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Mechanical size effects in a single crystalline equiatomic FeCrCoMnNi high entropy alloy
Scripta Materialia 129 (2017) 52–55
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Regular Article
Mechanical size effects in a single crystalline equiatomic FeCrCoMnNi high entropy alloy R. Raghavan a,⁎, C. Kirchlechner a,b, B.N. Jaya a, M. Feuerbacher c, G. Dehm a a b c
Max-Planck-Institut für Eisenforschung GmbH, Structure and Nano-/Micromechanics of Materials, Max-Planck-Strasse 1, 40237 Düsseldorf, Germany Department Material Physics, University of Leoben, Jahnstraße 12, A-8700 Leoben, Austria Peter Grünberg Institut and Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
a r t i c l e
i n f o
Article history: Received 4 August 2016 Received in revised form 19 October 2016 Accepted 21 October 2016 Available online xxxx Keywords: Size dependence Yield strength Plastic deformation Slip Compression
a b s t r a c t The size dependence of the mechanical behavior of a single crystalline equiatomic FeCrCoMnNi single phase high entropy alloy was studied using in situ SEM microcompression. Electron back-scattered diffraction was used in conjunction with high-resolution scanning electron microscopy to identify the dominant slip system activated for accommodating plastic flow. The scaling of the yield strength with the size of the micropillar is discussed in comparison with the size dependence observed in face-centered and body-centered cubic single crystalline metals. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Alloys forming a single-phase solid solution despite equal or nearly equal atomic concentrations of the multiple (N 5) constituent metals are known as high entropy alloys (HEAs) [1]. The transgression from the traditional metallurgical approach of adding alloying elements in small proportions to the parent metal (e.g. Ni-based superalloys, steels etc.) to exciting possibilities [2,3] and challenging questions posed by this ‘cocktail-alloying [4]’ has created a furor in the scientific community. Initially attributed to the high configurational entropy [5], recent studies revealed that the suppression of long-range diffusion due to the multicomponent nature could be the ‘kinetic’ factor contributing to the phase stability of a HEA [6,7]. Despite these advances in understanding the phase stability [6–8], correlations between microstructure and macro-scale mechanical behavior [9–11], systematic investigations into the mechanical response of HEA single crystals [12,13], especially at small scales, is lacking [14]. In particular, whether the strength of a HEA with an fcc crystal structure exhibits a scaling similar to that observed in pure metallic fcc crystals [15], is an open question. Hence, in this study, the effect of size on the strength and deformation mechanism of an equiatomic FeCoCrMnNi high entropy alloy was investigated using microcompression and electron crystallography. The experiments were carried out on single crystalline samples in order to exclude any influence of secondary phases or grain boundaries, on the deformation behavior. Thus, to the best of our knowledge this study is a first report 1) analyzing the size effect concerning yield stress in an fcc HEA, 2) ⁎ Corresponding author. E-mail address: raghavan/[email protected] (R. Raghavan).
http://dx.doi.org/10.1016/j.scriptamat.2016.10.026 1359-6462/© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
identifying the operating glide system, 3) measuring the resolved shear stress for the activated glide systems. The samples for our study were taken from a single crystal grown by means of the Czochralski technique from an equiatomic melt of highpurity elements Fe, Co, Cr, Mn, and Ni. The crystal, having a length of about 2 cm and a diameter of about 1 cm, was single crystalline according to Laue x-ray diffraction, showing consistent patterns over the entire surface. Careful inspection by scanning electron microscopy, however, revealed that it contained subgrain boundaries. These separate subgrains are of typically some mm in diameter, with relative orientations deviating by a few degrees. Details of the crystal-growth procedure and characterization will be published elsewhere [16]. An approximately 2 × 3 × 2 mm sized rectangular block free of subgrains was cut from the crystal and metallographically polished for structural and micromechanical characterization. Electron backscattered diffraction (EBSD) was carried out using a JEOL JSM-6490 scanning electron microscope (SEM) operated at 15 kV and a sample tilt of 70o. The EBSD patterns obtained were indexed by using fcc Nickel as the base crystal structure, and were analyzed using the commercially available EDAX® OIM™ Analysis 6.2 software. Micropillars with diameters of 10, 6, 3, 2 and 1 μm, and aspect ratio of 2.5 to 3 were machined within the crystal using a Zeiss Auriga® dual beam FIB workstation operated at 30 kV. Five to seven micropillars were tested for each diameter resulting in a total of 33 stress-strain curves. While currents ranging from 16 nA to 600 pA were used for coarse and fine milling to optimize the milling time, final polishing was conducted at 50 pA to achieve the desired dimensions for micropillars of all sizes. The compression tests
R. Raghavan et al. / Scripta Materialia 129 (2017) 52–55
were carried out by using the UNAT-SEM2® (ASMEC) in situ SEM indenter within a JEOL JSM-6490 SEM. While a conical diamond flat punch of 20 μm diameter was used for compressing the 6 and 10 μm diameter pillars, a 5 μm diameter punch was used for the smaller sizes. The load-displacement curves were corrected for instrument and substrate compliances [17] before converting them into engineering stress-strain curves using the top diameters of the micropillars. Stress values at 1% strain offsets of the engineering stress-strain curves were considered as the yield strengths of the respective films. The micropillars were imaged before and after compression to determine their exact dimensions and to obtain insight into the deformation geometry respectively, using the Gemini® electron column of the Zeiss dual beam FIB workstation. Fig. 1a is an orientation map obtained from the analysis of EBSD patterns from different regions of the metallographically prepared block. Its uniform color confirms its single crystalline nature. The surface normal being the crystallographic compression axis was determined to be close to the [11 3 5] direction from the corresponding inverse pole figures (inset of Fig. 1a & Fig. 1b). For reasons of clarity and establishing the orientation relationship between the specimen and crystal coordinate system, the longest edge of the specimen block was maintained horizontal as shown in Fig. S1 for all the measurements. Fig. 2 shows representative engineering stress-strain curves obtained from the compression of 10, 6, 3 and 1 μm diameter micropillars. In situ SEM compression of the micropillars revealed that the intermittent stress drops observed in the plastic regime of the stress-strain curves arise from the formation of parallel slip bands, which lead to offsets on the cylindrical and top surfaces of the micropillars. SEM imaging of the micropillars after compression (Fig. 3) revealed the formation of similar, finely-spaced slip band patterns, which deviate from the behavior of typical single crystalline fcc metals [18]. Fewer slip bands form larger offsets upon deformation of samples with smaller volumes of single crystalline fcc metals [19–21]. Additionally, the slip band patterns form throughout the entire length of the pillar despite the finite taper in the micropillars, which restricts plasticity to their upper (narrower) section. Since the HEA used in the present study is an fcc solid solution, the dominant slip system should be the one possessing the highest values of the Schmid factor among the 12 different possibilities arising from the family of the {111} ⟨110⟩ slip system. For a loading axis parallel to the [11 3 5] direction, the slip system with the highest Schmid factor of ~ 0.48 is the ð111Þ½110 , as shown in Table 1. Planar slip on the {111} ⟨110⟩ slip system was also observed as the dominant deformation mechanism at plastic strains up to 2% during the deformation of mmsized samples in polycrystalline HEAs of the same composition [9].
53
Fig. 2. Representative stress – strain curves obtained from in situ SEM compression of: (a) 10 μm, 6 μm, 3 μm and (b) 1 μm diameter micropillars.
Experimentally, the slip system activated in our samples was identified using both the information obtained by EBSD as well as the postmortem HRSEM images. Thereby, the activated slip plane was identified by projecting all possible {111} planes based on the given pillar compression axis and a known crystallographic in-plane direction
Fig. 1. EBSD analysis: (a) Orientation image map and inverse pole figure along [11 3 5] direction as inset, (b) inverse pole figure along [001] direction.
54
R. Raghavan et al. / Scripta Materialia 129 (2017) 52–55
Extensive research has been dedicated to reveal the scaling of strength and plastic deformation mechanisms of micron and sub-micron sized single crystals [15,22,23]. With primary focus on fcc metals using the microcompression technique [15], the strength of fcc single crystals approximately obeys the power law [22,24,25] scaling p τR D ¼A ; μ b
Fig. 3. HRSEM images obtained after in situ SEM compression of micropillars of: (a) 10 μm, (b) 6 μm, (c) 3 μm (trace of the ð111Þ slip plane being part of the slip system with the highest Schmid factor of 0.48 indicated in red) and (d) 1 μm diameter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(see Fig. 3c) with a user built Mathematica® code. Furthermore, the projection of all possible 〈110〉 Burgers vectors on the pillar top surface were used to identify the direction of slip offset in this view (Fig. S2). Following this procedure, we find that in our samples the ð111Þ½110 slip system exhibiting the highest Schmid factor of 0.48, is activated. This result is obtained for all micropillars of all diameters investigated, and confirms the fcc-like slip behavior of this specific HEA.
Table 1 Schmid factors calculated for perfect dislocations of {111} ⟨110⟩ slip systems oriented for compression in the [11 3 5] direction. ð111Þ
[110]
0.48
(111)
½110 [101]
0.40
½101
0.30
ð111Þ (111)
0.38
ð1Þ
where, τR is the shear stress resolved on the {111} ⟨110⟩ slip system, μ is the shear modulus, A is a constant, D is the diameter of the micropillar, b is the magnitude of the Burgers vector, and p the size exponent. The size exponent typically takes values between −0.6 and −1 [18, 26–29]. In contrast to these literature values, we interestingly find a smaller exponent of approximately − 0.32 for our samples, by fitting the 1% yield strength (error bars were estimated as the standard deviation of the 1% yield strength values) as a function of the micropillar diameter to a power-law of the form of Eq. (1) (Fig. 4). Smaller exponents ranging from −0.2 to −0.3 were observed for bcc Mo pillars [30], but exponents as high as −0.8 and a dependence on the test configuration were observed for bcc V [31], Nb, Ta and W [32,33]. These significant differences in the size exponents of bcc metals were attributed to the differing temperature dependence of the Peierls stresses [34]. Estimating the temperature-dependent Peierls stresses, it was reasoned that the Peierls stresses of fcc equiatomic alloys should be intermediate to those of pure fcc and bcc metals [35], which was confirmed for a B2 ordered Al-Co-Cr-Fe-Ni [36]. Statistical analysis used to describe the stochastic nature of plasticity in small volumes demonstrated that the bulk-to-theoretical-strength ratio governs the size exponent [37]. In particular, materials with higher bulk-to-theoretical strength ratio should exhibit a smaller size exponent. This prediction is in agreement with the high bulk-to-theoretical strength ratio observed in the HEA used in the present study, which can be explained by the high lattice friction substantially increasing the strength of the HEA. Hence, we reason that the lower size exponent exhibited by the HEA is due to the high bulk-to-theoretical strength ratio, i.e. the low mobility of dislocations due to a high Peierls stress. From a mechanistic perspective, the ‘starvation of dislocations’ [27] attributed to the attraction by image forces [28] or ‘mechanical annealing’ [38], requiring the activation of new dislocation sources could explain the aforementioned size dependence of the strength of micron-sized single crystals. In addition to confirming the starvation mechanism, further elegant in situ TEM investigations revealed that the geometrical confinement also leads to truncation of the dislocation sources [39,40]. However, the addition of a corresponding source-truncation contribution [41,42] to the Peierls stress and Taylor-hardening term used for bulk metallic single crystals [43,44] did not suffice to predict the strengths of single-crystalline Ni micropillars with diameters smaller than ≈5 μm [45]. In conclusion, planar slip on the ð111Þ½110 slip system was predominantly observed in in situ SEM microcompression of an equiatomic, single phase fcc FeCrCoMnNi HEA single crystal The observed slip system thus corresponds to that fcc slip system exhibiting the highest Schmid factor. However, in contrast to the stochastic nature of plastic flow observed in fcc single crystals, all sizes of the micropillars exhibited similarly fine-spaced slip band patterns. The dependence of the yield strength on the micropillar diameter follows a power law with an exponent of − 0.32. The exponent found for the FeCrCoMnNi HEA single crystals is thus smaller than that of −0.6 to −1 typically observed for pure fcc single crystals. This weaker dependence of the yield strength on the diameter of the micropillars is attributed to the high bulk-to-theoretical strength ratio of the HEA alloy compared to pure fcc metals. Supplementary data to this article can be found online at doi:10. 1016/j.scriptamat.2016.10.026.
R. Raghavan et al. / Scripta Materialia 129 (2017) 52–55
Fig. 4. Scaling of the yield strength with diameter of the micropillar; R2 - coefficient of determination. The yield strength obtained from bulk compression testing (105 MPa) has also been indicated (unpublished results).
Acknowledgements RR would like to thank Mrs. Angelika Bobrowski for technical assistance with polishing of the specimens. References [1] M.-H. Tsai, J.-W. Yeh, Math. Res. Lett. 2 (2014) 107–123. [2] B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, Science 345 (2014) 1153–1158. [3] Z. Zhang, M.M. Mao, J. Wang, B. Gludovatz, Z. Zhang, S.X. Mao, E.P. George, Q. Yu, R.O. Ritchie, Nat. Commun. 6 (2015) 10143. [4] S. Ranganathan, Curr. Sci. 85 (2003) 1404–1406. [5] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Adv. Eng. Mater. 6 (2004) 299–303. [6] F. Otto, Y. Yang, H. Bei, E.P. George, Acta Mater. 61 (2013) 2628–2638. [7] K.Y. Tsai, M.H. Tsai, J.W. Yeh, Acta Mater. 61 (2013) 4887–4897. [8] D. Ma, M. Yao, K.G. Pradeep, C.C. Tasan, H. Springer, D. Raabe, Acta Mater. 98 (2015) 288–296.
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Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Regular Article
Mechanical size effects in a single crystalline equiatomic FeCrCoMnNi high entropy alloy R. Raghavan a,⁎, C. Kirchlechner a,b, B.N. Jaya a, M. Feuerbacher c, G. Dehm a a b c
Max-Planck-Institut für Eisenforschung GmbH, Structure and Nano-/Micromechanics of Materials, Max-Planck-Strasse 1, 40237 Düsseldorf, Germany Department Material Physics, University of Leoben, Jahnstraße 12, A-8700 Leoben, Austria Peter Grünberg Institut and Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
a r t i c l e
i n f o
Article history: Received 4 August 2016 Received in revised form 19 October 2016 Accepted 21 October 2016 Available online xxxx Keywords: Size dependence Yield strength Plastic deformation Slip Compression
a b s t r a c t The size dependence of the mechanical behavior of a single crystalline equiatomic FeCrCoMnNi single phase high entropy alloy was studied using in situ SEM microcompression. Electron back-scattered diffraction was used in conjunction with high-resolution scanning electron microscopy to identify the dominant slip system activated for accommodating plastic flow. The scaling of the yield strength with the size of the micropillar is discussed in comparison with the size dependence observed in face-centered and body-centered cubic single crystalline metals. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Alloys forming a single-phase solid solution despite equal or nearly equal atomic concentrations of the multiple (N 5) constituent metals are known as high entropy alloys (HEAs) [1]. The transgression from the traditional metallurgical approach of adding alloying elements in small proportions to the parent metal (e.g. Ni-based superalloys, steels etc.) to exciting possibilities [2,3] and challenging questions posed by this ‘cocktail-alloying [4]’ has created a furor in the scientific community. Initially attributed to the high configurational entropy [5], recent studies revealed that the suppression of long-range diffusion due to the multicomponent nature could be the ‘kinetic’ factor contributing to the phase stability of a HEA [6,7]. Despite these advances in understanding the phase stability [6–8], correlations between microstructure and macro-scale mechanical behavior [9–11], systematic investigations into the mechanical response of HEA single crystals [12,13], especially at small scales, is lacking [14]. In particular, whether the strength of a HEA with an fcc crystal structure exhibits a scaling similar to that observed in pure metallic fcc crystals [15], is an open question. Hence, in this study, the effect of size on the strength and deformation mechanism of an equiatomic FeCoCrMnNi high entropy alloy was investigated using microcompression and electron crystallography. The experiments were carried out on single crystalline samples in order to exclude any influence of secondary phases or grain boundaries, on the deformation behavior. Thus, to the best of our knowledge this study is a first report 1) analyzing the size effect concerning yield stress in an fcc HEA, 2) ⁎ Corresponding author. E-mail address: raghavan/[email protected] (R. Raghavan).
http://dx.doi.org/10.1016/j.scriptamat.2016.10.026 1359-6462/© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
identifying the operating glide system, 3) measuring the resolved shear stress for the activated glide systems. The samples for our study were taken from a single crystal grown by means of the Czochralski technique from an equiatomic melt of highpurity elements Fe, Co, Cr, Mn, and Ni. The crystal, having a length of about 2 cm and a diameter of about 1 cm, was single crystalline according to Laue x-ray diffraction, showing consistent patterns over the entire surface. Careful inspection by scanning electron microscopy, however, revealed that it contained subgrain boundaries. These separate subgrains are of typically some mm in diameter, with relative orientations deviating by a few degrees. Details of the crystal-growth procedure and characterization will be published elsewhere [16]. An approximately 2 × 3 × 2 mm sized rectangular block free of subgrains was cut from the crystal and metallographically polished for structural and micromechanical characterization. Electron backscattered diffraction (EBSD) was carried out using a JEOL JSM-6490 scanning electron microscope (SEM) operated at 15 kV and a sample tilt of 70o. The EBSD patterns obtained were indexed by using fcc Nickel as the base crystal structure, and were analyzed using the commercially available EDAX® OIM™ Analysis 6.2 software. Micropillars with diameters of 10, 6, 3, 2 and 1 μm, and aspect ratio of 2.5 to 3 were machined within the crystal using a Zeiss Auriga® dual beam FIB workstation operated at 30 kV. Five to seven micropillars were tested for each diameter resulting in a total of 33 stress-strain curves. While currents ranging from 16 nA to 600 pA were used for coarse and fine milling to optimize the milling time, final polishing was conducted at 50 pA to achieve the desired dimensions for micropillars of all sizes. The compression tests
R. Raghavan et al. / Scripta Materialia 129 (2017) 52–55
were carried out by using the UNAT-SEM2® (ASMEC) in situ SEM indenter within a JEOL JSM-6490 SEM. While a conical diamond flat punch of 20 μm diameter was used for compressing the 6 and 10 μm diameter pillars, a 5 μm diameter punch was used for the smaller sizes. The load-displacement curves were corrected for instrument and substrate compliances [17] before converting them into engineering stress-strain curves using the top diameters of the micropillars. Stress values at 1% strain offsets of the engineering stress-strain curves were considered as the yield strengths of the respective films. The micropillars were imaged before and after compression to determine their exact dimensions and to obtain insight into the deformation geometry respectively, using the Gemini® electron column of the Zeiss dual beam FIB workstation. Fig. 1a is an orientation map obtained from the analysis of EBSD patterns from different regions of the metallographically prepared block. Its uniform color confirms its single crystalline nature. The surface normal being the crystallographic compression axis was determined to be close to the [11 3 5] direction from the corresponding inverse pole figures (inset of Fig. 1a & Fig. 1b). For reasons of clarity and establishing the orientation relationship between the specimen and crystal coordinate system, the longest edge of the specimen block was maintained horizontal as shown in Fig. S1 for all the measurements. Fig. 2 shows representative engineering stress-strain curves obtained from the compression of 10, 6, 3 and 1 μm diameter micropillars. In situ SEM compression of the micropillars revealed that the intermittent stress drops observed in the plastic regime of the stress-strain curves arise from the formation of parallel slip bands, which lead to offsets on the cylindrical and top surfaces of the micropillars. SEM imaging of the micropillars after compression (Fig. 3) revealed the formation of similar, finely-spaced slip band patterns, which deviate from the behavior of typical single crystalline fcc metals [18]. Fewer slip bands form larger offsets upon deformation of samples with smaller volumes of single crystalline fcc metals [19–21]. Additionally, the slip band patterns form throughout the entire length of the pillar despite the finite taper in the micropillars, which restricts plasticity to their upper (narrower) section. Since the HEA used in the present study is an fcc solid solution, the dominant slip system should be the one possessing the highest values of the Schmid factor among the 12 different possibilities arising from the family of the {111} ⟨110⟩ slip system. For a loading axis parallel to the [11 3 5] direction, the slip system with the highest Schmid factor of ~ 0.48 is the ð111Þ½110 , as shown in Table 1. Planar slip on the {111} ⟨110⟩ slip system was also observed as the dominant deformation mechanism at plastic strains up to 2% during the deformation of mmsized samples in polycrystalline HEAs of the same composition [9].
53
Fig. 2. Representative stress – strain curves obtained from in situ SEM compression of: (a) 10 μm, 6 μm, 3 μm and (b) 1 μm diameter micropillars.
Experimentally, the slip system activated in our samples was identified using both the information obtained by EBSD as well as the postmortem HRSEM images. Thereby, the activated slip plane was identified by projecting all possible {111} planes based on the given pillar compression axis and a known crystallographic in-plane direction
Fig. 1. EBSD analysis: (a) Orientation image map and inverse pole figure along [11 3 5] direction as inset, (b) inverse pole figure along [001] direction.
54
R. Raghavan et al. / Scripta Materialia 129 (2017) 52–55
Extensive research has been dedicated to reveal the scaling of strength and plastic deformation mechanisms of micron and sub-micron sized single crystals [15,22,23]. With primary focus on fcc metals using the microcompression technique [15], the strength of fcc single crystals approximately obeys the power law [22,24,25] scaling p τR D ¼A ; μ b
Fig. 3. HRSEM images obtained after in situ SEM compression of micropillars of: (a) 10 μm, (b) 6 μm, (c) 3 μm (trace of the ð111Þ slip plane being part of the slip system with the highest Schmid factor of 0.48 indicated in red) and (d) 1 μm diameter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(see Fig. 3c) with a user built Mathematica® code. Furthermore, the projection of all possible 〈110〉 Burgers vectors on the pillar top surface were used to identify the direction of slip offset in this view (Fig. S2). Following this procedure, we find that in our samples the ð111Þ½110 slip system exhibiting the highest Schmid factor of 0.48, is activated. This result is obtained for all micropillars of all diameters investigated, and confirms the fcc-like slip behavior of this specific HEA.
Table 1 Schmid factors calculated for perfect dislocations of {111} ⟨110⟩ slip systems oriented for compression in the [11 3 5] direction. ð111Þ
[110]
0.48
(111)
½110 [101]
0.40
½101
0.30
ð111Þ (111)
0.38
ð1Þ
where, τR is the shear stress resolved on the {111} ⟨110⟩ slip system, μ is the shear modulus, A is a constant, D is the diameter of the micropillar, b is the magnitude of the Burgers vector, and p the size exponent. The size exponent typically takes values between −0.6 and −1 [18, 26–29]. In contrast to these literature values, we interestingly find a smaller exponent of approximately − 0.32 for our samples, by fitting the 1% yield strength (error bars were estimated as the standard deviation of the 1% yield strength values) as a function of the micropillar diameter to a power-law of the form of Eq. (1) (Fig. 4). Smaller exponents ranging from −0.2 to −0.3 were observed for bcc Mo pillars [30], but exponents as high as −0.8 and a dependence on the test configuration were observed for bcc V [31], Nb, Ta and W [32,33]. These significant differences in the size exponents of bcc metals were attributed to the differing temperature dependence of the Peierls stresses [34]. Estimating the temperature-dependent Peierls stresses, it was reasoned that the Peierls stresses of fcc equiatomic alloys should be intermediate to those of pure fcc and bcc metals [35], which was confirmed for a B2 ordered Al-Co-Cr-Fe-Ni [36]. Statistical analysis used to describe the stochastic nature of plasticity in small volumes demonstrated that the bulk-to-theoretical-strength ratio governs the size exponent [37]. In particular, materials with higher bulk-to-theoretical strength ratio should exhibit a smaller size exponent. This prediction is in agreement with the high bulk-to-theoretical strength ratio observed in the HEA used in the present study, which can be explained by the high lattice friction substantially increasing the strength of the HEA. Hence, we reason that the lower size exponent exhibited by the HEA is due to the high bulk-to-theoretical strength ratio, i.e. the low mobility of dislocations due to a high Peierls stress. From a mechanistic perspective, the ‘starvation of dislocations’ [27] attributed to the attraction by image forces [28] or ‘mechanical annealing’ [38], requiring the activation of new dislocation sources could explain the aforementioned size dependence of the strength of micron-sized single crystals. In addition to confirming the starvation mechanism, further elegant in situ TEM investigations revealed that the geometrical confinement also leads to truncation of the dislocation sources [39,40]. However, the addition of a corresponding source-truncation contribution [41,42] to the Peierls stress and Taylor-hardening term used for bulk metallic single crystals [43,44] did not suffice to predict the strengths of single-crystalline Ni micropillars with diameters smaller than ≈5 μm [45]. In conclusion, planar slip on the ð111Þ½110 slip system was predominantly observed in in situ SEM microcompression of an equiatomic, single phase fcc FeCrCoMnNi HEA single crystal The observed slip system thus corresponds to that fcc slip system exhibiting the highest Schmid factor. However, in contrast to the stochastic nature of plastic flow observed in fcc single crystals, all sizes of the micropillars exhibited similarly fine-spaced slip band patterns. The dependence of the yield strength on the micropillar diameter follows a power law with an exponent of − 0.32. The exponent found for the FeCrCoMnNi HEA single crystals is thus smaller than that of −0.6 to −1 typically observed for pure fcc single crystals. This weaker dependence of the yield strength on the diameter of the micropillars is attributed to the high bulk-to-theoretical strength ratio of the HEA alloy compared to pure fcc metals. Supplementary data to this article can be found online at doi:10. 1016/j.scriptamat.2016.10.026.
R. Raghavan et al. / Scripta Materialia 129 (2017) 52–55
Fig. 4. Scaling of the yield strength with diameter of the micropillar; R2 - coefficient of determination. The yield strength obtained from bulk compression testing (105 MPa) has also been indicated (unpublished results).
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