Two aspects of high interfacial strength regarding the cracking behaviour of MCrAlY-coated superalloys

Abstract

In this study, we investigated the cracking behaviour of MCrAlY-coated superalloys having different interfacial strengths. A cyclic damage-coupled cohesive zone model is proposed to describe the fatigue crack initiation and propagation at the interface between the coating and the substrate. Our results indicate that a high interfacial strength leads to a significant stress concentration owing to the increasing interfacial stiffness. Moreover, high interfacial strength delays interfacial crack propagation but promotes the accumulation of deformation energy in the substrate, which accelerates fatigue crack initiation in the substrate. This work shows two aspects of high interfacial strength and can provide new insights into coating design.

Keywords

MCrAlY coating superalloys interfacial strength interfacial crack substrate crack

Introduction

MCrAlY coatings are widely applied to metallic surfaces such as those of gas turbines and aero-engines, which operate at elevated temperatures, to protect their components under corrosion and oxidation environments [1,2]. However, for MCrAlY-coated superalloys, several studies have indicated that the coating can lead to a reduction in fatigue life [3,4]. This effect is influenced by several factors, such as the loading level, coating composition, and temperature. Our previous study has shown that the coating-induced fatigue life reduction is significant when the strain range is greater than 1%. However, this effect is almost negligible when the strain range is lower than 0.8% [5]. Moreover, interfacial microstructural evolution also has a significant influence on the fatigue performance of coated superalloys. Specifically, when service temperature is greater than 980°C, interdiffusion between MCrAlY coating and superalloys resolves γ′ phase of substrate near the interface [6]. Interdiffusion destroys the solution-strengthened structures and reduces the bearing area of the coated superalloys, which leads to a significant reduction in the fatigue life [7,8]. In addition, according to Admin [9], the fatigue life reduction is significant when the temperature is lower than the ductile–brittle transition temperature (650°C for MCrAlY coatings [9] and 600°C for PtAl coatings [8]). The application of MCrAlY coating can prolong the service life of the components of gas turbines and aero-engines, but the negative effects, which are detrimental for flight safety [10,11], should also be considered.

Numerous studies have focused on the mechanism of fatigue life degradation of coated superalloys. First, the degradation can be attributed to surface crack initiation. Yang et al. [5] have shown that cracks easily initiate from the oxidation film of MCrAlY coating under cyclic loading. Subsequently, the coating crack propagates into the substrate and leads to the fracture of the coated superalloy [11,12].

Crack initiation from the coating–substrate interface and growth into the substrate also occurs due to interdiffusion [8], microstructural degradation [13], and interfacial defects of coatings [14]. Generally, crack deflection depends on the energy release rate of the interface and substrate [15]. Moreover, the deflected cracks in the substrate can cause early fracture of the coated substrate. During operation, the early failure of coated components (i.e. coated turbine blades of aero-engines) can lead to a catastrophic failure of structures. Besides, for MCrAlY-coated superalloys service at high temperatures, the interdiffusion, including the outward diffusion of Al, Ni, Co and inward diffusion of oxygen, also plays an important factor for life degradation. According to Ghadami et al. [16,17], after exposed at high temperature for several hours, the microstructures of coatings change significantly and lead early crack initiation. Furthermore, the evolution also can be delayed by many different methods, such as vacuum heat treatment, nano-crystallization, pre-oxidation, alloying with the reactive element or rare earth elements, dispersion of oxide particles, laser treatment, spark plasma sintering, hot isostatic pressing, and using multilayered/graded coating systems [18]. Therefore, understanding the propagation and deflection mechanisms of interfacial cracks could promote safety during operation. However, it should be noted that the interfacial crack deflection (focus of this study) is an important factor contributing to the early failure of the coated sample. Other factors, such as surface cracks and interfacial diffusions, are also worth investigating. Compared with surface cracks, interfacial cracks are invisible, which could lead to a catastrophic failure of components, and are worth studying in the field of engineering structures.

Owing to the limitation of high-temperature service environments, it is difficult to perform in situ tests on MCrAlY-coated samples. Therefore, several studies have used the finite element method (FEM) to investigate the fatigue failure process of coated samples. Zhang et al. [19] have used the extended FEM (XFEM) to simulate the surface crack propagation path with different interfacial roughness values. The results indicate that interface roughness has a significant influence on the stress distribution and strain energy release rate near the substrate. Wang et al. [20] have shown that the direction of crack propagation can influence the stress distribution and can change the final failure morphology of the coated superalloy. Moreover, Rehman et al. [21] have shown that the mechanical properties of the coating and substrate significantly influence the interfacial crack deflection behaviours. The coating crack is arrested at the interface when the substrate strength is approximately 1.73 times greater than the interfacial strength. However, owing to software limitations, few studies have investigated fatigue crack initiation and propagation in coated superalloys, and the competitive relationship between the interface and substrate cracks has been neglected.

In this study, the relationship between the interfacial and substrate cracks was analysed. We developed a cyclic damage-coupled cohesive element model (CZM) to simulate the fatigue cracking behaviour of the interface, and elastoplastic XFEM was employed to describe the substrate crack initiation. Based on this, the competitive initiation and growth behaviour of the interface and substrate cracks are discussed. Furthermore, the effect of the interfacial strength on the substrate crack is discussed. The results showed two aspects of high interfacial strength for coated superalloys, which could provide novel insight into coating design.

Finite element modelling

Geometry and mesh

A sine curve with an interfacial amplitude A of 3.55 μm and wavelength λ of 8.31 μm was employed to idealise the rough interface of the coated superalloys (Figure 1(b)). Owing to the periodic geometry of the interface (Figure 1(a)), only a quarter-period model was built with a refined mesh size near the interface (approximately 0.15 μm). In this study, a 2D plane strain FEM was developed to balance the efficiency and convergence of the simulations (Figure 1(c)). The plane strain calculation results might be different from the three-dimensional stress state [22], which is worth investigating in future studies. The interface geometry considers the average from previous experiments [6]. The thicknesses of the coating and substrate were 96 μm and 1 mm, respectively.

To describe the cracking behaviour of the coated superalloys, CZM and XFEM were employed to the interface and substrate, respectively. The model was composed of 6966 elements, including 298 CZM elements and 6668 plane strain elements. The CZM elements were employed on the coating–substrate interface to simulate interfacial crack initiation and growth. The plane strain elements on the substrate used an enrichment function in the XFEM simulation. The structure remained intact before the crack initiation. We mainly focused on the effect of interfacial strength on the crack initiation in the substrate; thus, the influence of cracks on the coating was neglected, which was already investigated in several previous studies [19,23].

Boundary conditions

Because of the dependence of the coating deformation on the substrate, an equation constraint was applied on the left and right sides of the model, such that the displacement on the boundary of the coating was equal to that of the substrate. The vertical degrees of freedom at the bottom were fixed (Figure 1(b)). Based on the service conditions of coated turbine blades [2], the temperature field was simplified by considering it to be uniform at 850°C. The loading conditions were similar to those in Ref. [6], with a maximum displacement of 1.2%, displacement ratio of 0.1 and loading rate of 1.5 Hz. Considering the efficiency of FEM, the simulation was stopped after 20 cycles.

Interfacial crack initiation and propagation using CZM

A cohesive element was employed at the interface to simulate interfacial crack initiation and propagation. Previous studies have used mixed models and shown that interface cracks generate and propagate owing to the complicated interfacial geometry [24,25]. Therefore, we employed Xu–Needleman [26] cohesive law that considered the coupling effect of tensile and shear loading. Notably, we employed only the cohesive law in Ref. [26], and a mechanical model was built based on the coating–substrate structures. The relation between traction T and displacement Δ is described as follows:

\begin{aligned} T = - \frac{\partial φ}{\partial Δ} . \end{aligned}

(1)

The work for interfacial separation φ is given by

\begin{aligned} φ (Δ) & = {φ_{n} + φ_{n} \exp (- \frac{Δ_{n}}{δ_{n}}) \\ \times [(1 - r + \frac{- Δ_{n}}{δ_{n}}) \frac{1 - q}{r - 1}] \\ - [q + (\frac{r - q}{r - 1}) \frac{Δ_{n}}{δ_{n}}] \exp (- \frac{{Δ^{2}}_{s}}{{δ^{2}}_{s}})}, \end{aligned}

(2)

with

\begin{aligned} q = φ_{s} / φ_{n} and r = Δ_{n}^{*} / δ_{n}, \end{aligned}

(3)

where the subscripts n and s denote tension and shear loads, respectively. The normal (T_n) and shear (T_s) attractions are expressed as follows:

\begin{aligned} T_{n} & = - \frac{φ_{n}}{δ_{n}} \exp (- \frac{Δ_{n}}{δ_{n}}) [\frac{Δ_{n}}{δ_{n}} \exp (- \frac{Δ_{s}^{2}}{δ_{s}^{2}}) \\ \times + (\frac{1 - q}{r - 1}) [1 - \exp (- \frac{Δ_{t}^{2}}{δ_{t}^{2}})] (r - \frac{Δ_{n}}{δ_{n}})], \end{aligned}

(4)

\begin{aligned} T_{s} & = 2 \frac{φ_{n}}{δ_{s}} \frac{Δ_{s}}{δ_{s}} [q + (\frac{r - q}{r - 1}) \frac{Δ_{n}}{δ_{n}}] \\ \times \exp (- \frac{Δ_{n}}{δ_{n}}) \exp (- \frac{Δ_{s}^{2}}{δ_{s}^{2}}) . \end{aligned}

(5)

The work for the complete separation of the interface with pure tension and shear loading is given as follows:

\begin{aligned} φ_{n} & = e σ_{n, max, 0} δ_{n}, \end{aligned}

(6)

\begin{aligned} φ_{s} & = \sqrt{e / 2} σ_{s, max, 0} δ_{s}, \end{aligned}

(7)

where σ_n_,max and σ_s_,max denote the tension and shear strengths of the interface, respectively. δ represents the critical displacement of the interface, which can be determined experimentally.

Moreover, considering the damage accumulation during cyclic loading, we introduce a cyclic damage variable D_c and monotonic damage D_m as follows [27]:

\begin{aligned} {\dot{D}}_{c} & = \frac{| {\dot{Δ}}_{c} |}{δ_{Σ}} (\frac{\bar{T}}{{\bar{σ}}_{max, 0}} - \frac{σ_{f}}{{\bar{σ}}_{max, 0}}) H (Δ_{c} - δ_{n}), \end{aligned}

(8)

\begin{aligned} {\dot{D}}_{m} & = \frac{max ({\bar{Δ}}_{t}) - max ({\bar{Δ}}_{t - Δ t})}{4 δ_{0}}, \end{aligned}

(9)

where δ₀ is the accumulated displacement of the interface, σ_f is the cohesive endurance and δ_Σ is the limit of accumulated cohesive length. The Heaviside function H indicates that damage is only effective when Δ _c is greater than δ_n, where

\bar{T}

and

{\bar{σ}}_{max, 0}

are the effective stress and strength, respectively, defined as follows:

\begin{aligned} \bar{T} & = \sqrt{T_{n}^{2} + T_{s}^{2} (2 e q^{2})} and \\ {\bar{σ}}_{max, 0} & = \sqrt{σ_{n, max, 0}^{2} + σ_{s, max, 0}^{2} (2 e q^{2})} . \end{aligned}

(10)

The total damage D is defined as follows:

\begin{aligned} D = \int max ({\dot{D}}_{m}, {\dot{D}}_{c}) d t . \end{aligned}

(11)

Then, the effective cohesive strength during cyclic load is expressed as

\begin{aligned} σ_{max, 0} = {σ^{'}}_{max, 0} (1 - D) . \end{aligned}

(12)

The user-defined material subroutine was employed to realise the finite element (FE) simulation of the CZM model. FE analysis was conducted using the commercial FE software ABAQUS. We first used a single-element model to verify the CZM model. The relationship between traction and displacement is shown in Figure 2.

Substrate crack initiation and propagation using XFEM

Considering the uncertainty of the crack growth path in substrate, we employed XFEM to describe the crack generation and growth in the substrate under cyclic loading, without a predefined crack growth path. The XFEM, first introduced by Belytschko and Black [28], allows local enrichment functions to be easily incorporated into a FE approximation. This method alleviates the shortcomings associated with the meshing of cracked surfaces. The presence of discontinuities is ensured by special enrichment functions, in conjunction with additional degrees of freedom. Herein, we employed a traction–separation cohesive-behaviour-based XFEM using the Abaqus/Standard software. This method differs from the CZM model, which requires the cohesive surfaces to align with element boundaries and the cracks propagate along a set of predefined paths. For XFEM, the crack growth does not depend on the element boundaries in a mesh, in which near-tip asymptotic singularity is not required, and only the displacement jump across a cracked element is considered. Crack propagation was determined by the stress/strain computed at the element centroid ahead of the crack tip [29]. The ultimate tensile stress (i.e. 1100 MPa for the superalloy at 850°C) was used as the damage initiation criterion law. The damage occurred as a linear traction–separation response once the damage initiation criterion was met. In this study, the XFEM was only activated in a superalloy substrate; thus, the substrate was selected as an enrichment feature, which allowed the presence of discontinuities in an element by enriching the degrees of freedom using special displacement functions (Figure 1(c)). Notably, owing to the limitations of the XFEM, only one crack was permitted in each element. Therefore, the branching and convergence of cracks were neglected.

Material parameters

The stress–strain curves of the substrate and coating are plotted in Figure 3 [30,31]. The thermal expansion coefficients are listed in Table 1 [32–35]. Notably, the fracture toughness of superalloys is approximately 100 MPa m^1/2 [36,37], thus the fracture density of the substrate is approximately 50 N/mm, estimated by $g_{f} = K_{I c}^{2} / E$ [38]. In this study, the fracture density was chosen as 20 N/mm to improve the calculation efficiency. Therefore, we discuss only the trend of crack initiation in substrates having different interfacial strengths.

Table 1

Temperature-dependent material properties of the coated superalloy [32–35].

Coating			Substrate
T (ˆC)	α × 10⁻⁶ (ˆC⁻¹)	υ	T (ˆC)	α × 10⁻⁶ (ˆC⁻¹)	υ
20	12.36	0.32	20	14	0.3
220	13.04	0.33	700	15	0.3
420	13.91	0.33	1000	16.6	0.3
620	14.97	0.34
820	16.22	0.35
1020	17.65	0.35

Previous experimental results have shown that the interfacial strength of MCrAlY-coated superalloys varies from 10 to 200 MPa depending on the manufacturer [39,40]. Therefore, in this study, the tension interfacial strengths σ_n_,max,0 were chosen as 20, 50, 100, and 200 MPa for different FE models (Figure 4). The shear strength σ_s_,max,0 was the same as σ_n_,max,0, according to the experimental results [39]. The model was regarded as continuous before the cracks initiated. The parameters of the traction–separation law are listed in Table 2 [27].

Table 2

Parameters for the traction–separation law model [27].

δ_n (mm)	δ_s (mm)	q	r	σ_f (MPa)
0.0002	0.0002	1	0	0.25

Moreover, we employed Norton’s power law to describe the creep behaviours of the coatings and substrate, which is defined as follows:

\begin{aligned} ε_{c r} = B σ^{n}, \end{aligned}

(13)

where ε _cr denotes creep strain. Parameters B (s⁻¹ MPa⁻ⁿ) and n represent the prefactor and power law exponents, respectively. The parameters are temperature-dependent constants and are obtained from experimental results [41,42], as shown in Table 3. It is worth mentioning that the creep effect of the coating and substrate is not significant at 850°C [43]. However, the creep option can be applied to higher temperatures. Notably, considering the difference in the deposition processes, the parameters of the coatings changed significantly. The average of the maximum and minimum values was adopted in the FE models. Furthermore, according to Ref. [20], the stress-free temperature was set as 650°C in this study.

Table 3

Creep parameters for coating and substrate [41,42].

	B (s⁻¹ MPa⁻ⁿ)	n	T (°C)
Coatings	6.5 × 10⁻¹⁹	4.6	≤600
2.2 × 10⁻¹²	3.0	700
1.8 × 10⁻⁷	1.6	≥800
Substrate	4.85 × 10⁻³⁶	1	20
2.25 × 10⁻⁹	3	1200

Results and discussion

Cracking behaviour of the coated substrate

First, the cracking behaviour of the coated substrate under cyclic loading was analysed. The interfacial strength was 20 MPa according to Ref. [39]. The results indicate that the maximum von Mises stress appears in the valley of the interface after five cycles, as shown in Figure 5(a). The stress increases from 1078 to 1227 MPa in 18 cycles. After 20 cycles, owing to the substrate crack growth, the maximum stress increases to 1532 MPa and appears on the substrate crack tip. The shear stress distribution is shown in Figure 6. The maximum shear stress appears at the off-top location near the interface, reaching 246 MPa after five cycles. Subsequently, the shear stress increases slowly with the number of cycles, increasing to 296 MPa after 18 cycles. However, after the initiation of the substrate crack, the maximum shear stress moves to the crack tip, as shown in Figure 6(d).

The simulation shows that interfacial cracks initiate earlier than substrate cracks because the interfacial strength is generally lower than that of the substrate [30,39]. The results show that interfacial crack nucleates at the off-peak location after five cycles, and then propagates along the coating–substrate interface, as shown in Figure 7(a,b). However, the substrate crack initiates near the interface valley after 18 cycles owing to the accumulated plastic deformation in the substrate, as shown in Figure 7(c). The failure process of the coated samples is shown in Figure 8. The interfacial crack initiates because of the stress mismatch between the coating and the substrate. Subsequently, the interfacial crack deflects into the coating and substrate under cyclic loading. However, it should be noted that the substrate crack can also be caused by cracks on the surface of the coatings, which has been investigated in previous studies [44,45]. In this study, we only discuss the effects of interfacial cracks.

The results indicate that the mechanisms of interfacial and substrate crack initiation are different. Under cyclic loading, the interfacial crack initiates at the off-peak location, which has the maximum shear stress. Therefore, the interfacial crack is mainly caused by shear stress and is more likely to be a type II crack. However, the substrate crack initiates near the valley of the interface in a complicated stress state, which could be the reason for the difficult prediction of substrate crack initiation in the coated samples. It is worth mentioning that the substrate crack generates before the interfacial crack reaches the valley, as shown in Figure 7(c). This phenomenon indicates that the substrate crack is not induced by interfacial crack deflection but by nucleation under cyclic deformation [46,47]. In other words, during operation, the interfacial crack contributes little to the substrate crack initiation.

Effect of interfacial strength on stress distributions

The stress distributions of the coated superalloys having different interfacial strengths are plotted in Figure 9. These results indicate that an increase in the interfacial strength can lead to an obvious stress concentration in the substrate. As shown in Figure 9(a–d), the maximum von Mises stress increases from 780 to 864 MPa when the interfacial strength increases from 20 to 200 MPa. However, the location of the maximum von Mises stress remains in the off-valley location of the interface, as shown in Figure 9.

The simulation shows that before crack initiation, the increase in interfacial strength does not change the location of the maximum von Mises stress but increases the stress value in the substrate. The increased stress level can be attributed to the different stiffnesses of the interfaces [46]. Generally, an increase in the interfacial strength results in higher interfacial stiffness, as shown in Figure 4. Therefore, when applied with the same boundary condition, a high-stiffness interface leads to a considerable stress concentration. Moreover, stress concentration can induce crack initiation and early failure of the substrate. In summary, the simulation results indicate that a high interfacial strength can facilitate coating adhesion but could be harmful to the substrate. It is worth mentioning that the results were based on the assumption of continuum mechanics. During the deposition of coatings, the change in the interfacial strength is usually accompanied by different microstructures (such as different sizes of micro-holes or micro-cracks) [48], which are harmful to the substrate and should be considered in future studies.

Effect of interfacial strength on cracking initiation of substrate

The cracking behaviours of the coated superalloys having different interfacial strengths are shown in Figure 10. Simulations show that models having different interfacial strengths have different failure morphologies. When the interfacial strength increases from 20 MPa to 100 MPa, the length of interfacial crack decreases from 8.8 to 7.2 μm after 20 cycles, as shown in Figure 10(a–c). The final length of the substrate crack reaches 0.60, 0.65 and 0.72 μm for models having interfacial strengths of 20, 50 and 100 MPa, respectively. For the model having an interfacial strength of 200 MPa, the calculation is nonconvergent and stops after 15 cycles, with an interfacial crack of 4.8 μm and a substrate crack of 2.57 μm, as shown in Figure 10(d). The number of cycles required for substrate crack initiation is plotted in Figure 11. For the model having an interfacial strength of 20 MPa, the substrate crack initiates after 18 cycles. However, for the model having an interfacial strength of 200 MPa, the substrate crack initiates after 12 cycles.

The simulation results indicate that the increase in interfacial strength can prevent the propagation of interfacial crack and promote the initiation of substrate crack. According to Madani et al. [49], for bi-material structures, the penetration or the deviation of the crack depends on the fracture energy of materials constituting the assembly. The propagation of substrate cracks usually leads more energy release rate [50]. For the coated superalloys, the long-time exposure at high temperature would lead to decrease the coating–substrate interface. Therefore, in those cases, the cracks are more likely to propagate along the interface instead of deflected into the substrate. Moreover, the interfacial crack propagation consumed the strain energy and delayed the substrate crack initiation. Therefore, the strength degradation (i.e. decline of strain energy release rate) of the substrate is beneficial to the interface crack deflection. The change in the substrate crack initiation could be attributed to the strain energy release in the coated superalloys. For models having a low interfacial strength, the interfacial crack initiates easily under cyclic loading, thereby releasing the strain energy of the coated superalloys. Conversely, a high interfacial strength prevents the interfacial crack from propagating; thus, the deformation energy accumulates in the coated superalloys and leads to crack initiation.

The simulation results indicated that a high interfacial strength might be harmful to substrate integrity. Many previous studies investigate the relation between the vertical and interfacial cracks in the coatings. Jian et al. [32] and Zhang et al. [19] using XFEM method simulate the crack propagation path of coatings under thermal fatigue loading. The results show that the cyclic thermal loading could lead to horizontal and vertical crack propagation in the coatings. Rehman et al. [21] investigated the vertical crack in coatings using CZM method, which is helpful to understand the mechanics of the stress transfer from a ductile substrate to a brittle coating and the failure of coating segments by normal cracking. However, the interdiffusion-induced strength degradation and substrate crack propagation still not received enough recognitions. According to Refs. [15,51], the interfacial crack can propagate into the substrate and lead to an early failure of the substrate when the interfacial energy release rate is greater than that of the substrate. Our simulation results also indicated that after exposed at high temperatures, the deflection of interfacial cracks might be one of the key factors for the decline of fatigue life. Therefore, a lower interfacial stress could maintain crack growth at the interface, delaying crack growth into the substrate. A suitable interfacial strength should be considered to improve both the adhesive performance of the coatings and the substrate strength under cyclic loading. However, this conclusion might neglect the effect of coating cracks. During service, surface cracks in coatings have a significant effect on the failure of the coated samples [45]. The change in interfacial strength could influence the strength of the coatings, which should be investigated in future studies.

Conclusions

In this study, an FEM was proposed to simulate interfacial and substrate crack initiation in coated superalloys under cyclic loading. A cyclical damage-coupled CZM was used for the interface, and an elastic–plastic XFEM was employed for the coating and substrate. The model could describe the interfacial and substrate cracking behaviours, which was in good agreement with the previous experimental results. The main conclusions are listed as follows:

The simulation indicated that the initiation of interfacial cracks was caused by shear stress at the off-peak location on the interface.

The substrate crack was generated from the off-valley location, which was induced by the stress concentration of the rough interface, instead of the deflection of the interfacial cracks.

The increase in the interfacial strength led to a high interfacial stiffness and increased the stress value in the coated superalloys.

The calculation results indicated that a high interfacial strength could prevent crack propagation at the interface but facilitated substrate crack initiation. Therefore, a suitable interfacial strength should be considered to prolong the fatigue life of the coated superalloys.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the authors.

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