Orientation Dependence of High Cycle Fatigue Behavior of a <111> Oriented Single-Crystal Nickel-Based Superalloy

High cycle fatigue failure has been recognized as one of the major forms of failure of aero-engine blades. This paper presents the high cycle fatigue testing of a Ni-based superalloy near <111> orientation at 800 °C. The fracture morphology and dislocation configuration were analyzed in detail by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to indicate the influence of orientation deviation degree on the high cycle fatigue properties. The results show that the orientation deviation significantly affects the initiation of the slip systems, which is closely related to fatigue performance. The best fatigue life appears on the precise <111> orientation, and the deformation behavior is controlled by multiple sets of equivalent <110> {111} slip systems. With the increase in orientation deviation, the fatigue properties of the alloy degenerate significantly. On the boundary of <111>-<001>, two groups of <110> {111} slip systems with the maximum Schmid shear stress dominate the deformation behavior. On the other hand, on the <111>-<011> boundary, the formation of stacking faults and rapid cutting of γ’ precipitates results in a negative effect on the fatigue life.


Introduction
Nickel-based single-crystal superalloys have been widely used as components in the hot end of advanced aircraft engines and gas turbines due to their excellent hightemperature strength, oxidation resistance and creep properties [1,2]. In the actual service process, turbine blades are often subjected to fatigue damage with cyclic loading, except for creep damage caused by constant centrifugal stress. Among the many factors that cause engine failure, high cycle fatigue (HCF) has proven to be the most common reason [3].
In the past few decades, high cycle fatigue has attracted much attention because of numerous influential factors. Temperature [4,5], frequency [6], load ratio [7], casting conditions [8] and trace elements [9] all have effects on the initiation and propagation of fatigue cracks. However, most of these studies focus on a specific [001] crystal orientation [10][11][12][13]. Vibration stresses resulting in fatigue damage scarcely follow a single axial direction when applied to turbine blades with complex structures. Therefore, crystal orientation, as a significant factor affecting mechanical properties, is noteworthy in the study of high cycle fatigue.
Previous research on the anisotropy of nickel-based single-crystal superalloys mainly focused on creep properties [14][15][16][17]. In Leverant and Kear's [18] paper, the [111] orientation of Mar M200 exhibits superior creep performance compared to [001] at 760 • C/689 MPa because of the lower Schmid factor of <112> {111} slip system. MacKay and Meier's early study on MarM247 SX superalloys indicated that orientation deviation significantly affected the creep properties near [001] orientation [19]. Creep lives of crystals near the <001>-<011> Metals 2021, 11, 1248 2 of 12 boundary of the stereographic triangle are significantly longer than that of the <001>-<111> boundary. Further studies of CMSX-4 by Sass [20] and Matan [21] showed that anisotropy of the primary creep rate is closely related to the number of dominant slip systems and the magnitude of shear stress. In general, the difference in the activation process of the slip systems during plastic deformation caused by different crystal orientation is considered to be the main reason for the creep anisotropy at immediate temperatures. However, the anisotropy of high cycle fatigue properties has only received limited attention.
In this paper, the high cycle fatigue behaviors of a Ni-based single-crystal superalloy with different orientations near <111> orientation were studied. Both coplanar double-slip orientation and non-coplanar double-slip orientation were considered to explain the orientation influencing factors of high cycle fatigue behaviors. Characteristics and mechanisms of fatigue fracture caused by orientation deviation angle and direction are revealed from macroscopic fracture mode and microscopic dislocation movement perspectives.

Materials and Methods
A model nickel-based single-crystal superalloy with nominal composition (wt.%) of (7.4-7.8) Al, (3.0-4.5) Ta, (8.9-9.3) Mo, (1.3-2.7) Cr, (1.4-1.6) Re and Ni as the balance, is used as the research object. The master alloy is prepared by vacuum induction melting, and the single-crystal (SX) rods with different deviations from [111] were prepared by highrate solidification (HRS) directional solidification with the seed crystal method. Twentymillimeter-long seeds with the same desired crystal orientation as the axial direction of test bars were cut directionally from the single-crystal specimens and placed at the bottom of the ceramic mold. Then, the master alloy was melted at 1600 • C and poured on the seeds. Finally, the ceramic mold was withdrawn from the furnace at a withdrawal rate of 3.5 mm/min. The crystal orientations were determined by Laue X-ray diffraction, as shown in Figure 1a. In this paper, test rods with four types of crystal orientations are chosen for this work, which are precise [111] orientation, labeled A, 14 • deviations from [111] orientation along the <111>-<001> boundary, labeled B, and 10 • and 15 • deviations from [111] orientation along the <111>-<011> boundary marked as C and D, respectively. After a full heat treatment with 1300 • C/2 h + 1310 • C/2 h + 1320 • C/2 h + 1330 • C/6 h + 1340 • C/10 h, air cooling (AC) + 1080 • C/2 h and AC + 870 • C/24 h, these rods are processed into test specimens with a gauge diameter of 4 mm and a length of 52 mm, as shown in Figure 1c. Two fatigue samples were machined for each orientation from the same bar.
All tests were performed in 800 • C/σ max = 445 MPa under load control at a stress ratio R = σ min /σ max = −1 and a frequency of 83.3 Hz. The specimens were loaded with sinusoidal wave by the rotating bending method. The fracture surfaces of specimens were observed by EVO-10 scanning electron microscope (SEM, Zeiss, Jena, Germany). Foils for the transmission electron microscope test were cut by a wire cutting machine along the direction perpendicular to the principal stress axis near the fatigue fracture surface, then mechanically ground and electro-chemically thinned at 20 • C in a solution (10 vol% perchloric acid in methanol). Whereafter, the dislocation configurations were analyzed by JEM-2100F transmission electron microscope (TEM, Tokyo, Japan). Observation regions of TEM were selected near the crack source to accurately represent the plastic deformation behavior.

HCF Properties
The results from HCF tests at 800 °C/σmax = 445 MPa for specimens with different crystal orientations are presented in both Table 1 and Figure 2. It is obvious that the HCF properties of this alloy exhibited significant small-angle deviation sensitivity. The precise [1 11] orientation showed the best HCF performance over 10 7 cycles. With the increased orientation deviation, the HCF properties degraded gradually, while the degree of decline varied according to the deviation direction. Fatigue life of specimens deviated by 15° from [1 11] towards [001] and decreased to an average of 2.42 × 10 6 cycles, whereas misorientations of 10° and 14° towards [011] directions resulted in a rapid decline in fatigue performance with 1.28 × 10 6 and 6.76 × 10 5 cycles, respectively.

HCF Properties
The results from HCF tests at 800 • C/σmax = 445 MPa for specimens with different crystal orientations are presented in both Table 1 and Figure 2. It is obvious that the HCF properties of this alloy exhibited significant small-angle deviation sensitivity.

SEM Fractography
SEM observations showed that mixed cleavage and tearing fracture modes exist in the vicinity of <111> orientation. Due to the rotary bending loading mode, the surface of the specimens bears the maximum cyclic stress, which results in the initial cracks mostly at or near the surface. Fractures of specimens with different orientations consist of crack initiation stage, crack propagation stage and final rupture stage, similar to numerous previous studies. However, with the change of deviation direction and angle, the fracture morphology exhibits obvious differences as shown in Figure 3a-d.
The observations from Figure 3a show typical multi-source fracture characteristics in precise <111> orientation. Fatigue cracks generate on the surface and propagate uniformly to the interior along multiple cleavage facets with distinct river pattern and obvious crystallographic characteristics. Many researchers have reported the stage 1 crack growth behavior in nickel-based SX superalloys. These smooth cleavage fracture facets formed during the stage of crack growth and are significantly dependent on the slip planes. Due to face-centered cubic structures, the dominating slip system of nickel-based SX superalloys operated at elevated temperatures is <110> {111} and <112> {111}, hence crack propagation will follow the habit plane {111} [22][23][24]. Fatigue steps are observed at the intersection of different cleavage surfaces as a result of the cross slip of dislocations under cyclic stress.
On the boundary of <111>-<001>, with the orientation deviating from <111>, although multi-source fracture patterns are still observed, crack propagation at stage 1 is not strictly uniform along different <111> planes, but mainly on two types of cleavage planes connected with ridges. Figure 4 shows the schematic diagram of {111} planes on which the different cleavage planes are located. In order to further determine the type of {111} plane, the method of calculating the angle relationship is adopted, as shown in Figure 4c. By measuring the angular relationship between the stress axis and the normal direction of the cleavage plane after cutting the sample longitudinally, one can observe that both fracture surfaces are 63° off the stress axis, which is close to the (111) and (111 ) planes (64°). Cracks propagate inward along these cleavage planes, resulting in a gradual decrease in the bearing capacity area and eventual failure under tensile overload. The occurrence of

SEM Fractography
SEM observations showed that mixed cleavage and tearing fracture modes exist in the vicinity of <111> orientation. Due to the rotary bending loading mode, the surface of the specimens bears the maximum cyclic stress, which results in the initial cracks mostly at or near the surface. Fractures of specimens with different orientations consist of crack initiation stage, crack propagation stage and final rupture stage, similar to numerous previous studies. However, with the change of deviation direction and angle, the fracture morphology exhibits obvious differences as shown in Figure 3a-d.
The observations from Figure 3a show typical multi-source fracture characteristics in precise <111> orientation. Fatigue cracks generate on the surface and propagate uniformly to the interior along multiple cleavage facets with distinct river pattern and obvious crystallographic characteristics. Many researchers have reported the stage 1 crack growth behavior in nickel-based SX superalloys. These smooth cleavage fracture facets formed during the stage of crack growth and are significantly dependent on the slip planes. Due to face-centered cubic structures, the dominating slip system of nickel-based SX superalloys operated at elevated temperatures is <110> {111} and <112> {111}, hence crack propagation will follow the habit plane {111} [22][23][24]. Fatigue steps are observed at the intersection of different cleavage surfaces as a result of the cross slip of dislocations under cyclic stress.
On the boundary of <111>-<001>, with the orientation deviating from <111>, although multi-source fracture patterns are still observed, crack propagation at stage 1 is not strictly uniform along different <111> planes, but mainly on two types of cleavage planes connected with ridges. Figure 4 shows the schematic diagram of {111} planes on which the different cleavage planes are located. In order to further determine the type of {111} plane, the method of calculating the angle relationship is adopted, as shown in Figure 4c. By measuring the angular relationship between the stress axis and the normal direction of the cleavage plane after cutting the sample longitudinally, one can observe that both fracture surfaces are 63 • off the stress axis, which is close to the (111) and (111) planes (64 • ). Cracks propagate inward along these cleavage planes, resulting in a gradual decrease in the bearing capacity area and eventual failure under tensile overload. The occurrence of river patterns provides evidence for cyclic plastic deformation, and the variation of distance between slip trace indicates that plastic deformation accelerates with crack growth.
A distinct fracture mode occurs when the orientation deviates towards [011] along the <111>-<011> boundary. Both Figure 3c,d show a unitary crack source regardless of whether misorientation is 10 • or 14 • . Crack propagation at a single cleavage plane with river patterns and stepwise features can be observed simultaneously. Angular relation calculations indicate that the fracture surface is (111) plane. It was also verified by Laue X-ray diffraction after polishing the cleavage plane of the sample, and the result was added in Appendix B. The fatigue fracture consists of a dominant stage 1 and a transient stage 2. Further comparison of Figure 3a-d indicates that with the increase in orientation deviation, the fracture pattern with a single cleavage plane becomes more evident. Moreover, this transformation of deformation behavior results in rapid degradation of fatigue performance. river patterns provides evidence for cyclic plastic deformation, and the variation of distance between slip trace indicates that plastic deformation accelerates with crack growth. A distinct fracture mode occurs when the orientation deviates towards [011] along the <111>-<011> boundary. Both Figure 3c,d show a unitary crack source regardless of whether misorientation is 10° or 14°. Crack propagation at a single cleavage plane with river patterns and stepwise features can be observed simultaneously. Angular relation calculations indicate that the fracture surface is (111) plane. It was also verified by Laue X-ray diffraction after polishing the cleavage plane of the sample, and the result was added in Appendix B. The fatigue fracture consists of a dominant stage 1 and a transient stage 2. Further comparison of Figure 3a-d indicates that with the increase in orientation deviation, the fracture pattern with a single cleavage plane becomes more evident. Moreover, this transformation of deformation behavior results in rapid degradation of fatigue performance.

Dislocation Configurations
TEM micrographs in Figure 5a show typical deformation substructures from the samples with orientation A after HCF failure. Under this test condition, the γ/γ' microstructures after fracture were roughly the same as that of the heat treated. The distribution of dislocations in the two phases is not uniform, but mainly concentrated in the γ matrix. Several groups of dislocations with different Burgers vectors in the matrix deposit on the γ/γ 'interface, forming dislocation networks. A few dislocations cut into the γ 'precipitate in the form of a/2 <110>, and no stacking faults cutting was observed. The basic characteristic of a nickel-based superalloy structure is that the cubic γ' phase is embedded in the γ matrix, resulting in the formation of three pairs of equivalent γ channels around the γ' cubic precipitate. When the applied stress is in the precise <111> orientation, three types of γ channels have the same stress state and similar dislocation distribution.
In the B oriented specimen, the dislocation configuration is similar to that of the sample with A orientation as shown in Figure 5b. Two types of a/2<110> dislocations were observed in the γ matrix and at the γ/γ' interface, while there were also very few present in the γ' precipitates. The nature of the dislocations cutting into the γ' precipitate was analyzed in detail under two-beam condition as shown in Figure 6. Typical dislocations b1 and b2 as indicated by the arrows are presented in Figure 6a Figure 5a show typical deformation substructures from the samples with orientation A after HCF failure. Under this test condition, the γ/γ' microstructures after fracture were roughly the same as that of the heat treated. The distribution of dislocations in the two phases is not uniform, but mainly concentrated in the γ matrix. Several groups of dislocations with different Burgers vectors in the matrix deposit on the γ/γ 'interface, forming dislocation networks. A few dislocations cut into the γ 'precipitate in the form of a/2 <110>, and no stacking faults cutting was observed. The basic characteristic of a nickel-based superalloy structure is that the cubic γ' phase is embedded in the γ matrix, resulting in the formation of three pairs of equivalent γ channels around the γ' cubic precipitate. When the applied stress is in the precise <111> orientation, three types of γ channels have the same stress state and similar dislocation distribution.

TEM micrographs in
In the B oriented specimen, the dislocation configuration is similar to that of the sample with A orientation as shown in Figure 5b. Two types of a/2<110> dislocations were observed in the γ matrix and at the γ/γ' interface, while there were also very few present in the γ' precipitates. The nature of the dislocations cutting into the γ' precipitate was analyzed in detail under two-beam condition as shown in Figure 6. Typical dislocations b1 and b2 as indicated by the arrows are presented in Figure 6a Compared with orientation A and B, the differences of samples on the <111>-<011> boundary are striking. Orientation deviation causes a variation of the stress state in the three different types of matrix channels, result in significant differences in the number of dislocations in different channels as shown in Figure 7. Meanwhile, in addition to highdensity dislocations in γ channels, there are many unidirectional stacking faults associated with <112> cutting both the γ matrix and γ' precipitates as presented in Figure 6b, which indicates that <112> {111} slip systems participate in the deformation instead of being dominated only by <110> {111} slip systems.   Compared with orientation A and B, the differences of samples on the <111>-<011> boundary are striking. Orientation deviation causes a variation of the stress state in the three different types of matrix channels, result in significant differences in the number of dislocations in different channels as shown in Figure 7. Meanwhile, in addition to highdensity dislocations in γ channels, there are many unidirectional stacking faults associated with <112> cutting both the γ matrix and γ' precipitates as presented in Figure 6b, which indicates that <112> {111} slip systems participate in the deformation instead of being dominated only by <110> {111} slip systems.   Compared with orientation A and B, the differences of samples on the <111>-<011> boundary are striking. Orientation deviation causes a variation of the stress state in the three different types of matrix channels, result in significant differences in the number of dislocations in different channels as shown in Figure 7. Meanwhile, in addition to highdensity dislocations in γ channels, there are many unidirectional stacking faults associated with <112> cutting both the γ matrix and γ' precipitates as presented in Figure 6b, which indicates that <112> {111} slip systems participate in the deformation instead of being dominated only by <110> {111} slip systems.

Discussion
Although HCF differs from creep in the manner of stress loading, both of them exhibit plastic behavior below yield strength. In this paper, the analysis of plastic behavior is mainly focused on the crack initiation on the sample surface to avoid the complex stress state in the late deformation. The initiation and propagation of fatigue cracks are the result of periodic slip of the slip system, that is, cyclic plastic deformation caused by dislocation movement. At elevated temperatures, the anisotropic behavior of nickel-based SX superalloys is closely related to the critical shearing stress of <110> {111} and <112> {111} slip systems [25]. Schmid factors of different specimens are shown in the Table 2. The value of the Schmid factor represents the ease with which the slip system is operated. It should be noted that the Schmid factors for all slip systems are not listed here. Only <110> {111} slip systems with the largest values and the <112> {111} slip systems that can be generated by the reaction are represented. Complete data for all slip systems are added in Appendix A. For the precise <111> orientation, TEM photographs in Figure 4a show that dislocation movement was mainly concentrated in the γ channel with few γ' precipitates cutting. It was indicated that plastic deformation was mainly controlled by the <110> {111} octahedral sliding system, since the shear stress of the <112> {111} sliding system on <111> orientation was relatively low. Six equivalent slip systems operated uniformly on three <111> planes, which was consistent with the macroscopic fracture. During the deformation process operated by multiple <110> {111} slip systems, dense dislocation networks were formed at the γ/γ 'interface through a continuous cross-slip and reaction of a/2[110] dislocations with different Burgers vectors. Previous studies [26] on creep behavior have shown that dense interfacial dislocation networks prevent dislocations in the γ matrix from cutting γ' precipitates, resulting in an obvious work hardening, which is an important reason for the transition from the first creep stage to the second. In the [111] oriented sample, since the Schmid factors of initial slip and cross slip planes are almost equivalent, the cross slip of screw dislocations in matrix channels occurs easily under the cyclic stress [27], which promotes the generation of γ/γ' interface dislocation networks. Furthermore, <110> {111} slip systems have the lowest shear stress in <111> direction. Both the low resolved shear stress and interfacial dislocation networks can contribute to resistance to the movement of dislocations, resulting in the best high cycle fatigue performance of <111> specimens.

Discussion
Although HCF differs from creep in the manner of stress loading, both of them exhibit plastic behavior below yield strength. In this paper, the analysis of plastic behavior is mainly focused on the crack initiation on the sample surface to avoid the complex stress state in the late deformation. The initiation and propagation of fatigue cracks are the result of periodic slip of the slip system, that is, cyclic plastic deformation caused by dislocation movement. At elevated temperatures, the anisotropic behavior of nickel-based SX superalloys is closely related to the critical shearing stress of <110> {111} and <112> {111} slip systems [25]. Schmid factors of different specimens are shown in the Table 2. The value of the Schmid factor represents the ease with which the slip system is operated. It should be noted that the Schmid factors for all slip systems are not listed here. Only <110> {111} slip systems with the largest values and the <112> {111} slip systems that can be generated by the reaction are represented. Complete data for all slip systems are added in Appendix A. For the precise <111> orientation, TEM photographs in Figure 4a show that dislocation movement was mainly concentrated in the γ channel with few γ' precipitates cutting. It was indicated that plastic deformation was mainly controlled by the <110> {111} octahedral sliding system, since the shear stress of the <112> {111} sliding system on <111> orientation was relatively low. Six equivalent slip systems operated uniformly on three <111> planes, which was consistent with the macroscopic fracture. During the deformation process operated by multiple <110> {111} slip systems, dense dislocation networks were formed at the γ/γ 'interface through a continuous cross-slip and reaction of a/2[110] dislocations with different Burgers vectors. Previous studies [26] on creep behavior have shown that dense interfacial dislocation networks prevent dislocations in the γ matrix from cutting γ' precipitates, resulting in an obvious work hardening, which is an important reason for the transition from the first creep stage to the second. In the [111] oriented sample, since the Schmid factors of initial slip and cross slip planes are almost equivalent, the cross slip of screw dislocations in matrix channels occurs easily under the cyclic stress [27], which promotes the generation of γ/γ' interface dislocation networks. Furthermore, <110> {111} slip systems have the lowest shear stress in <111> direction. Both the low resolved shear stress and interfacial dislocation networks can contribute to resistance to the movement of dislocations, resulting in the best high cycle fatigue performance of <111> specimens. For sufficiently applied stress, the a/3<112> dislocation may cut into γ' accompanied by rapid plastic deformation, while a/6<112> dislocations remain at the γ/γ' interface. Note that the reactions require appropriate dislocations rather than two arbitrary dislocations [29,30] Instead of uniform deformation on multiple slip planes, a coplanar double slip occurs when the orientation deviates from precise <111> by 10 • towards <011> along the <111>-<011> boundary. In other words, two dominant <110> {111} slip systems with maximum shear stress are located on the same plane. TEM observations in Figure 6 indicated that unidirectional stacking faults shear γ' is the dominative mechanism of plastic deformation. According to the analysis above, coplanar (111) [101] and (111) [ 110] slip systems can participate in the generation of (111) [211] dislocation distribution in the same (111) plane. Furthermore, the generated [211] dislocation was dominant in the dodecahedral slip system, which can continue to form stacking fault bands cutting into γ' precipitates. The resulting rapid plastic deformation promotes crack initiation and propagation and leads to a rapid decline in fatigue life.

Conclusions
The present study is focused on the effect of orientation deviation near <111> orientation on high cycle fatigue properties of a nickel-based single-crystal superalloy. High cycle fatigue tests were carried out at 800 • C (σ max = 445 MPa), and the fatigue deformation mechanism was studied from both macroscopic and microscopic levels, respectively. The conclusions are summarized as follows: (1) The precise <111> orientation showed the best fatigue performance. With the increase in orientation deviation, the fatigue properties degenerate significantly. (2) Fractographic investigation revealed that, under testing conditions, the precise <111> orientation shows a multi-source fracture mode, and its deformation is mainly controlled by multiple sets of equivalent <110> {111} slip systems in three γ channels with the same stress state. Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

Conflicts of Interest:
There are no conflict to declare.