Journal of Materials Science & Technology  2020 , 39 (0): 1-6 https://doi.org/10.1016/j.jmst.2019.09.010

Letter

Effect of grain size on fatigue cracking at twin boundaries in a CoCrFeMnNi high-entropy alloy

A.G. Wanga, X.H. Ana*, J. Gub, X.G. Wangc, L.L. Licd, W.L. Lia, M. Songb*, Q.Q. Duanc, Z.F. Zhangc, X.Z. Liaoa*

a School of Aerospace, Mechanical & Mechatronic Engineering, The University of Sydne0y, Sydney, Australia
b State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China
c Materials Fatigue and Fracture Division, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
d Max-Planck-Institut für Eisenforschung, Max-Planck-Straße 1, 40237 Düsseldorf, Germany

Corresponding authors:   * Corresponding authors. E-mail addresses: xianghai.an@sydney.edu.au (X.H. An), msong@csu.edu.cn (M. Song), xiaozhou.liao@sydney.edu.au (X.Z. Liao).* Corresponding authors. E-mail addresses: xianghai.an@sydney.edu.au (X.H. An), msong@csu.edu.cn (M. Song), xiaozhou.liao@sydney.edu.au (X.Z. Liao).* Corresponding authors. E-mail addresses: xianghai.an@sydney.edu.au (X.H. An), msong@csu.edu.cn (M. Song), xiaozhou.liao@sydney.edu.au (X.Z. Liao).

Received: 2019-06-14

Revised:  2019-08-30

Accepted:  2019-09-2

Online:  2020-02-15

Copyright:  2020 Editorial board of Journal of Materials Science & Technology Copyright reserved, Editorial board of Journal of Materials Science & Technology

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Abstract

The fatigue cracking behavior at twin boundaries (TBs) in a CoCrFeMnNi high-entropy alloy with three different grain sizes was systematically investigated under low-cycle fatigue. Irrespective of grain size, the change from slip band cracking to TB cracking occurred with increasing the difference in the Schmid factors (DSF) between matrix and twin. However, the required critical DSF for the transition of the dominant cracking mode decreases with decreasing grain size due to the reduced slip band spacing that increases the impingement sites on the TBs and facilitates the coalescence of defects and voids to initiate TB cracks.

Keywords: High-entropy alloy ; Fatigue cracking ; Twin boundary ; Slip band ; Grain size

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A.G. Wang, X.H. An, J. Gu, X.G. Wang, L.L. Li, W.L. Li, M. Song, Q.Q. Duan, Z.F. Zhang, X.Z. Liao. Effect of grain size on fatigue cracking at twin boundaries in a CoCrFeMnNi high-entropy alloy[J]. Journal of Materials Science & Technology, 2020, 39(0): 1-6 https://doi.org/10.1016/j.jmst.2019.09.010

High-entropy alloys (HEAs) that usually contain five or more principal elements with approximately equiatomic concentrations have been substantially investigated over the last decade [[1], [2], [3], [4]]. The unique features of HEAs induced by the mixture of multiple elements, such as the severe lattice distortion and sluggish diffusion, enable them to possess high structural stability and excellent mechanical properties [2,3]. Up to date, most researches concerning HEAs have focused on the formation and stability of simple crystal structures including face-centered cubic (FCC) [[5], [6], [7], [8], [9]], body-centered cubic [10,11], and hexagonal close-packed structures [12], design of novel HEAs to push the property boundary of possibility [[13], [14], [15]], deformation mechanisms, and structure-property relationships of HEAs [[16], [17], [18], [19], [20]]. Considering the application prospects of HEAs as promising candidate materials, their cyclic deformation response is a crucial concern, which is, nonetheless, less informed [[21], [22], [23], [24]]. Therefore, it is necessary to explore the fatigue behavior of HEAs, especially the fatigue cracking mechanism, to assess their potentials as safety-critical components.

It is well known that high-angle grain boundaries (HAGBs) play an essential role in strengthening polycrystalline materials by blocking dislocation movement, while they generally tend to be the preferential sites for the nucleation and propagation of fatigue cracks during cyclic deformation [25]. The culprit for HAGB cracking is local stress concentration induced by the impingement of slip bands (SBs) or strain incompatibilities due to grain boundary (GB) steps [[25], [26], [27], [28]]. Besides conventional HAGBs, twin boundaries (TBs), as a special kind of coherent interface with low energy, can interact with dislocations in different modes due to the special crystallographic characteristics of TBs [29]. For instance, TBs can serve as barriers to impede dislocation motion and can be slip planes to accommodate or be penetrated by dislocations [30,31]. The introduction of a high density of nanoscale TBs into materials can significantly improve their mechanical properties, including strength [[30], [31], [32], [33]], ductility [30,31], strain hardening [[30], [31], [32]], fracture toughness [32], and fatigue resistance [33].

Although it is believed that TBs are stronger in resisting fatigue cracking than conventional HAGBs, fatigue cracks initiated at TBs under high-cycle fatigue tests were observed due to the elastic anisotropy and concomitant local stress enhancement across the TBs [34]. In contrast, TB cracking behaviour under low-cycle fatigue (LCF) experiments is profoundly affected by the special dislocation-TB interactions that are controlled by stacking fault energy (SFE), dislocation slip mode and the difference in the Schmid factors (DSF) between matrix and twin [[35], [36], [37]]. With decreasing SFE and/or increasing DSF, the dominant cracking mode at TBs changed from SB cracking to TB cracking [35,36]. Although a semiquantitative model was established to understand the TB cracking mechanism [35,36], it is not clear if TB cracking behaviour is also affected by grain size that essentially determines dislocation configurations formed during cyclic deformation [38]. Since the GB strengthening efficiency of HEAs is apparently higher than that of conventional FCC metallic materials [5], CoCrFeMnNi HEA samples with three grain sizes were selected herein to investigate systematically the effect of grain size on the competition between SB cracking and TB cracking under LCF tests. The results will not only enrich our understanding on fatigue cracking and deformation behaviour of HEAs but also extend our capability to design advanced materials with excellent fatigue properties.

The equiatomic CoCrFeMnNi alloy with a single FCC phase was prepared by arc melting of a mixture of pure metals with high purity of above 99.99 wt% in an argon atmosphere. The alloy was remelted four times to ensure chemical homogeneity and then solution-annealed at 1473 K for 48 h. After that, the ingots were cold rolled to sheets with a thickness of ~ 4.5 mm and then were heat-treated in a vacuum furnace for 1 h at 1023 K, 1273 K and 1473 K to obtain fully recrystallized microstructures with three grain sizes. The fatigue specimens with the gauge section 16 mm × 5 mm × 4 mm were spark cut from the plates and then mechanically polished and electro-polished to produce mirror-like surface. Symmetric cyclic pull-push experiments were conducted on an Instron 8862 fatigue testing machine using a triangular waveform at room temperature under total strain amplitudes of 0.3% and 0.4% and an approximately constant strain rate of 1 × 10-3 s-1. An extensometer with a gauge length of 10 mm was applied to measure and control the strain instantaneously. Although the fatigue life increased slightly with reducing the grain sizes, fatigue failure occurred after about 2 ~ 2.3 × 104 cycles for all specimens, indicating that their accumulated plastic strains were comparable. Microstructures before and after fatigue tests were characterized using a Carl Zeiss Ultra Plus field emission gun scanning electron microscope (SEM) equipped with electron backscatter diffraction (EBSD), and a JEOL-2100 transmission electron microscope (TEM), to examine the grain size, crystallographic orientation, surface damage and fatigue damage mechanisms of the CoCrFeNiMn HEA.

The EBSD inverse pole figure (IPF) maps in Fig. 1(a)-(c) show typical microstructures of the CoCrFeMnNi HEA after annealing at different temperatures. All samples presented fully recrystallised microstructures with homogeneous equiaxed grains without apparent texture. Also, a large number of annealing twins were found frequently in all specimens. The average grain sizes measured by the linear intercept method are ~5 μm, ~30 μm and ~165 μm for annealing temperatures of 1023 K, 1273 K and 1473 K, respectively (excluding TBs). Fig. 2(a) displays a typical slip morphology near annealing TBs in a sample cyclically deformed cyclically at a total strain amplitude of 0.4%. Most of the slip bands (SBs) transferred through the TBs and maintained a good one-to-one correspondence with each other across the TBs [37]. Previously reports [6,37] suggested that representative deformation substructures in the CoCrFeMnNi HEA were dominated by the planar slip bands, as indicated by the black arrows in the Fig. 2(b), when the plastic strain is small.

Fig. 1.   EBSD IPF maps of the CoCrFeMnNi HEA annealed at 1023 K (a), 1273 K (b) and 1473 K (c), respectively. TBs, which were shown with red lines, were seen frequently.

Fig. 2.   (a) A typical SEM image shows slip bands passing through TBs as pointed by with arrows and (b) a typical TEM morphology presents planar slips bands as indicated by the black arrows, in the HEA fatigued under a total strain amplitude of 0.4%.

Since HAGBs are the weakest sites to resist fatigue cracking, most fatigue cracks initiated at HAGBs. Besides, the nucleation of fatigue cracks along SBs and TBs were also observed. Fig. 3(a) demonstrates the typical SB cracking mode in which cracks nucleated at SBs with apparent extrusion/intrusion and propagated along the SBs to penetrate TBs, while the TB cracking mode in which cracks initiated at and propagated along TBs is exhibited in Fig. 3(b). Based on the crystallographic relationships among the slip systems, different dislocation-TB interactions can be identified during cyclic deformation, while most of the interactions were determined to be the case with conjugated slip planes and two parallel dislocations on both sides of TBs [[35], [36], [37]]. The parameter of DSF was proposed based on this case [35]. Since the DSF between matrix and twin plays a crucial role in affecting the fatigue cracking mechanism at TBs, the measurement of this parameter is fundamentally important to compare cracking behaviour in the HEA with different grain sizes. As shown in Fig. 3(c), the crystallographic orientation of the matrix and twin in grains can be readily identified, while the activated slip plane can be determined based on the surface slip trace and four (111) planes of FCC structures. For instance, Fig. 3(d) shows the result derived from EBSD data in Fig. 3(c), indicating the activated slip plane of (11-1) in twin and (1-11) in matrix. By measuring the angles between the loading direction and the slip traces, the DSF between matrix and twin can be determined by using the equation ΔΩ = ΩMatrix -ΩTwin, where ΩMatrix and ΩTwin represent the Schmid factors in the matrix and twins, respectively [35]. Since the GB-affected zones may affect the accuracy of ΔΩ and then cracking behavior, especially in fine-grained materials, only the cracks formed away from GBs are considered in the present study.

Fig. 3.   Typical SEM images of (a) SB cracking and (b) TB cracking in the HEA with intermediate grains fatigued under a total strain amplitude of 0.4% (similar morphologies can be observed in the HEA with fine and coarse grains); (c) A typical IPF map showing the interaction between SBs and TBs (the white areas were not indexed due to the SB or TB cracking or severe extrusion/intrusion); (d) Determination of the slip planes in twin (top) and matrix (bottom) derived from (c) for the calculation of the DSF between matrix and twin.

In order to identify the effects of grain size and DSF on the TB cracking mechanism, nearly 100 SEM and EBSD images with fatigue cracks along either SBs or TBs were collected and analyzed from the samples under the total strain amplitudes of 0.3% and 0.4%, in which the sample surfaces were pretty smooth and suitable for EBSD analysis. As summarized in Fig. 4(a), the red dots at the upper part and black dots at the lower part represent TB cracking and SB cracking, respectively, while two parallel blue dashed lines cover the transition region where the two cracking modes coexisted. Two conclusions were reached from the statistical data in the DSF vs. D-1/2 (D is the grain size) coordinate system. First, irrespective of grain size, the dominant fatigue cracking mode tended to transform from SB cracking to TB cracking with increasing DSF. Second, the critical DSF for the transition of cracking modes decreases with the reduction of grain size, implying that decreasing grain size makes TB cracking relatively easier. The results clearly reveal that TB cracking is dependent on both DSF and grain size, which will be discussed in detail.

Fig. 4.   (a) Influence of DSF and grain size on the competition between SB cracking and TB cracking in the CoCrFeMnNi HEA; (b) Relationship between the spacing of SBs with extrusions/intrusions and grain size (The inset image demonstrates the measurement of SB spacing in the HEA); (c) Typical SEM images indicate that the SBs spacing increases with grain sizes.

The primary mechanism of fatigue cracking in metallic materials can be attributed to the cyclic slip irreversibility induced by the to-and-fro motion of dislocations [24,36]. In single crystal materials, the formation of extrusions/intrusions along SBs causes high stress/strain localisation, which facilitates the nucleation and propagation of fatigue cracks along the SBs [35]. In polycrystalline materials, since the intersection between HAGB and slip plane is not colinear, the activated SBs are not able to pass through the HAGBs, enabling significant piling-up of dislocations and vacancies. Previous investigations revealed that, independence of the angle between the loading direction and HAGBs, GBs that are impinged by SBs are always preferential cracking sites during cyclic deformation, leading to intergranular fatigue cracking [25]. Although TBs can act as barriers to block the movement of dislocations, TBs were proved to bear stronger in resisting fatigue cracking than HAGBs due to the special interactions between TBs and dislocations.

Systematic investigations proposed that different dislocation-TB interaction modes under cyclic loading essentially control the piling-up of dislocations against TBs, which causes distinct damage degree to TB and final cracking behaviour [37], while SFE, slip mode and crystallographic orientation play profound roles in affecting the dislocation-TB interaction mode [35,36]. Based on the dislocation pile-up theory, a criterion to predict the competition between TB cracking and SB cracking was established, indicating that TB cracking becomes more accessible with increasing DSF and/or lowering SFE and that the required critical DSF decreases with the reduction of SFE [35]. In the present study, the dependence of TB cracking on DSF was observed likewise in the CoCrFeMnNi HEA with different grain sizes. Based on the crystallographic analysis of dislocation-TB interactions, most cases are those that all activated slip planes are collinear on the two sides of TBs and the slip directions are parallel to the TB plane [[35], [36], [37]], which can also be substantiated by the twin-slip morphology of post-fatigue HEA samples. For this kind of dislocation-TB interactions, there is no residual dislocation or strain incompatibility at TBs [37,39], causing least damage to TBs and therefore making the TBs stronger in resisting fatigue cracking compared to HAGBs and even SBs [40]. However, the increase in DSF significantly enhances the degree of blocking dislocations at TBs, resulting in more severe piling-up of dislocation at TBs. Also, the dislocation-TB interaction modes that cause much higher fatigue damage to TBs will initiate [[35], [36], [37]]. These two aspects stemming from the increase in DSF essentially promote TB cracking. For the coarse-grained CoCrFeMnNi HEA, the critical DSF for the transition from SB cracking to TB cracking is alike to that of Cu-8 at.% Al alloy whose SFE (17 mJ/m2) [41] is similar to that of the HEA (18.3 mJ/m2) [42]. Since the SFE plays a crucial role in affecting the piling-up of dislocations, the above similarity can verify the reliability of our results.

Apart from DSF, present investigation reveals that decreasing grain size could reduce the required critical DSF, facilitating TB cracking. Although the previously established model proposed that increasing grain size makes the blockage of dislocations more serious, it was also mentioned that SB spacing might play a crucial role in promoting TB cracking [35]. As exhibited in Fig. 4(b) and (c), the spacing of SBs with extrusions/intrusions, within which high densities of defects were accumulated, decreases with reducing grain size, which can facilitate the minimisation of internal strain energy [43]. Therefore, it is in line with theoretical predication and experimental results in early studies [38,43,44]. Based on the dislocation pile-up theory, the previous model assumed that TB cracking occurred when the number of blocked dislocations at the TB reaches a critical value, which is basically a constant [35]. However, fatigue damage is a dynamic process involving the accumulation of vacancies to form voids, the coalescence of these voids to microcracks and final failure [25]. As schematically illustrated in Fig. 5, during cyclic deformation, SB formed via complicated dislocations activities, while high densities of dislocations and vacancies will accumulate within the SBs to form extrusions/intrusions. When the propagation of SBs was blocked by TBs, enabling the impingement of SBs to TBs, both dislocations and vacancies can be transferred from SBs to TBs [1], enabling the accumulation and combination of these defects that lead to the formation of voids and microcracks at the TBs. At a given length, the decreased SB spacing increases the number of impingement sites on the TBs and this enhances the possibility of the accumulation and growth of voids and microcrack coalescence, which catalyses the TB cracking during cyclic deformation. The crack growth along TBs in samples with small grain sizes due to the link of small voids is faster than that in large grain sizes due to the growth of voids at individual sites. Therefore, the decrease in grain size reduces the critical DSF for the transition of cracking mode and tends to promote TB cracking due to the narrower SB spacing. It should be mentioned that TB thickness has an insignificant effect on TB cracking in the present study due to the relatively high plastic deformation, making the influence of elastic anisotropy on the TB cracking behaviour negligible [45]. Our findings of the dependence of TB cracking on the grain size in the HEA can extend our understanding on fatigue cracking mechanism, which should also be applicable to other metallic materials.

Fig. 5.   Schematic illustration of the effect of grain size on the SB-TB interactions and TB cracking.

In summary, TB cracking behavior in the CoCrFeMnNi HEA with different grain sizes was investigated under LCF tests. Irrespective of grain size, with increasing DSF, the dominated damage mode transforms from SB cracking to TB cracking near TB regions. With the reduction of grain size, the critical DSF for the transition of cracking mode decreases, implying that reducing grain size promotes TB cracking due to the reduced SB spacing that facilitates the accumulation and coalescence of defects at TBs and consequently the initiation of TB cracks.

Acknowledgements

The authors appreciate the scientific and technical support from the Australian Microscopy & Microanalysis Research Facility at the University of Sydney. This work was supported financially by the Australian Research Council (Nos. DE170100053 and DP190102243), the Open Foundation of State Key Laboratory of Powder Metallurgy at Central South University, the National Natural Science Foundation of China (No. 51771229) and The University of Sydney under the Robinson Fellowship Scheme.


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