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Article

High-Cycle Fatigue Fracture Behavior and Stress Prediction of Ni-Based Single-Crystal Superalloy with Film Cooling Hole Drilled Using Femtosecond Laser

by
Zhen Li
1,2,3,4,
Yuanming Xu
1,
Xinling Liu
2,3,4,*,
Changkui Liu
2,3,4 and
Chunhu Tao
2,3,4
1
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
2
AECC Beijing Institute of Aeronautical Materials, Beijing 100095, China
3
AECC/AVIC Failure Analysis Center, Beijing 100095, China
4
Beijing Key Laboratory of Aeronautical Materials Testing and Evaluation, Beijing 100095, China
*
Author to whom correspondence should be addressed.
Metals 2024, 14(12), 1354; https://doi.org/10.3390/met14121354
Submission received: 11 October 2024 / Revised: 21 November 2024 / Accepted: 22 November 2024 / Published: 27 November 2024
Browse Figures
Figure 1
<p>Microstructural characteristics of enhanced phase (γ′-Ni<sub>3</sub>Al) morphology.</p> "> Figure 2
<p>(<b>a</b>) Structural morphology of pore walls in aerogel; (<b>b</b>) morphological characteristics of pore edge structure.</p> "> Figure 3
<p>(<b>a</b>) Geometrical dimensions of high-cycle fatigue specimens (all dimensions are in mm); (<b>b</b>) schematic diagram of the vibration excitation system; (<b>c</b>) monitoring position (red dot) and strain gauge position (yellow square) of the laser displacement sensor.</p> "> Figure 4
<p>High-cycle fatigue life of specimens with perforations compared to those without perforations (specimens marked in yellow for stress prediction analysis).</p> "> Figure 5
<p>(<b>a</b>) Microstructural characteristics of cross-section of M9; (<b>b</b>) Microstructural characteristics of cross-section of M1; (<b>c</b>) Microstructural characteristics of cross-section of M4.</p> "> Figure 6
<p>(<b>a</b>) Microstructural characteristics of the cross-section of M9; (<b>b</b>) Microstructural characteristics of the cross-section of M1; (<b>c</b>) Microstructural characteristics of the cross-section of M4.</p> "> Figure 7
<p>(<b>a</b>) Analysis of the morphologies of oxidized particles (The yellow box shows the EDS analysis area); (<b>b</b>) Euler angle results of oxidized particles (Different colors represent different grain orientations).</p> "> Figure 8
<p>(<b>a</b>) Back to bottom plot of HAADF elemental analysis; (<b>b</b>) Elemental distribution map.</p> "> Figure 9
<p>Characteristics of dislocation morphology.</p> "> Figure 10
<p>Schematic representation of the plastic deformation zone at the crack tip.</p> "> Figure 11
<p>Schematic representation of the EBSD sample preparation procedure.</p> "> Figure 12
<p>Results and data analysis of the KAM experiment.</p> "> Figure 13
<p>(<b>a</b>) Schematic representation of the elliptical corner crack model; (<b>b</b>) crack extension direction versus θ angle definition plot; (<b>c</b>) the cross-section of a high-cycle simulation specimen.</p> "> Figure 14
<p>Meshing and convergence study of M4 specimens.</p> "> Figure 15
<p>Finite element analysis of stress distribution at the chip placement interface of the M4 specimen (red marked positions).</p> "> Figure 16
<p>Stress along the crack propagation path for the M4 specimen.</p> ">
Versions Notes

Abstract

:
A high-temperature, high-cycle fatigue test was conducted on a nickel-based single-crystal superalloy with a pore structure. Optical and scanning electron microscopy were utilized to examine the crack propagation paths and fatigue fracture surfaces at the macro and micro scales. The analysis of crack initiation and propagation related to the pore structure facilitated the development of a crack shape factor reflecting these distinct fracture behaviors. Predictions about the high-cycle fatigue stress experienced by the specimen were made, accompanied by an error analysis, providing critical insights for precise stress calculations and structural optimization in engine blade design. The results reveal that high-cycle fatigue cracks originate from corner cracks at pore edges, with the initial propagation displaying smooth crystallographic plane features. Subsequent stages show clear fatigue arc patterns in the propagation zones. The fracture surface exhibits the significant layering of oxide layers, primarily composed of NiO, with traces of CoO displaying columnar growth. AL2O3 is predominantly found at the interfaces between the matrix and oxide layers. Short and straight dislocations near the oxide layers and within the matrix suggest that dislocation multiplication and planar slip dominate the slip mechanisms in this alloy. The orientation of the fracture surface is mainly perpendicular to the load direction, with minor inclined facets in localized areas. Correlations were established between the plastic zone dimensions at the crack tips and the corresponding fatigue stresses. Without grain boundaries in single-crystal alloys, these dimensions are easily derived as parameters for fatigue stress analysis. The selected crack shape factor, “elliptical corner crack at pore edges”, captures the initiation and propagation traits relevant to porous structures. Subsequent calculations, accounting for the impact of oxide layers on stress assessments, indicated an error ratio ranging from 1.00 to 1.21 compared to nominal stress values.

1. Introduction

Nickel-based single-crystal superalloys are extensively used in turbine blade manufacturing for aero-engines due to their superior high-temperature capabilities and distinct anisotropic mechanical properties [1,2,3]. To increase the operational temperature of turbine blades, thin film cooling hole (FCH) processing technology is implemented to facilitate effective cooling [4,5]. This technology alters the stress distribution around the film hole edge, transitioning from a uniaxial load to a complex multiaxial stress system, often leading to crack initiation at these locations and significant economic losses [6,7]. Researchers employ fracture surface analysis post-fatigue failure to predict the stresses endured by structures prior to failure. However, the variability in the structural details and material grades significantly affects the fatigue failure characteristics, reducing the applicability of the parameters, such as crack shape factors. Consequently, research on fatigue stress prediction in single-crystal alloys with film hole structures is limited [8].
Pore structures are believed to alter the stress distribution around the pore edge, with the fatigue fracture life resulting from the interplay between the maximum principal stress direction and the alloy’s optimal performance orientation. Stress analysis around the pore edge is typically performed using finite element analysis (FEA) numerical simulations [9]. Additionally, digital image correlation (DIC) technology has been employed to characterize the local plastic deformation at the crack tip and elucidate the stress field, although its application in detailed structural features remains challenging [10]. However, advancements in EBSD technology have simplified the characterization of the plastic zones at crack tips [11,12]. This paper uses the KAM function in EBSD to characterize the local plastic zone size at the crack tip in a nickel-based single-crystal alloy. Our study begins by examining the high-cycle fatigue fracture surfaces of pore membranes to summarize the crack initiation and propagation mechanisms. It also explores crack shape factors aligned with high-cycle fatigue characteristics. Utilizing KAM mapping within EBSD, we characterize the plastic zone at the crack tip and subsequently calculate and compare the stress distribution patterns around the pore edge with the results from the finite element method. The findings show strong correspondence between the experimental characterizations and theoretical predictions. This paper aims to explore quantitative prediction methodologies for stress rupture surface details in high-temperature single-crystal alloys with pore membrane structures relevant to engine blade design, thus providing insights for accurate stress calculations and structural optimization strategies.

2. Experimental Materials and Protocols

This study focuses on a second-generation nickel-based single-crystal superalloy oriented along the [001] direction, with its chemical composition detailed in Table 1. The experimental plates were fabricated using the spiral selection method within a directional solidification furnace, ensuring that the orientation deviation from the [001] direction was maintained within 10°, as verified by X-ray diffraction (XRD) analysis. Subsequent standard heat treatment procedures included heating at 1290 °C for 1 h, 1300 °C for 2 h, and then 1315 °C for 4 h under air cooling (AC). Additional treatments were carried out at 1120 °C for 4 h (AC) and at 870 °C for 32 h (AC). Figure 1 illustrates the morphologies of the reinforced phases, γ′ and γ, of the material after heat treatment, which retained the cubic morphology with robust, comprehensive performance.
Femtosecond laser technology was utilized to fabricate air film holes on the working sections of the blades, ensuring that the microstructure adjacent to the holes remained free from remelting layers, as shown in Figure 2. This process also maintained low inner wall roughness with Ra of ≤0.8 μm.
The specimens were designed with reference to HB5277–2020, “Vibration fatigue testing of engine blades and materials”. For the high-cycle fatigue testing under high-frequency vibration, the specimen was plate-shaped with a total length of 120 mm and a measurement length of 30 mm. To replicate the morphology of aerodynamic holes typical in actual turbine blades, the holes were angled at 36° relative to the specimen’s length, with a diameter (D) of 0.4 mm. The measurement section was polished with 1000# waterproof silicon carbide paper to achieve surface roughness below 0.8 μm, minimizing potential processing impacts on fatigue life.
Figure 3 shows a schematic diagram of the specimen size and fatigue test equipment. The specimen was designed as a plate type with one end clamped and the other end unconstrained. The Es–20 vibration exciter was used to force the specimen to perform symmetric reciprocating motion; the load type was a sinusoidal wave, and the stress ratio was R = −1. Electromagnetic induction heating was used to control the test temperature at 850 °C. The test was conducted in the working section of the specimen. During the experiment, strain gauges were pasted on the working section to obtain the relationship between the displacement of the free end of the specimen and the stress in the working section, and the control of the stress level was realized by detecting the displacement. The specific basis was as follows.
Turbine rotor blades often experience fatigue fractures at air film holes on the leading edge, where the engine design operating conditions can reach temperatures of up to 850 °C. Accordingly, the test temperature was set at 850 °C. The specimen underwent symmetrical reciprocating motion during vibration fatigue testing with a stress ratio (R) of −1. The Gofu heating method was employed, featuring high-density glass fiber insulation within the furnace to ensure temperature stability (temperature deviation ≤ 1.5 °C, temperature fluctuation ≤ 0.5 °C). Strain gauges were positioned near the membrane pores in the working section to measure the displacement from the farthest end of the holding section and the strain within the working section. The intrinsic frequency of the sample, verified using an MSW–7125A sweep instrument, served as a benchmark; the testing concluded when this frequency decreased by approximately 2.0%.
An ILD2310–50 laser displacement sensor measured the tip displacement in real time to regulate the stress levels in the working section. Multiple data sets were collected to minimize measurement errors associated with stress and displacement.
The Olympus DSX110X stereomicroscope (Olympus, Tokyo, Japan) documented the location and direction of primary crack propagation. The GEMiNi300 Zeiss field emission scanning electron microscope (SEM, Carl Zeiss AG, Jena, Germany) was utilized to examine the microscopic morphology and elemental distribution in the crack source region and surrounding areas. The FEI Talos F200S (TEM, FEI Company, Hillsboro, OR, USA), equipped with HADDF functionality, characterized the composition distribution beneath the section, while its high-resolution mode facilitated the characterization of the surface morphology, composition distribution, and dislocation configurations at the fracture surface. Additionally, the EBSD function of the GEMiNi300 Zeiss SEM, along with its corresponding KAM functionality, assessed the local plastic deformation within and below the crack section. The method is based on a core-area strain calculation method, which analyzes the local strain distribution and also calculates the geometrically necessary dislocation density. It applies to the strain distribution in crystalline materials after deformation. It can also be used to characterize the local mismatch angle of the crystalline material. Table 2 presents the phase selection criteria and fundamental parameters for the EBSD analysis.
Based on the fatigue fracture characteristics of nickel-based single-crystal high-temperature alloys, a stress prediction model was established, utilizing the plastic zone size at the crack tip (rp), the crack length (a), and the crack shape factor (Y) derived from the characterization data. These elements were integrated into the model to predict the stress levels.
The predicted stresses were compared with those obtained through finite element simulation. The error was quantified by calculating the ratio of the larger value to the smaller one between the two stress measurements. As orthotropic and anisotropic materials, nickel-based single-crystal high-temperature alloys necessitate the tailored definition of their intrinsic behavior. This behavior is described via a Fortran subroutine integrated through the UMAT interface with ABAQUS 6.14 for finite element simulations.
Following the principles of elastic mechanics, the stress–strain relationship for this material adheres to the generalized Hooke’s Law, presented in Equation (1). In the principal axis coordinate system of the single-crystal alloy, there is no coupling between the stress and strain components. The stiffness matrix C, reflecting the symmetry of the material’s stiffness, is outlined in Equation (2).
{ σ } = [ C ] { ε }
In the equation, {σ} is the stress matrix; {ε} is the strain matrix; and [C] is the stiffness matrix.
[ C ] = C 11 C 12 C 12 0 0 0 C 12 C 11 C 12 0 0 0 C 12 C 12 C 11 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44
In the formulae, C 11 = E ν − 1 2 ν − 1 ν + 1 , C 12 = − E ν 2 ν − 1 ν + 1 , and C 44 = G . E is the modulus of elasticity, G is the shear modulus of elasticity, and ν is the Poisson’s ratio. E [001] = 107.31 Gpa, ν = 0.383, G = 96.6 GPa.

3. Results and Analysis

3.1. High-Cycle Fatigue Life

Figure 4 presents the high-cycle fatigue test results for specimens with and without pores at 850 °C. The fatigue strength (σmax) of the specimen devoid of pores is approximately 300 MPa, while that of the specimen containing pores is around 250 MPa. The presence of pores alters the stress distribution within the working section of the specimen, leading to stress concentration at the pore edges, which significantly diminishes its fatigue strength. Integrating the findings from the finite element simulations in Section 3.6, the stress concentration coefficient Kt at the edge of the pore ranges from 2.5 to 3. In this paper, specimens with fatigue life Nf distributed in the range of 105~106 cycle times are selected for analysis and fatigue stress prediction to better demonstrate the characteristics of crack initiation and expansion and the stress prediction research process. “M” is the Chinese abbreviation for “mock-up”, and the numbers are the specimen numbers. They are M1(σmax = 320 MPa, Nf = 2.65 × 106), M4(σmax = 360 MPa, Nf = 5.58 × 105), and M9 (σmax = 320 MPa, Nf = 8.24 × 105).

3.2. Fracture Behavior and Morphological Characteristics of High-Cycle Fatigue

Figure 5 displays the crack trajectory and the macroscopic fracture morphology of a high-cycle fatigue-simulated sample featuring pore gas membranes. The cross-sections of specimens M9, M1, and M4 are primarily perpendicular to the samples’ lengths. Near the pore edge, specimens M9 and M1 show small inclined surfaces at an angle to the length, while M4 does not exhibit such features in the corresponding position. All cracks are observed to initiate from corner cracks at the pore edges. In the initial stages of expansion, smooth and flat crystallographic plane characteristics dominate; however, the later stages are marked by noticeable height variations characterized by fatigue stripe features [1].
Figure 6 illustrates the microscopic fracture morphology, highlighting small steps at the crack source area, followed by smooth crystallographic planes. During the advanced stages of fatigue propagation, the fatigue stripe features become prominent [13].
Figure 7 features a scanning electron microscope (SEM) image of the fracture surface, magnified to 10,000 times. This image shows densely packed spinel morphologies, approximately 0.4–0.6 μm in size. The EBSD background map and Euler angle map depict particle morphologies ranging from about 0.2 to 0.8 μm, indicating oxidation within the cross-section [14].
Figure 8 presents the results from a HAADF elemental face scan analysis, revealing a distinct layered structure within the surface oxide layer. The outermost layers primarily consist of NiO and CoO, transitioning to a layer mainly composed of Al2O3 and CrO; additionally, strengthening phases appear as filamentous aluminum oxides and non-crystalline structures similar to those in the original substrate phases, with notable oxygen content in both the surface and transition layers [14,15].
Finally, Figure 9 depicts typical dislocation images near the crack source areas, showing dislocations penetrating into the γ′ phases and the original dislocations present within both the γ and γ′ phases [16,17].

3.3. Stress Intensity Factor and Plastic Zone at Crack Tip

Unlike traditional aluminum alloys, steels, and other polycrystalline materials, crystallographic plane features are evident in the stable crack propagation stage of nickel-based single-crystal alloys without the typical fatigue stripe characteristics. This difference renders conventional methods, which utilize fatigue stripe features as analytical parameters, inapplicable for these materials. Therefore, it is crucial to establish appropriate fatigue analysis parameters corresponding to the fracture characteristics of nickel-based single-crystal superalloys [18,19,20].
Figure 10 depicts the morphology of the plastic zone at the crack tip during crack propagation. The size of this zone shows a positive correlation with the stress intensity factor K. According to the critical plane method, crack initiation and propagation are triggered when the shear stress on the primary slip system’s slip plane surpasses a critical threshold. Utilizing Tresca’s yield criterion, the relationship between the plastic zone size at the crack tip and the stress intensity factor K can be calculated. For scenarios under plane stress and plane strain, the formulas for single tensile and cyclic loading are given in (3) and (4), respectively [21,22,23].
r p ( γ ) = K 2 2 π 2 σ y s 2 cos ⁡ γ 2 ( 1 + sin ⁡ γ 2 ) + 2   Plane stress state
r p ( γ ) = K 2 2 π 2 σ y s 2 cos 2 ⁡ γ 2 ( 1 − 2 υ ) + sin ⁡ γ 2 2   Plane strain state
In the given equation, rp represents the size of the plastic zone at the crack tip, K denotes the stress intensity factor at this location, and γ is defined as the angle between the boundary of the plastic zone and the horizontal coordinate axis, set at γ = 90°, specified at the bottom of the fracture surface. Furthermore, σys signifies the yield strength and ν indicates Poisson’s ratio; both parameters are temperature-dependent. Lastly, π is a constant [24].
Equation (5) describes the stress intensity factor at the crack tip and the applied stress on the specimen, where Y represents the crack shape factor and a denotes the crack length. Consequently, a relationship can be established between the size of the plastic zone at the crack tip and the applied stress in the specimen using Equations (6) and (7). Research indicates that when a structure is subjected to only in-plane stresses, perpendicular stresses are negligible; thus, it is considered to be in a plane stress state. Under this condition, cracks typically initiate at the edge of the pore membrane, without material constraints on its wall surface, allowing calculations based on Equation (6). As cracks propagate perpendicularly into the material, transitioning to a plane strain state, Equation (7) is utilized for further analysis [22].
K = Y σ π a
r p = Y σ π a 2 2 π 2 σ   y s 2 × 1 2 × 1 + 2 2 2    Plane stress state
r p = ( Y σ π a ) 2 2 π ( 2 σ   y s ) 2 × 1 2 × 1 − 2 υ + 2 2 2     Plane strain state

3.4. Characterization and Determination of Dimensions of Plastic Zone at Crack Tip

Local plastic strain data beneath the fracture surface were obtained using the KAM map function in EBSD. An analysis of the high-cycle fatigue KAM data indicates that as the distance from the fracture surface increases, the KAM value stabilizes within a range of 0.2° to 0.25°. The first-order and second-order derivatives of the original KAM data were calculated and analyzed, as depicted in Figure 11 and Figure 12. The observed trends identified points where both the first-order and second-order derivatives equaled zero for the first time—coupled with alternating signs reaching a change rate of 10−3. These points mark the locations where the KAM value ceases to decrease. The distance from these points back to the starting position corresponds to the size of the plastic zone, with the results detailed in Table 3 [25,26].
Based on the spectrum analysis results depicted in Figure 7 and Figure 8, the primary components of the oxide layer on the fracture surface include O, Al, and Ni, with NiO being the predominant product. The formation of NiO involves a volume expansion, which follows from the chemical combination formula. The expansion ratio calculation utilizes the molar mass and density of both Ni and NiO. Table 3 provides data on the molar density, molar mass, and molar volume for Ni and NiO. The calculated molar volume ratio, determined to be 0.58, serves as the correction coefficient for these materials [27,28].
The plastic zone size can be accurately measured by accounting for the volume expansion due to oxidation. The correction formulas are detailed in Formulas (8) and (9), while Table 4 presents the results after applying these corrections to account for the oxide layer, thus refining the plastic zone size estimation.
H x = H 0 × 0.58
In the equation, H0 denotes the original thickness of the oxide layer, while Hx signifies the corrected thickness of the oxide layer.
r p = r p - native − ( H o × ( 1 − 0.58 ) )
In the equation, rp denotes the corrected plastic zone size, while rp-native refers to the original size.
Except for the crack length dimension, the valid figures in the table are retained to two decimal places.

3.5. Crack Shape Factor

The crack shape factor is fundamentally linked to various factors, including the load category, stress distribution, specimen geometry, crack location, and orientation. In high-cycle fatigue simulations in specimens with gas film holes, the crack behavior typically mirrors type I cracking, characterized by a cross-section perpendicular to the specimen’s length. Cracks typically initiate from a corner defect at the edge of the gas film hole and extend obliquely across the thickness of the specimen post-initiation, closely resembling a pair of elliptical corner cracks [22].
Given these characteristics, it is essential to reference the crack shape factor to that of an “elliptical corner crack subjected to bending and tension”. To calculate the stress intensity factor at the leading edge of a crack induced by bending moment M, the formula specifically accounts for a pair of corner cracks at the hole’s edge, denoted by the subscript d [27,28]. Since the specimen is subjected to a bending moment only, σ = 0 in Equation (10).
K Ι , d = σ + H σ M π a E k F ( b c b t r t r w c w θ )
Referring to the schematic diagram in Model 10, the parameters in the formula are defined as follows: a denotes the length of the crack, 2w represents the width of the working section, t indicates the thickness of the specimen, and r signifies the radius of the hole; all these values are derived from measurements. The parameter b refers to the length of the crack along the surface of the hole, while c denotes its length along the surface of the plate. The angle θ, formed between the crack extension path and surface c, varies gradually with the increasing crack length, See Figure 13. All parameters were measured from cross-sectional views, with lengths expressed in millimeters (mm) and angles in degrees °. Specific values for these parameters are documented in Table 5.
In this model, the crack shape factor Y and the terms E(k), F, and H, necessary to complete the stress intensity factor calculations, are determined using Formulas (11)–(14). The methodologies for the calculation of these parameters are detailed and can be referenced in the “Handbook of Stress Intensity Factors”, which is included in the appendix in [22,29,30,31].
Y = H E k × F
E k = 1 + 1.464 b c 1.65 1 / 2 b / c ≤ 1
F = M 1 + M 2 b t 2 + M 3 b t 4 × g 1 × g 2 × g 3 × g 4 × f ( θ ) × f ( w )
H = H 1 + H 2 − H 1 sin p θ
Except for the crack length dimension, the valid figures in the table are retained to two decimal places.

3.6. Prediction of Stress

Formulas (4) and (5) delineate the relationship between the plastic zone size at the crack tip and σ. Research indicates that the fatigue crack growth rate under constant-amplitude tensile and compressive loading (stress ratio R < 0) is significantly higher compared to that under constant-amplitude tensile loading (R > 0) as well as tensile–compressive cyclic loading scenarios. This higher growth rate for R < 0 is attributed to reverse compressive loading, which results in a larger reverse plastic zone, leading to more pronounced blunting damage at the crack tip and accelerating the crack growth rate [19,20,32,33,34]. In this study, high-frequency fatigue tests were performed with a stress ratio of (R = −1), where both tensile and compressive loads contributed to the formation of a plastic zone at the crack tip; thus, stress calculation Formulas (15) and (16) were derived [35,36,37,38].
The stress prediction for the specimen was carried out by substituting the values of the crack tip plastic zone rp and the crack shape factor Y for different crack lengths into Equations (15) and (16). The Poisson’s ratio ν and the yield strength σys used in these equations are temperature-dependent constants [39], the values of which are detailed in Table 6.
Δ σ = r p Y 2 a × 4 σ y s ( 1 + 2 / 2 )    Plane stress state
Δ σ = r p Y 2 a × 4 σ y s ( 1 − 2 υ + 2 / 2 )    Plane strain state
Except for the crack length dimension, the valid figures in the table are retained to two decimal places.

3.7. Finite Element Analysis and Error Assessment

In the convergence study on the grid size, when the minimum grid size is less than 0.01 mm, the fluctuation amplitude of the pore-side stress analysis results with the grid size is less than 5%, and the grid is converged. For the final determination of the basic cell size of 0.1 mm, in the vicinity of the air film holes and at a crack extension path cell size of 0.005 mm, see Figure 14.
In the boundary conditions, the temperature is set to be 850 °C, the same as in the test, and the loading frequency is the same as the intrinsic frequency of the specimen, which is M1 = 178 Hz, M4 = 173 Hz, and M9 = 178 Hz, respectively. The damping ratios are M1 = 0.45%, M4 = 0.37%, and M9 = 0.45%, respectively.
The harmonic response steady-state modal analysis method was utilized to simulate the one-dimensional bending vibration fatigue testing process of the specimen. This technique facilitated the calculation of the first-order resonant mode of the simulated specimen, from which the maximum stress amplitude σmax was extracted based on the frequency response curve. This simulated stress at the patch location closely aligns with the measured stress at the same position, as shown in Figure 15. For example, in the M4 specimen, the average stress at this patch location is σmax = 361.90 MPa, closely comparable to the strain gauge measurement from the actual sample (σmax = 360 MPa), thus validating the accuracy of the simulation [40,41,42,43].
Based on the fracture locations and crack propagation paths observed in real samples, a crack path was delineated; subsequently, the simulated stresses were measured at various points along this primary crack path, as illustrated in Figure 16.
According to established formulas, the predicted fatigue fracture stress corresponds to a stress range Δσ that is converted into σmax. A comparison between the finite element simulation values and the calculated results reveals ratios of larger and smaller values, as presented in Table 7, with factor errors ranging from 1.00 to 1.21.
According to references [44,45], for the commonly used polycrystalline materials titanium alloy and steel, a stress prediction error of about 20% or less can be achieved. Based on the current research status and technical maturity of the quantitative analysis industry, for nickel-based single-crystal high-temperature alloys, a new material, the application of the model is more difficult, and the final error reached 21% (1.21), which is a better result than those achieved so far. In addition, in engineering practice, we are unlikely to encounter a situation where the actual structure is exactly the same as the theoretical model. In this study, the closest theoretical model was selected based on the actual crack initiation and extension characteristics of the specimen, and the stress prediction and error calculation were carried out to achieve the above error results. The gap between the engineering reality and the theoretical model is also the reason for the error. This is where we need to improve our next work, by considering the correction factor between the theoretical model and the actual fracture specimen to further reduce the error.
σ max = Δ σ 1 − R
Except for the crack length dimension, the valid figures in the table are retained to two decimal places.

4. Conclusions

(1)
The fatigue strength σmax of the specimen without pores is approximately 300 MPa, whereas, for the specimen with pores, it is around 250 MPa. The presence of pores disrupts the stress distribution within the working section of the specimen and induces stress concentration at the edges of the pores, significantly reducing its fatigue strength.
(2)
The cross-section reveals a distinct oxidation layer accompanied by layering phenomena. The surface predominantly comprises NiO, with minor amounts of CoO. A significant quantity of Al2O3 is interspersed between the matrix and the oxide layer. Near the oxide layer and the matrix, cut-in dislocations within the γ′ phase are observed alongside the original dislocations in both the γ and γ′ phases. These dislocations are short and linear, measuring approximately 100–200 nm. The configuration of these dislocations suggests that the slip mechanism in this single-crystal alloy is predominantly governed by dislocation multiplication and planar slip.
(3)
During the crack propagation stage, no typical fatigue stripe features were observed in the simulated specimens of the high-cycle fatigue air film. Theoretical derivations suggest a correlation between the size of the plastic zone at the crack tip and the fatigue stress. The experimental results indicate that, in single-crystal alloys, it is relatively straightforward to determine the size of the plastic zone due to the absence of grain boundaries and other influencing factors. Given these favorable prediction outcomes, the size of the plastic zone at the crack tip can be effectively employed as a parameter for the analysis of fatigue stress.
(4)
The high-cycle-fatigue air-film porous specimen exhibited cracking in the form of an angular crack at the pore edges. The crack shape factor, termed the “pore edge elliptical corner crack”, was employed to predict the fatigue stress at the fracture surface, yielding relatively accurate results with an error range of 1.00 to 1.21.

Author Contributions

Conceptualization, X.L. and Z.L.; methodology, Z.L.; software, X.L.; validation, C.T., Y.X. and Z.L.; formal analysis, Z.L.; investigation, Y.X.; resources, C.T.; data curation, C.T.; writing—original draft preparation, Z.L.; writing—review and editing, C.L.; visualization, Z.L.; supervision, X.L. and C.L.; project administration, C.T.; funding acquisition, Y.X. and C.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by [the National Science and Technology Major Project] J2019-VI-0022-0138.

Data Availability Statement

The dataset for this thesis is covered by technical secrets and is not available at this time.

Acknowledgments

The authors would like to express their gratitude to EditSprings (https://www.editsprings.cn (accessed on 12 September 2024)) for the expert linguistic services provided.

Conflicts of Interest

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.

References

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Metals 14 01354 g001
Figure 1. Microstructural characteristics of enhanced phase (γ′-Ni3Al) morphology.
Figure 1. Microstructural characteristics of enhanced phase (γ′-Ni3Al) morphology.
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Metals 14 01354 g002
Figure 2. (a) Structural morphology of pore walls in aerogel; (b) morphological characteristics of pore edge structure.
Figure 2. (a) Structural morphology of pore walls in aerogel; (b) morphological characteristics of pore edge structure.
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Metals 14 01354 g003
Figure 3. (a) Geometrical dimensions of high-cycle fatigue specimens (all dimensions are in mm); (b) schematic diagram of the vibration excitation system; (c) monitoring position (red dot) and strain gauge position (yellow square) of the laser displacement sensor.
Figure 3. (a) Geometrical dimensions of high-cycle fatigue specimens (all dimensions are in mm); (b) schematic diagram of the vibration excitation system; (c) monitoring position (red dot) and strain gauge position (yellow square) of the laser displacement sensor.
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Figure 4. High-cycle fatigue life of specimens with perforations compared to those without perforations (specimens marked in yellow for stress prediction analysis).
Figure 4. High-cycle fatigue life of specimens with perforations compared to those without perforations (specimens marked in yellow for stress prediction analysis).
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Figure 5. (a) Microstructural characteristics of cross-section of M9; (b) Microstructural characteristics of cross-section of M1; (c) Microstructural characteristics of cross-section of M4.
Figure 5. (a) Microstructural characteristics of cross-section of M9; (b) Microstructural characteristics of cross-section of M1; (c) Microstructural characteristics of cross-section of M4.
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Figure 6. (a) Microstructural characteristics of the cross-section of M9; (b) Microstructural characteristics of the cross-section of M1; (c) Microstructural characteristics of the cross-section of M4.
Figure 6. (a) Microstructural characteristics of the cross-section of M9; (b) Microstructural characteristics of the cross-section of M1; (c) Microstructural characteristics of the cross-section of M4.
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Metals 14 01354 g007
Figure 7. (a) Analysis of the morphologies of oxidized particles (The yellow box shows the EDS analysis area); (b) Euler angle results of oxidized particles (Different colors represent different grain orientations).
Figure 7. (a) Analysis of the morphologies of oxidized particles (The yellow box shows the EDS analysis area); (b) Euler angle results of oxidized particles (Different colors represent different grain orientations).
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Figure 8. (a) Back to bottom plot of HAADF elemental analysis; (b) Elemental distribution map.
Figure 8. (a) Back to bottom plot of HAADF elemental analysis; (b) Elemental distribution map.
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Metals 14 01354 g009
Figure 9. Characteristics of dislocation morphology.
Figure 9. Characteristics of dislocation morphology.
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Figure 10. Schematic representation of the plastic deformation zone at the crack tip.
Figure 10. Schematic representation of the plastic deformation zone at the crack tip.
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Figure 11. Schematic representation of the EBSD sample preparation procedure.
Figure 11. Schematic representation of the EBSD sample preparation procedure.
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Metals 14 01354 g012
Figure 12. Results and data analysis of the KAM experiment.
Figure 12. Results and data analysis of the KAM experiment.
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Figure 13. (a) Schematic representation of the elliptical corner crack model; (b) crack extension direction versus θ angle definition plot; (c) the cross-section of a high-cycle simulation specimen.
Figure 13. (a) Schematic representation of the elliptical corner crack model; (b) crack extension direction versus θ angle definition plot; (c) the cross-section of a high-cycle simulation specimen.
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Metals 14 01354 g014
Figure 14. Meshing and convergence study of M4 specimens.
Figure 14. Meshing and convergence study of M4 specimens.
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Figure 15. Finite element analysis of stress distribution at the chip placement interface of the M4 specimen (red marked positions).
Figure 15. Finite element analysis of stress distribution at the chip placement interface of the M4 specimen (red marked positions).
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Figure 16. Stress along the crack propagation path for the M4 specimen.
Figure 16. Stress along the crack propagation path for the M4 specimen.
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Table 1. Chemical composition of nickel-based single-crystal superalloy (mass fraction, %).
Table 1. Chemical composition of nickel-based single-crystal superalloy (mass fraction, %).
ElementCCrCoWMo
wt%0.01~0.043.8~4.88.5~9.57.0~9.01.5–2.5
ElementAlTaHfReNi
wt%5.2–6.26.0~8.50.05~0.151.6~2.4Allowance
Table 2. Phase parameters required for EBSD characterization.
Table 2. Phase parameters required for EBSD characterization.
PhaseSpatial Structure of PhaseLattice ConstantSpace Group
Ni3AlFace-centered cubic structure4.157 Å225
NiOFace-centered cubic structure3.52 Å225
Table 3. Volume correction factor.
Table 3. Volume correction factor.
ElementMolar MassDensityMolar VolumeVolume Ratio
Ni58.7 g/mol8.902 g/cm³6.59 dm3/mol0.58
NiO74.7 g/mol6.6 g/cm³11.21 dm3/mol
Table 4. Size of the plastic zone at the crack tip for varying crack lengths.
Table 4. Size of the plastic zone at the crack tip for varying crack lengths.
Sample Identification NumberLength of the Crack a/mmDimensions of the Plastic Zone/μmRevised Dimensions of the Plastic Zone/μm
M90.0218.5618.43
0.058.848.84
0.109.189.18
0.1511.4811.48
0.208.788.78
0.258.748.74
0.509.119.11
0.808.117.90
M10.03513.1813.09
0.079.08 9.08
0.1013.59 13.59
0.155.67 5.67
0.2010.44 10.44
0.258.998.99
0.407.45 7.45
0.708.41 8.41
0.909.25 9.25
M40.0377.387.29
0.2088.1158.01
0.405.334.95
0.8010.059.84
1.2012.9712.64
Table 5. Results of calculations for crack shape factors.
Table 5. Results of calculations for crack shape factors.
Sample Identification NumberCrack Length
a/mm		c/bθ/°b/mmr/mmt/mmw/mmr/mmY
M90.02 1.00 300.02 0.20 2.71 5.00 0.20 1.31
0.051.00 450.05 0.20 2.71 5.00 0.20 1.08
0.101.00 450.10 0.20 2.71 5.00 0.20 0.85
0.151.00 450.15 0.20 2.71 5.00 0.20 0.97
0.201.00 450.20 0.20 2.71 5.00 0.20 0.86
0.251.00 450.25 0.20 2.71 5.00 0.20 0.77
0.500.65 500.77 0.20 2.71 5.00 0.20 0.60
0.800.50 701.61 0.20 2.71 5.00 0.20 0.58
M10.0351.00 300.0350.20 2.71 5.00 0.20 1.18
0.071.00 450.070.20 2.71 5.00 0.20 1.32
0.101.00 450.10.20 2.71 5.00 0.20 1.15
0.151.00 450.150.20 2.71 5.00 0.20 0.97
0.201.00 450.20.20 2.71 5.00 0.20 0.86
0.251.00 450.250.20 2.71 5.00 0.20 0.77
0.401.00 450.40.20 2.71 5.00 0.20 0.61
0.700.79 500.88 0.20 2.71 5.00 0.20 0.48
0.800.65 601.23 0.20 2.71 5.00 0.20 0.49
0.900.55 701.64 0.20 2.71 5.00 0.20 0.51
M40.0371.00 450.25 0.222.53 5.00 0.200.78
0.2081.00 450.34 0.222.53 5.00 0.200.67
0.401.00 450.44 0.222.53 5.00 0.200.58
0.800.56 700.48 0.222.53 5.00 0.200.68
1.200.51 800.90 0.222.53 5.00 0.200.53
Table 6. Results and errors of stress prediction calculations.
Table 6. Results and errors of stress prediction calculations.
Sample Identification Numbera/mm
Length of the Crack		Dimensions of the Plastic Zone/μmShape Factor of Cracks
Y		Prediction of the Stress Range
Δσ/MPa
M90.0218.431.311675.50
0.058.84 1.08 1615.02
0.109.18 0.85 1475.17
0.1511.48 0.97 1180.50
0.208.780.86 1017.79
0.258.74 0.77 1008.93
0.509.11 0.60 939.45
0.807.90 0.58 718.25
M10.03513.091.18 1189.69
0.079.08 1.32 1137.73
0.1013.59 1.15 1328.20
0.155.67 0.97 829.64
0.2010.44 0.86 1109.85
0.258.990.77 1023.26
0.407.45 0.61 931.25
0.708.41 0.48 950.94
0.909.25 0.51 825.09
M40.0377.290.78 1303.53
0.2088.01 0.67 1224.62
0.404.95 0.58 797.96
0.809.84 0.68 682.22
1.2012.64 0.53 798.57
Material Properties850 °C: Poisson’s ratio ν = 0.383, yield strength σys = 978 Mpa
Table 7. Results and errors of stress prediction calculations.
Table 7. Results and errors of stress prediction calculations.
Sample Identification NumberLength of the Crack
a/mm		Prediction of the Stress Range
Δσ/MPa		Predicted Maximum Stress Value
σmax/MPa		Finite Element Analysis of the Maximum Stress
σmax/MPa		Error Magnitude
M90.021675.50 837.75 915.20 1.09
0.051615.02 807.51 739.20 1.09
0.101475.17 737.59 640.00 1.15
0.151180.50 590.25 588.80 1.00
0.201017.79508.90 553.60 1.09
0.251008.93 504.47 528.00 1.05
0.50939.45 469.73 457.60 1.03
0.80718.25 359.13 416.00 1.16
M10.0351189.69 594.85 691.201.16
0.071137.73 568.87 611.201.07
0.101328.20 664.10 572.801.16
0.15829.64 414.82 534.401.29
0.201109.85 554.93 508.801.09
0.251023.26 511.63 486.401.05
0.40931.25 465.63 448.001.04
0.70950.94 475.47 406.401.17
0.90825.09 412.55 390.401.06
M40.0371303.53 651.77 756.001.16
0.2081224.62 612.31 505.601.21
0.40797.96 398.98 364.501.09
0.80682.22 341.11 327.501.04
1.20798.57 399.29 323.701.23
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Li, Z.; Xu, Y.; Liu, X.; Liu, C.; Tao, C. High-Cycle Fatigue Fracture Behavior and Stress Prediction of Ni-Based Single-Crystal Superalloy with Film Cooling Hole Drilled Using Femtosecond Laser. Metals 2024, 14, 1354. https://doi.org/10.3390/met14121354

AMA Style

Li Z, Xu Y, Liu X, Liu C, Tao C. High-Cycle Fatigue Fracture Behavior and Stress Prediction of Ni-Based Single-Crystal Superalloy with Film Cooling Hole Drilled Using Femtosecond Laser. Metals. 2024; 14(12):1354. https://doi.org/10.3390/met14121354

Chicago/Turabian Style

Li, Zhen, Yuanming Xu, Xinling Liu, Changkui Liu, and Chunhu Tao. 2024. "High-Cycle Fatigue Fracture Behavior and Stress Prediction of Ni-Based Single-Crystal Superalloy with Film Cooling Hole Drilled Using Femtosecond Laser" Metals 14, no. 12: 1354. https://doi.org/10.3390/met14121354

APA Style

Li, Z., Xu, Y., Liu, X., Liu, C., & Tao, C. (2024). High-Cycle Fatigue Fracture Behavior and Stress Prediction of Ni-Based Single-Crystal Superalloy with Film Cooling Hole Drilled Using Femtosecond Laser. Metals, 14(12), 1354. https://doi.org/10.3390/met14121354

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