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Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy
Journal Pre-proofs Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy Kai Suzuki, Motomochi Koyama, Shigeru Hamada, Kaneaki Tsuzaki, Hiroshi Noguchi PII: DOI: Reference:
S0142-1123(19)30522-5 https://doi.org/10.1016/j.ijfatigue.2019.105418 JIJF 105418
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
8 October 2019 19 November 2019 3 December 2019
Please cite this article as: Suzuki, K., Koyama, M., Hamada, S., Tsuzaki, K., Noguchi, H., Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy, International Journal of Fatigue (2019), doi: https://doi.org/10.1016/j.ijfatigue.2019.105418
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© 2019 Published by Elsevier Ltd.
International Journal of Fatigue
Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy
Kai Suzukia, Motomochi Koyamab, Shigeru Hamadac, Kaneaki Tsuzakic, Hiroshi Noguchic a Graduate b Institute c Faculty
School of Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka-shi, Fukuoka 819-0395, Japan
for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
of Engineering, Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka-shi, Fukuoka 819-0395, Japan
Corresponding author: [email protected]
Abstract High-cycle fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy were investigated using smooth specimens. The microstructural deformation characteristics, i.e., planar dislocation slip, significantly affected the fatigue crack initiation and small fatigue crack propagation. The deformation localization associated with dislocation planarity led to multiple crack initiation on the slip planes. The crack propagation mechanism comprised crack formation on slip planes around the main crack tip and subsequent coalescence. The fatigue crack propagation mechanism shifted to Mode I type as the crack length increased.
Keywords: High entropy alloy, planar slip, high cycle fatigue, fatigue crack initiation and propagation.
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1. Introduction Incorporation of compositional complexity in alloys has drawn attention as a novel strategy to create a new class of structural materials. Compositional complexity, namely, an increased configurational entropy, can result in extraordinary toughness, ductility, and strength [1-4]. An alloy group with a high configurational entropy has been referred to as high-entropy alloys (HEAs). Specifically, the equiatomic CrMnFeCoNi quinary alloy has been considered to have a representative composition of HEAs [5]. The excellent mechanical performance of equiatomic quinary HEA [6-10] is attributed to the characteristic dislocation behavior associated with its planarity [11] and thermal activation process [6]. From the viewpoint of mechanical performance, fatigue resistance is another important property for the practical use of HEA as a structural component. Dislocation planarity, which is high in the equiatomic quinary HEA, has been recognized as a significant factor affecting fatigue crack resistance as it influences various fatigue-related parameters: (1) work hardenability, (2) degree of crack tip stress shielding, and (3) ease of microstructural damage accumulation [12-14]. The first parameter is attributed to dislocation distribution, which means that high dislocation planarity delays self-accommodation of local stress. This effect increases the stored strain energy, which prevents further motion or multiplication of dislocations [15]. The second parameter is associated with the elastic strain field around the nearest dislocation from a crack tip. Because the dislocation planar array provides a high back stress, the elastic strain field at the nearest dislocation decreases the effective tensile stress at the crack tip, which delays crack opening [13]. The third parameter is related to the accumulation rate of lattice defects per cycle at a microstructurally local site. An enhanced dislocation planarity prevents dislocation annihilation, and localizes accumulation of dislocations or vacancies. Accelerated increase of local damage density alters the ease of crack initiation and fatigue crack propagation mechanism from Mode I to Mode II types [14][16]. Therefore, HEA with a high dislocation planarity is expected to exhibit the characteristic behavior of fatigue resistance. Growth behavior of mechanically long cracks in HEA (equiatomic CrMnFeCoNi) has been reported
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in a previous study [17], where compact tension tests with increasing ΔK were conducted at room temperature on the HEA and SUS316L which is austenitic stainless steel. The fatigue crack growth rates of the HEA were lower than those of SUS316L. Microstructure-dependent crack closure associated with crack roughness was considered as a factor enhancing the resistance to fatigue crack growth. It has been generally known that such microstructure effects, including influences of dislocation planarity, appear particularly when the crack is in an initiation stage and the crack length is small [18-20]. Such small cracks are referred to as mechanically and microstructurally small cracks and their propagation has two characteristics: significant hardness/yield strength dependence and selective propagation along microstructural features. Hence, the influence of the characteristic dislocation behaviors in HEA on fatigue crack initiation and small fatigue crack propagation must be elucidated. In this study, the characteristic dislocation behavior of HEA, such as dislocation planarity, which is expected to yield superior crack tip hardening and dislocation-driven stress shielding were investigated. Furthermore, dislocation planarity leads to localization of damage accumulation that is expected to cause slip-plane cracking and Mode II crack propagation, which may induce unconventional fatigue crack initiation and propagation phenomena. Therefore, this study aimed at elucidating the effect of high dislocation planarity on fatigue crack initiation and propagation in HEA.
2. Experimental procedure 2.1 Materials A 50 kg ingot of an equiatomic CrMnFeCoNi quinary alloy (hereafter, the chemical compositions are presented in at. %) was prepared by vacuum induction melting. The ingot was hot-rolled at 1373 K. The rolled bar was solution-treated at 1073 K and subsequently water-quenched. In addition, we used nonequiatomic solution-treated Fe-20Cr-14Ni ternary alloy as a reference material. Both of the alloys are non-magnetic fully face-centered cubic (FCC) alloys, which do not show martensitic transformation. In this study, the CrMnFeCoNi and Fe-20Cr-14Ni alloys are referred to as HEA and austenitic stainless
3
steel (ASS), respectively. The detailed chemical compositions of the alloys are listed in Table 1. The average grain sizes of the HEA and ASS were 41 μm and 38 μm, respectively, as shown in Fig. 1. The grain size was measured based on the cutting method, and the annealing twin boundaries were counted as grain boundaries. The stacking fault energies (SFE) of the ASS and HEA have been reported to be 35 [21] and 30 mJ m-2 [22], respectively. The solution-treated bars were cut by electro discharge machining to prepare tensile specimens, and machined by lathe to prepare fatigue test specimens. The specimen geometries are shown in Fig. 2. Table 1 Chemical compositions of the HEA and ASS [mass%]. Alloy
Fe
Mn
Ni
Co
Cr
C
S
P
Al
O
N
HEA
Bal
19.8
20.2
20.9
18.2
0.002
0.006
0.002
0.018
0.007
0.0087
ASS
Bal
0.001
14.6
18.8
0.002
0.001
0.001
Si
<0.001
Fig. 1 BSE image of as-solution-treated microstructures of the (a) ASS and (b) HEA.
2.2 Mechanical testing The specimens were mechanically and electrochemically polished before the tests. Tensile tests were conducted along the rolling direction (RD) at room temperature (RT: approximately 294 K) with an initial strain rate of 10-4 s-1. The strain was measured using a video extensometer. The specimen surface was mechanically and electrochemically polished. Therefore, the final diameter of the specimens was reduced by approximately 50 μm. Rotating bending fatigue tests were conducted
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at RT at a frequency of 30 Hz and a stress ratio of −1. The loading direction corresponded to the RD. In this experiment, the nominal stress was defined as the bending stress on the minimum radial part, and stress concentration due to the shape of the test specimen was not considered. The specimen surface during the fatigue tests was obtained using a replica method to measure the crack length. The replication was carried out under no-load conditions after immersing the replica sheet in methyl acetate. The replica images were taken by optical microscopy.In this experiment, the fatigue limit was defined as the stress amplitude where the specimen was not broken at 107 cycles. The fracture surfaces were observed by scanning electron microscopy (SEM) at an accelerating voltage of 15 kV.
Fig. 2 Specimen geometries of the (a) tensile test and (b) rotating bending fatigue specimens.
2.3 Microstructure characterization The fatigued specimens were mechanically polished using colloidal silica with a particle size of 60 nm. Electron backscatter diffraction (EBSD) measurements were performed around a subcrack with a beam step size of 500 nm. In addition, electron channeling contrast imaging (ECCI) was carried out on the fatigue-fractured specimens at an accelerating voltage of 30 kV.
3. Results
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3.1 Tensile and fatigue strength Fig. 3 (a) shows the engineering stress-strain curves of the ASS and HEA. Table 2 summarizes the obtained tensile properties. The tensile strength and 0.2 % proof strength of the HEA were higher than those of the ASS. However, the ASS was superior to the HEA in terms of fracture elongation. Fig. 3 (b) shows the true stress-true strain diagram up to the tensile strength. The large slope of the true stressstrain curve of HEA indicates that the work hardening capability of HEA is higher than that of ASS.
Fig. 3 (a) Engineering and (b) true stress-strain curves at an initial strain rate of 10-4 s-1.
Table 2 Tensile test results of the HEA and ASS. 𝝈𝐔𝐓𝐒, 𝝈𝟎.𝟐 and 𝜹 indicate ultimate tensile strength, 0.2 % proof strength and fracture elongation, respectively. Alloy
𝝈𝐔𝐓𝐒 [MPa]
𝝈𝟎.𝟐 [MPa]
𝜹 [%]
HEA
585
254
53
ASS
473
135
82
Fig. 4 (a) shows the stress amplitude as a function of the number of cycles to failure. The fatigue limits of the ASS and HEA were 200 and 250 MPa, respectively. In addition, since fatigue strength has been reported to be linearly correlated with tensile strength [23], the stress amplitude was normalized by the tensile strength, as shown in Fig. 4(b). The ratio of stress amplitude to tensile strength (σa/σUTS) plotted against the number of cycles to failure showed almost similar values.
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Fig. 4 (a) Stress amplitude-fatigue life diagram. (b) Ratio of stress amplitude to tensile strength, σa/σUTS -fatigue life diagram.
3.2 Fatigue crack growth behavior Fig. 5 shows the fatigue crack initiation and growth behavior for the ASS and HEA at the same ratio of stress amplitude to tensile strength, σa/σUTS as exhibited in Fig. 4. The results of the five longest cracks are shown for each alloy. The stress amplitudes for the ASS and HEA were selected to be 220 and 270 MPa, respectively. The fatigue lives of the ASS at 220 MPa and HEA at 270 MPa were 5.0×105 and 1.1×106 cycles, respectively, as indicated in Fig. 4. Fig. 5 (a) shows the number of cracks at 4.7×105 cycles in ASS and 106 cycles in HEA. The number of cracks with a crack length over 200 μm was 76 in ASS and 80 in HEA. The difference appeared in the number of cracks with a crack length of 100-200 μm. The number of cracks with a crack length of 100-200 μm was 122 in ASS and 435 in HEA. In other words, the number of small fatigue cracks with a crack length of 100-200 μm in HEA was larger than in ASS. Fig. 5 (c) shows the fatigue crack growth rates plotted against the crack length for five fatigue cracks, respectively. Comparing the crack growth rates of the ASS with those of the HEA, we can see that most of the crack growth rate data showed similar general trend when plotted against the crack length. An important difference was observed in the stage where the crack length was small. That is, the
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fatigue crack growth rate of HEA with a length of <500 μm was lower than that of ASS. In addition, the small cracks in the HEA temporarily stopped to grow. Crack coalescence was observed in both materials. In ASS, crack coalescences were observed with crack lengths of 422.4 μm, 655.7 μm, 656.8 μm, 1007 μm, 1040 μm. In HEA, crack coalescences were observed with crack lengths of 175.0 μm, 325.0 μm, 363.0 μm, 394.5 μm, 414.0 μm, 735.5 μm, 753.0 μm. This result indicates that crack coalescences of HEA occur at early crack stage.
Fig. 5 Growth behavior of the longest five cracks for the ASS at 220 MPa and the HEA at 270 MPa for the same ratio of stress amplitude to tensile strength, σa/σUTS. (a) Number of cracks plotted against fatigue crack length (b) Fatigue crack length plotted against the number of cycles. (c) Fatigue crack growth rate plotted against fatigue crack length.
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3.3 Fatigue crack propagation path To understand the factors causing the difference in the fatigue crack growth rate, the fatigue crack propagation path was observed. Figs. 6 and 7 show the replica images of fatigue sub cracks in ASS and HEA. The white arrows indicate the crack tips. In the ASS (Fig.6), the fatigue crack occurred along slip lines. The fatigue crack propagation behaviors of ASS can be classified into two cases: propagations (1) along and (2) across the slip lines, as indicated by the blue circle and red lines in Fig. 6 (e), respectively. In the HEA (Fig.7), the fatigue crack also occurred along slip lines. However, fatigue crack propagation across the slip lines was not observed in HEA. Hence, the ratio of propagation along slip lines to the fatigue crack length in HEA was larger than that in ASS (Fig. 6 (e) and Fig. 7 (e)). Furthermore, multiple crack initiation was frequently observed in HEA, which resulted in crack coalescence during the growth, as shown in Figs. 7 (c) to (d). The crack coalescence of HEA was observed particularly at the early fatigue stage where the crack length was up to 500 µm.
Fig.6 A set of replica images showing a fatigue sub crack at (a) 2×105, (b) 2.8×105, (c) 3.4×105, (d) 4.0×105, (e) 4.3×105 cycles in the ASS tested at 220 MPa. White arrows indicate crack tips. Red lines
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indicate regions of crack propagation along slip lines. Blue circle indicates an example of crack propagation across slip lines.
Fig. 7 A set of replica images showing fatigue sub cracks at (a) 4×105, (b) 7.5×105, (c)9.5×105, (d)1.0×106 (e) 1.05×106 cycles in the HEA tested at 270 MPa. White arrows indicate crack tips. Red lines indicate regions of crack propagation along slip lines.
3.4 Fractography Fig. 8 and Fig. 9 show SEM fractographs of ASS and HEA, respectively. The yellow dashed line traces the white streaks that formed by crack coalescence. Namely, yellow dashed lines indicate the boundaries of multiple cracks. In both materials, multiple cracks were observed on the fractographs, and their propagation and coalescence led to fracture. In the central parts of the fracture surface, dimples were observed (Fig. 8 (a) and Fig. 9 (a)). In the surface crack observation, as discussed in Section 3.3, the number of crack initiation sites was large in HEA, and the same tendency was observed in the fractograph. Fig. 8 (b) and Fig. 9 (b) show parts near the specimen surfaces with the crack initiation sites. In HEA, three crack initiation sites were observed, as indicated by orange circles. In both ASS and
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HEA, the crack initiation parts showed transgranular facets, as depicted in Fig. 8 (c) and Fig. 9 (c). A difference was observed in the fracture surface around the crack length at 500 µm (Fig. 8 (d) and Fig. 9 (d)). Transgranular facets were observed for both materials, but the facet size of HEA was larger than that of ASS. Considering that the grain size of both materials is about 40 µm, the facet size of ASS is less than 1 grain size and that of HEA is 1 to 2 grain size. Fig. 8 (e) and Fig. 9 (e) show the fractograph near the dimple, that is, where the fatigue crack length is large. For both materials, striations were observed in the part where the crack length was about 1 to 2 mm.
Fig. 8 SEM fractographs of the ASS (σa=220 MPa): (a) overview of the fracture surface, (b) a part near specimen surface (c) crack initiation site, (d) crack length around 500 µm, (e) striations. Yellow dashed lines in (a) indicate boundaries of multiple cracks. The orange circle in (b) indicates a crack initiation site.
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Fig. 9 SEM fractographs of the HEA (σa=270 MPa): (a) overview of the fracture surface, (b) a part near specimen surface (c) crack initiation site, (d) crack length around 500 µm, (e) striations. Yellow dashed lines in (a) indicate boundaries of multiple cracks. Orange circles in (b) indicate crack initiation sites.
3.5 Dislocation substructure evolution associated with fatigue cracks. Compared to ASS, HEA showed intensive crack propagation along slip lines. To understand the crack propagation behavior, we first observed the dislocation substructure near the fatigue crack of ASS, as shown in Fig. 10 (a). Here, the crack propagated along the (111) plane that is parallel to the annealing twin boundary. In addition, dislocation cell formed in the vicinity of the fatigue crack tip in ASS, as shown in Fig. 10 (b). Since the number of fatigue cracks of HEA was larger than that of ASS, it is important to understand the crack initiation mechanism. Fig. 11 shows corresponding rolling direction (RD//loading direction)Inverse Pole Figure map and ECC images around the sub crack initiation site. As shown in Fig. 11 (c) (d), highly planar dislocation array was observed around the crack initiation site. The fatigue crack plane at the initiation site was along the (111) plane, but the planar dislocation array was aligned on the (111) plane. The crack in Fig.11 propagated along the slip plane after crack initiation. Fig. 12 shows the ECC images around the crack propagation region. Planar dislocation arrays in two slip systems were
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observed around the fatigue crack. Incidentally, deformation twinning was not observed in the grains where the fatigue crack propagated.
Fig. 10 ECC images showing dislocation structure near the subcracks in ASS (σa = 220 MPa). (a) planar slip and (b) cell formation were observed. Yellow lines in (a) indicate slip plane traces. A yellow circle in (b) indicates the portion where dislocation cell structure is formed.
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Fig. 11 (a) Overview around one of the subcracks near the main crack, and (b) corresponding rolling direction (RD//loading direction)-IPF map in HEA (σa = 270 MPa). (c, d) Magnified ECC images of the crack initiation site. Arrows in (a) indicate the crack tips. Red lines in (c) indicate slip plane traces. Yellow lines in (d) indicate two slip plane traces where dislocation patterns are aligned.
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Fig. 12 (a) A magnified ECC image of the region indicated in Fig, 11(a) (HEA).
(b) Magnified image
corresponding to Fig. 12(a). The arrow in (a) indicates the crack tip. Yellow lines in (b) indicate two slip plane traces where dislocation patterns are aligned.
4. Discussion The ratio of stress amplitude to tensile strength (σa/σUTS) plotted against the number of cycles to failure showed almost similar values for ASS and HEA. However, there were differences in the number of fatigue cracks, fatigue crack growth rate, and crack propagation path. These factors might have been affected by the dislocation planarity of HEA. In this section, we elucidate the role of dislocation planarity in fatigue crack initiation and propagation.
4.1 Fatigue crack initiation The number of fatigue cracks of HEA was larger than that of ASS. Multiple crack initiation of HEA led to crack coalescence at the early stage of fatigue. The increase in the number of cracks can be interpreted in terms of the geometrical relationship between the crack initiation site and the dislocation
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structure. As shown in Fig. 11(d), the crack initiation site in HEA was along the {111} plane but not parallel to the planar dislocation array that was aligned on a different {111} plane. However, the replica images demonstrated that the localized slip line/band formation acted as a fatigue crack initiation site in HEA (Fig. 7). This observation indicates that dislocation accumulation occurred along the slip plane prior to the crack initiation, which apparently contradicts the fact observed by the post-mortem analysis. This contradiction can be explained as follows. Slip deformation highly localized on a single {111} atomistic layer where the crack initiated. Since the single plane layer where dislocation accumulated was cracked, we could not observe the corresponding planar dislocation array. Here, we note two observations from the replica images shown in Fig. 7: (1) number of slip lines of HEA was less than that of ASS, and (2) because the deformation was concentrated on the slip planes where the slip lines were formed, the slip lines appeared more intensive in HEA compared to those in ASS. These findings are consistent with the above discussion, which thus explains the contradiction between the replica-based analysis and post-mortem analysis. Moreover, we note the crack initiation life and the number of cracks in ASS and HEA. As shown in Fig 5 (a), the crack initiation life of ASS and HEA were 2.0×105 and 4.0×105 cycles, respectively. The factors that enhanced the crack initiation life of HEA were (1) high proof stress by solid solution strengthening and (2) high work hardening rate due to low SFE. Since these two factors suppressed slip deformation at the specimen surface, the crack initiation life of HEA was larger than that of ASS. On the other hand, the number of cracks of HEA was larger than that of ASS. This result is due to localization of plastic deformation in HEA, as discussed earlier. In HEA, the short range ordering (SRO) effect has been reported [24]. Although SRO associated with attractive atomic interaction can increase strength, it also causes local softening when the atomic order is broken by dislocation motion [25], which leads to localized accumulation of lattice defects. Therefore, once slip deformation initiates, deformation can easily concentrate on the single slip plane until the slip plane becomes a crack. This characteristic is the reason behind the increase in the number of cracks.
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4.2 Dislocation-driven crack tip hardening and stress shielding As shown in Fig. 5 (c), in the comparison between HEA and ASS, the highest crack growth rate did not show a significant difference. However, the fatigue crack growth rate of HEA was lower than that of ASS when the crack length was less than 500 μm. Furthermore, growth of small fatigue cracks with a length of < 500 μm was observed to temporarily stop in HEA. Therefore, we must consider some factors that can enhance the resistance to small crack propagation in HEA. Two factors, which enhanced the crack propagation resistance, were dislocation-driven crack tip hardening and stress shielding. Dislocation-driven crack tip hardening which is work hardening at crack tip can be enhanced because of the low SFE of HEA. The low SFE prevents cross slip, which suppresses dislocation re-arrangement. Because this effect constrains the dislocation structure as a high energy state in grains even under high external stress, further dislocation motion is prevented, which leads to crack tip hardening. The SRO in HEA may enhance this effect. However, it should be noted here that work hardening is expected to play a minor role in enhancing the resistance to small fatigue crack propagation in HEA; this is because the comparison shown in Fig. 5 and associated characterizations were performed for specimens tested at the identical ratio of stress amplitude to tensile strength. Moreover, in the same line, the planar dislocation motion associated with low SFE increases the dislocation density on specific slip planes and stress arising from the nearest dislocation to the crack tip, which strongly shields crack tip stress during loading. This effect is referred to as dislocation-driven stress shielding. Fig. 13 shows a schematic diagram of dislocation-driven stress shielding. Dislocation pile-up stress increases with increase in the number of dislocations that accumulate on one slip plane. Therefore, the high dislocation planarity in HEA may lead to an enhanced pile-up stress to a dislocation emitted from the crack tip. In addition, as shown in Fig. 12, dislocation planar array was observed on the two slip systems. When dislocations move on such two slip systems, the Lomer-Cottrell reaction occurs at the intersection of dislocations [13][26]. Since Lomer-Cottrell sessile dislocation hinders the
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motion of dislocation, the formation of Lomer-Cottrell sessile dislocation may enhance the effect of stress shielding, as shown in Fig. 13.
Fig.13 Schematic diagrams of effects of dislocation-driven stress shielding.
4.3 Fatigue crack propagation mechanism of HEA In both materials, striations were observed on the fractographs that correspond to the long crack propagation stage. In contrast, the small crack propagation stage in HEA showed significant difference in the crack propagation behavior compared to that in ASS. That is, small fatigue cracks of HEA frequently propagated along slip lines. Focusing on this difference in the crack propagation path, the fatigue crack propagation mechanism of HEA is discussed below. Here, considering the crack propagation mechanism, we recognize two modes: (A) Mode I type driven by dislocation emission from a crack tip, and (B) Mode II type associated with dislocation accumulation on limited slip planes ahead of crack tip. In ASS, the fatigue crack propagated perpendicularly to the loading direction without large zigzag features, as shown in Fig. 6, and only a small portion of the fatigue crack was along the slip lines. Moreover, even when the fatigue crack propagated partially along the slip lines, it did not fully propagate along the slip lines from the edge of the grain to the other edge (Fig. 6 (e) and Fig. 10 (a)). As shown in
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Fig. 8 (d), facets observed in the fractograph of crack propagation provide evidence of crack propagation along a specific crystallographic plane such as the slip plane. The size of a facet in ASS is less than 1 grain, which is consistent with the result of replica observation. From these observations, the predominant fatigue crack propagation mode in ASS is concluded to be (A) Mode I type controlled by dislocation emission at a crack tip. On the other hand, the fatigue crack of HEA, as shown in Fig. 7, propagated along slip lines from the edge of the grain to the other edge, which led to a coarse zig-zag propagation. On the fractograph, facets were observed in the region corresponding to the crack length of around 500 µm, similar to ASS (Fig. 9 (d)). However, the size of each facet was larger than that of ASS, namely, the facet size of HEA roughly corresponded to 1~2 grain size. This observation provides evidence of crack propagation fully along a single slip plane in some grains. In addition, the ratio of propagation along slip lines to the fatigue crack length was larger than that in ASS, as shown in Fig. 7 (e). Hence, (B) Mode II by dislocation accumulation to a slip plane must have been promoted in HEA by some effects. The cause of promotion of Mode II crack propagation in HEA can be explained as follows. As mentioned in Section 4.1, dislocation planarity enhanced the degree of slip localization on a single slip plane (Fig. 11), which led to multiple crack initiation. In this context, the lattice defects can be localized to a slip plane where the slip lines formed. In addition, dislocation-driven stress shielding, which is explained in Section 4.2, might suppress (A) Mode I associated with dislocation emission at a crack tip. (B) Mode II by dislocation accumulation to a slip plane was promoted because Mode I crack propagation was suppressed and instead shear-induced damage was localized along a slip plane where the slip lines formed. Based on the above discussion, the crack propagation model of HEA is proposed, as depicted in Fig. 14. When the crack tip approaches the slip line, the stress field at the crack tip promotes slip deformation on the slip line, as shown in Figs. 14 (a) to (b). Dislocations are localized on a few slip planes due to dislocation planarity. Therefore, accumulation of dislocation dipoles or stress concentration at intrusion triggers subcrack initiation [27], as shown in Fig. 14 (b) to (c). Then, the crack propagates via coalescence with
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subcrack. This process can constitute the mechanism of Mode II crack propagation in HEA under the experimental condition of this study. However, as described at the beginning of this section, striations were observed on the fractographs in the long crack propagation stage. That is, as the fatigue crack becomes longer, the above-mentioned effect of dislocation planarity weakens and the fatigue crack propagation mechanism of HEA shifts to Mode I type. As the crack length and the applied stress increases, multiple slips occur near the crack tip. This hinders dislocation pile-up and damage localization on a slip plane. The degree of the effect of dislocation planarity depends on the crack length and applied stress. Considering that dislocation planarity promotes Mode II crack propagation, investigation on the correlation between these mechanical factors (crack length and applied stress) and the crack propagation mode will be undertaken in a future work.
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Fig. 14 Schematic diagram of the fatigue crack propagation mechanism of Mode II type promoted by HEA’s dislocation planarity. (a) Slip line formed during cyclic loading. (b) Slip deformation promoted by crack-tip stress field. (c) Sub crack initiation. (d) Crack coalescence.
5. Conclusions In this study, we characterized the influence of planar slip on the fatigue crack initiation and propagation behavior of the equiatomic CrMnFeCoNi HEA. (1) Dislocation planarity of HEA leads to slip localization, which causes slip-plane cracking. The planar-slip-driven crack initiation did not reduce the crack initiation life, but increased the number of fatigue cracks. (2) Dislocation planar array was observed around the fatigue crack of HEA. Dislocation planarity of HEA might suppress crack opening for Mode I crack propagation through a decrease in the effective stress at the crack tip. In fact, the decrease in crack growth rate was remarkable at the small crack stage. (3) In HEA, Mode II type crack propagation acted as the primary mechanism. Specifically, Mode I crack propagation might be suppressed by dislocation-driven stress shielding and the lattice defects were preferentially accumulated on the slip plane. Hence, subcracks initiated near the crack tip, which led to fatigue crack propagation via crack coalescence. Acknowledgements This work was financially supported by JSPS KAKENHI (JP16H06365 and JP17H04956).
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Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi highentropy alloy
Highlights
Fatigue crack initiation and propagation in a high entropy alloy were investigated.
Planar slip in high entropy alloy affected the fatigue crack initiation and propagation.
The deformation localization led to multiple crack initiation on the slip planes.
Crack propagation comprised crack formation around the crack tip and coalescence.
The crack propagation mechanism shifted to Mode I as the crack length increased.
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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.
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S0142-1123(19)30522-5 https://doi.org/10.1016/j.ijfatigue.2019.105418 JIJF 105418
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
8 October 2019 19 November 2019 3 December 2019
Please cite this article as: Suzuki, K., Koyama, M., Hamada, S., Tsuzaki, K., Noguchi, H., Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy, International Journal of Fatigue (2019), doi: https://doi.org/10.1016/j.ijfatigue.2019.105418
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© 2019 Published by Elsevier Ltd.
International Journal of Fatigue
Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy
Kai Suzukia, Motomochi Koyamab, Shigeru Hamadac, Kaneaki Tsuzakic, Hiroshi Noguchic a Graduate b Institute c Faculty
School of Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka-shi, Fukuoka 819-0395, Japan
for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
of Engineering, Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka-shi, Fukuoka 819-0395, Japan
Corresponding author: [email protected]
Abstract High-cycle fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi high-entropy alloy were investigated using smooth specimens. The microstructural deformation characteristics, i.e., planar dislocation slip, significantly affected the fatigue crack initiation and small fatigue crack propagation. The deformation localization associated with dislocation planarity led to multiple crack initiation on the slip planes. The crack propagation mechanism comprised crack formation on slip planes around the main crack tip and subsequent coalescence. The fatigue crack propagation mechanism shifted to Mode I type as the crack length increased.
Keywords: High entropy alloy, planar slip, high cycle fatigue, fatigue crack initiation and propagation.
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1. Introduction Incorporation of compositional complexity in alloys has drawn attention as a novel strategy to create a new class of structural materials. Compositional complexity, namely, an increased configurational entropy, can result in extraordinary toughness, ductility, and strength [1-4]. An alloy group with a high configurational entropy has been referred to as high-entropy alloys (HEAs). Specifically, the equiatomic CrMnFeCoNi quinary alloy has been considered to have a representative composition of HEAs [5]. The excellent mechanical performance of equiatomic quinary HEA [6-10] is attributed to the characteristic dislocation behavior associated with its planarity [11] and thermal activation process [6]. From the viewpoint of mechanical performance, fatigue resistance is another important property for the practical use of HEA as a structural component. Dislocation planarity, which is high in the equiatomic quinary HEA, has been recognized as a significant factor affecting fatigue crack resistance as it influences various fatigue-related parameters: (1) work hardenability, (2) degree of crack tip stress shielding, and (3) ease of microstructural damage accumulation [12-14]. The first parameter is attributed to dislocation distribution, which means that high dislocation planarity delays self-accommodation of local stress. This effect increases the stored strain energy, which prevents further motion or multiplication of dislocations [15]. The second parameter is associated with the elastic strain field around the nearest dislocation from a crack tip. Because the dislocation planar array provides a high back stress, the elastic strain field at the nearest dislocation decreases the effective tensile stress at the crack tip, which delays crack opening [13]. The third parameter is related to the accumulation rate of lattice defects per cycle at a microstructurally local site. An enhanced dislocation planarity prevents dislocation annihilation, and localizes accumulation of dislocations or vacancies. Accelerated increase of local damage density alters the ease of crack initiation and fatigue crack propagation mechanism from Mode I to Mode II types [14][16]. Therefore, HEA with a high dislocation planarity is expected to exhibit the characteristic behavior of fatigue resistance. Growth behavior of mechanically long cracks in HEA (equiatomic CrMnFeCoNi) has been reported
2
in a previous study [17], where compact tension tests with increasing ΔK were conducted at room temperature on the HEA and SUS316L which is austenitic stainless steel. The fatigue crack growth rates of the HEA were lower than those of SUS316L. Microstructure-dependent crack closure associated with crack roughness was considered as a factor enhancing the resistance to fatigue crack growth. It has been generally known that such microstructure effects, including influences of dislocation planarity, appear particularly when the crack is in an initiation stage and the crack length is small [18-20]. Such small cracks are referred to as mechanically and microstructurally small cracks and their propagation has two characteristics: significant hardness/yield strength dependence and selective propagation along microstructural features. Hence, the influence of the characteristic dislocation behaviors in HEA on fatigue crack initiation and small fatigue crack propagation must be elucidated. In this study, the characteristic dislocation behavior of HEA, such as dislocation planarity, which is expected to yield superior crack tip hardening and dislocation-driven stress shielding were investigated. Furthermore, dislocation planarity leads to localization of damage accumulation that is expected to cause slip-plane cracking and Mode II crack propagation, which may induce unconventional fatigue crack initiation and propagation phenomena. Therefore, this study aimed at elucidating the effect of high dislocation planarity on fatigue crack initiation and propagation in HEA.
2. Experimental procedure 2.1 Materials A 50 kg ingot of an equiatomic CrMnFeCoNi quinary alloy (hereafter, the chemical compositions are presented in at. %) was prepared by vacuum induction melting. The ingot was hot-rolled at 1373 K. The rolled bar was solution-treated at 1073 K and subsequently water-quenched. In addition, we used nonequiatomic solution-treated Fe-20Cr-14Ni ternary alloy as a reference material. Both of the alloys are non-magnetic fully face-centered cubic (FCC) alloys, which do not show martensitic transformation. In this study, the CrMnFeCoNi and Fe-20Cr-14Ni alloys are referred to as HEA and austenitic stainless
3
steel (ASS), respectively. The detailed chemical compositions of the alloys are listed in Table 1. The average grain sizes of the HEA and ASS were 41 μm and 38 μm, respectively, as shown in Fig. 1. The grain size was measured based on the cutting method, and the annealing twin boundaries were counted as grain boundaries. The stacking fault energies (SFE) of the ASS and HEA have been reported to be 35 [21] and 30 mJ m-2 [22], respectively. The solution-treated bars were cut by electro discharge machining to prepare tensile specimens, and machined by lathe to prepare fatigue test specimens. The specimen geometries are shown in Fig. 2. Table 1 Chemical compositions of the HEA and ASS [mass%]. Alloy
Fe
Mn
Ni
Co
Cr
C
S
P
Al
O
N
HEA
Bal
19.8
20.2
20.9
18.2
0.002
0.006
0.002
0.018
0.007
0.0087
ASS
Bal
0.001
14.6
18.8
0.002
0.001
0.001
Si
<0.001
Fig. 1 BSE image of as-solution-treated microstructures of the (a) ASS and (b) HEA.
2.2 Mechanical testing The specimens were mechanically and electrochemically polished before the tests. Tensile tests were conducted along the rolling direction (RD) at room temperature (RT: approximately 294 K) with an initial strain rate of 10-4 s-1. The strain was measured using a video extensometer. The specimen surface was mechanically and electrochemically polished. Therefore, the final diameter of the specimens was reduced by approximately 50 μm. Rotating bending fatigue tests were conducted
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at RT at a frequency of 30 Hz and a stress ratio of −1. The loading direction corresponded to the RD. In this experiment, the nominal stress was defined as the bending stress on the minimum radial part, and stress concentration due to the shape of the test specimen was not considered. The specimen surface during the fatigue tests was obtained using a replica method to measure the crack length. The replication was carried out under no-load conditions after immersing the replica sheet in methyl acetate. The replica images were taken by optical microscopy.In this experiment, the fatigue limit was defined as the stress amplitude where the specimen was not broken at 107 cycles. The fracture surfaces were observed by scanning electron microscopy (SEM) at an accelerating voltage of 15 kV.
Fig. 2 Specimen geometries of the (a) tensile test and (b) rotating bending fatigue specimens.
2.3 Microstructure characterization The fatigued specimens were mechanically polished using colloidal silica with a particle size of 60 nm. Electron backscatter diffraction (EBSD) measurements were performed around a subcrack with a beam step size of 500 nm. In addition, electron channeling contrast imaging (ECCI) was carried out on the fatigue-fractured specimens at an accelerating voltage of 30 kV.
3. Results
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3.1 Tensile and fatigue strength Fig. 3 (a) shows the engineering stress-strain curves of the ASS and HEA. Table 2 summarizes the obtained tensile properties. The tensile strength and 0.2 % proof strength of the HEA were higher than those of the ASS. However, the ASS was superior to the HEA in terms of fracture elongation. Fig. 3 (b) shows the true stress-true strain diagram up to the tensile strength. The large slope of the true stressstrain curve of HEA indicates that the work hardening capability of HEA is higher than that of ASS.
Fig. 3 (a) Engineering and (b) true stress-strain curves at an initial strain rate of 10-4 s-1.
Table 2 Tensile test results of the HEA and ASS. 𝝈𝐔𝐓𝐒, 𝝈𝟎.𝟐 and 𝜹 indicate ultimate tensile strength, 0.2 % proof strength and fracture elongation, respectively. Alloy
𝝈𝐔𝐓𝐒 [MPa]
𝝈𝟎.𝟐 [MPa]
𝜹 [%]
HEA
585
254
53
ASS
473
135
82
Fig. 4 (a) shows the stress amplitude as a function of the number of cycles to failure. The fatigue limits of the ASS and HEA were 200 and 250 MPa, respectively. In addition, since fatigue strength has been reported to be linearly correlated with tensile strength [23], the stress amplitude was normalized by the tensile strength, as shown in Fig. 4(b). The ratio of stress amplitude to tensile strength (σa/σUTS) plotted against the number of cycles to failure showed almost similar values.
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Fig. 4 (a) Stress amplitude-fatigue life diagram. (b) Ratio of stress amplitude to tensile strength, σa/σUTS -fatigue life diagram.
3.2 Fatigue crack growth behavior Fig. 5 shows the fatigue crack initiation and growth behavior for the ASS and HEA at the same ratio of stress amplitude to tensile strength, σa/σUTS as exhibited in Fig. 4. The results of the five longest cracks are shown for each alloy. The stress amplitudes for the ASS and HEA were selected to be 220 and 270 MPa, respectively. The fatigue lives of the ASS at 220 MPa and HEA at 270 MPa were 5.0×105 and 1.1×106 cycles, respectively, as indicated in Fig. 4. Fig. 5 (a) shows the number of cracks at 4.7×105 cycles in ASS and 106 cycles in HEA. The number of cracks with a crack length over 200 μm was 76 in ASS and 80 in HEA. The difference appeared in the number of cracks with a crack length of 100-200 μm. The number of cracks with a crack length of 100-200 μm was 122 in ASS and 435 in HEA. In other words, the number of small fatigue cracks with a crack length of 100-200 μm in HEA was larger than in ASS. Fig. 5 (c) shows the fatigue crack growth rates plotted against the crack length for five fatigue cracks, respectively. Comparing the crack growth rates of the ASS with those of the HEA, we can see that most of the crack growth rate data showed similar general trend when plotted against the crack length. An important difference was observed in the stage where the crack length was small. That is, the
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fatigue crack growth rate of HEA with a length of <500 μm was lower than that of ASS. In addition, the small cracks in the HEA temporarily stopped to grow. Crack coalescence was observed in both materials. In ASS, crack coalescences were observed with crack lengths of 422.4 μm, 655.7 μm, 656.8 μm, 1007 μm, 1040 μm. In HEA, crack coalescences were observed with crack lengths of 175.0 μm, 325.0 μm, 363.0 μm, 394.5 μm, 414.0 μm, 735.5 μm, 753.0 μm. This result indicates that crack coalescences of HEA occur at early crack stage.
Fig. 5 Growth behavior of the longest five cracks for the ASS at 220 MPa and the HEA at 270 MPa for the same ratio of stress amplitude to tensile strength, σa/σUTS. (a) Number of cracks plotted against fatigue crack length (b) Fatigue crack length plotted against the number of cycles. (c) Fatigue crack growth rate plotted against fatigue crack length.
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3.3 Fatigue crack propagation path To understand the factors causing the difference in the fatigue crack growth rate, the fatigue crack propagation path was observed. Figs. 6 and 7 show the replica images of fatigue sub cracks in ASS and HEA. The white arrows indicate the crack tips. In the ASS (Fig.6), the fatigue crack occurred along slip lines. The fatigue crack propagation behaviors of ASS can be classified into two cases: propagations (1) along and (2) across the slip lines, as indicated by the blue circle and red lines in Fig. 6 (e), respectively. In the HEA (Fig.7), the fatigue crack also occurred along slip lines. However, fatigue crack propagation across the slip lines was not observed in HEA. Hence, the ratio of propagation along slip lines to the fatigue crack length in HEA was larger than that in ASS (Fig. 6 (e) and Fig. 7 (e)). Furthermore, multiple crack initiation was frequently observed in HEA, which resulted in crack coalescence during the growth, as shown in Figs. 7 (c) to (d). The crack coalescence of HEA was observed particularly at the early fatigue stage where the crack length was up to 500 µm.
Fig.6 A set of replica images showing a fatigue sub crack at (a) 2×105, (b) 2.8×105, (c) 3.4×105, (d) 4.0×105, (e) 4.3×105 cycles in the ASS tested at 220 MPa. White arrows indicate crack tips. Red lines
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indicate regions of crack propagation along slip lines. Blue circle indicates an example of crack propagation across slip lines.
Fig. 7 A set of replica images showing fatigue sub cracks at (a) 4×105, (b) 7.5×105, (c)9.5×105, (d)1.0×106 (e) 1.05×106 cycles in the HEA tested at 270 MPa. White arrows indicate crack tips. Red lines indicate regions of crack propagation along slip lines.
3.4 Fractography Fig. 8 and Fig. 9 show SEM fractographs of ASS and HEA, respectively. The yellow dashed line traces the white streaks that formed by crack coalescence. Namely, yellow dashed lines indicate the boundaries of multiple cracks. In both materials, multiple cracks were observed on the fractographs, and their propagation and coalescence led to fracture. In the central parts of the fracture surface, dimples were observed (Fig. 8 (a) and Fig. 9 (a)). In the surface crack observation, as discussed in Section 3.3, the number of crack initiation sites was large in HEA, and the same tendency was observed in the fractograph. Fig. 8 (b) and Fig. 9 (b) show parts near the specimen surfaces with the crack initiation sites. In HEA, three crack initiation sites were observed, as indicated by orange circles. In both ASS and
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HEA, the crack initiation parts showed transgranular facets, as depicted in Fig. 8 (c) and Fig. 9 (c). A difference was observed in the fracture surface around the crack length at 500 µm (Fig. 8 (d) and Fig. 9 (d)). Transgranular facets were observed for both materials, but the facet size of HEA was larger than that of ASS. Considering that the grain size of both materials is about 40 µm, the facet size of ASS is less than 1 grain size and that of HEA is 1 to 2 grain size. Fig. 8 (e) and Fig. 9 (e) show the fractograph near the dimple, that is, where the fatigue crack length is large. For both materials, striations were observed in the part where the crack length was about 1 to 2 mm.
Fig. 8 SEM fractographs of the ASS (σa=220 MPa): (a) overview of the fracture surface, (b) a part near specimen surface (c) crack initiation site, (d) crack length around 500 µm, (e) striations. Yellow dashed lines in (a) indicate boundaries of multiple cracks. The orange circle in (b) indicates a crack initiation site.
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Fig. 9 SEM fractographs of the HEA (σa=270 MPa): (a) overview of the fracture surface, (b) a part near specimen surface (c) crack initiation site, (d) crack length around 500 µm, (e) striations. Yellow dashed lines in (a) indicate boundaries of multiple cracks. Orange circles in (b) indicate crack initiation sites.
3.5 Dislocation substructure evolution associated with fatigue cracks. Compared to ASS, HEA showed intensive crack propagation along slip lines. To understand the crack propagation behavior, we first observed the dislocation substructure near the fatigue crack of ASS, as shown in Fig. 10 (a). Here, the crack propagated along the (111) plane that is parallel to the annealing twin boundary. In addition, dislocation cell formed in the vicinity of the fatigue crack tip in ASS, as shown in Fig. 10 (b). Since the number of fatigue cracks of HEA was larger than that of ASS, it is important to understand the crack initiation mechanism. Fig. 11 shows corresponding rolling direction (RD//loading direction)Inverse Pole Figure map and ECC images around the sub crack initiation site. As shown in Fig. 11 (c) (d), highly planar dislocation array was observed around the crack initiation site. The fatigue crack plane at the initiation site was along the (111) plane, but the planar dislocation array was aligned on the (111) plane. The crack in Fig.11 propagated along the slip plane after crack initiation. Fig. 12 shows the ECC images around the crack propagation region. Planar dislocation arrays in two slip systems were
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observed around the fatigue crack. Incidentally, deformation twinning was not observed in the grains where the fatigue crack propagated.
Fig. 10 ECC images showing dislocation structure near the subcracks in ASS (σa = 220 MPa). (a) planar slip and (b) cell formation were observed. Yellow lines in (a) indicate slip plane traces. A yellow circle in (b) indicates the portion where dislocation cell structure is formed.
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Fig. 11 (a) Overview around one of the subcracks near the main crack, and (b) corresponding rolling direction (RD//loading direction)-IPF map in HEA (σa = 270 MPa). (c, d) Magnified ECC images of the crack initiation site. Arrows in (a) indicate the crack tips. Red lines in (c) indicate slip plane traces. Yellow lines in (d) indicate two slip plane traces where dislocation patterns are aligned.
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Fig. 12 (a) A magnified ECC image of the region indicated in Fig, 11(a) (HEA).
(b) Magnified image
corresponding to Fig. 12(a). The arrow in (a) indicates the crack tip. Yellow lines in (b) indicate two slip plane traces where dislocation patterns are aligned.
4. Discussion The ratio of stress amplitude to tensile strength (σa/σUTS) plotted against the number of cycles to failure showed almost similar values for ASS and HEA. However, there were differences in the number of fatigue cracks, fatigue crack growth rate, and crack propagation path. These factors might have been affected by the dislocation planarity of HEA. In this section, we elucidate the role of dislocation planarity in fatigue crack initiation and propagation.
4.1 Fatigue crack initiation The number of fatigue cracks of HEA was larger than that of ASS. Multiple crack initiation of HEA led to crack coalescence at the early stage of fatigue. The increase in the number of cracks can be interpreted in terms of the geometrical relationship between the crack initiation site and the dislocation
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structure. As shown in Fig. 11(d), the crack initiation site in HEA was along the {111} plane but not parallel to the planar dislocation array that was aligned on a different {111} plane. However, the replica images demonstrated that the localized slip line/band formation acted as a fatigue crack initiation site in HEA (Fig. 7). This observation indicates that dislocation accumulation occurred along the slip plane prior to the crack initiation, which apparently contradicts the fact observed by the post-mortem analysis. This contradiction can be explained as follows. Slip deformation highly localized on a single {111} atomistic layer where the crack initiated. Since the single plane layer where dislocation accumulated was cracked, we could not observe the corresponding planar dislocation array. Here, we note two observations from the replica images shown in Fig. 7: (1) number of slip lines of HEA was less than that of ASS, and (2) because the deformation was concentrated on the slip planes where the slip lines were formed, the slip lines appeared more intensive in HEA compared to those in ASS. These findings are consistent with the above discussion, which thus explains the contradiction between the replica-based analysis and post-mortem analysis. Moreover, we note the crack initiation life and the number of cracks in ASS and HEA. As shown in Fig 5 (a), the crack initiation life of ASS and HEA were 2.0×105 and 4.0×105 cycles, respectively. The factors that enhanced the crack initiation life of HEA were (1) high proof stress by solid solution strengthening and (2) high work hardening rate due to low SFE. Since these two factors suppressed slip deformation at the specimen surface, the crack initiation life of HEA was larger than that of ASS. On the other hand, the number of cracks of HEA was larger than that of ASS. This result is due to localization of plastic deformation in HEA, as discussed earlier. In HEA, the short range ordering (SRO) effect has been reported [24]. Although SRO associated with attractive atomic interaction can increase strength, it also causes local softening when the atomic order is broken by dislocation motion [25], which leads to localized accumulation of lattice defects. Therefore, once slip deformation initiates, deformation can easily concentrate on the single slip plane until the slip plane becomes a crack. This characteristic is the reason behind the increase in the number of cracks.
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4.2 Dislocation-driven crack tip hardening and stress shielding As shown in Fig. 5 (c), in the comparison between HEA and ASS, the highest crack growth rate did not show a significant difference. However, the fatigue crack growth rate of HEA was lower than that of ASS when the crack length was less than 500 μm. Furthermore, growth of small fatigue cracks with a length of < 500 μm was observed to temporarily stop in HEA. Therefore, we must consider some factors that can enhance the resistance to small crack propagation in HEA. Two factors, which enhanced the crack propagation resistance, were dislocation-driven crack tip hardening and stress shielding. Dislocation-driven crack tip hardening which is work hardening at crack tip can be enhanced because of the low SFE of HEA. The low SFE prevents cross slip, which suppresses dislocation re-arrangement. Because this effect constrains the dislocation structure as a high energy state in grains even under high external stress, further dislocation motion is prevented, which leads to crack tip hardening. The SRO in HEA may enhance this effect. However, it should be noted here that work hardening is expected to play a minor role in enhancing the resistance to small fatigue crack propagation in HEA; this is because the comparison shown in Fig. 5 and associated characterizations were performed for specimens tested at the identical ratio of stress amplitude to tensile strength. Moreover, in the same line, the planar dislocation motion associated with low SFE increases the dislocation density on specific slip planes and stress arising from the nearest dislocation to the crack tip, which strongly shields crack tip stress during loading. This effect is referred to as dislocation-driven stress shielding. Fig. 13 shows a schematic diagram of dislocation-driven stress shielding. Dislocation pile-up stress increases with increase in the number of dislocations that accumulate on one slip plane. Therefore, the high dislocation planarity in HEA may lead to an enhanced pile-up stress to a dislocation emitted from the crack tip. In addition, as shown in Fig. 12, dislocation planar array was observed on the two slip systems. When dislocations move on such two slip systems, the Lomer-Cottrell reaction occurs at the intersection of dislocations [13][26]. Since Lomer-Cottrell sessile dislocation hinders the
17
motion of dislocation, the formation of Lomer-Cottrell sessile dislocation may enhance the effect of stress shielding, as shown in Fig. 13.
Fig.13 Schematic diagrams of effects of dislocation-driven stress shielding.
4.3 Fatigue crack propagation mechanism of HEA In both materials, striations were observed on the fractographs that correspond to the long crack propagation stage. In contrast, the small crack propagation stage in HEA showed significant difference in the crack propagation behavior compared to that in ASS. That is, small fatigue cracks of HEA frequently propagated along slip lines. Focusing on this difference in the crack propagation path, the fatigue crack propagation mechanism of HEA is discussed below. Here, considering the crack propagation mechanism, we recognize two modes: (A) Mode I type driven by dislocation emission from a crack tip, and (B) Mode II type associated with dislocation accumulation on limited slip planes ahead of crack tip. In ASS, the fatigue crack propagated perpendicularly to the loading direction without large zigzag features, as shown in Fig. 6, and only a small portion of the fatigue crack was along the slip lines. Moreover, even when the fatigue crack propagated partially along the slip lines, it did not fully propagate along the slip lines from the edge of the grain to the other edge (Fig. 6 (e) and Fig. 10 (a)). As shown in
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Fig. 8 (d), facets observed in the fractograph of crack propagation provide evidence of crack propagation along a specific crystallographic plane such as the slip plane. The size of a facet in ASS is less than 1 grain, which is consistent with the result of replica observation. From these observations, the predominant fatigue crack propagation mode in ASS is concluded to be (A) Mode I type controlled by dislocation emission at a crack tip. On the other hand, the fatigue crack of HEA, as shown in Fig. 7, propagated along slip lines from the edge of the grain to the other edge, which led to a coarse zig-zag propagation. On the fractograph, facets were observed in the region corresponding to the crack length of around 500 µm, similar to ASS (Fig. 9 (d)). However, the size of each facet was larger than that of ASS, namely, the facet size of HEA roughly corresponded to 1~2 grain size. This observation provides evidence of crack propagation fully along a single slip plane in some grains. In addition, the ratio of propagation along slip lines to the fatigue crack length was larger than that in ASS, as shown in Fig. 7 (e). Hence, (B) Mode II by dislocation accumulation to a slip plane must have been promoted in HEA by some effects. The cause of promotion of Mode II crack propagation in HEA can be explained as follows. As mentioned in Section 4.1, dislocation planarity enhanced the degree of slip localization on a single slip plane (Fig. 11), which led to multiple crack initiation. In this context, the lattice defects can be localized to a slip plane where the slip lines formed. In addition, dislocation-driven stress shielding, which is explained in Section 4.2, might suppress (A) Mode I associated with dislocation emission at a crack tip. (B) Mode II by dislocation accumulation to a slip plane was promoted because Mode I crack propagation was suppressed and instead shear-induced damage was localized along a slip plane where the slip lines formed. Based on the above discussion, the crack propagation model of HEA is proposed, as depicted in Fig. 14. When the crack tip approaches the slip line, the stress field at the crack tip promotes slip deformation on the slip line, as shown in Figs. 14 (a) to (b). Dislocations are localized on a few slip planes due to dislocation planarity. Therefore, accumulation of dislocation dipoles or stress concentration at intrusion triggers subcrack initiation [27], as shown in Fig. 14 (b) to (c). Then, the crack propagates via coalescence with
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subcrack. This process can constitute the mechanism of Mode II crack propagation in HEA under the experimental condition of this study. However, as described at the beginning of this section, striations were observed on the fractographs in the long crack propagation stage. That is, as the fatigue crack becomes longer, the above-mentioned effect of dislocation planarity weakens and the fatigue crack propagation mechanism of HEA shifts to Mode I type. As the crack length and the applied stress increases, multiple slips occur near the crack tip. This hinders dislocation pile-up and damage localization on a slip plane. The degree of the effect of dislocation planarity depends on the crack length and applied stress. Considering that dislocation planarity promotes Mode II crack propagation, investigation on the correlation between these mechanical factors (crack length and applied stress) and the crack propagation mode will be undertaken in a future work.
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Fig. 14 Schematic diagram of the fatigue crack propagation mechanism of Mode II type promoted by HEA’s dislocation planarity. (a) Slip line formed during cyclic loading. (b) Slip deformation promoted by crack-tip stress field. (c) Sub crack initiation. (d) Crack coalescence.
5. Conclusions In this study, we characterized the influence of planar slip on the fatigue crack initiation and propagation behavior of the equiatomic CrMnFeCoNi HEA. (1) Dislocation planarity of HEA leads to slip localization, which causes slip-plane cracking. The planar-slip-driven crack initiation did not reduce the crack initiation life, but increased the number of fatigue cracks. (2) Dislocation planar array was observed around the fatigue crack of HEA. Dislocation planarity of HEA might suppress crack opening for Mode I crack propagation through a decrease in the effective stress at the crack tip. In fact, the decrease in crack growth rate was remarkable at the small crack stage. (3) In HEA, Mode II type crack propagation acted as the primary mechanism. Specifically, Mode I crack propagation might be suppressed by dislocation-driven stress shielding and the lattice defects were preferentially accumulated on the slip plane. Hence, subcracks initiated near the crack tip, which led to fatigue crack propagation via crack coalescence. Acknowledgements This work was financially supported by JSPS KAKENHI (JP16H06365 and JP17H04956).
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Planar slip-driven fatigue crack initiation and propagation in an equiatomic CrMnFeCoNi highentropy alloy
Highlights
Fatigue crack initiation and propagation in a high entropy alloy were investigated.
Planar slip in high entropy alloy affected the fatigue crack initiation and propagation.
The deformation localization led to multiple crack initiation on the slip planes.
Crack propagation comprised crack formation around the crack tip and coalescence.
The crack propagation mechanism shifted to Mode I as the crack length increased.
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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.
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