary character was plotted as shown in Fig. 2. (c, d). The sample deformed at high strain rate is characterized by the presence of lenticular deformation twins, which are absent in the sample deformed at low strain rate. In order to verify the presence of deformation twins point to point misorientation across the line AB and CD was plotted as shown in Fig. 2. (f). Misorientation plot along both the lines show misorientation of 60° indicating the presence of 6
deformation twins in the sample which was subjected to high strain rate. The misorientation axis distribution plot for the entire map of the high strain rate deformed sample shows clustering near <111> direction for misorientations between 57° - 63° confirming the presence of deformation twins. Another important observation is the shift in peak KAM value (Fig. 2. (e)) to a higher number for the quasistatic deformed sample compared to high strain rate deformed sample that indicates higher density of dislocations in quasistatic regime. In order to further understand the deformation behaviour, geometrically necessary (GND) dislocation density map [25] was plotted for the octahedral #111% < 110 > slip systems. Sample tested at higher strain rates shows high GND density near the grain boundaries [26] whereas in the sample deformed at low strain rate GNDs are not localized at grain boundaries as shown in Fig. 3. (a). Heavy accumulation of GNDs near grain boundaries is expected to be the cause of grain fragmentation at high strain rate resulting in considerable reduction in grain size as postulated in variety of metals and alloys by Meyers et al. [26, 27]. Additional information on the evolution of area average grain size, intragranular misorientation in terms of KAM, average GND density and grain boundary character for the CoCuFeMnNi sample deformed at low and high strain rate obtained from EBSD is depicted in Table I. It is observed that the high strain rate deformed sample is characterized by lower grain size and higher sigma 3 coincident site lattice boundaries which correspond to deformation twinning in FCC materials. However, the high strain rate sample shows lower average GND density and low angle grain boundary fraction. 3.4 Bulk texture The evolution of deformation texture in compression for CoCuFeMnNi HEA at low and high strain rate is depicted in terms of inverse pole figure in Fig. 3. (b). A pronounced <101> fibre texture along the compression direction which is a characteristic of FCC materials is observed in samples deformed at low and high strain rate with the later showing a weaker 7
texture compared to that of the former. The evolution of crystallographic texture is related to plastic spin as a result of operation of different slip systems to accommodate imposed plastic deformation. The relationship between plastic spin (dω), lattice spin (dΩ) and rigid body rotation (dβ) is provided below dΩ ++++ = dβ+ − dω ++++ (iv) For deformation in compression, the rigid body rotation is zero and hence the plastic spin contributes to lattice spin and dictates texture evolution. Canova et al. [28] had proposed that there is an increase in the number of active slip systems with increase in strain rate that contributes to lower plastic spin. This contributes to weakening of texture for tension and compression where the rigid body rotation is zero [29–31] whereas texture strengthening is observed in torsion that has non zero rigid body rotation [32]. The weakening of texture in the present investigation can be attributed to operation of multiple slip systems as well as twinning at high strain rate deformation of CoCuFeMnNi high entropy alloy. Deformation twinning contributes to grain fragmentation that further leads to weakening of texture [29, 30]. 3.5 Constitutive model Johnson-Cook model is utilized to model the constitutive response for two different rates [33]. It is an empirical model where von Mises flow stress is given by the following equation. =
+/
4
78 79
01 + 12 34 56 01 − 37
:
;
5 6 8 7 9
Here, σ is the flow stress, ε is the plastic strain,
(v)
is the plastic strain rate, T is the
experimental temperature, < and <; are the reference temperature and melting point, respectively, A, B, n and C are material constants corresponding to yield strength at reference 8
strain rate, strain hardening co-efficient, strain hardening exponent and strain rate hardening co-efficient respectively. Temperature related parameters in the Johnson Cook equation were not considered in the present investigation as all the experiments were carried out at room temperature and no softening was evident in the sample deformed at high strain rate due to adiabatic heating. A strain rate of 1 s-1 was chosen as the reference strain rate for fitting the constitutive response of CoCuFeMnNi high entropy alloy, and constitutive parameters were determined to obtain the best fit for the two strain rates. The predicted stress-strain response and its comparison with the experimental data is provided in Fig. 4 with the values of the constitutive parameters provided in the inset. Material constants A, B, n and C calculated for CoCuFeMnNi HEA alloy are greater than the corresponding constants for pure metals [12] indicating the high yield strength, high strain hardening ability and higher strain rate hardening respectively for the HEA. 5. Summary The high strain rate deformation of FCC CoCuFeMnNi HEA is characterized by significant strain rate hardening accompanied with substantial deformation twin induced grain fragmentation compared to quasistatic deformation. The high strain rate deformed sample exhibited weaker texture but higher strain hardening rate due to twinning and operation of multiple slip systems. Johnson-Cook model successfully captures the constitutive response of the alloy for the quasistatic and dynamic strain rate regime and indicates superior strain hardening and strain rate hardening behaviour of CoCuFeMnNi HEA compared to pure metals. Acknowledgements The authors would like to acknowledge the funding from Science and Engineering Research Board, Department of Science and Technology, India.
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List of figures Fig. 1 (a) Inverse pole figure (IPF) map of annealed CoCuFeMnNi high entropy alloy (b) Stress-strain and strain hardening behaviour of CoCuFeMnNi high entropy alloy at low and high strain rate. Fig. 2 Compression direction inverse pole figure map (a, b) and image quality map with high angle and co-incident site lattice Σ3 boundaries (c, d) for CoCuFeMnNi high entropy alloy deformed at low (left) and high strain rate (right). (e) Kernel average misorientation (KAM)
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distribution and (f) Misorientation profile along the two lines AB and CD (d) with misorientation axis distribution plot (inset) for the entire map in the microstructure of CoCuFeMnNi high entropy alloy deformed at high strain rate. Fig. 3 (a) Geometrically necessary dislocation (GND) density maps from electron back scatter diffraction and (b) Inverse pole figures along the compression axis from X-ray bulk texture measurement for the CoCuFeMnNi high entropy alloy sample deformed at low and high strain rate. Fig. 4 Johnson-Cook correlation and its comparison with experimental results at different strain rates for CoCuFeMnNi high entropy alloy.
List of tables Table I Evolution of average kernel average misorientation (KAM), geometrically necessary dislocation density (GND), grain boundary character (GBC) and grain size for the annealed and deformed CoCuFeMnNi high entropy alloy samples from EBSD.
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Tables Table I Evolution of average kernel average misorientation (KAM), geometrically necessary dislocation density (GND), grain boundary character (GBC) and grain size for the annealed and deformed CoCuFeMnNi high entropy alloy samples from EBSD.
Strain rate (s-1) Annealed 10-3 3000
Grain size (µm) 95 48 35
Average KAM (◦)
Average GND density (× 1014 m-2)
0.32 0.85 0.75
0.06 2.0 1.6
16
Grain boundary character LAGBs HAGBs CSL (%) (%) (%) 17.6 36 46.2 91.7 7.0 1.1 74.9 21.0 4.9
Figures
(a)
(b) Fig. 1 (a) Inverse pole figure (IPF) map of annealed CoCuFeMnNi high entropy alloy (b) Stress-strain and strain hardening behaviour of CoCuFeMnNi high entropy alloy at low and high strain rate.
17
Fig. 2 Compression direction inverse pole figure map (a, b) and image quality map with high angle and co-incident site lattice boundaries (c, d) for CoCuFeMnNi high entropy alloy deformed at low (left) and high strain rate (right). (e) Kernel average misorientation (KAM) distribution and (f) Misorientation profile along the two lines AB and CD (d) with misorientation axis distribution plot (inset) for the entire map in the microstructure of CoCuFeMnNi high entropy alloy deformed at high strain rate.
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Fig. 3 (a) Geometrically necessary dislocation (GND) density maps from electron back scatter diffraction and (b) Inverse pole figures along the compression axis from X-ray bulk texture measurement for the CoCuFeMnNi high entropy alloy sample deformed at low and high strain rate.
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Fig. 4 Johnson Cook correlation and its comparison with experimental results at different strain rates for CoCuFeMnNi high entropy alloy.
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Highlights •
Significant strain rate hardening in CoCuFeMnNi HEA
•
High strain hardening due to twinning at high strain rate
•
Twinning causes grain fragmentation
•
Characteristic <101> compression texture weakens at high strain rate
•
Johnson-Cook model explains better constitutive response of CoCuFeMnNi HEA
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0925-8388(20)30126-2
DOI:
https://doi.org/10.1016/j.jallcom.2020.153763
Reference:
JALCOM 153763
To appear in:
Journal of Alloys and Compounds
Received Date: 31 August 2019 Revised Date:
1 January 2020
Accepted Date: 8 January 2020
Please cite this article as: R. Sonkusare, R. Jain, K. Biswas, V. Parameswaran, N.P. Gurao, High strain rate compression behaviour of single phase CoCuFeMnNi high entropy alloy, Journal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/j.jallcom.2020.153763. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Credit Author statement Reshma Sonkusare and Roopam Jain performed all the experiments, carried out data analysis and prepared the first draft of the manuscript. Krishanu Biswas, Venkitanarayanan Parameswaran and N. P. Gurao conceptualised and supervised the project as well as edited the final manuscript.
High Strain Rate Compression Behaviour of Single Phase CoCuFeMnNi High Entropy Alloy Reshma Sonkusare1, Roopam Jain1, Krishanu Biswas1, Venkitanarayanan Parameswaran2, N. P. Gurao1* 1
Department of Materials Science and Engineering, Indian Institute of Technology Kanpur, Kanpur208016, India 2
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur-208016, India
*corresponding author (email ID : [email protected] ) Abstract Deformation behaviour of FCC CoCuFeMnNi single phase high entropy alloy (HEA) was studied under quasistatic and dynamic loading conditions in compression at strain rate of 0.001 s-1 and 3000 s-1 using screw driven universal testing machine and Split Hopkinson Pressure Bar respectively. A detailed microstructural characterization was carried out using electron back scatter diffraction (EBSD) while bulk texture measurement was carried out using X-ray diffraction. The high strain rate deformed sample shows high strain rate hardening as well as higher strain hardening that is attributed to operation of deformation twinning as observed from EBSD. The operation of deformation twinning and multiple slip systems leads to grain fragmentation and weakening of characteristic <101> compression texture in sample subjected to high strain rate. Constitutive behaviour of the CoCuFeMnNi HEA explained using the Johnson-Cook phenomenological model further justifies better strain rate and strain hardening response of the alloy compared to individual elements.
Keywords: metals and alloys, mechanical properties, microstructure, dislocations and disclinations, scanning electron microscopy 1
1. Introduction High entropy alloys (HEAs) are a new class of materials with minimum five principal elements having concentration varying from 5 to 35 atomic percentage that show many interesting mechanical and functional properties. The high configurational entropy of mixing (∆
≥ 1.5R, where R is the universal gas constant) stabilizes the solid solution phases
over brittle intermetallic phases [1–4]. HEAs exhibit exceptional mechanical properties and therefore, they have been a subject of tremendous research in the last few years [5–8]. Various investigations have probed the mechanical properties of HEAs across wide strain, strain rate and temperature regimes and have indicated excellent mechanical properties. Tensile behaviour of single phase FCC CoCrFeMnNi HEA shows a very strong dependence on temperature indicating that the thermal component of stress is very important in FCC HEAs unlike conventional pure FCC metals but similar to conventional substitutional solid solution alloys [9,10]. It is therefore, imperative to study the effect of strain rate on deformation behaviour of HEAs [11] to fully understand the fundamentals of deformation processes in HEAs vis a vis traditional alloy. Of particular importance is the dynamic deformation (strain rate > 103 s-1) behaviour of HEAs as additional mechanisms like twinning, shear banding and phase transformation have been reported to occur in conventional metals and alloys at high strain rate deformation [12]. The high strain rate (HSR) behaviour of very few HEAs have been studied so far with major focus on the very first high entropy alloy developed by Cantor et al. [13] due to its unique mechanical properties. Recently, Tsai et al. [14] showed that high strain rate deformation of the Cantor alloy leads to significant rise in yield stress, strain hardening rate and strain rate sensitivity due to extensive nano-twinning and stacking fault hardening. High strain rate behaviour of other HEAs also indicate the higher strain rate sensitivity and excellent work hardening [15– 17] in the dynamic deformation regime. Kumar et al. [15] reported that HSR deformation of
2
Al0.1CrFeCoNi HEA was similar to low stacking fault energy (SFE) materials. Multiple deformation mechanism like thermal softening, dislocation drag, solid solution strengthening, nano twinning, forest dislocation strengthening have been reported to be operative in the dynamic regime for metallic materials [18–21]. Efforts have been made to model the constitutive response using phenomenological and physics based constitutive models [16, 17]. Wang et al. [17] have shown the utility of the physics based Zerilli–Armstrong model [22] which corresponds well with the experimental results. However, a detailed investigation combining mechanical testing with detailed microstructural and textural characterization of single phase high entropy alloy is still missing. The present investigations aims to study the evolution of microstructure and mechanical properties in newly developed equiatomic FCC CoCuFeMnNi HEA with copper-rich nanoclusters (~2.5) [23] for quasistatic and dynamic deformation
in
compression
using state of the art
characterization
tools
and
phenomenological modelling. 2. Materials and methods High purity Co, Cu, Fe, Mn and Ni nuggets were used to prepare the alloy using vacuum arc melting technique with water-cooled copper hearth and non-consumable tungsten electrode. The alloy was homogenized at 1273 K for 24 hours to achieve chemical homogeneity and then water quenched to retain the single phase microstructure. Cylindrical samples with 6 mm diameter and 9 mm height and 6 mm diameter and 6 mm height were machined for quasistatic and dynamic tests respectively using electric discharge machining. Both quasistatic and dynamic tests were conducted at room temperature. Strain rate of 10-3 s-1 and 3000 s-1 were chosen to compare the stress strain response of the two regimes. High strain rate tests were performed using the compression split Hopkinson bar setup which is a widely accepted instrument for intermediate regime of strain rate (102 – 104 s-1). Compression samples were subjected to stress pulse by varying the striker velocity to obtain a strain rate of 3
3000 s-1. Incident, reflected and transmitted pulses were recorded using strain gauges attached on incident and transmitter using which the stress strain relationship was derived [12]. Compression samples were sandwiched between incident (3 m) and transmitted (2 m) bars made of maraging steel of 20 mm diameter. A 300 mm long striker bar was propelled using a gas gun at 6 kg/cm2 pressure to achieve strain rate close to 3000 s-1. For high strain rate experiments stress, strain and strain rate can be calculated from the following equations. = −
(i) = −
(ii) =
(iii) Here,
is longitudional wave velocity in the bars,
is length of the specimen,
and
are respectively the experimentally measured reflected and transmitted strain histories, is the cross-sectional area of the specimen, transmission bars and,
is the cross-sectional area of the incident and
is the elastic modulus of the incident as well as transmission bars.
Three tests were performed at the two strain rates to obtain statistically significant data. The deformed samples were machined along the compression axis from the centre using diamond saw and one half was metallographically prepared by polishing with emery paper followed by alumina cloth polishing and finally with colloidal silica polishing (Vibromet) for electron back scatter diffraction (EBSD). The microstructural examination was carried out in field emission scanning electron microscope Nano Nova SEM 450 FE-SEM operating at 20 kV. EBSD measurement was carried out using EDAX TSL-OIM setup with step size of 0.15 μ".
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Data analysis was carried out using TSL-OIM version 8 data analysis software. Bulk texture measurements were carried out using Rigaku Ultima diffractometer with Cu Kα radiation, in reflection mode. Three incomplete pole figures 111, 200 and 220 were measured and Resmat software was used to calculate orientation distribution function (ODF) as well as compression direction inverse pole figure (IPF) for all the deformed samples. 3. Results & Discussion 3.1 Initial sample Fig. 1. (a) shows the crystal orientation or inverse pole figure (IPF) map of annealed sample of CoCuFeMnNi HEA with a grain size of 96 µm and is characterized by presence of few annealing twins. Earlier investigations have shown that this HEA is characterized by the presence of CoCuFeMnNi FCC matrix and copper rich nanoclusters with size of 2.5 nm from atom probe tomography results [23]. The presence of few annealing twins in the sample is similar to that of medium stacking fault energy copper and has been reported in previous investigations by the authors [10, 24]. 3.2 Mechanical behaviour True stress - true strain curves at the strain rate of 10-3 s-1 and 3000 s-1 are shown in Fig. 1. (b) for comparing the mechanical behaviour of CoCuFeMnNi HEA. A noticeable strain rate hardening is observed in dynamically deformed sample. In order to obtain better insight of the strain hardening behaviour at different strain rates, Kocks-Mecking plots that provide the evolution of strain hardening rate with plastic stress were determined and are represented in Fig. 1 (b). The Kocks-Mecking plot for the sample tested at low strain rate shows gradual decrease in strain hardening rate with increase in stress indicating delayed dynamic recovery. Earlier investigation by the authors on rolling of CoCuFeMnNi alloy attributed the evolution of Goss-Brass type texture to the operation of planar partial slip in addition to conventional 5
octahedral slip [24]. Thus, the delayed onset of recovery can be attributed to operation of octahedral and partial slip at low strain rate. The strain hardening response of the sample tested at high strain rate is characterized by initial decrease in strain hardening rate followed by a plateau. The plateau in strain hardening curve indicates additional strain hardening from operation of twinning or phase transformation in FCC materials [12]. The Kocks-Mecking plot clearly indicates that there is significant increase in strain hardening with increase in strain rate and more importantly characteristic difference in the nature of the curves indicates operation of different micro-mechanism at high strain rate. In order to decipher the operative micro-mechanism of deformation, detailed microstructural characterization was carried out using electron back scatter diffraction and is discussed in the next section. 3.3 Microstructural evolution In order to isolate the effect of strain rate, CoCuFeMnNi HEA samples were subjected to similar amount of strain in quasistatic and dynamic loading. The crystal orientation or inverse pole figure map along the compression direction on the longitudinal plane of the two samples deformed at quasistatic and dynamic strain rates is shown in Fig. 2. (a, b). Inverse pole figure maps for both the samples are characterized by large colour gradient within the grains with the sample deformed at high strain rate showing lower grain size compared to sample deformed at low strain rate. The colour gradient within the grains corresponds to the orientation gradient and indicates intense slip activity. In order to obtain more insight about the evolution of microstructure, composite map comprising of image quality and grain boundary character was plotted as shown in Fig. 2. (c, d). The sample deformed at high strain rate is characterized by the presence of lenticular deformation twins, which are absent in the sample deformed at low strain rate. In order to verify the presence of deformation twins point to point misorientation across the line AB and CD was plotted as shown in Fig. 2. (f). Misorientation plot along both the lines show misorientation of 60° indicating the presence of 6
deformation twins in the sample which was subjected to high strain rate. The misorientation axis distribution plot for the entire map of the high strain rate deformed sample shows clustering near <111> direction for misorientations between 57° - 63° confirming the presence of deformation twins. Another important observation is the shift in peak KAM value (Fig. 2. (e)) to a higher number for the quasistatic deformed sample compared to high strain rate deformed sample that indicates higher density of dislocations in quasistatic regime. In order to further understand the deformation behaviour, geometrically necessary (GND) dislocation density map [25] was plotted for the octahedral #111% < 110 > slip systems. Sample tested at higher strain rates shows high GND density near the grain boundaries [26] whereas in the sample deformed at low strain rate GNDs are not localized at grain boundaries as shown in Fig. 3. (a). Heavy accumulation of GNDs near grain boundaries is expected to be the cause of grain fragmentation at high strain rate resulting in considerable reduction in grain size as postulated in variety of metals and alloys by Meyers et al. [26, 27]. Additional information on the evolution of area average grain size, intragranular misorientation in terms of KAM, average GND density and grain boundary character for the CoCuFeMnNi sample deformed at low and high strain rate obtained from EBSD is depicted in Table I. It is observed that the high strain rate deformed sample is characterized by lower grain size and higher sigma 3 coincident site lattice boundaries which correspond to deformation twinning in FCC materials. However, the high strain rate sample shows lower average GND density and low angle grain boundary fraction. 3.4 Bulk texture The evolution of deformation texture in compression for CoCuFeMnNi HEA at low and high strain rate is depicted in terms of inverse pole figure in Fig. 3. (b). A pronounced <101> fibre texture along the compression direction which is a characteristic of FCC materials is observed in samples deformed at low and high strain rate with the later showing a weaker 7
texture compared to that of the former. The evolution of crystallographic texture is related to plastic spin as a result of operation of different slip systems to accommodate imposed plastic deformation. The relationship between plastic spin (dω), lattice spin (dΩ) and rigid body rotation (dβ) is provided below dΩ ++++ = dβ+ − dω ++++ (iv) For deformation in compression, the rigid body rotation is zero and hence the plastic spin contributes to lattice spin and dictates texture evolution. Canova et al. [28] had proposed that there is an increase in the number of active slip systems with increase in strain rate that contributes to lower plastic spin. This contributes to weakening of texture for tension and compression where the rigid body rotation is zero [29–31] whereas texture strengthening is observed in torsion that has non zero rigid body rotation [32]. The weakening of texture in the present investigation can be attributed to operation of multiple slip systems as well as twinning at high strain rate deformation of CoCuFeMnNi high entropy alloy. Deformation twinning contributes to grain fragmentation that further leads to weakening of texture [29, 30]. 3.5 Constitutive model Johnson-Cook model is utilized to model the constitutive response for two different rates [33]. It is an empirical model where von Mises flow stress is given by the following equation. =
+/
4
78 79
01 + 12 34 56 01 − 37
:
;
5 6 8 7 9
Here, σ is the flow stress, ε is the plastic strain,
(v)
is the plastic strain rate, T is the
experimental temperature, < and <; are the reference temperature and melting point, respectively, A, B, n and C are material constants corresponding to yield strength at reference 8
strain rate, strain hardening co-efficient, strain hardening exponent and strain rate hardening co-efficient respectively. Temperature related parameters in the Johnson Cook equation were not considered in the present investigation as all the experiments were carried out at room temperature and no softening was evident in the sample deformed at high strain rate due to adiabatic heating. A strain rate of 1 s-1 was chosen as the reference strain rate for fitting the constitutive response of CoCuFeMnNi high entropy alloy, and constitutive parameters were determined to obtain the best fit for the two strain rates. The predicted stress-strain response and its comparison with the experimental data is provided in Fig. 4 with the values of the constitutive parameters provided in the inset. Material constants A, B, n and C calculated for CoCuFeMnNi HEA alloy are greater than the corresponding constants for pure metals [12] indicating the high yield strength, high strain hardening ability and higher strain rate hardening respectively for the HEA. 5. Summary The high strain rate deformation of FCC CoCuFeMnNi HEA is characterized by significant strain rate hardening accompanied with substantial deformation twin induced grain fragmentation compared to quasistatic deformation. The high strain rate deformed sample exhibited weaker texture but higher strain hardening rate due to twinning and operation of multiple slip systems. Johnson-Cook model successfully captures the constitutive response of the alloy for the quasistatic and dynamic strain rate regime and indicates superior strain hardening and strain rate hardening behaviour of CoCuFeMnNi HEA compared to pure metals. Acknowledgements The authors would like to acknowledge the funding from Science and Engineering Research Board, Department of Science and Technology, India.
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List of figures Fig. 1 (a) Inverse pole figure (IPF) map of annealed CoCuFeMnNi high entropy alloy (b) Stress-strain and strain hardening behaviour of CoCuFeMnNi high entropy alloy at low and high strain rate. Fig. 2 Compression direction inverse pole figure map (a, b) and image quality map with high angle and co-incident site lattice Σ3 boundaries (c, d) for CoCuFeMnNi high entropy alloy deformed at low (left) and high strain rate (right). (e) Kernel average misorientation (KAM)
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distribution and (f) Misorientation profile along the two lines AB and CD (d) with misorientation axis distribution plot (inset) for the entire map in the microstructure of CoCuFeMnNi high entropy alloy deformed at high strain rate. Fig. 3 (a) Geometrically necessary dislocation (GND) density maps from electron back scatter diffraction and (b) Inverse pole figures along the compression axis from X-ray bulk texture measurement for the CoCuFeMnNi high entropy alloy sample deformed at low and high strain rate. Fig. 4 Johnson-Cook correlation and its comparison with experimental results at different strain rates for CoCuFeMnNi high entropy alloy.
List of tables Table I Evolution of average kernel average misorientation (KAM), geometrically necessary dislocation density (GND), grain boundary character (GBC) and grain size for the annealed and deformed CoCuFeMnNi high entropy alloy samples from EBSD.
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Tables Table I Evolution of average kernel average misorientation (KAM), geometrically necessary dislocation density (GND), grain boundary character (GBC) and grain size for the annealed and deformed CoCuFeMnNi high entropy alloy samples from EBSD.
Strain rate (s-1) Annealed 10-3 3000
Grain size (µm) 95 48 35
Average KAM (◦)
Average GND density (× 1014 m-2)
0.32 0.85 0.75
0.06 2.0 1.6
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Grain boundary character LAGBs HAGBs CSL (%) (%) (%) 17.6 36 46.2 91.7 7.0 1.1 74.9 21.0 4.9
Figures
(a)
(b) Fig. 1 (a) Inverse pole figure (IPF) map of annealed CoCuFeMnNi high entropy alloy (b) Stress-strain and strain hardening behaviour of CoCuFeMnNi high entropy alloy at low and high strain rate.
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Fig. 2 Compression direction inverse pole figure map (a, b) and image quality map with high angle and co-incident site lattice boundaries (c, d) for CoCuFeMnNi high entropy alloy deformed at low (left) and high strain rate (right). (e) Kernel average misorientation (KAM) distribution and (f) Misorientation profile along the two lines AB and CD (d) with misorientation axis distribution plot (inset) for the entire map in the microstructure of CoCuFeMnNi high entropy alloy deformed at high strain rate.
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Fig. 3 (a) Geometrically necessary dislocation (GND) density maps from electron back scatter diffraction and (b) Inverse pole figures along the compression axis from X-ray bulk texture measurement for the CoCuFeMnNi high entropy alloy sample deformed at low and high strain rate.
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Fig. 4 Johnson Cook correlation and its comparison with experimental results at different strain rates for CoCuFeMnNi high entropy alloy.
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Highlights •
Significant strain rate hardening in CoCuFeMnNi HEA
•
High strain hardening due to twinning at high strain rate
•
Twinning causes grain fragmentation
•
Characteristic <101> compression texture weakens at high strain rate
•
Johnson-Cook model explains better constitutive response of CoCuFeMnNi HEA
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: