Effects of ultrasonic surface mechanical attrition treatment on microstructures and mechanical properties of high entropy alloys

Effects of ultrasonic surface mechanical attrition treatment on microstructures and mechanical properties of high entropy alloys

Intermetallics 93 (2018) 113–121 Contents lists available at ScienceDirect Intermetallics journal homepage: www.elsevier.com/locate/intermet Effects...

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Intermetallics 93 (2018) 113–121

Contents lists available at ScienceDirect

Intermetallics journal homepage: www.elsevier.com/locate/intermet

Effects of ultrasonic surface mechanical attrition treatment on microstructures and mechanical properties of high entropy alloys

T

M.T. Tsaia, J.C. Huanga,b,∗, W.Y. Tsaia, T.H. Choua, Chin-Fu Chenc, T.H. Lid, J.S.C. Jangd a

Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC Institute for Advanced Study; Department of Materials Science & Engineering, City University of Hong Kong, Kowloon, Hong Kong c Metal Industries Research & Development Centre, Kaohsiung, 811, Taiwan, ROC d Institute of Materials Science and Engineering, Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan, ROC b

A R T I C L E I N F O

A B S T R A C T

Keywords: High entropy alloy Surface mechanical attrition treatment Microstructure Hardness Strengthening mechanism

Most high entropy alloys (HEAs) are cast to form single phase solid solution. Their hardness and strength at room temperature under the as-cast condition are typically lower than expectation. In the research, the ultrasonic surface mechanical attrition treatment (SMAT) is conducted on the surface of two HEAs, FeCoNiCrMn and FeCoNiCrMn-Al, to upgrade their room temperature surface characteristics. By proper SMAT multiple paths, the grain size can be reduced from ∼50 μm down to ∼0.1–1 μm, the hardness increased from ∼2.5–5.0 GPa up to ∼5.0–8.5 GPa, and the tensile strength and elongation can be nearly doubled. The gradient refined and strengthened surface layers are demonstrated to appreciably upgrade the HEA performance. The strengthening mechanisms and superposition rules are established and are compared well with the experimental measurements.

1. Introduction Recently, multiple elemental high entropy alloys (HEAs) [1–3], either of the single phase face-centered cubic (FCC) solid solution or of the dual FCC and body-centered cubic (BCC) phases mixture, have attracted attention in terms of their alloy-composition optimization, mechanical-property exploration, and related physical and chemical characteristics [4–9]. While the high temperature heat resistance and sluggish diffusion have opened the window for various HEAs for creep and radiation resistance applications, the room temperature hardness and yield strength, especially for the single FCC phase solid solution, are often lower than expectation, as compared with Ni or Fe based superalloys [10–12]. A newly developed surface nano-crystallization process, surface mechanical attrition treatment (SMAT) [13,14], is modified from shot peening, which uses much large size of balls (1–10 mm), higher frequencies (10–100 kHz), and slower impact velocities (1–20 m/s) [15,16]. Comparing with shot peening, the impact directions of the balls onto the sample surface are rather random due to the random flying directions of the balls inside the vibration chamber. Each impact will induce plastic deformation with a high strain rate in the surface layer of the sample, as schematically shown in Fig. 1. Conventional shot peening is a directional process in which the angle between the shot jet



and the sample surface is normally fixed, close to 90° in many cases. But in the SMAT, random directional impacts of the balls onto the sample are needed in order to facilitate the grain refinement process. It is well known that many material failures are related to the surface conditions, so a proper surface modification may improve the life span and behavior. SMAT is a decent way to introduce a gradient grain refinement and nano-crystallization near the surface. Meanwhile, the properties of the bulk materials can be preserved because of the undeformed matrix inside. Compared with conventional surface nanocrystallization coating and electrodeposition such as physical vapor deposition (PVD) or chemical vapor deposition (CVD), which may be concerned about the chemical composition of the film and the quality of the bonding between the coated nanostructured layer and substrate, SMAT is the advanced way to retain the overall phases and composition [17], and the gradient SMAT-affected zone can be extended to several hundreds of micrometers in depth. Previous efforts have been made to explore the SMAT effects on various pure metals and alloys, such as Fe, Cu, 304 stainless steel, etc. [18–23]. In this research, we adopt the SMAT as surface processing for two common HEAs, namely, the FeCoNiCrMn (single FCC phase solid solution) and FeCoNiCrMn-Al (a mixture of dual FCC and BCC phases). By multiple SMATs paths, the resulting microstructure and mechanical properties are systematically examined and discussed. The

Corresponding author. Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC. E-mail address: [email protected] (J.C. Huang).

https://doi.org/10.1016/j.intermet.2017.11.018 Received 28 July 2017; Received in revised form 13 October 2017; Accepted 27 November 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.

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Zeiss Supra 55 SEM with an EBSD system. To enhance the pattern quality, the specimens were further electropolished with an electrolyte, prior to the establishment of Kikuchi patterns by EBSD. Crystal information is obtained from the EDAX Genesis analytical system computer software. The morphology of grains/subgrains and dispersion of reinforcement phase in matrix and interface between the reinforcement and matrix were examined by Tecnai G20 field emission transmission electron microscopy with an operating voltage of 200 kV. The crosssectional transmission electron microscopy (TEM) foils of the SMAT samples were fabricated using the dual-3beam focused-ion-beam (FIB) system (Seiko, SMI3050) with an operating voltage of 30 kV and an ion beam current of 1 pA. In order to observe the nanocrystal structure near the treated surface, the TEM samples of the HEAs were prepared in the dual FIB using a trenching and liftout technique. The Vickers hardness (Hv) was measured by the SHIMADZU HMV-2 system and with a load of 500 g for 15 s. The hardness of the SMAT specimens was measured from the cross-sectional surface that each datum was tested with an interval of 5 μm by the MTS Nano Indenter XP System. The tests were operated with the displacement rate about 10 nm/s under the continuous stiffness measurement (CSM) mode, and the allowable vibration drift of the environment were controlled under 0.05 nm/s. The indented depth limit was set to be 1200 nm. The as-cast and SMATed samples, which were bombarded at the both sides for the same time period, were then processed into tensile test specimens. The tensile tests using the reduced dog-bone tensile specimens in accordance with the E8M standard, with a gauge length of 12 mm, gauge width of 3 mm and gauge thickness of 2 mm, were performed using the Instron machine, deformed at the initial strain rate of 1 × 10−3 s−1, well within the quasi-steady state.

Fig. 1. Schematic illustration of the SMAT set up.

strengthening mechanisms are also explorted. 2. Experimental procedures In this study, two high entropy alloys are adopted as the tested materials, namely, Fe20Co20Ni20Cr20Mn20 (in at%) with single FCC phase and Fe18Co18Ni18Cr18Mn18Al10 (in at%) with dual FCC and BCC phases. These two alloys were cast by drop casting system with induction furnace in an atmosphere of high-purity argon and the ingots were re-melted three times to ensure chemical homogenization. The starting pure elements are all in high purity greater than 99.9 wt%. Table 1 summarizes the resulting compositions measured form the two as-cast alloys. The SMAT set-up in Fig. 1 contains a cylindrical chamber measuring 70 mm in diameter and 20 mm in height. A plate measuring 40 × 20 × 2 mm was set on the top of the SMAT chamber. The plate sample is fixed tightly on the top holder by four screws in avoiding loosening during SMAT. The SUJ2 bearing steel balls with smooth surface and high hardness in the RC scale of 62 are applied as the energy deliverer and are placed in a reflecting chamber that is vibrated by a vibration generator with a fixed vibration frequency ν = 20 kHz. The vibration amplitude, A, was chosen to 60 μm. The size of the ball was selected the 2 mm in diameter. The density of the ball of size, D, is fixed to be 7.8 g/cm3. In order to maintain the fixed ball coverage area of 25% inside the chamber, the 2 mm ball case would install 10 g of the total ball weight. Throughout the SMAT experiment, the SMAT time duration is set to be 15 min for each specimen. The analysis of X-ray diffraction (XRD) was performed by using the SIEMENS D5000 X-ray diffractometer, with Cu Kα radiation λ = 1.5406 Å. The working voltage and current were set to be 40 keV and 30 mA. The SMAT samples with ultra-fine grain microstructure were characterized by scanning electron microscopy (SEM), using the etching reagent of acetic acid + perchloric acid + ethanol (with the volume ratio of 16:4:5). The orientation tests were conducted by using a Gatan Alto 2500 Cryotransfer system interfaced to a field emission gun

3. Results and discussionora 3.1. X-ray diffraction analysis Fig. 2(a) presents the XRD scans of the as-cast and SMATed FeCoNiCrMn samples. For the SMATed sample, XRD was performed on the plane already subject to SMAT bombard. They can well be indexed by the FCC crystal structure, with a lattice parameter of 0.362 nm. For both the as-cast and SMATed samples, the (111) planar texture appears to be remained. But by careful measurements, the peak height ratio of (111) peak versus (200) peak seems to be lowered, from 8.0 for the ascast sample down to 4.5 for the SMATed sample. This suggests that the FCC grain orientation distribution in the SMATed sample has become more random by the SMAT deformation. In comparison, Fig. 2(b) shows the XRD results of the as-cast and SMATed FeCoNiCrMn-Al samples, which are of the duplex phase with the FCC (with a lattice parameter of 0.362 nm) and BCC structure (with a lattice parameter of 0.282 nm). The volume fraction of the FCC and BCC phases is ∼80% and ∼20%, respectively, based on the summation of the all FCC and BCC integral peak intensity. From the XRD (111) and (200) FCC peak ratio, the as-cast and SMAT samples appears to possess similar FCC texture. This FCC + BCC two-phase structure in the as-cast sample appears to be more difficult to be altered by SMAT, due to mutual restriction for grain orientation rotation. Finally, the peak widths increase apparently, suggesting strong grain size refinement and the presence of atomic-level lattice strain. 3.2. EDS and SEM analyses

Table 1 The SEM-EDS composition results of the FeCoNiCrMn and FeCoNiCrMn-Al specimens (all in at%). Elements

Fe

Co

Ni

Cr

Mn

Al

FeCoNiCrMn FeCoNiCrMn-Al

19 ± 2 17 ± 2

20 ± 1 19 ± 1

22 ± 3 20 ± 3

20 ± 1 19 ± 1

19 ± 2 17 ± 2

– 8 ± 1

All cast alloys were confirmed for their resulting compositions by SEM/EDS. Table 1 lists the results. Though there is scattering, the alloy compositions still fall into the range initially designed. Fig. 3 presents the SEM micrographs taken form the cross sections of the SMATed FeCoNiCrMn and FeCoNiCrMn-Al specimens, at three different depths from the free surface that was subject to SMAT 114

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up to about 50 μm at a depth of 500 μm. Some of the measured grain size data at various depth levels from the SMAT surface are included in Table 4, as will be discussed for the grain size strengthening later. Based on the XRD results in Fig. 2(a), taken from the flat surface subject to SMAT bombarding, there is a (111) texture. Now, the EBSD in Fig. 4(a) was taken from the cross-sectional plane, 90° with respect to the flat surface. There is very few (111) grains in this EBSD image, consistently with the XRD scans. In parallel, Fig. 5(a) and (b) present the typical EBSD FeCoNiCrMnAl specimens. The initial grain size in the as-cast alloy is about 10 μm. And the refined grain size near the SMAT surface is about 0.3–1 μm, with the average of 0.6 μm. Some of the measured grain size data at various depth levels are also included in Table 4. The representative TEM micrographs for the SMATed samples near the SMAT surface regime are presented in Fig. 6. It can be seen that there are abundant dislocations, forming refined subgrains and grains. The average grain size is consistent within 0.6–0.7 μm. From the substructures and the associated selected area diffraction patterns, the grain lattices appear to contain slight distortion and retained internal stress. Such SMAT gradient surface layers would contribute work hardening appreciably, in addition to grain size strengthening, as discussed below. 3.4. Hardness measurements The hardness was evaluated by both the Hv micro-hardness measurement, performed on the flat surface subject to SMAT bombarding, and the nanoindentation, conducted from the cross-sectional plane. The basic data are summarized in Table 2. According to Table 2, the hardness readings of the FeCoNiCrMn and FeCoNiCrMn-Al samples before and after SMAT are 147–290 Hv and 370–650 Hv, respectively. The hardness data presented in Table 2 are the average of fifty datum point. Fig. 7 illustrates the variation trends of the nanoindentation hardness as a function of depth from the free surface for both the FeCoNiCrMn and FeCoNiCrMn-Al SMAT samples. The nano-scaled hardness readings for the FeCoNiCrMn sample in Fig. 7(a) decrease from about 5.0 GPa at the sample free surface down to about 2.5 GPa at a depth ∼500 μm, maintaining around 2.5 GPa afterward. The SMAT affected zone is thus estimated to be about 500 μm. The hardness increase from ∼2.5 GPa up to ∼5.0 GPa is already a double increment (200%). In parallel, the nano-scaled hardness readings for the FeCoNiCrMnAl sample in Fig. 7(b) decrease from about 8.5 GPa at the sample free surface down to about 5.0 GPa at a depth ∼400 μm. The SMAT affected zone is thus estimated to be about 400 μm. The increase from ∼5.0 GPa to ∼8.5 GPa is almost a double increment (170%).

Fig. 2. XRD profiles taken from (a) the flat surface of the as-cast and SMATed FeCoNiCrMn FCC HEA samples (facing SMAT bombarding), and (b) the flat surface of the as-cast and SMATed FeCoNiCrMn-Al FCC + BCC HEA samples (facing SMAT bombarding).

bombard. Since the affected depth of the current SMAT experiment was only about 500 μm (as later shown by the nanoindentation results), the SEM micrographs shown for the center region, i.e., Fig. 3(b) and (e), in fact represent the grain structure in the as-cast samples, showing the very simple coarse FCC grains in the FeCoNiCrMn sample and the nearly eutectic structure of FCC + BCC in the FeCoNiCrMn-Al sample. By using the current etching reagent, only the FCC and BCC phases can be differentiated. The grain size within the FCC or BCC phase cannot be revealed. Thus, the refined grain structures after SMAT have also been examined by EBSD and TEM. Since the grain size is rather small, the SMATed surface layers do not contain nano-twins. But the twin density increases with increasing sample depth into the inner portion.

3.5. Tensile results The comparison of the tensile engineering stress-strain curve results for the as-cast and SMAT samples is shown in Fig. 8 for both the FeCoNiCrMn and FeCoNiCrMn-Al alloys. The flat top and bottom sample surfaces have both been subject to SMAT, resulting fine equiaxed grains about 0.3–1 μm (with an average about 0.7 μm for FeCoNiCrMn and about 0.6 μm for FeCoNiCrMn-Al). The data on the yield stress (YS), ultimate tensile stress (UTS), tensile elongation (ε), work hardening rate (θ = dσ/dε), and work hardening exponent (n = dlnσ/dlnε) are all compiled in Table 3. For the FCC single phase FeCoNiCrMn alloy, the YS, UTS and ε data have increased from about 230 MPa, 400 MPa and 33% under the as cast condition up to about 450 MPa, 600 MPa and 60% under the SMAT condition, about 100% double increment, as compared in Table 3. The apparent grain refinement gradient layer on both surface have significantly improve the tensile performance. The work hardening rate values at ε = 7% and 20% are ∼1000 and 400 MPa for the as-cast samples and ∼700 and 350 MPa for the SMATed samples, respectively.

3.3. EBSD and TEM analysis Fig. 4(a) and (b) show the EBSD images taken form the cross-sectional planes of the as-cast and SMATed FeCoNiCrMn specimens, respectively. The grain sizes can be more readily seen from the EBSD micrographs, being about 50 μm for the as-cast sample, and about 0.3–1 μm near the free surface of the SMATed sample, with the average of 0.7 μm. The grain size can be significantly refined by SMAT, and the grain size gradually increases from about 300 nm at the SMAT surface 115

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Fig. 3. (a) Illustration of the microstructure extraction from the SMATed samples. (b) (c) (d) are the SEM micrographs taken from the SMAT FeCoNiCrMn edge-on side surface, for the three sections marked in (a). (e) (f) (g) are the SEM micrographs taken from the SMAT FeCoNiCrMn-Al edge-on side surface, for the three sections marked in (a). Note that the BCC grains are in bright contrast and the FCC grains are in dark contrast. The grain size cannot be clearly revealed by such SEM micrographs. Need to be revealed by EBSD below.

Fig. 4. EBSD image taken from (a) the as-cast FeCoNiCrMn sample, showing that the initial FCC grain size is about 50 μm, and (b) the SMATed FeCoNiCrMn sample, with the free surface directly subject to SMAT bombarding on the right, indicating that the FCC grain size has been significantly reduced down to about 0.3–1 μm.

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Fig. 5. (a) (b) EBSD images taken from the as-cast FeCoNiCrMn-Al sample. The FCC (in blue color) and BCC (in red color) can be clearly distinguished in (a), and the initial grain size can be estimated to be about 15 μm. (c) (d) EBSD images taken from the SMATed FeCoNiCrMn-Al with the free surface on the right. The grain size near the free surface subject to SMAT has been significantly reduced down to about 0.3–1 μm.

4. Strengthening analyses by rule of mixture

The extracted n exponent is 0.55 for the as-cast samples and 0.35 for the SMATed samples. Note that θ and n for the SMATed samples are both lower than those of the as-cast ones, even though the tensile elongation of the former is higher. This means that the general observation for the uniform tensile strain εu is about the value of n (εu = n) for necking criterion is not the only cause for the current tensile elongation performance. The gradient surface layers of the SMATed samples have significantly helped in extending the tensile elongation from 33% to 60%, though their θ rate and n exponent are lower. In addition, since the YS levels for the SMAT samples are already raised up by the induced dislocations in the gradient regime, the work hardening effect will be lowered accordingly, reducing the θ and n values. For the FCC + BCC FeCoNiCrMn-Al alloy, the YS, UTS and ε data have also increased from about 500 MPa, 750 MPa and 9% under the as cast condition up to about 750 MPa, 1100 MPa and 13% under the SMAT condition, about 50% increment, also compared in Table 3. The work hardening rate value at ε = 7% is ∼1500 MPa for the as-cast samples and ∼1200 MPa for the SMATed samples, respectively. The extracted n exponent is 0.45 for the as-cast samples and 0.35 for the SMATed samples. The trend is basically similar to that observed from the FCC FeCoNiCrMn alloy.

The SMAT surface treatment by mechanical bombarding has been demonstrated to upgrade the HEAs appreciably. From previous research on pure metals [24,25], the gradient surface layers appear to be highly effective, especially the gradient layer does not have sharp interfaces, thus the load transfer and distribution over the deforming gauge section can be quite smooth. In order to evaluate the strengthening contribution, further analyses are conducted below. Firstly, we intend to check how the gradient surface layer would contribute to the gauge sample during tensile loading, based on the common model for laminated composite materials. Since the layers are parallel to the loading axis, it should follow the equal strain condition, or the Rule of Mixture (ROM) [26],

σtotal = σ1V1 + σ2V2,

(1)

where σtotal, σ1, and σ2 is the total sample strength, strength contribution from layer 1, and strength contribution from layer 2, respectively, and V1 and V2 is the volume fraction of layer 1 and layer 2, respectively. Since the gradient layer has the gradual and gradient variation of the grain size and dislocations/twins by SMAT, we can either integrate the strength over this gradient layer, or simply approximate the case by 117

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Fig. 6. Representative TEM micrographs taken from the regime near the SMAT surface of the SMATed FeCoNiCrMn alloy.

than the ROM level. The gradient distribution of refined grains (with extra strengthening from the dislocations/twins work hardening) can effect update the alloy tensile performance, to a higher strength level greater than the ROM prediction as well as a higher tensile elongation. From the higher tensile strength and elongation, the fracture toughness or the fatigue resistance of the SMATed samples is also expected to be higher. The same ROM calculation for the FCC + BCC FeCoNiCrMn-Al alloy is applied, namely,

using several thinner layers with different strength levels. In order to evaluate the individual strength level for each thin layer, we can take advantage of the measured hardness by nanoindentation in Fig. 7. By rough estimation, the tensile flow stress level can be obtained by dividing the hardness by 3 [27], for example, the nano-scaled hardness of 2.5 GPa at the inner portion without any SMAT influence for FeCoNiCrMn in Fig. 7(a) can be transformed into tensile flow stress about 2500/3 = 833 MPa. But this high strength of 833 MPa is only valid in nano-scales. There is an apparent sample size effect, as widely seen in many metallic materials [28–31]. To estimate the tensile strength in the bulk (or in mini-scales), we can refer the YS of 250 MPa and UTS of 450 MPa in Table 3. Since the hardness measurement usually does not indent until fracture, but must have exceeded yielding, thus it is logical to estimate that the tensile flow stress to be about 350 MPa at mini-scales. Thus, the sample size effect from nano to mini scales will be ∼833/350–2.4. Using the sample size factor of 2.4, we can estimate the tensile flow stress from the inner portion without any SMAT influence, three intermediate gradient layers, and the outer surface layer to be about 350, 420, 490, 595, and 700 MPa, respectively. By the Rule of Mixture in Equation (1), the tensile strength σtotal for the as-cast FCC FeCoNiCrMn sample can be roughly estimated as

σtotal ∼ 490 × 0.6 + 660 × 0.1 + 830 × 0.1 + 1000 × 0.1 + 1180 × 0.1 The tensile flow stress (750 + 1100)/2–925 MPa (Table 3) appears to be much higher than the ROM prediction of 661 MPa. The gradient effect is even more apparent. 5. Strengthening analyses in terms of grain size and work hardening strengthening Attempt has also made on the strengthening contributions. Based on the microstructure examination and hardness measurement from the cross-section of the SMATed samples, the two major strengthening contributions are considered to be the grain size (GS) and work hardening (WH). The rough contributed strength increments are estimated below. Previous studies have demonstrated that the Victor's hardness of the FeCoNiCrMn based alloys follow the Hall-Petch relationship well, with the following expression [32].

σtotal ∼ 350 × 0.5 + 420 × 0.125 + 490 × 0.125 + 595 × 0.125 (2)

+ 700 × 0.125 ∼ 451 MPa,

(3)

∼ 661 MPa.

which can be compared to the tensile flow stress of the SMATed sample, namely, (450 + 600)/2–525 MPa (Table 3). It can be seen that the ROM predicted value of 451 MPa is still lower than the experimentally measured data of 525 MPa. This suggests that the gradient refined grains by SMAT can result in a tensile strengthening level even higher

Hv (in MPa) = Hvo + 677 d−1/2,

(4)

Table 2 The Vicker's hardness Hv values taken form the top surface and the nanoindentation data taken from the cross-section of the FeCoNiCrMn and FeCoNiCrMn-Al as-cast and SMATed specimens. Alloy

FeCoNiCrMn FeCoNiCrMn-Al

As-cast

SMATed

Hv

Nano-indent

Hv

Nano-indent (Near free surface)

Nano-indent (250 μm in depth)

Nano-indent (500 μm in depth)

147 ± 4 290 ± 5

2.5 ± 0.2 GPa 5.0 ± 0.2 GPa

370 ± 50 650 ± 50

5.0 ± 0.3 GPa 8.5 ± 0.3 GPa

3.5 ± 0.2 GPa 6.5 ± 0.1 GPa

2.5 ± 0.1 GPa 5.0 ± 0.2 GPa

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Fig. 8. Representative room temperature tensile engineering stress –strain curves for (a) FeCoNiCrMn and (b) FeCoNiCrMn-Al. Each condition has been tested for at least three times to ensure reproducibility. Fig. 7. The gradient variation of the nanoindentation hardness data measured from the cross section of representative SMAT samples: (a) FeCoNiCrMn and (b) FeCoNiCrMn-Al. The SMAT affected zone appears to be about 500 μm for FeCoNiCrMn and about 400 μm for FeCoNiCrMn-Al.

the SMAT surface, as listed in Table 4. With increasing depth into the inner portion, the work hardening contribution will be gradually decreasing. With the help from careful TEM observations, the defect density ρ at the depth of 250 μm from the SMAT surface has been reduced to about one half (0.5). According to common stage II work hardening mechanism, the strain ε would be linearly proportional to the defect density ρ, i.e.,

where the slope K has the unit of MPa.μm−1/2. This can be roughly corresponding to

σGS (in MPa) = σo + 226 d−1/2.

(5)

ε ∝ ρ,

Then, with the help of the variations from the SMAT surface into the inner portion of the grain size and hardness, the Hall-Petch plots for the YS date of the two alloys can be plotted. Though there are some scattering, the strengthening contribution from grain size refinement is given by

ΔσGS = σGS − σo = K(d−1/2 − dmatrix −1/2).

(7)

and the stress σ would be related to ε and ρ by

σ ∝ e1/2 ∝ ρ1/2.

(8)

with a parabolic work hardening exponent n about 1/2. This would lead to the work hardening contribution at the depth of 250 μm from the SMAT surface to be (0.5)1/2, namely, ∼0.7 of σWH = 150 MPa for FeCoNiCrMn at the SMAT surface (106 MPa). Table 4 lists the determined values of the work hardening contribution. The addition rule for grain size and work hardening strengthening contributions is generally expressed by the generalized superposition rule [33–35],

(6)

With the measured grain size at various depths from the SMAT surface, the contributions from the grain size strengthening are listed in Table 4. As for the work hardening, the induced defects such as dislocations within the SMAT affected zone are ascribed as the total work hardening contribution. From Fig. 8(a) and (b), the work hardening contribution for the FeCoNiCrMn and FeCoNiCrMn-Al alloys over the strain levels from 5% to 20% and 4% to 6% are consistently about 150 and 330 MPa in average, respectively. This is considered to be the range that the induced defects can strengthen the alloy by the work hardening mechanism by the SMAT bombard. Thus, in this study, we attribute σWH = 150 MPa for FeCoNiCrMn and 330 MPa for FeCoNiCrMn-Al at

q σ q = σ GS + σ qWH,

(9)

where q is an adjustable exponent, mostly lying within 1–2. When q is equal to 1, it is the simple linear superposition rule, and when q is equal to 2, it becomes the Pythagorean superposition rule, namely,

σ = σGS + σWH , 119

(10)

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Table 3 Comparison of the average tensile results of the as-cast and SMATed FeCoNiCrMn and FeCoNiCrMn-Al specimens. At least three samples were tested for each condition. The elastic modulus E for the FeCoNiCrMn and FeCoNiCrMn-Al is consistently around 110 GPa and 120 GPa, respectively, independent of the as-cast or SMAT condition. The work hardening rate θ was all taken from ε = 7% for comparison. Alloy

FeCoNiCrMn FeCoNiCrMn-A

As-cast

SMATed

YS (MPa)

UTS (MPa)

ε %

θ (MPa)

n

YS (MPa)

UTS (MPa)

e %

θ (MPa)

n

230 ± 2 500 ± 8

400 ± 5 750 ± 9

33 ± 3 9 ± 1

∼1000 ∼1500

∼0.55 ∼0.45

450 ± 2 750 ± 3

600 ± 4 1100 ± 8

60 ± 4 13 ± 1

∼700 ∼1200

∼0.35 ∼0.35

Table 4 Comparison of the strengthening analyses from theoretical predictions and experimental measurements of the stress increment with respect to the stress of the base alloy (without SMAT, i.e., with d of ∼50 μm and nill work hardening). D is the distance from the SMAT surface, and d is the grain size at that position. The experimentally obtained flow stress data are extracted from the nanoindentation data (by dividing by 3 to transforming the hardness into flow stress). The flow stress in this study is referred to the tensile flow stress at strain e about 15% for FeCoNiCrMn and about 7% for FeCoNiCrMn-Al. Alloy

FeCoNiCrMn

FeCoNiCrMn-Al

2 σ 2 = σ GS + σ 2WH.

D, μm

0 50 100 250 0 50 100 200

d, μm

0.7 1.5 5.0 18 0.6 1.4 3.0 6.0

Theroretical prediction

Experimental measurement

ΔσGS (MPa)

ΔσWH (MPa)

Δσ (q = 1) (MPa)

Δσ (q = 2) (MPa)

Δσflow-stress (MPa)

238 152 68 21 220 120 59 21

150 146 142 106 330 302 289 231

388 298 210 127 550 422 348 252

281 211 157 108 397 325 295 232

347 278 208 125 486 382 313 236

increase from 2.5 GPa at the inner central region up to 5.0 GPa at the surface, an increment of 2 times. In parallel, the hardness of FeCoNiCrMn-Al can increase from 5.0 GPa up to 8.5 GPa, also an increment of 1.7 times. The tensile tests also demonstrate that the tensile UTS and elongation can be improved by SMAT from 400 MPa and 33% up to 600 MPa and 60% for FeCoNiCrMn, and from 750 MPa and 9% up to 1100 MPa and 13% for FeCoNiCrMnAl. (4) The joint strengthening effects from ΔσGS and ΔσWH can strengthen the alloys by Δσflow-stress ∼347–486 MPa at the SMAT surface and nil at the inner central region. By comparing the experimentally measured data and the theoretically predicted values for the strengthening, the linear superposition rule (q = 1) can adequately predict the experimental strength, but the addition rule with q∼1.2 gives the best match.

(11)

Taking the grain size strengthening contribution for σGS and the determined work hardening contribution for σWH into Equations (10) and (11), the values for the overall strength can be calculated and then compared with experimental data, as compared in Table 4. It can be seen that the experimentally measured strengthening data, Δσflow-stress, are all within the theoretically predicted values using q = 1 and q = 2. By close examination, the experimental data are closer to those predicted values with q = 1. The best fit appears to the case while using q = 1.2. This is logical since the two types of obstacles of the grain boundaries and dislocations are relatively in wide difference in obstacle size and intrinsic strength, thus the better fit of the addition rule should be closer to the linear superposition addition rule with q = 1. For two types of obstacles with similar obstacle size and intrinsic strength, for example, precipitates and dislocations for precipitation hardening and work hardening, the addition rule would be closer to the Pythagorean superposition rule with q = 2. The current case, q = 1.2 appears to be the best match.

Acknowledgement The authors gratefully acknowledge the support from Ministry of Science and Technology of Taiwan, ROC, under the grant no. MOST105-2221-E-110-019-MY31. The support by Metal Industries Research & Development Center is also acknowledged.

6. Conclusion By a simple surface mechanical attrition treatment (SMAT) on the FeCoNiCrMn and FeCoNiCrMn-Al HEAs, the apparent surface hardening and grain size refinement in a gradient manner from the SMAT surface into the inner portion, the samples become much stronger and tougher, resulting in the following conclusions.

Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx. doi.org/10.1016/j.intermet.2017.11.018.

(1) The surface grain size can be refined from the initial ∼50 μm for FeCoNiCrMn and ∼10 μm for FeCoNiCrMn-Al down to ∼0.3–1 μm in a gradual gradient manner, contributing significant grain size strengthening ΔσGS from over 200 MPa near the surface gradually down to nil in the inner central region. (2) The SMAT will also induce significant work hardening ΔσWH from the surface into the inner portion, from ∼150 to 170 MPa at the surface gradually down to nil in the inner central region. (3) Experimentally, the cross-sectional hardness of FeCoNiCrMn can

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