Prediction of High-Cycle Fatigue Performance of 1Cr11Ni2W2MoV Stainless Steel Plate after Foreign Object Damage

High-cycle fatigue (HCF) properties of 1Cr11Ni2W2MoV stainless steel impacted by a high-speed steel ball were studied by the foreign object damage (FOD) test and HCF test. The results show that the damage depth 
 
 Z
 
 has the most obvious effect on the HCF limit of notched flat plate specimens, and the fatigue limit decreases with the increase of depth 
 
 Z
 
 . The microcharacteristics of the FOD notch and HCF fracture of 1Cr11Ni2W2MoV stainless steel were observed by a scanning electron microscope (SEM). The results show that the microdamage features such as plastic deformation, loss of material, and microcracks promote the initiation and propagation of fatigue cracks, and the fatigue source area lies near the root of the notch. The Peterson formula and Worst Case Notch (WCN) mode were used to predict the HCF limit of flat plate specimens after FOD. The crack growth threshold was obtained by the crack growth test. The results show that the prediction results of both methods are conservative. For the notch with damage depth 
 
 Z
 <
 1
 
  mm, the prediction accuracy of the WCN model is higher (
 
 error
  
 range
 <
 30
 %
 
 ). For the notch with damage depth 
 
 Z
 >
 1
 
  mm, the prediction results of both methods have large errors (>30%) with the WCN model being slightly more accurate.


Introduction
During the service of aeroengine, it is unavoidable to draw nearby particles into the flow path of the engine, including birds, ice, and small hard objects. The impact of birds and ice belongs to soft impact, namely, bird strike [1] and ice impact [2], and the impact of small hard objects such as bolts, nuts, sand, and stones is called foreign object damage (FOD) [3]. FOD often occurs near the ground during the operation, forming a dent or notch at the leading edge of the blade [4]. FOD has become a key issue which must be considered in the design of aeroengine blades.
The FOD on aeroengine blades is a complex transient dynamic problem, which involves the nonlinearity, contact, and large deformation of materials. Many scholars have paid more and more attention to FOD in recent years. The most intuitive way to study the FOD problem is to test the impact damage prefabricated. The most used method is the air cannon method [5]. Peters et al. [6] used an air cannon to launch steel balls to impact the surface of the Ti-6A1-4V plate and observed the bottom of the notch by a scanning electron microscope (SEM) and found obvious microcrack damage caused by high-speed impact. Farahani et al. [7] carried out ballistic impact tests by air cannon, launching steel foreign objects of different shapes on Udimet-500 nickelbased alloy (the first-stage rotor material of the Fiat gas turbine engine) with different impact velocities and incident angles. The result shows that there are many microcracks at the damage caused by cube foreign object incident at a 45°angle. Bache et al. [8] conducted FOD tests using ballistic systems. The Ti-6A1-4V plate samples were impacted with 2 mm diameter steel balls at different incident speeds. The results show that there are ductile indentations at the impact position under low energy impacts, while loss of material (LOM) was observed on the edge of damaged samples under high energy impacts.
With the development of finite element analysis technology, the process of simulating the impact of foreign objects on the blade by finite element software has also become a common method in studying FOD. Oakley and Nowell [9] and Duó et al. [10] used software such as LS-DYNA, DYTRAN, ABAQUS, and material models such as Bammann and Johnson-Cook to perform dynamic simulation analysis for the foreign object impacting process. The damage morphology obtained by the simulation is in good agreement with the experimental results, which proves the applicability of simulation analysis on blade FOD. Chen and Hutchinson [11] used ABAQUS finite element software to simulate the process of steel ball striking the edge of the Ti-6A1-4V flat plate. After studying the residual stress distribution at the FOD location, it was found that a significant residual tension area is formed at the raised tip at the bottom of the notch due to lateral expansion and then resulted in fatigue cracks. Marandi et al. [12] used the finite element method and the experimental method to investigate the stress concentration factor at the notch root of the turbine blade leading edge. The results showed that the finite element calculation results agree well with the experimental data.
Aeroengine blades are subjected to high-cycle fatigue (HCF) loads caused by vibration and short-time resonance during operation. Stress concentrations, residual stresses, and microscopic damage at the FOD location will accelerate the initiation of cracks under HCF, resulting in premature fatigue damage to engine blades in its designed cycles. That means FOD is an important factor limiting the high-cycle fatigue performance of engine blades [13]. Ruschau et al. [14] performed high-cycle fatigue tests on Ti-6Al-4V blades which were impacted by glass beads at different incident angles. Bache et al. [8] studied the effects of different foreign object sizes and shapes on the fatigue strength of the FOD flat specimen. Martinez et al. [15] performed high-cycle fatigue tests on FOD flat specimens with different radii at the leading edges and then studied the effect of different leading-edge radii on the high-cycle fatigue strength of FOD blades. Witek, a scholar at the Rzeszow University of Science and Technology in Poland, used a shaker to directly perform high-cycle vibration fatigue test research on real blades and achieved good results. He used ABAQUS software to calculate the stress distribution during blade vibration. The results showed that the blades would generate high stress loads due to vibration under the first-order mode, and there was a high stress gradient in the blade's first-order nodal line cross-section [16]. Based on the research on high-cycle fatigue test or complete blade, Witek [17] prefabricated different shapes of notches on the leading edge of the PZL-10W engine compressor blade and conducted a high-cycle fatigue test to study the effect of the notch shape on the fatigue strength of the blade. When studying the cause of fatigue failure of a certain type of naval helicopter engine blade, Witek et al. [18] found that the cor-rosion pits at the blade leading edge caused by salt spray seriously endangered the HCF performance of blades, just like the defects at the blade leading edge caused by FOD. In order to improve the anti-FOD capability of engine blades, surface strengthening processes such as shot peening [19] and laser shock peening [20] have been performed to blades in recent years. The impact of these processes on the fatigue strength of FOD blades has also become focuses on FOD-related research.
Structural fatigue problems usually occur during the engineering application of metal components, especially in high stress concentration positions such as notches and welded joints [21,22]. Based on the idea of structural elements, Neuber [23] proposed an average stress model to predict notched fatigue strength and gave a Neuber formula to calculate notched fatigue coefficients K f . Peterson [24] proposed a simpler Peterson formula based on Neuber's research, which is widely used in engineering. Ruschau et al. [25] took the FOD damage made by an air cannon as a notch and predicted the HCF strength of the damaged TC4 specimen through the above-mentioned empirical formula of fatigue notch coefficient. It was found that the predicted values were higher than experimental results. Based on the research by Neuber and Peterson, Taylor [26] developed a method called the Theory of Critical Distance (TCD), which took the average stress of stresses within a certain area around the root cross-section of the notch as the effective stress to predict the fatigue limit. Hudak et al. [27] proposed a Worst Case Notch (WCN) model for HCF strength prediction for damaged parts. This model assumes that microcracks generate at the root of damage since the initial fatigue loading stage; thus, the HCF fatigue strength of damaged parts could be predicted by the boundary conditions of crack propagation. The boundary conditions of crack propagation can be used to estimate the HCF strength. Nowell et al. [28] applied a short crack arrest model which is similar to the WCN model to predict the HCF strength of three different-sized FOD notches. The prediction result is significantly lower than the experimental value. They believes that the main factor affecting the prediction accuracy is that the model does not consider the effect of compressive residual stress at the damage root on the crack propagation boundary. Chaves et al. [29] proposed a method of fatigue limit prediction through stress gradient and linear elastic analysis under remote loading based on the microstructural fracture mechanics model (Navarro and De los Rios [30]). The prediction model was applied to circle holes and V-notches under I-mode loading. The results show that the prediction error is within 12% and the accuracy is high. This paper focuses on the effect of FOD on the HCF limit of a 1Cr11Ni2W2MoV stainless steel flat plate specimen, as well as on the prediction method for the HCF limit. Through FOD and HCF tests, the influences of damage parameters on the notch fatigue limit were analysed, and the microcharacteristics of notch and fracture were observed. Both the average stress model and the WCN model were used to predict the fatigue limit of FOD notch, and the high accuracy range of the WCN model was given after the research.  Table 1.
A flat plate specimen is designed for the FOD test. The size of the specimen is shown in Figure 1.
The foreign objects used in the FOD test are GCr15 steel balls with diameters of 2 mm, 3 mm, and 4 mm, respectively, which are fixed by a cylindrical nylon sabot. Material properties of GCr15 at room temperature are shown in Table 1.

Device
Details. FOD tests on flat plate specimens were carried out by an air cannon system to obtain damages more consistent with features of that in real service. The test system consists of a gas cylinder, a gas storage tank, a loading mechanism, a pressure sensor, a target chamber, solenoid valves, and other components. The picture of the air cannon system is shown in Figure 2.
After the FOD test, a HIROX KH-7700 three-dimensional stereomicroscope was used to observe the macrofeatures of the damage notch, whose minimum resolution is 1 μm.

Test Method.
The impact speed was 290 m/s in the test, with an incident angle of 0°. The impact diagram is shown in Figure 3.

Fatigue Test
2.2.1. Specimen Details. The HCF test specimens are divided into the smooth rectangular section specimen and notched specimen. The smooth rectangular section specimen designed according to GB3075-82 (a Chinese national standard for metal axial fatigue test) [31] is shown in Figure 4 and used to obtain the fatigue limit of 1Cr11Ni2W2MoV at stress ratio R = 0:8 (working stress ratio of aeroengine at cruise state). The notched specimen is a flat plate sample after the FOD test in Section 2.1. In fact, the residual stress at the notch root caused by FOD will affect the stress ratio, which cannot be maintained at 0.8. However, considering the complexity of quantitative analysis on and the inconvenience of measurement on residual stress in engineering application, in-depth research on this point is not conducted in the paper. Thus, all tests are carried out with the stress ratio R = 0:8.

Device Details.
The HCF tests on both smooth rectangular section specimens and notched specimens were carried out by QBQ-100 a high-frequency fatigue testing machine.

Test
Method. The step-loading method (Maxwell and Nicholas [32]) was used to perform HCF tests to obtain the HCF limit of each smooth rectangular section specimen and notched specimen at the life of 10 7 cycles.
The method is described as follows. If the specimen survived the initial step of loading, the stress level would be increased by 10% and the test repeated. This would continue until the specimen failed in less than 10 7 cycles. If we assume that the fatigue damage accumulates linearly in the last step of loading, the fatigue limit for the life of 10 7 cycles could be calculated by the following formula: where σ e is the fatigue limit at 10 7 cycles, σ pr is the maximum stress level of the previous stress step, N f is the number of cycles when the last stress step fails, and σ f is the maximum stress level of the last stress step. The load spectrum of the notched specimen is shown in Figure 5. The device parameters are as follows: (i  [33], and then, the sample is processed by wire cutting before the test. The designing size of the crack growth test specimen is shown in Figure 6. The crack growth direction is perpendicular to the rolling direction.

Device Details.
The tests were carried out by the 809 axial/torsional test system (MTS), and the crack length was measured by a Crack Opening Displacement (COD) gauge, as shown in Figure 7. Before the crack growth test, the precracking test [34,35] was carried out and the length of precracking is 1.7 mm. The controlled stress ratio during the

Test Method.
The K gradient method controlled by constant force was used in the test. During the test, the gradient value C of stress intensity factor K is constant, and the calculation method of stress intensity factor range ΔK is given by the following formula. The compliance method was used to measure the crack length: where α = a/W, ΔP is the range of load, a is the calculated crack length, B is the thickness of the specimen, and W is the width of the specimen.    During the steady-state crack growth stage, the relationship between the crack growth rate da/dN and stress intensity factor amplitude ΔK can be described by the Paris power function: Take logarithm operation on both sides of the above formula, Generally, at least 5 pairs of ðda/dNÞ i and corresponding ðΔKÞ i which satisfy 10 −7 mm/cycle ≤ da/dN ≤ 10 −6 mm/   International Journal of Aerospace Engineering cycle should be taken as the threshold value for fatigue crack calculation [35]. lg ðda/dNÞ in formula (4) is taken as the independent variable for the matching of lg ðda/dNÞ − lg ðΔKÞ data points by the linear regression method. The fatigue crack growth threshold ΔK th is ΔK corresponding to da/dN = 10 −7 mm/cycle according to the matching results.

FOD Test Results
3.1.1. FOD Size. FOD tests were conducted on 13 flat plate specimens. The maximum damage size along the length direction of the specimen is defined as the damage width X, the maximum damage size along the thickness direction of the specimen is defined as the damage thickness Y, and the maximum damage size along the width direction of the specimen is defined as the damage depth Z. The definition of damage sizes is shown in Figure 8.
The FOD test results of flat plate specimens are shown in Table 2. The relationship between damage size and steel ball diameter is shown in Figure 9, where the straight line formed by blue stars represents the mean value of damage size. It can be found from Figure 9 that the width X, thickness Y, and depth Z of the damage notch all increase with the diameter of the steel ball. The damage width X and depth Z are relatively stable with the same diameter of the impact steel ball, while damage thickness Y shows great fluctuation due to the deviation of impacting position in the thickness direction.  Figure 10. It can be seen from the figure that there is a relatively smooth extrusion area at the root of the notch formed by the high-speed impact of the steel ball, and there is obvious plastic deformation accompanied by loss of material (LOM) on the side of the notch. If further amplified by the notch root area, it can be found that there are lamellar structures forming at the side of the notch due to the shear stress in the impacting process, accompanying with microcracks. These microdamage characteristics provide favourable conditions for the initiation and propagation of fatigue cracks and reduce the fatigue performances of materials at the notch.

Fatigue Test Results
3.2.1. Fatigue Limit. The fatigue limit results of smooth rectangular section specimens at the life of 10 7 cycles with stress ratio 0.8 are shown in Table 3.    International Journal of Aerospace Engineering The fatigue limit results of 13 notched specimens at the life of 10 7 cycles with stress ratio 0.8 are shown in Table 2.
The relationship between the HCF limit of FOD flat plate specimens and FOD parameters is shown in Figure 10 and the parameters including damage width X, damage depth Z, and steel ball diameter. Figures 11(a) and 11(b) show the relationship between the HCF limit and damage size, in which the red line is the   7 International Journal of Aerospace Engineering fitting curve of the HCF limit. It is obvious that the HCF limit decreases with the increase of damage depth Z and damage width X. However, the dispersion of damage width X and HCF limit is larger than that of damage depth Z. It shows that the effect of notch depth on HCF is larger than that of notch width.
The relationship between the HCF limit and steel ball diameter is shown in Figure 11(c), in which the straight line formed by blue stars represents the mean value of the HCF limit. It can be seen that the HCF limit decreases with the increase of steel ball diameter, which is consistent with the relationship between damage depth Z and steel ball diameter shown in Figure 9(c). The HCF limit under the same steel ball diameter has certain dispersion, which is caused by the characteristics of the air cannon system.

Fracture Microscopic Features. The fatigue fractures on
No. 9 notched specimens were observed and analysed by SEM, as shown in Figure 12. It can be seen from the figure that the fatigue fracture occurs at the root surface of the FOD notch. There are two fatigue source zones, Zones A and B in Figure 11(a), which are located on both sides of the thickness direction of the flat plate specimen and near the notch tip. The fatigue source zone usually occurs at the notch tip where the notch root surface meets the specimen surface. The crack initiation becomes flat and fine since it is torn open and extruded repeatedly by HCF loads. The fracture surface can be distinguished from the fatigue source area (dark) and the crack growth area (light). The darker colour of the fatigue source area is due to the long exposure time in the air and the oxidation of the material after the crack initiation. The red arrow in Figure 12(a) indicates the incident direction of the steel ball. Zone A and Zone B are the locations of the fatigue source area. Since the crack started at different heights during the initiation process, it would meet each other in the propagation process, and then, a river pattern came out converging to the fatigue source (Figure 12(b)). The adiabatic shear band (ASB) can be observed near the notch root surface in Zone C, caused by steel ball impact [36]. What is more, loss of material (LOM) and plastic deformation can be  Figure 11: The relationship between HCF limit and FOD parameters: (a) HCF limit with damage width X; (b) HCF limit with damage depth Z; (c) HCF limit with steel ball diameter. 8 International Journal of Aerospace Engineering observed in the fatigue source area, indicating that FOD provides favourable conditions for the initiation of fatigue cracks. Under the action of the fatigue load, the fatigue crack gets rapid growth and finally causes the specimen fracture failure.

Crack Growth Test
Results. The crack growth rate measured by the crack growth test is shown in Figure 13, from which the crack growth threshold of 1Cr11Ni2W2MoV can be calculated as 6.23 MPa ffiffiffiffi m p when the stress ratio R = 0:8.

Fatigue Limit Prediction.
The stress concentration caused by the notch has a significant effect on the fatigue performance of the components. The theoretical stress concentration factor K t is based on the assumption that the material is elastic, and it only depends on the geometry of the component. However, in engineering practice, there is plastic deformation in varying degrees of the notch. Therefore, it is necessary to use the fatigue notch factor K f to characterize the fatigue strength of notched components. The fatigue notch factor K f is defined as the ratio between the fatigue limit of the smooth rectangular section specimen and the fatigue limit of the notched specimen under the same conditions and cycles. The formula is as follows: where σ smooth = 949:83 MPa, as shown in Table 3.

Prediction Model for FOD Specimen Fatigue Limit
Based on Peterson Formula. On the basis of Neuber's research [23], Peterson assumed that stress decreases linearly from the notch root inward. When the average stress within a certain distance from the notch root is greater than or equal to the fatigue limit of the smooth specimen, the fatigue failure will occur. The Peterson formula is as follows: where ρ is the radius of the notch root, which is approximately equal to the radius of the steel ball in this paper. a p is the material constant under the influence of tensile stress value, which could be determined by the empirical formula a p = ð270/σ b Þ 1:8 . σ b is tensile strength of 1Cr11Ni2W2MoV, which equals to 955 MPa. For sharp notches, the following equation can be used to calculate K t [37]: where d is the depth of the notch, ρ is the radius of the notch root, and f ðρ/dÞ is given by the following equation: The theoretical stress concentration factor K t can be calculated according to formula (7), and the prediction fatigue notch factor K f can be calculated according to formula (6). The fatigue limit of the notched specimen can be predicted according to formula (6). The calculation results and error analysis are listed in Table 4.
The error distribution on the fatigue limit of FOD flat plate specimens predicted by the Peterson formula is shown in Figure 14, and the error is defined by the following formula. It can be seen from the figure that the prediction error lies within the range of (-55%, -30%), except one 13.7%.

International Journal of Aerospace Engineering
Prediction values for all FOD flat plate specimens are lower than test values, which is considered conservative: 3.6. Prediction Model for FOD Specimen Fatigue Limit Based on WCN Model. Microcracks and corresponding cracks which do not propagate along the stress gradient direction of the notch could be regarded as the WCN model [27]. The WCN model takes the nominal stress threshold as a function of elastic stress concentration factor K t and crack size a. The nominal stress threshold decreases with the increase of K t and notch sensitivity. However, the nominal stress threshold does not decrease with the increase of K t when the predicted K t (by the WCN model) exceeds the limit value. It is mainly caused by the generation of end crack and nonpropagating crack. For the notch with fixed depth and different root radii, the nominal stress threshold increases with radius, and there is a limit radius. When the radius exceeds the limit radius, the crack will not propagate. The aim of the WCN model is to quantify the correlation among notch depth, root radius, stress concentration factor, and other parameters, so as to solve the problem of the notch fatigue limit in a systematic way. Because of the great amount of microdamages in the notch caused by FOD and the fatigue cracks initiated at the microcrack or micronotch, the WCN model is selected to predict the fatigue limit of the notched flat plate specimen.
Generally speaking, the stress threshold is a function of the FOD notch size, the loading mode, and the material parameters. In this paper, the crack propagation threshold of 1Cr11Ni2W2MoV is obtained by the crack growth test.
The formula of the WCN model is where ΔS e is stress amplitude at the root of the notch, a 0 is small crack parameters, ΔK th is the crack propagation threshold (obtained from the crack growth test result in Section 3.3), F is the finite-thickness correction function (if the crack depth is much smaller than its length, F is about 1.12, and most cases of FOD are those where cracks are small [37]), and Δσ e is the fatigue limit of the smooth specimen at 10 7 cycles. Small crack parameters a 0 can be calculated by formula (11), and the stress amplitude ΔS e can be calculated by formula (10). According to the relationship between stress amplitude ΔS e and stress ratio R, the prediction value of the

10
International Journal of Aerospace Engineering HCF limit of the notch root can be calculated. The prediction results are shown in Table 4, and the error distribution graph is shown in Figure 15. It can be seen from the figure that the prediction error lies within the range of (-50%, 6%). Most prediction values of FOD flat plate specimens are lower than test values, which is considered conservative, just like the prediction results by the Peterson formula.

3.7.
Comparison. It can be seen from Figure 16 and Table 4 that the fatigue limit predicted by the Peterson formula and WCN model is both conservative, and almost all prediction error of the Peterson formula is between (-55%, -30%), while that of the WCN model is between (-50%, 20%). For the notch with damage depth Z greater than 1 mm, the predictions by the Peterson formula and WCN model are similar, and the errors are all more than 30%. The predictions by the WCN model are slightly accurate. For the notch with damage depth Z less than 1 mm, the prediction accuracy of the WCN model is higher than that of the Peterson formula, and the error lies within 32%. The results show that the WCN model is more accurate for the HCF limit prediction for specimens with small damage depth (<1 mm). The possible reasons for the prediction error are as follows. The Peterson formula is based on the point stress model. It is assumed in the Peterson formula that there is only uniaxial stress at the notch of the specimen, without considering the strengthening effect, three-dimensional stress concentration, loading conditions, and complex microdamage characteristics at the notch. Therefore, the prediction results are conservative. In the WCN model, when the notch size is small, the parameter notch depth d in formula (10) is accurate. However, when the notch size is large, the parameter is not accurate enough, so it is necessary to research the model expression more deeply.

Conclusions
FOD tests, HCF tests, and crack growth tests under stress ratio R = 0:8 were carried out for 1Cr11Ni2W2MoV stainless steel specimens. The Peterson formula and WCN model were used to predict the HCF limit of notched specimens. The results obtained in this study allow us to draw the following conclusions: (1) FOD notch sizes (damage width X, damage thickness Y, and damage depth Z) increase with the steel ball diameter, and the damage thickness Y shows great fluctuation (2) The high-speed impact of the steel ball results in a smooth extrusion area at the notch root, accompanying plastic deformation, loss of material, and microcracks at the side of the notch. These microdamage characteristics promote the initiation and propagation of fatigue cracks. Therefore, fatigue fracture occurs at the root of the FOD notch, which displays a dark fatigue source area (3) The HCF limit of FOD flat plate specimens was predicted by the Peterson formula and WCN model. The predictions by the Peterson formula are conservative, and the error lies within (-55%, -30%), except one 13.7%. The predictions by the WCN model are more accurate, especially for the damage depth Z < 1 mm (errors less than 32%). The prediction errors of the notch fatigue limit for damage depth Z > 1 mm are more than 30%, but most of them are still better than the predictions by the Peterson formula Z: damage depth; K t : calculation stress concentration factor; K f : predicted notch fatigue factor; σ P : HCF limit  Worst case notch Z < 1 mm Worst case notch 1 mm < Z < 2 mm Peterson Z < 1 mm Error 0 Error -50% Error -30% Error -55% Peterson 1 mm < Z < 2 mm

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International Journal of Aerospace Engineering predicted by Peterson formula; ΔS e : stress amplitude at the root of notch; σ W : HCF limit predicted by WCN model; σ test : HCF limit tested by HCF test; ErrorP: prediction error of Peterson formula; ErrorW: prediction error of WCN model.

Data Availability
The test data used to support the findings of this study are included within the article.

Additional Points
Highlights. (i) FOD notch size (damage width X, damage thickness Y, and damage depth Z) increases with the increase of steel ball diameter. (ii) The high-speed impact of the steel ball results in the smooth extrusion area at the notch root, accompanying plastic deformation, loss of material, and microcracks at the side of the notch. (iii) The prediction results of the Peterson formula are conservative, and the error range is (-55%, -30%). (iv) The prediction results of "Worst Case Notch" model are more accurate, especially for the damage depth Z < 1 mm, whose errors are within 32%.

Conflicts of Interest
The authors declare that they have no conflicts of interest.