Low-cycle fatigue of MCrAlY-coated superalloys: A fracture mechanics-based analysis

Abstract

A fracture mechanics-based method was proposed to quantify the low-cycle fatigue (LCF) life reduction of superalloys deposited with MCrAlY coating. A series of LCF tests were conducted under different temperatures to verify the accuracy of the model. The effect of the coating shows temperature-related behaviour. At 980°C, the coating reduced the LCF life of the samples. Furthermore, the coating-induced fatigue life reduction increased with the stress amplitude. However, at 850°C, the coating was beneficial to the fatigue life at low-stress amplitudes but harmful at high stress amplitudes. Based on the aforementioned data, a life-prediction model of the coated superalloy was proposed that agreed well with the test results.

Keywords

Life prediction fracture mechanics MCrAlY coating LCF directional superalloy

Introduction

Owing to excellent properties, such as oxidation and corrosion resistance, MCrAlY (M presents Ni or/and Co) coatings are widely applied to turbine blades of aero engines to increase the service temperature of the blade [1,2]. However, some studies showed that the coating might be harmful to the fatigue or creep rupture life of Ni-based substrates [3,4]. The life degradation of superalloys after coating with MCrAlY could be attributed to the interdiffusion between MCrAlY coatings and substrate. According to Ref. [4 -6], after coating with MCrAlY, hard and brittle particles were easily initiated on the interface between the coating and substrate, which is referred to as the interdiffusion zone (IDZ). On one hand, the generation of IDZ changes the mechanical properties and expansion of the coating–substrate interface, thereby resulting in the life degradation of the coated substrate. According to Texier [7], the coating decreases the tensile strength of IDZ due to the interdiffusion between the coating and Ni-based substrate. On the other hand, defects, such as voids and non-adherent grit-blasting particles in the IDZ, could become the source of fatigue cracks under cyclic loading and induce fatigue life degradation of MCrAlY-coated superalloys [8,9].

Several previous studies investigated the low-cycle fatigue (LCF) behaviours of coated superalloys. Many previous studies compared the microstructure of coated and uncoated superalloys and showed that the coating process could change the microstructure of the substrate surface [10,11]. Moreover, for some Ni-based superalloys, the change could result in fatigue strength degradation of the substrate [7,12]. However, other studies showed that the coating is beneficial to the LCF performance of superalloys as the coating protects the substrate from oxidation at elevated temperatures and prolongs the fatigue life of coated superalloys [4,13]. Generally, by considering the microstructure and fracture behaviour of coatings, the fatigue life of coated samples can be influenced by various factors, including the material of coating and substrate, coating manufacturing process test temperature, and stress amplitude [3,14]. Furthermore, considering that fatigue cracks are likely to initiate on the coating–substrate interface, the bond strength of the interface also has a significant influence on the fatigue life of the coated samples [12,15 -17].

However, it is difficult to characterise fatigue crack initiation or propagation life in the coating, especially at elevated temperatures. Thus, the effect of coating on fatigue life reduction cannot be quantified. Several previous studies investigated the fatigue life of coated samples, and many types of continuum damage method (CDM) life-prediction models were built [3,14,18]. However, those life models could only characterise the fatigue life of entire samples, which cannot separate the contribution of the coating on the fatigue life change. Compared to CDM, fracture mechanics can divide the fatigue life of samples into different steps and analyse the contribution of each part quantitatively. Hence, the fracture mechanics-based fatigue life-prediction method was applied to samples with different surface states [19,20] and test environments [21].

In this study, a fracture mechanics-based fatigue life model was proposed to calculate the fatigue life of coated samples, which quantified the fatigue life of the coating and base materials. Based on the microstructure of the coated samples, the fatigue life was divided into two parts, i.e. the life of the coating and substrate. Subsequently, LCF tests were conducted at 850 and 980°C to verify the accuracy of the fatigue life model.

Life-prediction model

Substrate cracking behaviour

The fatigue life of the MCrAlY-coated samples can be divided into three parts: (i) fatigue life of the MCrAlY coating, (ii) fatigue life of IDZ, and (iii) fatigue life of the substrate. Thus, the fatigue life of the MCrAlY-coated samples can be formulated using Equation (1). (1) where N_coating, N_IDZ, and N_SUB represent the fatigue life of the coating, IDZ, and substrate, respectively. Generally, fatigue cracks are more likely to initiate from surface-coated samples that are subjected to LCF loading [13,14,22]. However, Equation (1) is only valid for failure induced by surface cracks.

Moreover, the fatigue life of specimens can be divided into two stages. (2) Here, N_CAA represents the fatigue life of the coating-affected area, including the fatigue life of the coating and IDZ. A schematic of the surface crack growth is shown in Figure 1. The fatigue life of the oxidation layer is included in N_CAA. Moreover, as the duration of the LCF test was short, the thickness of the oxidation layers under different temperatures was assumed to be similar. Considering the thickness ratios of the oxidation layers and MCrAlY coating, this assumption is acceptable.

Compared to the substrate, there are more defects in the coating; therefore, the cracks are more likely to initiate from the coating [7,22,23]. Furthermore, the cracks in the coating would change the stress state and accelerate crack growth in the substrate [24,25]. However, it is difficult to measure the fatigue life in this area. In this study, we estimated the fatigue life of coating-affected areas by calculating the residual fatigue life of the substrate based on fracture mechanics. In this study, the surface crack was assumed to be of an elliptical shape, which was adopted in many previous studies [23,26,27]. Generally, the stress intensity factor of a surface crack is calculated by Newman's method [28]. (3) where Δσ represents the remote uniform tension stress and a is the crack depth. Q and F are the functions of the crack shape. To simplify the calculation process, we used an empirical equation to calculate the stress intensity factor at the crack front, where Q and F were replaced by an empirical function g, as follows [29]: (4) (5) and the empirical parameters , , , , and were calculated, as shown in Equation (6). (6)

Here, parameter a is the crack depth and c is the width of the cracks, as shown in Figure 2. The aspect ratio of the surface crack was set to 0.45. φ represents the location of the crack tip and t is the thickness of the samples, which was assumed to be 6 mm in this study. Nevertheless, above parameters were consistent with our experimental results [3].

When the surface crack propagates into the substrate, the residual fatigue life can be described using the Paris law [22,30 -33]: (7) where P and m are temperature-dependent coefficients calculated from the crack growth test [34]. Thus, the fatigue life of the substrate was calculated using the integral equation of Equation (6), as follows: (8) where a₀ is the initial crack length equal to the thickness of the coating (41.5 µm), as observed in section “Microstructure of MCrAlY-coated superalloys”. The critical crack length a_t, which was equal to 0.6 mm, was determined by fracture toughness [35,36] observed from the fracture surface.

Therefore, after obtaining N_sub, the fatigue life of the coating-affected area can be calculated using Equation (2). As mentioned above, when subjected to LCF loading, the MCrAlY coating induces surface degradation of the substrate due to the generation of IDZ and element diffusion. In this study, we define degradation as a kind of initial damage, and the fatigue life of a coating affected by N_CAA is presented using the Chaboche model [37,38].

Life model of coating

Fracture mechanics are suitable for crack-containing solids and used to calculate the residual crack propagation life of the component. However, it is difficult to predict the crack-initiation life using the fracture mechanics method. Therefore, in this study, we calculated the fatigue life of the coating-affected area N_CAA using continuum damage mechanics. The fatigue life model is shown in Equation (9) [37,38]. (9)

The integral form of Equation (8) is shown in Equation (10). (10)

The empirical constants D_f, M₀, α, β, and b can be fitted using experimental data.

As the coating decreases the fatigue life of the substrate [10,11], we used the initial damage D₀ to characterise the damage induced by the coating process based on the effective loading area of the substrate [39 -42]. (11) where r and d_IDZ represent the radius of the samples and depth of IDZ, respectively, related to the microstructure morphology of the as-deposited samples. In this study, r is equal to 3 mm and d_IDZ is 15 µm, as discussed in section “Microstructure of MCrAlY-coated superalloys”.

The fatigue life of the coating-affected area and substrate were calculated using Equations (7) and (9), respectively. Thus, the fatigue life of the coated samples can be predicted. Furthermore, the effect of the coating on fatigue life degradation was analysed quantitatively.

Experimental verification

To verify the accuracy of the fatigue life-prediction model, we conducted LCF tests on MCrAlY-coated directional superalloys.

The {001} crystal direction of the substrate is similar to the load direction, and the chemical composition is plotted in Table 1. The MCrAlY (in this study, M represents Ni) coating was deposited using the electron beam physical vapour deposition method at a deposition temperature of 850°C and pressure of 10⁻² Pa. The chemical composition of the coating is shown in Table 2. The coated specimen was cut and the cross-section was polished. The microstructure of the polished section was subjected to scanning electron microscopy (SEM), as shown in Figure 3.

Table 1

Nominal chemical compositions of the substrate (wt-%).

Elements	Ni	C	Cr	Co	W	Mo	Al	Ti	Ta	Hf	B
Wt-%	Bal	0.1	8.90	10	7	2	5.20	0.9	3.8	1.5	0.015

Table 2

Nominal chemical compositions of the MCrAlY coating (wt-%).

Elements	Al	Cr	Ni	Y
wt-%	6.42	12.48	80.33	0.76

The load-controlled LCF test was conducted using a SHIMAZU hydraulic universal testing machine and electric. Considering the service temperature of the turbine blade substrate, the experiments were conducted at 850 and 980°C. Because the yield stress and Young's modulus of the substrate changes with temperature. In this study, the maximum stresses were 800, 760, 720, 680, and 640 MPa at 850°C and 480, 440, 400, and 360 MPa at 980°C to obtain appropriate results. The load conditions and temperatures of the LCF test are listed in Table 3. At each loading condition, the LCF test was conducted on coated and uncoated samples to investigate the effect of coatings on the LCF life of superalloys. Additionally, the mean stress was calculated based on the geometry of the bare samples. The stress ratio R was equal to zero and the loading rate was 400 MPa s⁻¹. Both coated and uncoated samples were tested at the same loads and temperatures to investigate the coating effect.

Table 3

Loading and temperature condition of LCF tests.

No.	Surface condition	Temperature (°C)	Maximum stress (MPa)
980-B1	Bare	980	480
980-B2			440
980-B3			400
980-B4			360
980-C1	Coated	980	480
980-C2			440
980-C3			400
980-C4			400
980-C5			360
850-B1	Bare	850	800
850-B2			760
850-B3			760
850-B4			720
850-B5			720
850-B6			720
850-B7			680
850-B8			680
850-B9			640
850-B10			640
850-B11			640
850-C1	Coated	850	800
850-C2			800
850-C3			760
850-C4			760
850-C5			720
850-C6			680
850-C7			680
850-C8			640

Furthermore, a microhardness test was conducted to determine the variation of hardness along the thickness direction for a load of 0.3 kg and dwell time of 15 s [43]. Thus, 20 nodes were selected on the cross-section of the coated specimens near the coating-substrate interface. The hardness of each node was determined as the average of three measurements.

Results and discussion

Microstructure of MCrAlY-coated superalloys

The microstructures of the MCrAlY-coated samples are shown in Figure 3. The coating, which was approximately 41.5 µm thick, was deposited on directional superalloys, with a columnar crystal structure.

The IDZ layer, which was approximately 1.5 µm thick, was generated during the deposition process owing to the element interdiffusion behaviour of the substrate and coating [5,6]. However, hardness is a function of the elastic modulus and material strength, which can present the mechanical properties of materials qualitatively. In this study, we measured the hardness along the radial direction of the longitudinal section of the coated samples. Several isometric points were conducted; the results are shown in Figure 4. According to the results, the hardness of the coating increases with depth initially and then decreases to 472 HV near the interface. Furthermore, the hardness of IDZ was greater than that of the substrate, as shown in Figure 4. The increase in hardness near the interface was mainly caused by residual stress and interdiffusion during the deposition process [5,9]. However, the change in hardness at elevated temperatures would be different from that at room temperature [44]. Nevertheless, the hardness change indicates that the coating process has some effect on the mechanical behaviour of the substrate.

Fatigue crack propagation behaviour

The longitudinal section of the coated sample and fracture surface was observed via SEM. The effect of temperature and stress amplitude on the crack behaviour of the coated and uncoated samples was characterised by microstructural observations.

Owing to the defects caused during deposition, fatigue cracks were more likely to initiate in the coating at elevated temperatures [23]. During the LCF tests, as shown in Figure 5, cracks generated in the coating and propagated into the substrate. Therefore, the model introduced above can be applied to the tests. Furthermore, the cracks in the coating would induce stress concentration and oxidation-associated crack growth, thereby accelerating the failure of the substrate.

Effect of MCrAlY coating on crack initiation and propagation

As mentioned above, the fatigue life of the coating affected by N_CAA can be calculated using fracture mechanics. The effect of stress amplitude and temperature on the fracture behaviour is shown in Figures 6 and 7. For bare samples, N_CAA represents the fatigue life of crack initiation and propagation when the crack length is equal to the thickness of the coating-affected area. This shows the effect of coating on crack-initiation life.

Compared to bare samples, the coating might reduce the crack-initiation and -propagation life at 980°C. As shown in Figure 6, the coating-induced fatigue-life reduction changed with the stress amplitude at 480, 440, and 400 MPa. Considering the variation in the LCF tests, we employed the error bar to present the dispersibility of test results. Moreover, according to the linear regression results, the difference in N_CAA between the coated and uncoated samples increased with stress amplitude. When the stress amplitude decreased to 360 MPa, the coating seemed to have a smaller influence on the fatigue life of the substrate compared to other stress amplitudes.

However, at 850°C, the stress amplitude seemed to have a greater influence on N_CAA. As plotted in Figure 7, the coating decreases N_CAA at 800 MPa. However, when the stress amplitude was reduced to 760 MPa, the difference in N_CAA between the coated and uncoated samples was small. Furthermore, if the stress amplitude was lower than 720 MPa, the N_CAA of the coated sample was greater than that of the uncoated samples. This indicates that the samples coated at 850°C subjected to lower stress amplitude would have a longer fatigue life [3]. The entire fatigue life N_f has the same trend as N_CAA, suggesting that the difference in fatigue life between coated and uncoated samples might be related to the fatigue life of the coating-affected areas.

The value of N_CAA/N_f could represent the contribution of surface crack initiation to sample failure.

The increase in N_CAA/N_f indicates that more cycles were consumed by the initiation of surface cracks. When the value of N_CAA/N_f reaches 1, the surface crack-initiation life is equal to the entire fatigue life of the sample; this could be considered as brittle fracture.

As shown in Figure 8, for the applied lower stress amplitude at 980°C, the crack-initiation life is approximately 97% of the entire fatigue life for the coated and uncoated samples. As the stress amplitude is increased, the value of N_CAA/N_f decreases quickly. The reduction in N_CAA/N_f value indicated that the cracks can easily initiate and propagate into the substrate at high stress amplitudes, as shown in Figure 8. The proportion of N_CAA/N_f presented a nonlinear relationship with the stress amplitude. Moreover, the proportion drops from 95 to 77% when the stress amplitude increases from 440 to 480 MPa. This reduction might be related to the fracture of the brittle oxidation layer and oxidation-associated crack growth of bare samples, considering that the high-temperature fatigue tests were conducted in the atmospheric environment [45,46]. Compared to the bare samples, the coated samples showed a linear decrease when the stress amplitude was increased. Furthermore, the proportion of coated samples was still less than that of the uncoated samples. Thus, the cracks are more likely to initiate in the coating-affected area, which would be a major reason for coating-induced fatigue life degradation. Notably, the conclusion is valid for the stress amplitude and temperature mentioned above. Moreover, different loading and service temperatures would change the mechanical behaviour of the coating, resulting in different conclusions [47].

Contrarily, according to the calculation results, the coated and uncoated samples had a higher N_CAA/N_f value at 850°C than that obtained at 980°C, as shown in Figure. 9. Moreover, the results indicated that surface crack initiation is important for both coated and uncoated samples. However, the proportion decreased linearly with the stress amplitude. Furthermore, a critical stress amplitude was observed at approximately 680 MPa for the MCrAlY-coated samples. Interestingly, the proportion had the same trend as N_CAA, as plotted in Figure 6. The calculation results indicate that the uncoated samples seemed to have a lower fatigue life proportion of N_CAA/N_f decreasing rate than that of the coated samples. According to previous studies, the coating has a negative effect on surface-crack initiation and decreases the fatigue life of superalloys, especially at high stress amplitudes [10,11]. However, due to the limitation of LCF in this study, the conclusion should be verified using additional experimental studies.

In this study, we found the critical stress amplitude for MCrAlY-coated samples. When the stress amplitude was greater than the critical value, the coating was harmful to the fatigue life of the substrate in which cracks were easily initiated in the coating and propagated into the substrate [48,49]. Furthermore, the cracks cause the coating to lose antioxidant protection [50] and accelerate crack propagation [51]. When the loadings are lower than the critical stress, the cracks are not easily initiated in the coating. Therefore, the coating could prevent the substrate from oxidation and prolong the fatigue life.

As the mechanical behaviour and coating strength are influenced by temperature [51], the critical stress of the coated samples showed temperature-related behaviour. The critical stress was approximately 360 MPa at 850°C. Furthermore, the critical stress increased to 760 MPa when the temperature reached 980°C. Thus, the critical stress, which is related to the facture behaviour of the coating, is increased with temperatures [52]. It is worth mentioning that the critical stress is influenced by different materials and manufacturers. In this study, the value of critical stress is only applicable to special manufacturing, as mentioned in the Section “Results and discussion”. Furthermore, considering the dispersibility of LCF tests, we only discussed the change in trend for coated and uncoated superalloys. However, additional experimental results are needed to obtain an accurate value of critical stress, which should be analysed in future work.

Life prediction

During the application of the model, it was assumed that there was no initial damage to the bare samples. For coated samples, the interdiffusion and manufacturing process would induce microstructural changes near the interface during the spring process, as mentioned in the Section “Microstructure of MCrAlY-coated superalloys”. Thus, we defined the initial damage to be 0.0047 based on the depth of microstructure change, as obtained using Equation (10). Here, the initial damage D₀ is a dimensionless variable related to the microstructure of the specimens. Therefore, the initial damage would be different when the coating is deposited by different manufacturing process. However, the process has no effect on the calculation method, as illustrated in Equation (10), and the fatigue life model is applicable.

The accuracy of the fatigue life-prediction model was verified by the LCF test at different temperatures. The parameters of Equation (9) were fitted using parts of the fatigue test results, as plotted in Tables 4 and 5. Furthermore, another result of the LCF test was used to verify the accuracy of the models and parameters. The prediction results are plotted in Figures 10 and 11 for the coated samples at different temperatures. The solid node presenting the data was used for parameter fitting in the fatigue life model, and the hollow node was the calculation result to verify the accuracy of the model. The calculated fatigue life of the coated samples fitted well with the LCF test results, and the scattering zone of the predicted fatigue life was less than 1.8, which implies that the predicted fatigue life was 1.8 times more (or less) than the experimental results. This indicated that the proposed model captured the coating effect properly.

Table 4

The parameters of life prediction model under 980°C.

α ₁	β ₁	M ₀₁	b ₁	D_f ₁
31.66	14.62	4.86	0	0.99

Table 5

The parameters of life prediction model under 850°C.

α ₂	β ₂	M ₀₂	b ₂	D_f ₂
28.19	13.09	9.08	0	0.99

Conclusion

In this study, a fracture mechanics-based life-prediction model was proposed to calculate the fatigue crack-initiation and -propagation life of a coated superalloy, which quantified the coating-induced fatigue life reduction. A series of LCF tests were conducted at different temperatures to verify the accuracy of the fatigue life model. The results are summarised as follows:

The coating reduced the crack-initiation life and accelerated the failure of the coated samples at 980°C. The increase in stress amplitude would significantly reduce the proportion of crack initiation life of the coated samples at 980°C.

Critical stress was observed for MCrAlY-coated samples at 850°C. When the applied loading was greater than the critical stress, the coating accelerated the initiation of surface cracks, whereas the coating protected the substrate from oxidation at elevated temperatures and delayed the initiation of fatigue cracks. The proportion of crack-initiation life decreased slightly with the stress amplitude at 850°C. Additionally, critical stress of fatigue life was observed for coated samples.

The new fatigue life-prediction model fitted well for coated samples, both at 980 and 850°C.

Footnotes

Acknowledgments

The authors would like to thank the National Natural Science Foundation of China (No. 51605015), the Fundamental Research Funds for the Central Universities (No. YWF-19-BJ-J-338) and the Academic Excellence Foundation of BUAA for PhD Students for the support given to this research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

References

Nicholls

JR.

Advances in coating design for high-performance gas turbines. MRS Bull. 2003; 28(9):659–670.

Walston

Cetel

MacKay

Joint development of a fourth generation single crystal superalloy. NASA STI Report Series. 2004: 15–24.

Yang

Effect of MCrAlY coating on the low-cycle fatigue behavior of a directionally solidified nickel-base superalloy at different temperatures. Int J Fatigue. 2015; 75:126–134.

Huang

Wang

Zhu

Effect of HVOF Sprayed MCrAlY coating on Thermomechanical and Isothermal fatigue life of superalloy M963. Key Eng Mater. 2008; 373-374:23–26.

Elsaβ

Frommherz

Scholz

Interdiffusion in MCrAlY coated nickel-base superalloys. Surf Coat Technol. 2016: 307: 565–573.

Taylor

Pragnell

Evans

HE.

Evidence for the formation of Al-rich reservoir phases resulting from interdiffusion between MCrAlY coating and Ni-based substrate. Mater Sci Forum. 2004; 461-464:239–246.

Texier

Monceau

Hervier

Effect of interdiffusion on mechanical and thermal expansion properties at high temperature of a MCrAlY coated Ni-based superalloy. Surf Coat Technol. 2016; 307:81–90.

McGrann

RTR

Greving

Shadley

The effect of coating residual stress on the fatigue life of thermal spray-coated steel and aluminum. Surf Coat Technol. 1998; 108-109(none):59–64.

de Camargo

JAM

Cornelis

Odila Hilário Cioffi

Coating residual stress effects on fatigue performance of 7050-T7451 aluminum alloy. Surf Coat Technol. 2007; 201(24):9448–9455.

10.

Ray

Dwarakadasa

Das

Fatigue behavior of a thermal barrier coated superalloy at 800 C. Mater Sci Eng, A. 2007; 448(1):294–298.

11.

Rhys-Jones

Cunningham

TP.

The influence of surface coatings on the fatigue behaviour of aero engine materials. Surf Coat Technol. 1990; 42(1):13–19.

12.

Pollock

Laux

Brundidge

Oxide-assisted degradation of Ni-base single crystals during cyclic loading: the role of coatings. J Am Ceram Soc. 2011; 94:s136–s145.

13.

Wood

MI.

Mechanical interactions between coatings and superalloys under conditions of fatigue. Surf Coat Technol. 1989; 39:29–42.

14.

H-Y

Yang

J-S

Yang

X-G

Fatigue behavior of uncoated and MCrAlY-coated DS nickelbased superalloys pre-exposed in hot corrosion condition. Rare Met. 2018; 11: 936–941.

15.

Ito

Saito

Ishiwata

Bending fatigue life properties of MCrAlY alloy coating systems: study of life properties of high-temperature corrosion-resistant coating systems (4th report). Weld Int. 1999; 13(2):6.

16.

Uematsu

Tokaji

Takekawa

Effect of thick DLC coating on fatigue behaviour of magnesium alloy in laboratory air and demineralised water. Fatigue Fract Eng Mater Struct. 2010; 33(9):607–616.

17.

Fukui

Murakami

R-i

Yonekura

Effects of dynamic ion mixing coating condition for fatigue properties of Stainless Steel with TiN film. Key Eng Mater. 2007; 353-358:1875–1878.

18.

Chataigner

Remy

Thermomechanical fatigue behaviour of coated and bare Nickel-based superalloy single crystals. In: Thermomechanical fatigue behavior of materials: second volume. ed. M. Verrilli and M. Castelli. West Conshohocken, PA: ASTM International; 1996. p. 3–26.

19.

Golden

Calcaterra

JR.

A fracture mechanics life prediction methodology applied to dovetail fretting. Tribol Int. 2006; 39(10):1172–1180.

20.

Liu

Chen

Fatigue and crack growth behavior of pre-corroded aluminum alloy 2024-T62 and its life prediction based on fracture mechanics. Acta Aeronaut Astronaut Sin. 2011; 32(1):107–116.

21.

Gnagloff

RP.

Crack tip modeling of hydrogen environement embrittlement: application to fracture mechanics life prediction. Mater Sci Eng, A. 1988; 103(1):157–166.

22.

Shi

Influence of surface recrystallization on the low cycle fatigue behaviour of a single crystal superalloy. Fatigue Fract Eng Mater Struct. 2015; 38(3):340–351.

23.

Bussac

Lautridou

JC.

A probabilistic model for prediction of LCF surface crack initiation in PM alloys. Fatigue Fract Eng Mater Struct. 1993; 16:861–874.

24.

Rahmani

Nategh

Influence of aluminide diffusion coating on low cycle fatigue properties of René 80. Mater Sci Eng, A. 2008; 486(1):686–695.

25.

Rahmani

Nategh

Mechanical properties of uncoated and aluminidecoated René 80. Metall Mater Trans A. 2010; 41(1):125–137.

26.

Murakami

Keer

LM.

Stress intensity factors handbook, Vol. 3; 1989.

27.

Soady

Mellor

Fatigue crack growth behaviour in the LCF regime in a shot peened steam turbine blade material. Int J Fatigue. 2016; 82:280–291.

28.

Newman

Raju

IS.

An empirical stress-intensity factor equation for the surface crack. Eng Fract Mech. 1981; 15:185–192.

29.

Xiang

Zhixue

New empirical stress-intensity-factor equations for surface cracks. Eng Mech. 2008; 25(7):35–39. (in Chinese).

30.

Raju

Newman

JC.

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates. Eng Fract Mech. 1979; 11(4):817–829.

31.

Kou

KP.

Stress intensity factor of a Wide Range of Semi-elliptical partly through-wall crack in a finite-thickness plate. Computational Methods in Engineering & Science. Springer, Berlin, Heidelberg. 2006: 197–197.

32.

Hayashi

Abé

Stress intensity factors for a semi-elliptical crack in the surface of a semi-infinite solid. Int J Fract. 1980; 16(3):275–285.

33.

Anderson

TL.

Fracture mechanics: fundamentals and applications. CRC Press; 1991. New York, US.

34.

Shi

Yang

Influence of orientation and temperature on the fatigue crack growth of directionally solidification superalloys DZ125. MATEC Web of Conferences 2018, 165, 13014.

35.

Shi

Yang

The effect of inclusion factors on fatigue life and fracture-mechanics-based life method for a P/M superalloy at elevated temperature. Int J Fatigue. 2019; 131: 105–365.

36.

Shi

Yang

The influence of temperature and orientation on fatigue crack growth behavior of a directional solidification nickel-based superalloy: experimental investigation and modelling. Int J Fatigue. 2019; 125:505–519.

37.

Chaboche

Lesne

PM.

A non-linear continuous fatigue damage model. Fatigue Fract Eng Mater Struct. 1988; 11:1–17.

38.

Chaboche

JL.

Continuum damage mechanics: part II damage growth, crack initiation, and crack growth. J Appl Mech. 1988; 55:65–72.

39.

Kim

Kang

Yeom

Continuum damage mechanics-based creep-fatigue-interacted life prediction of nickel-based superalloy at high temperature. Scripta Mater. 2007; 57:1149–1152.

40.

Dattoma

Giancane

Nobile

Fatigue life prediction under variable loading based on a new non-linear continuum damage mechanics model. Int J Fatigue. 2006; 28:89–95.

41.

Giancane

Nobile

Panella

Fatigue life prediction of notched components based on a new nonlinear continuum damage mechanics model. Procedia Eng. 2010; 1:1317–1325.

42.

Shang

Sun

Deng

Nonlinear cumulative damage model for multiaxial fatigue. Front Mech Eng China. 2006; 1:265–269.

43.

Osman

Hoziefa

Escuder

Comparative study between high-velocity oxygen fuel and flame spraying using MCrAlY coats on a 304 stainless steel substrate. J Mater Res Technol. 2019; 8(5):4253–4263.

44.

Passilly

Kanoute

Leroy

High temperature instrumented microindentation: applications to thermal barrier coating constituent materials. Philos Mag. 2006; 86(33-35):5739–5752.

45.

Zhang

Influence of oxidation on the cracks of DZ125L nickel-based superalloy thin-walled parts in laser metal direct forming. Rapid Prototyp J. 2013; 19(6):446–451.

46.

H-Y

Liang

X-B

S-L

High-temperature oxidation behavior of DZ125 Ni-based superalloy under tensile stress. Rare Met. 2016; 1: 1–6.

47.

Lafata

Rettberg

Mercer

Sustained peak low-cycle fatigue in single crystals with equilibrium γ-γ′ coatings/superalloys 2016: Proceedings of the 13th Intenational Symposium of Superalloys. Hoboken, NJ: Wiley; 2016, pp. 405–413.

48.

Ranke

Durst

Microstructure and local mechanical properties of Pt-modified nickel aluminides on nickel-base superalloys after thermo-mechanical fatigue. Mater Sci Eng, A. 2007; 467(1):15–23.

49.

Oskay

Rudolphi

Evolution of microstructure and mechanical properties of NiAl diffusion coatings after thermocyclic exposure. Intermetallics. 2017; 89:22–31.

50.

Chen

Wang

Zhu

SJ.

Tensile fracture behavior of thermal barrier coatings on superalloy. Surf Coat Technol. 2011; 205(15):3931–3938.

51.

Obrtlík

Pospíšilová

Juliš

Effect of Al and Al-Si diffusion coating on the low cycle fatigue behavior of Inconel 713LC. Procedia Eng. 2011; 10(7):1361–1366.

52.

Texier

Monceau

Crabos

Tensile properties of a non-line-of-sight processed β-γ-γ′ MCrAlY coating at high temperature. Surf Coat Technol. 2017; 326:28–36.