High temperature in-situ SEM observation and crystal plasticity simulation on fretting fatigue of Ni-based single crystal superalloys

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High temperature in-situ SEM observation and crystal plasticity simulation on fretting fatigue of Ni-based single crystal superalloys Yue Su a, Qi-Nan Han b, c, **, Wenhui Qiu d, Zhiwu He a, e, Yi-Bo Shang a, f, HuiJi Shi a, ***, Li-Sha Niu a, * a

AML, School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China c Aero-engine Thermal Environment and Structure Key Laboratory of Ministry of Industry and Information Technology, Nanjing, 210016, China d Midea Residential Air Conditioning Division, Foshan, Guangdong, 528311, China e Guangdong Bright Dream Robotics Co., Ltd, Foshan, Guangdong, 528312, China f Beijing Jingwei Hirain Technologies Co., Ltd., Beijing, 100191, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Ni-based single crystal superalloy Crystal plasticity Finite elements In-situ fretting fatigue test Crystal orientation

The fretting fatigue behavior of Ni-based single crystal (NBSX) superalloy specimens with different crystal orientations ([110] and [010]) was investigated by in-situ scanning electron microscopy at 400 � C. The slip lines on the surface of the specimens were captured during the test, and crack paths were recorded. These results show that the dominant deformation mode of fretting fatigue at 400 � C is the crystallographic slip. Fretting contact conditions were simulated by the crystal plasticity finite element (CPFE) method. It was found that the activated slip systems and planes in the numerical results are correlated to crystal orientations. The predicted slip lines corresponding to the dominant slip planes obtained by the simulations are in good agreement with the experimental observations. And the crack initiation sites in the experiment coincide with the equivalent plastic strain in the simulation.

1. Introduction Fretting fatigue occurs when two bodies in contact subjected to a small relative motion (usually less than 100 μm) which is caused by cyclic bulk loading or oscillating force (Goh et al., 2003; Hills, 1994; Sabnis et al., 2013; Waterhouse, 1981). It produces stress concentration and severe stress gradient at the contact surface, resulting in material degradation and accelerated crack initiation. This poses a severe threat to the industrial application, such as bolted joints (Juoksukangas et al., 2016), ropes (Peterka et al., 2014), splined couplings (Houghton et al., 2009) and railway axles (Foletti et al., 2016; Makino et al., 2011). Especially, fretting fatigue is usually observed at the joints of the gas turbine blades and disks due to the centrifugal and aerodynamic force in turbine engine (Barella et al., 2011; Rajasekaran and Nowell, 2006; Sabnis et al., 2013). U.S. Air Force research shows that one-sixth of failures were caused by

* Corresponding author. Room N-519, Mong Man Wai Building of Science and Technology, Tsinghua University, Beijing, 100084, China. ** Corresponding author. College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China. *** Corresponding author. Room N-513, Mong Man Wai Building of Science and Technology, Tsinghua University, Beijing, 100084, China. E-mail addresses: [email protected] (H.-J. Shi), [email protected] (L.-S. Niu). https://doi.org/10.1016/j.ijplas.2019.102645 Received 6 September 2019; Received in revised form 30 November 2019; Accepted 10 December 2019 Available online 14 December 2019 0749-6419/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Yue Su, International Journal of Plasticity, https://doi.org/10.1016/j.ijplas.2019.102645

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fretting, among the aircraft engine accidents related to the high-cycle fatigue (Farris et al., 2000). Hence, the analysis of fretting fatigue at the turbine blade-disk attachment needs to be analyzed. Over the last five decades, extensive fretting fatigue testing has been carried out, and a lot of fretting fatigue data for aluminum alloy (Navarro et al., 2008; Szolwinski and Farris, 1998), stainless steel (Nakazawa et al., 2003) and titanium alloy (Goh et al., 2003; Golden et al., 2008; Lavella and Botto, 2018; Ruiz et al., 1984) have also been obtained. Ni-based single crystal (NBSX) superalloy is widely used in the casting of turbine blades and vanes for the gas turbine engine, due to its excellent elevated temperature mechanical properties and corrosion resistance (Graverend et al., 2014; Han et al., 2019b; Reed, 2008; Rodas and Neu, 2018; Zhou et al., 2019). Recently, researches on fretting fatigue behavior of NBSX superalloys has also been reported. For example, Murthy et al. (2006) re­ ported an experimental setup to perform fretting fatigue of NBSX superalloys at 610 � C. Matlik et al. (2006) observed that the fretting fracture surface of NBSX superalloys was along the {111} slip plane at 649 � C. Rengaraj et al. (2016) also investigated the effect of tangential force on fretting fatigue life of NBSX superalloys. Su et al. (2019) revealed the effect of temperature on the fatigue properties of single crystal superalloys. However, their works are limited to macroscopic fatigue test and post-experimental observation, and the microscopic mechanism of temperature effects is lacking. Besides, an in-situ fretting fatigue experimental setup in scanning electron microscopy (SEM) environment was designed by Han et al. (2018, 2016; Han et al., 2019a). The 2-D radiographs of cracks were observed in the in-situ fretting fatigue test at a synchrotron facility by de Pannemaecker et al. (2017). Compared with the fracture analysis after macro-test, these in-situ tests mentioned above show that the crack initiation and propagation of fretting fatigue at room temperature. However, these results are limited to room temperature, the in-situ observation of fretting fatigue crack for NBSX su­ peralloys at elevated temperature is rare. More importantly, the temperature at the turbine blade and disk attachment can reach 400–650 � C (Reyhani et al., 2013). And previous works on NBSX superalloys have identified that the temperature is one of the primary

Fig. 1. (a) Schematic diagram of fretting fatigue experimental system, (b) the observation window in SEM equipment, the dimensions for (c) specimen and (d) fretting pad (all dimensions are in mm), (e) the servo-hydraulic testing machine equipped with scanning electron microscope, (f) The loading system for fretting fatigue tests. 2

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factors which affect the mechanical properties (Desmorat et al., 2017; Fedelich, 2002; Huang et al., 2012; Li et al., 2019; Matlik et al., 2009). Thus, the in-situ observation and mechanism analysis at high temperatures are necessary and critical to understand the fretting fatigue crack evolution of NBSX superalloys. For the NBSX superalloys, the crystal orientation relative to the loading direction is an important factor which could affect the mechanical properties (le Graverend, 2019; Sabnis et al., 2012; Xu et al., 2018). Some studies pointed out that the [001] orientation has the lowest modulus and superior plain fatigue resistance, compared to the [110] and [111] orientation (Estrada Rodas and Neu, 2018; Reed, 2008). Huang et al. (2009) conducted the fretting experiments at room temperature to identify the crystallographic effects on the fretting response and coefficient of friction. Gao et al. (2014) investigated the effect of the crystal orientation of NBSX su­ peralloys on the fatigue crack formation direction. In addition, numerical analysis has also been made to estimate the fretting stress of turbine blade attachment with different crystal orientation (Arakere and Swanson, 2001). More recently, the influence of crystal orientation of NBSX superalloys on fretting fatigue life has been reported at elevated temperature (Fleury et al., 2014; Su et al., 2019). However, the role of crystal orientation in the fretting crack initiation and evaluation mechanics has not yet been fully understood. A lot of work has been carried out to study the deformation mechanism of NBSX superalloys under various condition. These works indicate that plastic deformation exists at the fretting contact zones (Hu et al., 2016; Richter et al., 2018), and dislocations play an important role in the deformation behavior below 700 � C (Huang et al., 2018; Neu and McDowell, 2008; Sabnis et al., 2013; Wu et al., 2017). Crystal plasticity finite element (CPFE) was a desirable tool to model the deformation behavior of NBSX superalloy under tensile (Hama and Takuda, 2011; Sabnis et al., 2012), fatigue (Sinha and Ghosh, 2006; Turkmen et al., 2003) and creep test (Barba et al., 2018; Venkatramani et al., 2007). This method can simulate the microscopic and plastic response such as crystallographic slip. And this slip line generated by the dislocation motion is consistent with the experimental observation. The CPFE simulation of NBSX su­ peralloys fretting fatigue at room temperature has been completed by Han et al. (2016). In order to better understand the fretting fatigue properties, the simulation at high temperatures is necessary. Therefore, the CPFE method is used to model the fretting fatigue behavior of NBSX superalloys at high temperature. The main purpose of this study was to observe in situ the fretting fatigue crack evolution of NBSX superalloys at high temperatures. And two fretting experiments with different crystal orientations were carried out to explore the deformation mechanism of fretting fatigue. To this end, Section 2 introduces a high temperature fretting fatigue experimental device using in-situ SEM observation system, and the materials and test procedure. The CPFE model and finite element implementation are described in Section 3. Section 4 presents the in-situ observations of fretting fatigue crack evolution. The state of the slip system and stress-strain behavior are investigated by the CPFE method. The main conclusions are summarized in Section 5. 2. Materials and experiment 2.1. In-situ fretting fatigue experimental fixture and material As shown in Fig. 1a, an experimental fixture is designed to conduct the fretting fatigue testing at elevated temperature in the SEM system. The experimental device (Fig. 1e) consists of the loading, observation (SEM) and control system, which was provided by Shimadzu. The in-situ tests were carried out in the chamber of the SEM with a servo-hydraulic loading system. In the loading system, two flared loading heads are used to fix the specimen, as shown in Fig. 1f. The loading head on the left side is fixed, and the cyclic load is applied along the length direction by the movement of the right head. Normal contact force is applied by the proving ring and screw. Thus, four cylinder-on-flat contacts (Fig. 1b) are formed between the specimen and fretting pads, which are denoted as C1. C2, C3, and C4. These materials, including the specimen and fretting pad, are heated by tungsten arranged in a certain form. Two type K-ther­ mocouples are used to measure the temperature in the fretting contact zone, as shown in Fig. 1a. The temperature can reach about 800 � C. In the vacuum chamber of the SEM, the high temperature environment is separated by a heat insulation shell. A circular hole with a diameter of 5 mm on the heat insulation is used as the observation window. During the fretting fatigue process, all four contacts are captured in the observation window (Fig. 1b). Therefore, it is possible to capture all potential fretting crack initiation site and crack evolution processes by SEM. In this work, the specimen is machined from the NBSX superalloys, which represents the turbine blade. And a Ni-based poly­ crystalline superalloys, which represents the turbine disk, is used as the fretting pad. The chemical composition of these materials is detailed in Tables 1 and 2. The purpose is to make the contact is consistent with the actual working condition at turbine blade-disk attachment. The geometry and dimensions of the specimen and fretting pads are shown in Fig. 1c and d, which is designed based on the ASTM (2015) and JSME (2009). A dog-bone shape of the specimen with thickness of 1.2 mm is used. There are two cylindrical surfaces with a radius of 0.75 mm on the fretting pad. The thickness of the fretting pad is increased to 2 mm to ensure contact in the thickness direction of the specimen. In order to avoid the contact zone being blocked, the thickness of the top of the proving ring is reduced. What’s more, the normal contact force at elevated temperature can be maintained due to the proving ring made of Ni-based polycrystalline superalloys. In a word, four cylinder-on-flat fretting contacts appear in the observation window at elevated

Table 1 The chemical composition of the NBSX superalloys (wt. %). Cr

Co

Mo

Al

Ti

Ta

W

C

Ni

12.2

9.0

1.9

3.6

4.1

5.0

3.8

0.07

balance

3

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Table 2 The chemical composition of the Ni-based polycrystalline superalloys (wt. %). Cr

Co

W

Mo

Nb

Al

Ti

B

Zr

C

Fe

Ni

16

13

4

4

0.7

2.1

3.7

0.015

0.05

0.05

�0.05

balance

temperature. 2.2. Material orientation It is well known that the crystalline orientation of NBSX superalloys plays a major role in the mechanical properties. In general, the preferred growth direction for NBSX turbine blade is [001], since the lowest modulus and superior fatigue resistance. Besides, the rotation about the [001] direction is defined as the secondary orientation, and which is parallel to the blade root attachment (Savage, 2012; Zhou et al., 2019). However, the secondary orientation is not controlled during the blade manufacturing process, which is different from the primary orientation. Hence, two specimens with typical orientation are tested in our work, as shown in Fig. 2, to explore the effect of secondary orientation on fretting fatigue. Firstly, the length direction of specimens is parallel to [001], which represents the growth direction of the NBSX turbine blade. Then, [010] and [110] orientation are selected as the contact direction, which is defined as Orientation A and B, respectively. This alignment of crystal orientation caused by the casting variability is within 6–8� , which is acceptable in industrial manufacture. In short, these orientations not only are consistent with the actual blade used in industry but also suitable for understanding the influence of the secondary orientation on fretting fatigue behavior. 2.3. Experimental procedure In the present work, fretting fatigue tests were run at 400 � C using a servo-hydraulic fatigue testing machine equipped with in-situ SEM. Two different specimens (Orientation A and B) were tested. These loading parameters details are listed in Table 3. For each test, the sinusoidal load with a frequency of 10 Hz was applied along the length direction of the specimen. The load ratio was 0.1, and the maximum cycle load was 1.0 kN. The normal contact force (Fn) of 426 N was assumed to be constant during the test. All specimens and fretting pads were machined by wire electrical discharge machining, and the finish surface roughness was less than 0.20 μm. Besides, the observation surface was ground by SiC paper down to 2000 grit, and then polished with 0.15 μm diamond paste. Thus, the surface machining marks were removed to achieve a mirror finish. Prior to testing, specimen and fretting pads were cleaned with acetone. These methods make it possible to observe the evolution of cracks and microstructures in SEM. The temperature at the NBSX blade root attachment can reach 400–650 � C during turbine engine operation (Reyhani et al., 2013). Several studies have demonstrated that there is a threshold temperature (750 � C) in the failure of NBSX superalloy (Ma et al., 2008). In general, the crystallographic fracture model is the main failure mechanism below the threshold temperature. In turn, model I fracture (non-crystallographic fracture) occurs above the threshold temperature. In order to explore the crystallographic deformation below 750 � C, while considering imaging quality of the SEM system at high temperature. The experiments at 400 � C were carried out in this

Fig. 2. (a) The contact in fretting fatigue test device (b) crystal orientation of the specimen. 4

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Table 3 These loading parameters in this study. Load ratio

Frequency

Waveform

Maximum cycle load

Normal contact load (Fn)

0.1

10 Hz

Sine wave

1.0 kN

426 N

paper, and this is consistent with the temperature in industrial applications. 3. Numerical simulation The CPFE approach is suitable for simulating the microstructure evolution of single crystal materials. Section 3.1 introduces the crystal plasticity constitutive model used in this work. The finite element implementation and definition of the dominant slip system are given in Section 3.2 and 3.3, respectively. 3.1. Crystal plasticity constitutive model A rate-dependent crystal plasticity constitutive model is developed from the frame work of elastic-plastic constitutive theory proposed by Asaro (1983); Asaro and Rice (1977); Hill and Rice (1972); Peirce et al. (1982); (1983). Within a finite deformation framework, it can be assumed that the deformation gradient, F is multiplicatively decomposed into elastic and plastic components as: (1)

F ¼ Fe Fp The evolution of F can be expressed using the following relationship with the slip rate: p

p F_ ¼ Lp Fp

(2)

X Lp ¼ γ_ ðαÞ sðαÞ � mðαÞ

(3)

α

where Lp is the plastic velocity gradient, γ_ ðαÞ denotes a dislocation slip rate on α th slip system, s(α) and m(α) are the slip direction and the normal direction of slip plane on the α th active slip system, respectively. the rate-dependent power function of slip rate γ_ ðαÞ is established based on Peirce et al. (1983), which is related to the back stress X(α), resolved shear stress τ(α) and slip resistance g(α), as the following expression: � ðαÞ �n �τ X ðαÞ �� γ_ ðαÞ ¼ γ_ 0 sgnðτðαÞ X ðαÞ Þ�� (4) � ð Þ α g here γ_ 0 represents a reference value of the slip rate and n is the rate exponent. The resolved shear stress τ(α) can be expressed using the Schmid law: (5)

τðαÞ ¼ σ : ðsðαÞ � mðαÞ Þ where σ is the Cauchy stress. The back-stress rate X(α) can be calculated using the Chaboche (1989) model: ðαÞ X_ ¼ ζðαÞ ðrðαÞ γ_ ðαÞ

(6)

X ðαÞ j_γðαÞ jÞ

where ζ(α) and r(α) are the material coefficients. Based on the law proposed by Peirce et al. (1982), the slip resistance can be given by: g_ðαÞ ðγÞ ¼

n X

(7)

hαβ ðγÞj_γ ðβÞ j

β

hαβ ðγÞ ¼ hðγÞ½q þ ð1 � hðγÞ ¼ h0 sech2

γ¼

h0 γ

τs

(8)

qÞδαβ � �

(9)

τ0

Z X β¼1 jdγðβÞ j

(10)

n

in which q and h0 are the latent and initial hardening parameters, respectively. τ0 represents the initial slip resistances, and τs rep­ resents the saturation slip resistances. By fitting the experimental results of Ma et al. (2008), these parameters used in the above model have been determined, which are summarized in Table 4.

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3.2. Finite element implementation A half finite element model (see Fig. 3) has been created to simulate the contact condition in the ABAQUS commercially software, taking into account the geometric symmetry of the experimental fixture. The dimensions of specimen and fretting pad are consistent with the actual test setup. As shown in Fig. 3a, a fixed condition is applied on the left side of the specimen. And the bottom of the specimen is symmetrical along the y direction. Besides, loading conditions are established in three loading steps based on the testing process. In the first step, a pre-load of 0.01 kN is applied at the top of the fretting pad. So the interaction between the specimen and pad is established. In the second step, the normal force of 426 N is applied on the pad, and the pre-load is unloaded. Finally, a cycle load with sinusoidal form is applied to the right side of the specimen along the x direction. Overall, 20 cycles are used to ensure that these constitutive model parameters reach a stabilized state, which is advantageous to reduce the calculation cost. Eight-node brick elements (C3D8I) are employed. As shown in Fig. 3b, the mesh density in the contact region is higher than other since the non-linearity of the contact problem. In order to verify the mesh convergence, the mesh with different sizes at the contact zone is considered. The convergence criterion is defined as the stress change less than 8% when the density is doubled. Thus, the mesh size of 5 � 5 μm is used on the contact interface in this simulation. ABAQUS contact parameters, including finite sliding and surface-tosurface assumptions, are used between the contact pair. The semi-cylindrical surface of the fretting pad is defined as a master surface and the specimen is the slave surface. The penalty method is employed to establish the frictional contact, and the friction coefficient of 0.3 is set according to the experimental results (Lavella, 2016). In this model, an isotropic elastic constitutive is selected for the fretting pad. And the constitutive model described in Section 3.1 is implemented on the specimen by a user-defined subroutine (UMAT). These material parameters are listed in Tables 4 and 5. Newton-Raphson iteration is chosen to solve the non-linearity in contact problems. For the CPFE simulation, the analysis under different crystal orientation was carried out to match the experimental work. 3.3. Definition of dominant slip system For the NBSX superalloys with FCC crystal structure, there are four {111} octahedral slip plane. Three slip directions <110> exist on each slip plane. So, a total of 12 slip systems have the potential to be activated. When the dislocations move along the slip system, the slip steps left on the free surface is defined as the slip line. Fig. 4 shows the schematic of the octahedral slip plane and crystal orientation on the specimen. It can be seen that the distribution of the slip system on the specimen is different due to the changes in crystal orientation. Thus, these slip lines that can be observed in SEM are also different as shown in Fig. 5. For Orientation A, there are two groups of potential slip lines (A-I and A-II) on the free surface perpendicular to the observation direction. These are 45� inclined to the contact direction. In detail, A-I, A-II, A-III and A-IV correspond to the ð111Þ, ð111Þ, ð111Þ and ð111Þ slip plane respectively. However, there are three groups of slip lines (B–I, B-II and B-III) on the free surface for Orientation B. For example, B–I and B-II are both 54.7� inclined to the contact direction, which corresponds to the (111) and ð111Þ slip plane, respectively. The B-III and B-IV are parallel to the contact direction, which corresponds to the ð111Þ and ð111Þ slip plane, respectively. The resolved shear stress projected onto the slip system is the main cause of the slip system activation. When the load is applied to the specimen, the amount of plastic slip on each slip system is different. Sabnis et al. (2013) and Biswas et al. (2013) pointed out that the slip system with the maximum plastic slip has a higher possibility to generate the slip line on the free surface. Therefore, the slip system with the maximum plastic slip is defined as the dominant slip system. In order to determine the dominant slip system, the plastic slip of all 12 slip system on every computational node is calculated. Besides, the slip plane corresponding to the dominant slip system is marked as the dominant slip plane. A contour map containing the dominant slip system/plane at each computational point will be discussed in detail in Section 4.2. Thus, the predicted slip lines in fretting fatigue test of NBSX superalloys will be obtained, and the comparison with the experimental results is also analyzed. 4. Results and analysis 4.1. In-situ observation results Fig. 6 shows the in-situ image on the surface of the specimen in the fretting fatigue test at 400 � C. Fig. 7 displays the typical fracture surface after the fretting fatigue tests for Orientation A and B. As shown in Fig. 7, the fracture crack initiates in the pore at the edge of the sample for the Orientation A and B, and then propagation along the crystallographic planes until the final fracture occurred. The crack initiated site is located on the surface of the sample that is observed in the SEM. Hence, the in situ observations reflect both initiates at the contact zone as shown in Fig. 6. In addition, the crystallographic fracture occurs in both orientations. For Orientation A, the crack only appears at the C2 contact point, which is 45� inclined to the contact direction. The crack path matches the direction of the slip line A-I. However, the crack at C3 contact point grows along the contact direction for Orientation B, which is also approxi­ mately parallel to the slip lines B-III and B-IV. The crack path is deflected due to the presence of inclusions. Therefore, there is a Table 4 The material parameters of the NBSX superalloys used in the CPFE simulation. C11 (GPa) 214.84

C22 (GPa) 133.19

C44 (GPa) 113.19

γ_ 0 10

6

n

ζðαÞ (GPa)

rðαÞ

hαβ (MPa)

h0 (MPa)

τ0 (MPa)

τs (MPa)

q

3.6

210.87

1960

1

548

60.64

100.64

1

6

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Fig. 3. (a) Schematic diagram of the finite element model and (b) mesh in the contact zone. Table 5 The material parameters of the Ni-based poly­ crystalline superalloys used in the CPFE simulation. E (GPa)

ν

180

0.32

significant difference in crack propagation path between the Orientation A and B. The effect of contact orientation on fretting fatigue performance has also been found in this work. For Orientation A, the fracture failure of the sample occurs, when the number of fatigue cycles reaches 200998. And the sample with Orientation B fractured after 67952 cycles. Thus, Orientation A exhibits a better fatigue performance, which corresponds to the [010] contact orientation. Meanwhile, Rengaraj et al. (2017) performed macroscopic fretting fatigue tests of NBSX superalloys under different contact orien­ tations. Their study showed that the sample with <011> contact orientation failed faster than <010> orientation, which is in agreement with our work. The crack morphology for Orientation A under different cycles can be seen in Fig. 8. It is clear that the fretting fatigue crack initiates from the contact area. Then, the crack grows in a direction that is 45� inclined to the contact direction. When the number of cycles reach 200091, the crack path is deflected. This shows that inclusions play an important role in the crack evolution. Finally, the fracture failure of the specimen occurs after 200998 cycles. Thus, the fretting fatigue crack was observed in-situ for NBSX superalloys at 400 � C in this work. 7

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Fig. 4. (a) Schematic diagram of the octahedral slip systems on the specimen for (a) Orientation A and (b) Orientation B.

Fig. 5. The slip lines that can be observed in SEM on the specimen surface for (a) Orientation A and (b) Orientation B.

Fig. 6. The in-situ image on the surface of the specimen for (a) Orientation A and (b) Orientation B in the fretting fatigue test at 400 � C. (Note: N ¼ number of fatigue cycles).

More recently, some researches have revealed that slip lines appear on the free surface of the fretting contact area at room tem­ perature. These slip lines represent the dislocation motion along the corresponding slip system, which reflects the plastic deformation in fretting fatigue of NBSX superalloys. In this work, as shown in Fig. 9, the density of the slip line is lower than the results at room temperature (Han et al., 2018). Similar features related to slip line are also present in other contact locations. The crack tip of Orientation A and B are displayed in Fig. 9c and d. It can be seen that the slip lines are still observed at the crack tip. For Orientation A, the slip line has a 49–52� inclined with the contact direction (Fig. 9c), which corresponds to the predicted slip lines A-III and A-IV. For Orientation B, the slip line is 2–5� inclined to the contact direction, which corresponds to the predicted slip lines B-III and B-IV. This 8

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Fig. 7. Typical fracture surface for (a1) Orientation A and (b1) B after the tests, and (a2) (b2) the crack initiation region.

Fig. 8. The crack morphology for Orientation A under different cycles (Note: N ¼ number of fatigue cycles).

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Fig. 9. The slip lines on the surface of the specimen in SEM for (a) Orientation A (b) Orientation B, (c) and (d) the enlarged image of slip line in the (a) (b), the slip line at room temperature for (e) Orientation A (f) Orientation B by Han et al. (2018) (Note: N ¼ number of fatigue cycles).

deviation of slip line from the predicted direction can be explained by the crystal orientation error during the casting process. The reduced slip line density is also pointed out in the plain fatigue of Ni-based superalloys at high temperatures by Pineau and Antolovich (2009). The result indicates that the plastic deformation is lower than at room temperature. The decrease in the density of the slip zone indicates that the plastic deformation is weakened. 4.2. Predicted slip system by CPFE simulation In this simulation, the dominant slip system cloud diagram in different contact orientation is shown in Fig. 10. The color of the contour map represents the activated slip system, not the numerical size. The slip amount of this slip system at this calculation node is the largest among all 12 octahedral slip systems, which is defined as the dominant slip system as mentioned in Section 3.3. For Orientation A, there are six dominant slip systems in the contact area of the specimen as shown in Fig. 10a. From the left to the right side of the specimen, the dominant slip systems are ð111Þ½011�, ð111Þ½101�, ð111Þ½011�, ð111Þ½011�, ð111Þ½101� and ð111Þ½011�. For Orientation B, as shown in Fig. 10b, there are five dominant slip systems appear in the contact area. They are ð111Þ½011�, ð111Þ½011�, ð111Þ½101�, ð111Þ½101� and ð111Þ½011�. As shown in Fig. 4, the dominant slip planes are the same on the adjacent slip systems. For example, the dominant slip plane of the ð111Þ½101� and ð111Þ½011� are both is (111). In this work, the dominant slip plane contour maps are shown in Fig. 11 according to the 10

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Fig. 10. Dominant slip system cloud diagram for (a) Orientation A (b) Orientation B. The color of the contour map represents the activated slip system. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 11. Dominant slip plane contour maps for (a1) Orientation A (b1) Orientation B, the straight lines present the predicted slip line corresponding to the slip plane. The slip lines on the surface in SEM observation for (a2) Orientation A (b2) Orientation B, which are also shown in Fig. 9c and d.

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crystal structure. It can be seen that there are four dominant slip planes in the contact area for Orientation A, which are ð111Þ, ð111Þ, ð111Þ and ð111Þ, respectively. For Orientation B, four dominant slip planes appear in the contact area, which are ð111Þ, ð111Þ, ð111Þ and ð111Þ, respectively. Further, the predicted slip lines left on the free surface of the specimen are marked as straight line in Fig. 11, because the corre­ sponding slip system is activated. It is obvious that the predicted slip lines are different between the two contact orientations. For Orientation A, two sets of slip lines that are at 45� inclined to the contact direction appear in the free surface (Fig. 11a). However, there are three slip lines on the free surface for Orientation B. This contains two groups of slip lines which are both 54.7� inclined to the contact direction, and a slip line parallel to the contact normal direction. As described above, the slip lines are rare at the contact area in this experimental observation. But, some slip lines are still observed at the crack tip, as shown in Fig. 11(a2) and 11(b2). For Orientation A, the slip lines are 49–52� inclined to the normal contact direction, which are marked by the dashed line. There is 4–7� deviation, compared with the predicted title angle of 45� . In addition, the slip line inclined 2–5� to the normal direction appears on the crack path for Orientation B. This is a 2–5� error from the predicted slip line parallel to the contact normal direction. Crystal orientation deviation during the casting process is a factor that causes the deviation of the slip line direction. There are 6–8� in the angular de­ viation of the crystal orientation for the NBSX superalloys, which is mainly caused by the casting error. This error is within an acceptable range in industrial manufacturing. Therefore, in spite of the angular deviation, the in-situ experimental observation results can still be predicted by CPFE simulation. 4.3. The crack initiation location and direction It is clear that there are significant differences in the crack behavior between two orientations according to the in-situ experimental results. In this section, the crack initiation and propagation will be discussed in detail by CPFE simulation. Equivalent plastic strain has been used to predict the crack initiation location for NBSX superalloys (Han et al., 2018; Su et al., 2019), which is defined as rffiffiffiffiffiffiffiffiffiffiffi 2 p p (11) ε¼ εε 3 ij ij

Fig. 12. The superposition of equivalent plastic strain fields and dominant slip plane of the specimens for (a) Orientation A (b) Orientation B. (Note: Slip line at crack initiation site are marked by white line). 12

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εp ¼

X γ ðαÞ ðsðαÞ � mðαÞ Þ

(12)

α

where εpij is the plastic strain component. So the equivalent plastic strain is obtained in the simulation. Fig. 12 show the equivalent

plastic strain fields of the specimens for Orientation A and B. It can be seen that the peak of the equivalent plastic strain in both orientations appears at the edge of the contact area, which is consistent with the location of the crack initiation observed in this test (Fig. 6). In order to explore the crack initiation direction from the simulation results, the equivalent plastic strain contour maps are superimposed upon the dominant slip plane maps, as shown in Fig. 12. Slip line at the crack initiation site is marked by the white line. For Orientation A, the activated dominant slip plane at the peak of equivalent strain is ð111Þ. The corresponding predicted slip line is 45� inclined to the contact direction, and the observed crack during the initiation stage is 45� inclined to the contact normal direction. Besides, the dominant slip plane at the strain peak is ð111Þ for Orientation B. So the corresponding predicted slip line is parallel to the contact normal direction, which is confirmed by the crack initiation parallel to the contact normal direction in the in-situ experiment. Hence, this indicates that the crystallographic slip still plays a key role in the fretting fatigue failure for NBSX superalloys at 400 � C. And the crack initiation direction in the experiment coincide with the slip line corresponding to the activated slip system in the simulation. The crack initiation location and direction can be predicted by the CPFE simulation, which is in agreement with our in-situ experimental observation. 5. Conclusions In this study, an in-situ fretting fatigue experimental fixture with high temperatures testing capability was designed to realize fretting contact condition. The effect of secondary orientation on fretting fatigue behavior of NBSX superalloys was investigated at 400 � C, including the crack path and slip line. The in-situ observation shows that the slip line density was reduced at 400 � C, compared with the room temperature (Han et al., 2018, 2016). Besides, for Orientation A, slip lines appear on the crack tip, which are 49–52� inclined to the contact normal direction. But, the slip line is 2–5� inclined to the normal contact direction for Orientation B. Consequently, the crystallographic fracture is the main deformation mode of fretting fatigue for NBSX superalloys at 400 � C. The crack grows along the {111} slip plane in two orientations. The three-dimensional numerical analysis of fretting fatigue was carried out using the CPFE method. Activated dominant slip systems/planes were obtained by the CPFE simulation. The result confirms the difference in the dominant slip systems/planes in the two contact orientations. The predicted slip lines corresponding to the dominant slip planes were found to be in good agreements with the in-situ experimental results. This analysis indicates that equivalent plastic strain is effective for predicting crack initiation location. Furthermore, the growth direction of the crack can be predicted by CPFE simulation for both orientations. Declaration of competing interest We declare that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. CRediT authorship contribution statement Yue Su: Conceptualization, Methodology, Investigation, Software, Formal analysis, Writing - original draft, Writing - review & editing. Qi-Nan Han: Conceptualization, Methodology, Validation, Formal analysis, Writing - review & editing. Wenhui Qiu: Soft­ ware, Writing - review & editing. Zhiwu He: Investigation, Software. Yi-Bo Shang: Methodology, Writing - review & editing. Hui-Ji Shi: Conceptualization, Formal analysis, Writing - review & editing, Supervision, Funding acquisition. Li-Sha Niu: Supervision, Re­ sources, Visualization, Conceptualization, Methodology, Writing - review & editing, Project administration. Acknowledgment This work is financially supported by the National Natural Science Foundation of China (Nos.11632010, 11572171, 11672151 and 91860101), National Science and Technology Major Project (2017-VI-0003-0073). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijplas.2019.102645.

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