Interface fracture toughness in thermal barrier coatings by cross-sectional indentation

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Acta Materialia 60 (2012) 6152–6163 www.elsevier.com/locate/actamat

Interface fracture toughness in thermal barrier coatings by cross-sectional indentation Xin Wang a,⇑, Changjiang Wang b, Alan Atkinson a b

a Department of Materials, Imperial College, London SW7 2BP, UK School of Engineering and the Built Environment, University of Wolverhampton, Wolverhampton WV1 1LY, UK

Received 7 July 2012; received in revised form 26 July 2012; accepted 28 July 2012 Available online 23 August 2012

Abstract The interface fracture toughness of thermal barrier coatings (TBCs) on high-pressure turbine blades manufactured by electron beam physical vapour deposition was measured by a cross-sectional indentation (CSI) method. Scanning electron microscopy and luminescence mapping were employed to reveal that coating delamination induced by CSI was predominantly along the thermally grown oxide–bond coat interface and the shape of the delaminated area was approximately semicircular. The critical energy release rate (Gc) for delamination was calculated based on a clamped circular plate model. Analysis of the stored energy release revealed that the residual stresses in the coating do not contribute to the total energy release rate provided that the delaminated area of the coating does not buckle. Therefore, for this method, detailed information of residual stresses is not necessary for the determination of interface fracture toughness. However, intercolumnar microfracture and shear displacement in the YSZ top coat can lead to significant overestimation of the interface fracture toughness in some situations. A method of specimen preparation is described to inhibit these effects. The interface fracture resistance of the TBCs was found to be 29 ± 9 J m2 after between 35 and 100 thermal cycles (from room temperature to 1150 °C with 1 h duration). Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Thermal barrier coating (TBC); Interface toughness; Cross-sectional indentation (CSI); Residual stress; Finite-element modelling (FEM)

1. Introduction Thermal barrier coatings (TBCs) are employed in the hot sections of turbine engines to protect the superalloy components and improve the efficiency of the engines. Most commercial TBCs have a multilayer structure. Nibased superalloy employs a metallic bond coat on its surface to give protection against high-temperature oxidation and a yttria-partially stabilized zirconia (YSZ) coating is deposited on top as the outer low-conductivity thermal barrier. For turbine blades the YSZ is usually deposited by electron beam physical vapour deposition (EBPVD) and is typically between 100 and 200 lm in thickness. Between the bond coat and the YSZ, a thermally grown ⇑ Corresponding author. Tel.: +44 20 75496809; fax: +44 20 75946757.

E-mail address: [email protected] (X. Wang).

oxide (TGO) layer of mainly Al2O3 forms as a result of oxidation of the metallic bond coat. After a certain period of service the ceramic layer(s) can delaminate (spall) from the metallic components, leaving them in an unprotected state. Coating lifetime is strongly dependent on the interplay between the driving force for delamination (release of the stored energy in the ceramic layers) and the resistance to crack propagation (toughness or work of fracture) of the relevant interfaces. Reliable test methods for measuring the interface toughness for TBCs are critical to achieve fundamental understanding of their failure mechanisms and establish reliable lifetime models, and ultimately to guarantee the reproducibility of the deposition processes and the integrity of the coated components [1,2]. A fundamental quantity which characterizes the adhesion of an interface between dissimilar materials is the ideal work of separation, i.e. the reversible work needed to sep-

1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.07.058

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arate the interface into two free surfaces [3]. Under realworld mechanical tests, the “reversible” separation process is seldom achievable, and so the measured interface fracture energy is substantially larger than the thermodynamic work of separation. The deviation from the ideal work of separation can have many contributions, such as crack shielding by non-planarity of the interface [4], and plastic dissipation in the constituent layers [5,6]. Typically, interface fracture energy is found to increase with phase angle (W) of loading [7], which is a measure of the relative shear to opening mode loading experienced at the crack tip: W = 0° corresponds to pure opening with no shear; W = 90° corresponds to pure shear with no opening. The phase angle of loading depends on the choice of the testing method and specimen. Therefore the interface toughness measured by mechanical methods normally depends on the test method employed. Ideally the loading in the test method should be similar to that experienced by the coating in actual service conditions. Several different test methods have been investigated for measuring the fracture toughness for metal–ceramic interfaces, such as: scratch test [1,8]; double cantilever beam [9]; four-point bending [10]; double-cleavage drilled compression [11]; indentation method [1,12,13]; wedge impression [14]; and barb test [2,15]. These methods encompass a range of loading modes, with the phase angle of loading ranging between 0 (e.g. double-cantilever beam) to 90 (e.g. barb test). However, many of these methods have limited applicability to EBPVD TBCs. This is due to the relatively strong bonding of the EBPVD coating to the metallic bond coat and relatively weak, non-uniform columnar structure of the top coat. Two major extra challenges associated with the testing of TBCs are: (i) the crack path is difficult to control; and (ii) the elastic properties of the YSZ top coat are anisotropic and poorly characterized. Cracks often tend to divert away from the interface of interest into the vertical columns of the YSZ, which prevents the interface of interest being measured. Additionally all test methods need input of the elastic properties of the YSZ top coat in order to quantify interface fracture resistance. However, the porous columnar microstructure of the top coat results in complicated anisotropic and potentially non-linear mechanical properties. Different test methods, e.g. indentation from the top surface [12] and the “barb test” [2,15], have been used for quantitative determination of the interface toughness of EBPVD TBCs. One common feature for these two methods is that both apply in-plane compression to the top coat. In-plane compression to the top coat (which would close the intercolumnar gaps, thereby stiffening and strengthening the top coat) has the desirable effect of encouraging crack propagation along in-plane interfaces (either the TGO–bond coat or TGO–YSZ interface) and inhibits crack deflection into the YSZ. Another feature of these two methods is that the loading is close to mode II. However, delamination of the TBCs in real service conditions can occur not only in a mixed mode at a phase angle of

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50 < W < 90, but also in pure mode I (i.e. W = 0) [15]. Given this diversity of mode mixity, it is important to develop test methods capable of probing the TBC interface toughness at different modes [15]. A particular complication of tests involving increasing in-plane compression is that the energy associated with the residual stresses in the coating (which are also in-plane) contributes to the driving force for delamination in the test. Recently Zhao et al. [16] used a “strain to fail” method to measure mode I interfacial fracture toughness of EBPVD TBCs. This method is based on the principle of plate buckling by applying extra compression to the coating (and substrate). It also requires input of residual stresses in the TGO and YSZ layers, which means that uncertainties in the determination of residual stresses in different layers could lead to errors in the evaluation of interfacial fracture toughness. Cross-sectional nanoindentation (CSN) at the interface of interest has been successfully employed in thin-film interfacial adhesion characterization [17–19]. In this approach stable interfacial fracture is achieved by nanoindentation into the interface on a cross-section. A model based on elastic plate theory has been developed to quantify the interfacial critical energy release rate. CSN has several advantages over other interface fracture test techniques. First, it is a simple, quick method to produce controlled interface fracture; and secondly, it allows the interface crack path to be observed directly [18]. However, one problem is to place the indent tip reliably on the interface. This is often complicated when the materials forming the interface have very different hardness (as in the case of TBCs) and as a result the indent tends to deflect into the softer material. Therefore in this work we investigate cross-section indentation in the substrate close to the interface. In order to generate sufficiently large displacements, we have used microscopic indentation rather than nanoindentation. The experiments were performed on EBPVD TBC specimens cut from real turbine blades and subjected to various degrees of thermal cycling. The interface crack path was examined by luminescence mapping in combination with scanning electron microscopy (SEM). Finite-element modelling (FEM) was used to model the indentation and determine interface deformation. Finally, a clamped plate model was used to extract interface toughness. A theoretical analysis is given which shows that the energy release rate during interface fracture in this method is independent of the residual stresses in the different layers in the EBPVD TBCs. 2. Materials and methods 2.1. Sample preparation The TBC samples investigated in this work were taken from high-pressure turbine blades provided by Rolls Royce plc. The bond coat was formed by diffusion of a Pt coating into the superalloy substrate (CMSX4) and then 130 lm

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YSZ top coat (3 mol.% Y2O3) was applied by EBPVD at 1000 °C in an argon/oxygen atmosphere. All the specimens for the CSI test were in the form of cross-sections parallel to the blade chord, with a width of 2.5 mm parallel to blade axis, and cut from the blades using a diamond saw. A schematic of the shape of the cut specimens was given as Fig. 1 in an earlier paper [20]. The indentation was placed such that the TBC being tested was on the approximately flat part of the blade suction surface (region F in Ref. [20]). The blade axis is parallel to the [0 0 1] crystallographic axis of the base alloy, in other words the cut cross-sections were parallel to the (0 0 1) crystallographic planes. The cross-sections were polished to 1 lm finish using diamond paste. In the current investigation, all the test samples, after cutting from the blades, were exposed to different degrees of thermal cycling. The thermal cycling was conducted by moving the specimens periodically in and out of a furnace by a computer-controlled motorized stage. The temperature of the furnace was maintained at 1150 °C. Immediately after being removed from the furnace the specimens were fan-cooled by laboratory air. The thermal cycling was run with a 1 h scheme in which the specimen dwelt at high temperature for 1 h and stayed outside the furnace for 0.5 h. After thermal cycling, the cross-sections were repolished to 1 lm finish using diamond paste. 2.2. Indentation test Indentation was carried out using a hardness testing machine (Indentec Ltd., UK) which provides six loading options from 9.8 to 294 N (1–30 kg). A sharp cone diamond indenter with an apex angle of 2h = 90° was used for the tests. A schematic of the CSI arrangement is shown in Fig. 1. The specimen was placed on a precision X–Y stage which allows the indentation tests to be performed at specific positions. Typically the distance between the centre of the indent mark to the TGO–bond coat interface was in the range of 200–300 lm. Preliminary tests found the interface crack length to be dependent on both applied load and distance from the interface. It was found that the interface crack generated by a load of <98 N was generally

Indentation mark

Interface crack

Substrate YSZ/TGO

Fig. 1. Schematic of the cross-section indentation (CSI) test arrangement. The broken line indicates the extent of the delaminated region induced by the indent.

too small to be analyzed using the elastic plate model (which requires a crack length significantly larger than the coating thickness). In contrast, a loading of 196 N was found to produce well-defined interface cracks with the lengths significantly larger than the coating thickness. Therefore, a fixed loading of 196 N was used in the subsequent experiments. 2.3. Interface delamination detection The crack path identification and crack length measurement are vitally important for investigating the interface fracture of the TBC system. In this work, the interface delamination was detected by employing two different techniques: luminescence mapping and SEM examination. Luminescence mapping measures the in-plane distribution of stress in the TGO and is able to detect, non-destructively, defects that reduce TGO stress through the top coat in the TBC system [21]. Both peak shift and spectral shape parameters (peak width ratio and peak separation) were found in previous work to deviate significantly from their “usual” values if local damage exists in the TGO, such as delamination. Therefore the maps of peak shift and spectral shape parameters can be used to identify the interface delamination area [21]. A Renishaw Raman optical microprobe (model 2000) fitted with a motorized mapping stage was used for the luminescence mapping measurements. The laser source was a green Ar+ laser with a wavelength of 514.5 nm. Measurements were taken on a grid of 2000  500 lm with a pitch of 20 lm. More details of the luminescence mapping technique can be found in Ref. [21]. The interface delamination was also examined directly on the cross-sections after indentation using SEM (JEOL JSM-840A). The crack length measured by SEM was compared with that measured by luminescence mapping. 3. Results 3.1. Identification of crack path and measurement of the crack length Fig. 2a presents a typical example of interface cracking caused by the CSI test. An interface crack normally could be observed when the distance from the indentation to the interface was short enough. Often, vertical cracks along some intercolumn gaps in the YSZ would also appear as indicated in Fig. 2a. Instead of the circular indentation mark expected when a conical diamond indenter is placed in an isotropic material, the indentation imprint on the blade substrate and/or bond coat regions was found to be always slightly distorted. Furthermore, the interface fracture was also found to be slightly asymmetric with respect to the centre of the indentation—typically with the crack on the left flank longer than that on the right. Both effects are probably due to the anisotropic mechanical (both elastic and plastic) properties of the single-crystal Ni superalloy.

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(a) Vertical cracks

up

TBC

DCI

Interface crack Substrate

Indentation imprint

(b) YSZ

TGO Crack

Bond Coat

Fig. 2. An example of an interface crack induced by cross-sectional indentation (the sample had been subjected to 50 thermal cycles): (a) SE image covering the full length of the interface crack; (b) a highermagnification SE image close to the left end the interface crack.

The interface fracture path was predominantly along TGO–bond coat interface, although the fracture path occasionally crossed through the TGO over deep valleys due to the sharp local curvature of the interface (as illustrated in Fig. 2b). The interface roughness was estimated based on SEM micrographs of exposed substrate (Fig. 9 in Ref. [20]) and cross sections (Fig. 2a and b). The major peak-to-peak wavelength was estimated to be 15 lm, and the amplitude of waviness (quantified by determining the standard deviation of the interface profile) was 2.1 lm. While SEM examination on the cross-sections can only reveal one-dimensional features of the interface fracture, the luminescence mapping reveals two-dimensional details of the delamination. In the luminescence “peak shift” map shown in Fig. 3a, the approximately semicircular dark area corresponds to the delaminated area. The interface fracture causes damage to the TGO, leading to partial residual stress relaxation locally in the TGO. This results in a smaller peak shift in the delaminated area. In the luminescence “peak width ratio” map as shown in Fig. 3b, the bright area matches very well to the dark area in Fig. 3a.

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This is because the modification of residual stress in the TGO caused by interface fracture leads to changes in the spectral shape (here specifically the peak width ratio) due to the presence of different stress levels in the probed volume. More details regarding how interface fracture would affect the peak shift and spectral shape can be found in the literature [21–23]. The diameter of the semicircle measured by luminescence mapping (semicircle having the same area as the approximately semicircular delaminated area) was found to be in good agreement with the crack length measured by SEM. For example, Figs. 2 and 3 are for the same sample. The crack length measured by SEM was 1291 ± 50 lm (Fig. 2), whereas the dark semicircular area in Fig. 3a was measured to be 6.6  105 ± 3300 lm2 by image analysis, which corresponds to a diameter of 1296 ± 29 lm for a semicircle of the same area. Furthermore, the luminescence “signal intensity” map can be used to identify whether the interface fracture is along the TGO–substrate or YSZ– TGO interface. Due to a stronger reflection of light from a TGO–air interface than from a TGO–bond coat interface, a fracture path along the TGO–bond coat interface gives a stronger luminescence signal intensity compared to that of the undelaminated region, whereas a YSZ– TGO interface delamination gives relatively weaker signal intensity. As shown in Fig. 3c, the brighter area in the intensity map corresponds to the dark area in Fig. 3a and thus confirms that the fracture path induced by CSI is mainly along TGO–bond coat interface in agreement with the SEM observations. 3.2. The effect of indentation position on crack length A fixed load of 196 N was used for all the indentations. When the indenter was placed at different distances with respect to the interface, the interface crack length was found to change systematically. Fig. 4 shows the crack radius as a function of the distance from the indentation centre to the interface (hereafter referred to as DCI) for two different sets of specimens. One set had been exposed for 2 thermal cycles and the other for 100 cycles. Although the data scattering is quite large, there is a clear trend of crack radius decreasing with increasing DCI for both 100cycle and 2-cycle specimens. In addition, the crack radii for the 100-cycle specimen were significantly larger than for the 2-cycle specimen. 3.3. The effect of thermal exposure on interface crack length Fig. 5 gives the crack length as a function of thermal exposure when DCI was fixed at 230 lm. There was a large increase of the interface crack length in the first 35 cycles. The crack length at 35 cycles was about three times that at 2 cycles. The interface crack length appeared to be a maximum at about 50 cycles and then maintained a constant level afterwards.

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Fig. 3. An example of luminescence mapping of an interface delamination induced by CSI (the same specimen as in Fig. 2). The maps are through the YSZ from the “vertical” face of the specimen and the centre of the X-axis is in line with the centre of the indent: (a) peak shift map; (b) peak width ratio map; and (c) signal intensity map. X and Y axis scales correspond to distances in lm.

Fig. 4. Crack radius as a function of distance from the centre of the indentation to the interface. The circles are for a specimen after 100 thermal cycles and the triangles for a specimen after 2 cycles.

Fig. 5. Influence of thermal cycling exposure on the interface crack length.

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4. Discussion 4.1. Clamped circular plate model for energy release rate Figs. 2 and 3 indicate that the interface crack generated by CSI was a half-penny-shaped crack parallel to the coating surface. The delaminated area of coating can be regarded as a semicircular plate with a fixed periphery. This can be further approximated by a clamped semicircular plate, for which the energy release rate G with respect to crack radius, a, can be expressed as (for its derivation see Appendixes A and B): GC ¼

2Ec h3c Du2 3a4 ð1  m2 Þ

ð1Þ

where Ec is the effective in-plane Young’s modulus of the delaminated coating (YSZ plus TGO), m is its Poisson’s ratio, hc is the thickness of the coating, a is crack radius, and u is the displacement of the coating caused by the indentation at the point in line with the centre of the indent (i.e. the central out-of-plane displacement of the clamped plate). 4.2. Determination of displacement (u) by FEM In order to calculate Gc from Eq. (1), we have to determine the out-of-plane displacement u. The displacement is small and consists of both elastic and plastic deformation. Therefore it is difficult to measure it accurately experimentally. For this reason we used FEM to model the cross-sectional indentation displacements. The FEM was performed using ANSYS software (for details, see Appendix C) with solid element type SOLID185, which has large plasticity, large deflection and large strain capabilities. The deformation during indentation is determined by both the elastic and plastic properties of the materials involved. The effective Young’s modulus of Ni-based superalloy single crystals determined by indentation has been reported to be in the range 156–225 GPa depending on the orientation of the indenter loading direction [24]. The elastic properties of the Pt-diffusion bond coat should be similar to those of the Ni-based superalloy since it has the same crystal structure. Therefore, the Young’s modulus and Poisson’s ratio were assumed to be 190 GPa and 0.3, respectively, for both the superalloy and the bond coat considered as an equivalent isotropic material for the modelling of indentation. The plasticity of the metal substrate was modelled as a bilinear strain-hardening material. The coefficient of friction between the diamond indenter and the superalloy substrate was chosen such that in the modelling result neither pile-up nor sink-in around the indentation mark occurs (which was observed to be true in the actual experiments). The yield stress and tangent modulus of the metal substrate were determined by matching the modelled indentation mark size to the experimental results (Fig. 6a). In this way, the yield stress of the substrate was

Fig. 6. (a) Indentation mark size as a function of the indentation distance with an indentation load of 196 N, where the solid squares are modelling results, the hollow circles are measured values. (b) Surface maximum displacement as a function of indentation distance with an indentation load of 196 N, where the solid squares are the modelling results (elastic plus plastic) and the hollow circles are measured plastic deformation.

determined to be 1200 MPa and the tangent modulus 700 MPa. The coefficient of friction between the diamond and the superalloy was 0.15. As shown in Fig. 6a, the modelled indentation mark diameter (solid squares) agrees well with the experimental results (hollow circles). Both experimental and modelling results show an increase in the mark size with a decrease in DCI as expected from the lower constraint as the free surface is approached. Fig. 6b gives the displacement (u) as a function of DCI using a fixed load of 196 N. The correlation between displacement and DCI (all distances in lm) can be expressed as: u ¼ 72:6  0:35DCI þ 0:00046D2CI

ð2Þ

The residual plastic displacement of the interface (up) can be measured from the SEM images as shown in Fig. 2a and is also shown in Fig. 6b. Since the total displacement (u) consists of both plastic component (up) and elastic component (ue), up is expected to be smaller than u. As shown in Fig. 6b, both the experimentally determined up and modelled total displacement u show a similar decreasing trend with an increasing DCI. It is recognized that the isotropic approximation used here does not fully describe the complexity of elastic and plastic deformation around the indent in the anisotropic single crystal. How-

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Table 1 The effective in-plane Young’s modulus of the YSZ–TGO bilayer after different thermal cycles [25]. Thermal cycles Ec (GPa)

2 7.5a

35 14

40 17

100 13.5

a

This value was determined by extrapolation of the data shown in Fig. 6 in Ref. [25].

ever, the error in estimating the total displacement normal to the coating is expected to be small because the plastic response has been fitted to the residual indent mark size and the elastic contribution is only part of the total displacement. 4.3. Calculated energy for interface fracture For the calculation of Gc, the displacement u was taken from Fig. 6b or calculated by Eq. (2) and the crack length data were taken from Fig. 5. The other required parameters (Table 1) were hc = 120–140 lm, m = 0.3 and EC (the effective in-plane Young’s modulus of the bilayer TBC coating). EC was measured previously on free-standing TBC specimens also prepared from Rolls Royce high-pressure turbine blades [25]. The calculated value of interface fracture energy as a function of the thermal exposure is shown in Fig. 7a. Apart from the specimen that had been exposed to only 2 thermal

cycles, which gives a much larger value of Gc (2300 J m2), all other specimens give a more or less similar value (42 J m2). 4.4. Uncertainties and potential errors in the derivation of Gc In order to understand the results in Fig. 7a, it is necessary to evaluate the uncertainties and potential errors in both the experiments and the analysis. Some conditions during the experiments could have deviated from those assumed in the theoretical model. Also there is uncertainty in the material properties, particularly the elastic properties of the bilayer ceramic coating. A detailed discussion is given in the following sections. 4.4.1. Buckling of the delaminated coating Eq. (1) applies in the absence of elastic buckling of the delaminated area. If buckling occurs, additional stored strain energy would be partially released, leading to a larger driving force for coating delamination. In such a case (for derivation, see Appendix B): G¼

2Eh3 u2 0:617ð1  mÞhðrR  rC Þ2 þ ; 3a4 ð1  m2 Þ E

ð3Þ

where rC is the critical edge stress for buckling and rR is the residual stress in the coating before buckling. Hence, if buckling occurs, measurement of the residual stress is required for the calculation of Gc. We now estimate the conditions for buckling to occur. The critical edge force per unit length, fCR, for buckling of an edge-clamped circular plate is a function of its flexural rigidity, D, and radius (crack size) [26]: fCR ¼

14:68D a2

ð4Þ

According Eq. (4), the critical edge force can be transformed to specify a critical crack radius if the edge force is known.  aCR ¼

Fig. 7. (a) The apparent interface fracture toughness as a function of thermal exposure: the solid circular points are for specimens without epoxy coating, the square point giving the measured Gc after applying an epoxy coating on the 50-cycle specimens, which shows a decrease of Gc from of 42 to 29 J m2. (b) The apparent interface fracture toughness as a function of indentation distance for 50-cycle specimens.

1=2  1=2 14:68D 14:68Eh3 ¼ fCR 12f CR ð1  m2 Þ

ð5Þ

(Here E is the effective modulus for bending of the composite coating.) According to the literature, the residual compressive stress in the TGO (rTGO) is about 4 GPa [27] and that in the YSZ (rYSZ) is typically less than 200 MPa [28,29]. Thus, if the thickness of TGO (hTGO) is taken as 3 lm and thickness of YSZ (hYSZ) as 128 lm, the largest possible edge force applied to a delaminated TBC (f = hTGOrTGO + hYSZrYSZ) is 3.76  104 N m1. The critical buckling crack radius for a 130 lm thick TBC coating can thereby be calculated as 886 lm. From Figs. 4 and 5, the interface crack radii measured in our experiments were all smaller than 850 lm and therefore would not be expected to buckle. In addition, even if the residual stresses are slightly larger than the critical stress for buckling, the extra contribution from buckling would still be small as

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it is proportional to (rR  rC)2 according to Eq. (3). Therefore, the residual stresses in the TBCs should not have a significant influence on the interface toughness measured in the current experiments. 4.4.2. Crack size Interface crack size is an important parameter as it not only determines which model to use for the calculation of Gc but also appears to the fourth power in the calculation. If the crack size is larger than the critical size for buckling, then Eq. (3) should be used to include the buckling contribution. However, if the crack size is too small compared to the central displacement and the coating thickness, shear in the coating will become an important issue. In the derivation of the Eq. (1) (or Eq. (A5) in Appendix A), the displacements and strains are assumed to be exclusively due to bending and shear is neglected. The displacement due to shear in the plate is directly proportional to (h/a)2 for a given central displacement [26], so it will increase quickly with a decrease in crack size. Too small a crack size entails a significant deviation from the model, which would become unreliable. According to Ref. [26], the ratio of the displacement due to shear (uS) to that due to bending (uB) is: uS =uB ¼ 4h2 =ða2 ð1  mÞÞ

ð6Þ

Under a testing condition of DCI = 230 lm, the crack radius was about 600 lm (in Fig. 4 except for the 2-cycle specimen), which means h/a = 130/600 = 0.21. The displacement due to shear can be calculated from Eq. (6) to be about 26% of that due to bending, which means that u could be overestimated by 20% at the most in this case. However, for the 2-cycle specimen, the crack length was smaller than 300 lm, (i.e. h/a > 0.33), and therefore the displacement due to shear could account for more than 50% of the total displacement in this case. Furthermore, the shear modulus of the YSZ coating is expected to be very small due to the weak bonding between columns. Hence neglecting the displacement due to shear could lead to significant overestimation of the stored energy (driving force) for crack propagation when the crack is short. 4.4.3. Indentation distance The indentation distance DCI determines the central displacement of the coating, which in turn determines the crack size. If the indentation is placed at a position too far away from the interface, the interface crack size so generated can be too small for the application of the circular plate model for G. If the indenter is placed too close to the interface, a slight misalignment of the indenter in the vertical direction or a slight deviation from vertical direction of the interface in the specimen can lead to significant uncertainties in the displacement. In Fig. 7b, Gc is plotted as a function of DCI. The Gc values are quite scattered but can be regarded as constant when DCI is smaller than 250 lm. When DCI is larger, the crack length is too small to apply the clamped plate model

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reliably. The unusually large Gc value is due to shear being neglected, as discussed earlier. 4.4.4. Young’s modulus of the bilayer TBC For the clamped circular plate model, G is directly proportional to the Young’s modulus of the plate. However, the delaminated TBC is a bilayer (TGO and YSZ) and moreover the YSZ coating has a complex anisotropic microstructure. This results in literature values of Young’s modulus for the coating being dependent on the measurement method. For example, the indentation method [30,31] generally gives much higher values (typically 70– 100 GPa) than the bending method (10–30 GPa) [32–34]. In order to employ the clamped circular plate model, only the ones measured by bending of bilayers are applicable. Even using the same bending method, the measured stiffness has been found to depend on whether the YSZ columns are being pushed together or pulled apart [25]. Additionally, intercolumn microfracture and shear can lead to a significant decrease of the apparent stiffness [25]. In the present experiments, it was frequently found that vertical cracks were formed around the point with

Vertical cracks

Shear displacement

Interface crack

Epoxy coating TBC

Fig. 8. (a) Significant shear displacement and microfractures observed after CSI on a specimen thermally exposed for 2 cycles. (b) The microfracture (initially seen in the specimens without epoxy coating as shown in Fig. 2) was largely suppressed after an epoxy coating was applied. Note that a 50 lm epoxy coating is shown here for illustration, whereas in most cases the thickness of the epoxy coating was 10–15 lm.

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the maximum out-of-plane displacement (as shown in Fig. 2). Such vertical cracks would, from the stiffness point of view, decrease the apparent Young’s modulus of the coating, or from the energy point of view, release some of the stored strain energy in the delaminated ‘plate’, leading to an overestimation of Gc. In order to investigate the potential impact of these vertical cracks, an epoxy adhesive resin was applied to the top of the coating on the specimen that had been thermally cycled for 50 times. This had the objective of inhibiting intercolumn microfracture and relative vertical movement between columns. After being subjected to the same cross-sectional indentation tests, the vertical cracks were found to have been largely prevented (as shown in Fig. 8b). At the same time, the interface crack sizes of the epoxy-coated specimen were approximately 10% larger than those on specimens without the epoxy coating. The observed 10% increase of crack radius implies that Gc (in Fig. 7a) would be overestimated by approximately 46% (Gc is proportional to 1/a4) when vertical cracking occurred. In addition, interface roughness can give rise to local tensile and shear residual stresses [27]. The residual stress variability associated with the local waviness may interfere with the crack propagation. However, since the wavelength of the interface waviness was relatively short (15 lm) compared to the typical delamination diameter (>1000 lm), this type of short-range variation in local stresses is not expected to cause systematic change in delamination area. The measured interface fracture energy is representative of long-range crack propagation. 4.5. Interface fracture toughness of TBC As discussed above, if the measured crack size is too small, Eq. (1) leads to a significant overestimate of Gc. The Gc value for the specimen after 2 cycles shown in Fig. 7a is greatly overestimated because the crack radius for this specimen is only about 200 lm. In addition, as shown in Fig. 8, significant shear displacement and vertical cracks were observed after indentation of this specimen. This could be due to the fact that, after only 2 cycles, the TGO layer was still thin and the intercolumn bonding was particularly weak due to a lack of sintering. Intercolumnar microfracture and shear displacement in the YSZ could become the dominant energy release mechanisms in this case, greatly reducing the strain energy available to drive interface cracking. Although such unusually high apparent Gc values for TBCs with short thermal exposure still reflects a strong capability for resisting delamination, it does not reflect the intrinsic interfacial fracture energy. Therefore, the CSI method used here is not suitable for measuring the interface fracture energy for TBCs with short thermal exposure. For TBCs with longer thermal exposures (e.g. >35 cycles in this study), the problem of microfracture and shear displacement can be largely overcome by using a thin epoxy

resin coating. As discussed above, the Gc value from experiments without the epoxy was concluded to be overestimated by 46%. This means that a more accurate value for the interface fracture energy should be 29 J m2, instead of the 42 J m2 shown in Fig. 7a. Guo et al. [2] and Liu et al. [15] measured the TGO– bond coat interface fracture energy to be 35 J m2 (W = 65°) to 70 J m2 (W = 90°) by using the barb test method. These values are slightly higher than the value of 29 J m2 measured in the present study. The crack tip loading in barb tests has a large fraction of shear mode (mode II): the phase angle for the barb test is in the range 65–90° [2,15]. Interface toughness tends to increase when the phase angle is larger than 65° due to contact and friction along the non-planar delamination surfaces [35]. For the CSI test, the exact phase angle is not known, but it is reasonable to expect the phase angle in CSI is much smaller than that in the barb test because of the out-of-plane displacements. Therefore, the interface fracture toughness measured by CSI can be regarded as consistent with those measured by the barb test method. Zhao et al. [16], using a “strain to buckling” approach, obtained much smaller interfacial fracture toughness values for similar coatings and substrates. The “mode I” interfacial toughness they obtained was 10 J m2 for a specimen after 2 h exposure at 1150 °C and decreased to 0.79 J m2 for a sample thermally exposed for 60 h. These values are much smaller than the values obtained by our CSI method and by others [2,15] using the barb test method, even after the phase angle has been taken into consideration. For EBPVD TBCs, the stiffness of the coating is expected to be higher in compression than in bending, because bending always allows partial opening of the columns, and even intercolumnar microfracture if the bending is large [25]. In Ref. [16] the residual stress in the YSZ layer was calculated based on stiffness measurements in bending. This would lead to underestimation of the residual stress in the YSZ and therefore, underestimation of Gc for interface fracture. Hence it is not surprising that the CSI method gives higher interfacial fracture values than the strain to buckling method. The results from the current CSI method also differ qualitatively from the results of Zhao et al. in that no decrease of interfacial fracture toughness with thermal exposure up to 100 cycles was seen in the present study. This is contrast to the large decrease of interfacial fracture toughness with thermal exposure reported in Ref. [16]. The cause of this discrepancy between the different methods is not clear in this stage and further work is needed to clarify this. 5. Conclusions

(1) The locus and extent of the coating delamination in the CSI test can be reliably monitored non-destructively by luminescence mapping. The interface frac-

X. Wang et al. / Acta Materialia 60 (2012) 6152–6163

(2)

(3)

(4)

(5)

ture for the TBC specimens after thermal cycling was predominantly along the TGO–bond coat interface. The shape of the interface crack generated by the CSI test was found to be approximately semicircular by luminescence mapping. The crack size measured by luminescence mapping was in good agreement with that measured by SEM in cross-section. Although significant compressive residual stresses exist in the YSZ and TGO, they do not affect the measured Gc value, provided that the delaminated area does not buckle. Under these conditions the Gc value derived from a simple clamped circular plate model is sufficiently accurate to determine the actual critical energy release rate for the interface fracture. This makes the interface fracture energy measurement much simpler because no detailed information of residual stresses is required. Even when the delaminated area buckles, the error in Gc remains small and a correction can be made for the effect of the residual stress. Intercolumnar microfracture and shear displacements in the YSZ could become dominant energy release mechanisms in TBCs with short thermal exposure because the YSZ has weak intercolumn bonding at this stage. This leads to large overestimation of Gc using the clamped plate model and therefore the CSI method is not suitable for the determination of interface fracture energy for TBCs with short thermal exposure. For TBCs with longer thermal exposure, the microfracture and shear displacements can be largely prevented by applying a thin epoxy coating on the outer surface of the YSZ to inhibit shear between YSZ columns. The interface fracture resistance of the TBCs was found to be independent of thermal cycling for specimens having 35–100 cycles. A specimen subjected to only 2 cycles showed a higher apparent interface fracture resistance, but this is concluded to be unreliable as the specimen did not satisfy the requirements for the test to be valid. The interface fracture toughness of the TBC system thermally exposed for more than 35 cycles was determined to be approximately 29 ± 9 J m2. This is consistent with results measured by others using the barb test, after taking into consideration the different crack loading angles. However, it is higher than those reported by Zhao et al. using a “strain to buckle” method, probably because they underestimated the modulus of the YSZ in the compressed condition of their test.

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the Department of Physics at Imperial College for access to the Raman microprobe. The authors are grateful to D. Rickerby of Rolls-Royce plc for provision of specimens. Appendix A. Energy release rate of a penny-shaped crack based on clamped circular plate model For an all-around clamped circular plate subjected to a concentrated force at the centre as shown in Fig. A1, the vertical displacement at the centre is a function of the load P and the flexural rigidity of the plate D [26]: u¼

Pa2 16pD

ðA1Þ

where D¼

Eh3 12ð1  m2 Þ

ðA2Þ

The stored bending energy in the plate: UB ¼

Pu 8pDu2 ¼ 2 a2

ðA3Þ

When the displacement u is a constant, the stored elastic energy in the plate U would decrease with an increase of the plate (or crack) size a. The energy release rate with respect to crack size is: G¼

1 dU B  2pa da

ðA4Þ

Upon combination of Eqs. (A2)–(A4), G can be expressed by: G¼

2Ec h3c u2 3a4 ð1  m2 Þ

ðA5Þ

Appendix B. Influence of residual stress in the coating on G The influence of the residual stress in the coating can be evaluated by a hypothetical operation approach as used by Marshall and Evans [36]. As shown in Fig. A2, instead of applying a concentrated force at the centre directly to a plate which is already subjected an in-plane residual stress rR, the plate is imagined to undergo three reversible operations. In step 1 the coating section above the crack is cut and removed and forces equal and opposite to rR are applied to the faces of the cut to hold the uncut section.

a

u

Acknowledgements The authors would like to thank EPSRC for financial support in Grants GR/S26149/01 and GR/T07329/01. The authors would also like to thank Prof. L. Cohen of

P Fig. A1. All-around clamped circular plate subjected to a concentrated force at the centre.

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In the case without buckling, the radius of the plate shrinks by DR = (1  m)rRa/E. Since no further bending is occurring and if u  h, the elastic behaviour of the bent plate can be assumed to be the same as a flat plate. The applied edge stress required to generate a radius shrinkage of DR is rP = EDR/a(1  m) = rR, therefore the stored energy change in step 3: 2pahrP  2pða þ DR Þhr0 DR 2 ¼ phð1  mÞr2R a2 =E

UP ¼

ðA9Þ

Since rP = rR and ro = 0, then: U P ¼ phð1  mÞr2R a2 =E

ðA10Þ

Note that UP and UR are equal and opposite, so they cancel out. Therefore, the total stored energy in the system is the same as the simple clamped circular bending energy, EB (U = UR + EB + UP = EB), and G can still be expressed by Eq. (A5) for this case. In the case with buckling, the buckling reduces the strain energy in step 3. The difference is [36]: Fig. A2. Hypothetical operations to calculate the stored energy in the delaminated coating.

The residual stress in the removed section is then allowed to relax to zero. In step 2, the stress-free plate is clamped and a concentrated force is applied at the centre to generate a vertical displacement u. This step is exactly the same as in Fig. A1. In step 3, a stress is applied to the bent plate on the edge to generate a radial contraction so that the final size of the plate fits the cut hole. The plate is then replaced in the hole, sides are rewelded and the stress is relaxed. In step 1, the plate radius expands by DR = (1  m)rRa/E and the stored energy change in the system is [36]: U R ¼ phð1  mÞr2R a2 =E

ðA6Þ

In step 2, the bending energy is the same as Eq. (A3). The edge stress distribution of the bent plate is [26]: rr ¼

4Eu z;  m2 Þ

a2 ð1

h=2 < z < h=2

The average edge stress is: Z 1 h=2 4Eu ro ¼ z dz ¼ 0 h h=2 a2 ð1  m2 Þ

dU ¼ 0:617pð1  mÞhðrR  rC Þ2 a2 =E

ðA11Þ

where rC is the critical edge stress for buckling. Although ub > u, the difference will be small if the buckle is small. Hence for this case G can be approximated as: G¼

2Eh3 u2 0:617ð1  mÞhðrR  rC Þ þ 3a4 ð1  m2 Þ E

2

ðA12Þ

Upon comparing Eq. (A12) with Eq. (A5), it is clear that the crack driving force is larger when there is buckling. Appendix C. Numerical modelling of cross-sectional indentation A finite-element model including superalloy substrate, thermal barrier coating (TGO and YSZ) and diamond indenter was created in ANSYS software [35] as shown in Diamond indenter

Superalloy

ðA7Þ TBC

Top surface

ðA8Þ

and so the average edge stress is zero after step 2. In step 3, there are two different situations: with or without buckling. When the applied edge force is smaller than the critical force for buckling, the plate will not bend further (therefore there is no change in u) and the work done by the edge external force will be transformed into compressive strain energy. In contrast, when the applied force is larger than the critical force for buckling, the bending energy will be increased (therefore, ub > u) and the compressive strain energy is also increased.

Front surface

Fig. A3. Finite-element model of superalloy substrate, thermal barrier coatings and diamond indenter.

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remaining surfaces are constrained in their normal directions. One example of the modelled displacement in sideways of the indented superalloy and TBC is given in Fig. A5, for which a load of 196 N is applied to the diamond indenter and the indentation distance is 230 lm. References

Fig. A4. Details of the finite-element mesh of the diamond indenter and superalloy substrate.

Fig. A5. The modelled displacement with a load of 196 N and indentation distance of 230 lm.

Fig. A3. The details of the finite-element mesh are shown in Fig. A4. The ANSYS solid element type SOLID185, which has large plasticity, large deflection and large strain capabilities, was used in the model. The ANSYS contact element type CONTA173 and target element type TARGE170 were employed to simulate contact and sliding between the indenter and supperalloy substrate. The model consists of 12836 solid elements and 1860 contact elements. The finite-element model is 2 mm long, 2 mm high and 1.4 mm wide. The thickness of the thermal barrier coating is 0.13 mm, and there are five element divisions cross the thickness. The interface between the thermal barrier coating and the superalloy substrate is bonded in the finite-element model. Apart from the top and front surfaces, the

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