Introduction

Alloys or coatings designed for high temperature applications largely depend on the formation of an alumina scale for corrosion and oxidation resistance [1]. At room temperature, the oxide scale is usually subjected to a residual compression, caused primarily by the thermal mismatch between the oxide and the substrate. In many cases, a compressive growth stress is superposed and provides a substantial contribution to the total stress. For example, it has been reported that the growth stress in the oxide formed on FeCrAlY alloy can be up to 1 GPa at oxidation temperature [2]. According to classic elastic theory, the scale spallation is driven by the strain energy in the oxide, and resisted by the interfacial toughness. Therefore, it is generally believed that reducing the stress would be helpful in preventing the spallation of oxide scales.

However, Tolpygo and Clarke reported a quite different result [3]. They investigated the spallation behaviour of an alumina scale formed on a FeCrAl alloy. It was found that the extent of spalling does not decrease by reducing the residual stress in the oxide. For example, at a given cooling rate, spalling is more pronounced on a thinner substrate when the oxide stress is smaller. In addition, for a given substrate thickness, the alumina scale only spalls after intermediate cooling rates, but remains adherent after very fast or slow cooling. They attributed this phenomenon to the relaxation of the substrate [3]. However, this theory cannot give a consistent explanation on the spallation behaviour for the alumina scales formed on the FeCrAlY alloy. Our previous work [4] has shown that, at any given cooling rate, the thicker substrate exhibits more spallation although the relaxation in the substrate is smaller.

Hou’s group conducted a series of work on the compositions at Al2O3/FeCrAl Interfaces after oxidation at high temperatures [5–7]. It was found that impurity segregation such as sulfur along with carbon and chromium enrichments at the interfaces had a strong presence, which was prone to lead to the spallation of Al2O3 scales. However, the “adherent” Y-doped FeCrAl system exhibited very different behaviour, i.e., all most no sulfur was detected at the interface on the FeCrAlY alloy. Tolpygo and Viefhaus suggested that stresses and plastic deformation associated with the growth of alumina scales may induce the different concentration of sulfur segregation [8].

According to established theory, for a film under compression, the spontaneous buckling requires the presence of pre-existing interface separation between the film and the substrate [9]. In addition, the spallation should occur immediately once the stress level in the oxide exceeds a critical value. However, the experimental observations both in this study and previous works seem to contradict this theory [2, 4]. That is, the spallation does not occur immediately after cooling to the room temperature, but requires a period of incubation. This suggests that the interfacial separation should develop through a crack nucleation and coalescence process. This similar phenomenon reported by Smialek et al. was referred as moisture-induced delayed spallation (MIDS) and desktop spalling (DTS) [10–13]. Exposure of Al2O3 scales/superalloy system to moisture could lead to spontaneous interfacial failure; while the specimens were intact at ambient conditions; then their delamination and buckling was delayed until well after cooling down. Hydrogen embrittlement owing to the presence of water vapor, resulting from the reaction of \({\text{Al}}_{\text{alloy}} + 3\left( {{\text{H}}_{2} {\text{O}}} \right)_{\text{air}} = {\text{ Al}}\left( {\text{OH}} \right)_{3} + 3{\text{H}}^{ + } + 3{\text{e}}^{ - }\), was considered to be the main cause of the degradation. The moisture increased growth rates of cracks in bulk alumina, and reduced the interfacial strength and toughness. It should be noted that, in all the literatures above [10–13], MIDS and DTS are a secondary mechanistic detail, not as important as the sulfur segregation and reactive element additions. This indicates that moisture effects appear to be more prominent in systems where S and Y levels are modest. Moreover, the MIDS and DTS effects were all observed after cyclic thermal treatment [10–13] or after a considerable scale had been built up [14].

Carbon has been addressed as a weaker interface modifier as compared to H and S from first principle studies [15, 16]. In Smialek and Pint’s work [14], carbon has not been implicated as a spallation fact, which tied up with Hf as the carbide. However, in another work [17], it was reported that the carbon content in the FeCrAlY alloy affected the segregation at an alumina scale/alloy interface and substrate grain boundaries, which led to a different oxidation kinetics due to various levels of spallation.

Therefore, the objective of this work is to advance the understanding on the spallation behaviour of an alumina scale formed on FeCrAlY alloy. Both the effects of the stress, the interfacial chemistry and the interface morphology will be examined. The residual stresses in the alumina scale were controlled by appropriate choice of the cooling rate and the substrate thickness. The oxide–metal adhesion was evaluated and related to the interfacial chemistry. The morphology at the interface was quantified using atomic force microscopy (AFM). Based on established models, the local stresses at the undulated interface were analyzed. Their effects on the spallation of alumina scales were also discussed.

Experimental Procedures

A commercial FeCrAlY alloy (Goodfellow, UK) with a nominal composition of 72.8Fe–22Cr–5Al–0.1Y–0.1 Zr–0.02C (in wt%) was used in this study. It also contains trace concentration of Mn, Si, Zr and C [4]. Disc shape specimens with a diameter of 25.4 mm were cut from a rod and then mechanically polished to 0.25 μm finish on both sides. Two groups of specimens were prepared. One group has the same thickness of about 1.4 mm, and the other group has different thicknesses of 0.48, 1.4, 3.4 and 7.6 mm.

Oxidation testing was carried out at 1200 °C for 25 h using a chamber furnace, with a heating rate of 3 °C/min. After oxidation, the specimens were cooled to room temperature at various rates varying from 1 to 100 °C/min (1, 5, 10, 30 °C/min and air cooling). Slow cooling was conducted inside the furnace at a constant rate. For higher cooling rates, the specimens were removed from the furnace rapidly. In these cases, the cooling rate was not a constant, so the average value was estimated from the period of time required to reach a temperature below about 100 °C, i.e., the air cooling rate was estimated as ~100 °C/min.

The residual stress in the oxides was measured at room temperature using photostimulated luminescence piezospectroscopy (PLPS). The observed frequency shift (Δν) of the R-line peak can be converted to elastic biaxial stress (σox) in the oxides by [18]:

$$\Delta \nu = 5.06\sigma_{ox}$$
(1)

The microstructure of the specimens was examined by optical microscope (Olympus BH2-UMA) and scanning electron microscopy (SEM, Philips XL30). Mapping of concentration measurements were acquired using energy dispersive spectroscopy (EDX).

The wrinkled morphology of the alumina scales was quantified using AFM. Several images of the oxide surface, 50 × 50 µm2 in size, were scanned on each specimen. Assuming a sine wave, the geometry parameters of the wrinkles, such as amplitude and wavelength, can be quantified from the image. The amplitude was characterized by the root-mean-square roughness parameter, Rq, which is defined as the standard deviation of the height of each point on the surface relative to the average value. The wavelength was evaluated from the whole area of each AFM image, using a fast Fourier transformation method. The wavelength determined from this method is similar to that obtained directly from the SEM images.

A compression test was conducted at room temperature to qualitatively compare the interfacial toughness of TBCs specimens (thickness of substrate = 1.4 mm, cooling rate = 1 °C/min for Group A and air cooling for Group B) after 25 h oxidation at 1200 °C. Before the test, specimens were cut into square with a size of 10 × 10 mm2. The compression was applied along the direction parallel to the substrate by using a MTS Alliance RT/100 mechanical testing machine [19]. The loading rate was set to be 5 µm/s. The buckling process of specimens was monitored and recorded by a high-speed camera. The records were transferred to digital images and analyzed using DaVis 7.2 image processing software.

Radio frequency glow-discharged optical emission spectroscopy (GDOES, GD Profiler 2, Horiba Jobin–Yvon, France) was utilised to determine the impurities across the oxide. The measurements were performed using argon gas plasma at power and pressure of 35 W and 700 Pa respectively. The distributions of elements were monitored using a polychromator. Prior to depth profiling, pre-sputtering of sacrificial monocrystalline silicon wafer was undertaken to minimise the influence of contamination of the glow discharge source.

Results

Effect of Stress on Scale Spallation

To investigate the influence of the residual stress in the oxide on the spallation of alumina scales, substrates with various thicknesses from 0.5 to 7.6 mm were oxidized at 1200 °C for 25 h, and then cooled at different rates. In this manner, different stress levels can be created in the oxide. Figure 1 shows the room temperature stress as a function of the cooling rate for the scales formed on 1.4 mm thick substrate. With an increase in cooling rate, the residual stresses in the alumina scale increase from −2.96 GPa to −4.67 GPa. Conversely, the extent of alumina spallation is not proportional to the stress in the scale. The alumina scale only exhibits noticeable spallation at intermediate cooling rates, i.e., between 5 °C and 30 °C/min, but remains intact during both slow cooling (1 °C/min) and fast cooling (air cooling). This observation is consistent with the previous report on the FeCrAl substrate [3], which implies that the stress in the alumina oxide is not the sole reason for the scale failure.

Fig. 1
figure 1

Residual stresses in alumina scale formed on FeCrAlY substrate (1.4 mm thick) as a function of cooling rate after 25 h oxidation at 1200 °C. The stresses were measured by photostimulated luminescence piezospectroscopy (PLPS) at room temperature. The insets are corresponding optical images of oxide surface at different cooling at rate

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The fact that spalling becomes more pronounced at intermediate cooling rates indicates that there is a combination of two opposite effects. As proposed by Tolpygo and Clarke, the strain relaxation in the substrate plays an important role on the scale failure [3]. It acts in conjunction with the residual stress to control the spallation. At a high cooling rate, although the residual stress is large, the relaxation strain is negligible and thus no spalling; at a very slow cooling rate, the relaxation strain is large, but the residual stress is too small to spall. According to this scenario, for a given cooling rate, the relaxation strain is smaller on a thicker substrate. Therefore, less spallation should be produced. The stress relaxation involves two processes, i.e., the plastic deformation of the alloy (providing elongation of the substrate plate) and the creep in the alumina scale [3]. The plastic relaxation is more pronounced at lower cooling rates and thinner substrates. During slow cooling, the thermal misfit stress in the alloy substrate slowly increases while provides more time for elongation of the substrate, until the creep strength of the alloy is sufficient to prevent further plastic deformation. On the contrary, no relaxation is possible during fast cooling. For specimens with different substrate thicknesses, the thicker alloy possesses a smaller plastic deformation in the substrate at the same cooling rate due to the fact that thicker substrate is harder to deform to the extent of a thinner one to accommodate the creeping alumina scale. However, the experiment result described in the following appears inconsistent with this hypothesis.

To investigate if the relaxation strain in the substrate is a dominant factor, substrates with different thickness were oxidized at 1200 °C for 25 h and cooled at the same rate (30 °C/min). Figure 2 presents the residual stress in the alumina scale as a function of substrate thickness, for a cooling rate of 30 °C/min. As expected, the oxide stress increases with an increase in the substrate thickness. In this case, the impurities at the interface in all specimens should be the same. However, the spallation of alumina scale is more pronounced for a thicker substrate (Fig. 2 insets). This observation clearly suggested that the relaxation of the substrate is not the dominant factor for spallation. Nevertheless, this behaviour is consistent with the existing models of spalling of compressed film, in which a larger compressive stress will promote the delamination due to a higher strain energy.

Fig. 2
figure 2

Residual stresses in the alumina scale formed on FeCrAlY substrate with different thickness, at a cooling rate of 30 °C/min after 25 h oxidation at 1200 °C. The stresses were measured by PLPS at room temperature. The insets are corresponding optical images of oxide surface formed on different thick substrate

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The Dynamic Buckling Process

Figure 3a shows the SEM image of a typical spalled area. The exposed metal surface exhibits imprints of alumina grains, indicating spallation occurs from the oxide–metal interface. Small craters formed by Zr-containing oxide inclusions can also be found (Fig. 3b). However, no relationship between the craters and the spallation can be correlated. The circular shape of the spalls indicates that buckling is the major mode of spallation, which is driven by the strain energy in the alumina scale and resisted by the interfacial toughness between the oxide and the metal substrate.

Fig. 3
figure 3

a SEM image of a spalled area, in which the wrinkles are evident on the exposed metal surface and the oxide surface; b detailed region of the small crater formed by Zr-rich oxide. The substrate thickness is 1.4 mm and cooling rate is 30 °C/min. Specimens were oxidized at 1200 °C for 25 h

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Figure 4 summarized the buckling size as a function of residual stress in the alumina scale. The buckling size was estimated from 10 to 30 circular spalls on each specimen, and the residual stress was measured in the adherent scale remote from the spalls. The buckling size shows a clear correlation with the residual stress: it decreases with an increase in the compressive stress in the oxide. Similar observation has been reported for the alumina scales grown on FeCrAl alloy [20].

Fig. 4
figure 4

The buckling size as a function of residual stress in the alumina scale. A comparison of measured (data points) and calculated (curve line) tend is shown. The data points show the diameter of circular spalls measured on specimens of different thickness (0.48, 1.4, 3.4 and 7.6 mm; under 30 °C/min) and after different cooling rates (1, 5, 10, 30 °C/min and air cooling; for thickness of 1.4 mm) after 25 h oxidation at 1200 °C. The critical buckling size calculated from Eq. (3) as a function of residual stress for a given oxide thickness (h ox  = 4.9 µm) was also superimposed (curve line)

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According to the buckling theory, an essential requirement for buckling to occur is the presence of pre-existing interface separation between the film and the substrate [9]. For films subjected to biaxial compression, the critical separation size, d, for axisymmetric buckling at stress, σ ox , is [20, 21]:

$$\frac{d}{{h_{ox} }} = 2.2\sqrt {\frac{{E_{ox} }}{{\sigma_{ox} }}}$$
(2)

The predicted critical separation size is plotted as a function of residual stress (Fig. 4, solid curve). At a given stress, the oxide scale spontaneously buckles once the interfacial separation exceeds the critical size.

However, there is no initial separation of detectable size existing at the oxide–metal interface immediately after cooling to the room temperature. As shown in Fig. 5, after a period of incubation, initial separation appears at the oxide–metal interface. It usually starts from a smaller size, and then grows with time, until abruptly increasing and spalling. This suggests that the buckling develops through a crack nucleation and coalescence process, and thus exhibits a time-dependence. Although this phenomenon has been reported on the FeCrAl alloy, no satisfactory explanation was given [20].

Fig. 5
figure 5

Optical images showing the evolution of an incipient buckle and sudden spallation. Buckling growth but intact scale is shown at 15 and 40 min, spallation is shown at 42 min. The substrate thickness is 7.5 mm and cooling rate is 30 °C/min. Specimens were oxidized at 1200 °C for 25 h. The images were obtained by placing the specimens under the microscope immediately after cooling

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Quantification of Interfacial Morphology

After oxidation, the surface of the oxide scale usually exhibits a wrinkled or undulated morphology (Fig. 3), which is caused by the creep of the oxide, either at high temperature or during cooling. Cross-sectional observation reveals the oxide thickness is rather uniform. Therefore, the undulation is not cause by the variations of oxide thickness. After spalling, the substrate surface is clean and covered with imprints of alumina grains, implying that the substrate deformed together with the oxide scale at high temperature. Thus, the roughness of the oxide–metal interface is similar to that of the scale surface. The interfacial cracks, if any, must occur during cooling.

The typical AFM image of the scale surface is presented in Fig. 6a. The surface exhibits some periodicity, which can be assumed as a sine wave (Fig. 6b). The geometric parameters such as the amplitude (A) and the wavelength (2L) of the wrinkles can be extracted from AFM image. The wrinkle amplitude was related to the root-mean-square roughness (Rq): A = 2Rq. Figure 7 gives the amplitude for the alumina scale formed by different cooling rates and on substrates of different thickness. For a given substrate thickness, the creep of the oxide at oxidation temperature should be the same. Thus the amplitude only depends on the creep during cooling. Since a fast cooling generates less creep in the oxide, the amplitude decreases with increasing cooling rate. For a given cooling rate, the oxide on a thicker substrate creeps more, both at high temperature and during cooling. Therefore, the amplitude increases with an increase in the substrate thickness. However, for all specimens studied in this work, the wrinkles exhibit a similar wavelength of ~15 ± 2 µm.

Fig. 6
figure 6

a the AFM morphology of an alumina scale formed on the substrate (1.4 mm thick, cooling at 1 °C/min) after 25 h oxidation at 1200 °C; b Schematic of the wrinkled surface. By assuming a sine wave, the geometry parameters such as amplitude (A) and half wavelength (L) are indicated

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Fig. 7
figure 7

The amplitude (A) of wrinkles on the alumina scale formed at a different cooling rate and b different substrate thickness. Specimens were oxidized at 1200 °C for 25 h

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Discussion

Two findings in this work are particularly noteworthy: (i) the extent of spallation is not only dependent on the residual stress in the oxide, but also dependent on the cooling rate; (ii) The spallation does not occur immediately after cooling, but requires a period of incubation. The buckles typically start from a size much smaller than that predicted by theory, and then expand with the time until abrupt buckling occurs. The first finding indicates that, besides the stress, there should be another factor that affects the spallation. The second one indicates that there should be a crack nucleation and coalescence process, leading to a time-dependent effect. The mechanisms that govern those phenomena will be discussed in the following.

Interface Degrade by Impurity Segregation

Since the influence of relaxation of the substrate has been ruled out, the most plausible reason is the impurity segregation at the interface, which should be affected by the cooling rate. Generally, the impurity level at high temperature is lower due to a higher solubility in the alloy as compared to that at room temperature. It may remain at a lower impurity level after fast cooling. However, during slow cooling, impurities have enough time to segregate and degrade the interface.

To see if the interface adhesion changes or not, we first examine the interface toughness. According to the mechanics analysis, the spall diameter, d, could be associated with the ratio of the interface toughness, \({\varGamma_{i}^{0}}\), to the fracture toughness of the oxide, Г ox [21]:

$$\frac{d}{h} = 2.2\sqrt {\frac{{E_{ox} }}{{\sigma_{ox} }}} \exp \left( {0.7\frac{{\varGamma_{ox} }}{{\varGamma_{i}^{0} }} - 1.25} \right)$$
(3)

where σ ox is the compressive stress in the oxide, h ox is the oxide thickness, E ox is Young’s modulus. Using the data presented in Fig. 4, with Γ ox  = 20 Jm−2, the estimated mode I interfacial toughness is shown in Fig. 8. All values are higher than that formed on an undoped FeCrAl substrate, which can be attributed to the beneficial effect of the Y addition [1].

Fig. 8
figure 8

Mode I interfacial toughness as a function of cooling rate and substrate thickness. Specimens were oxidized at 1200 °C for 25 h. The thickness of the alumina scale in this calculation is about 4.9 µm, the Young’s modulus Eox = 400 GPa. For 1 °C/min and air cooling, the toughness was estimated based on the buckles near the edge of the spalled disc. The value of an alumina scale grown on an undoped FeCrAl alloy is also superposed

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As shown in Fig. 8, for a given substrate thickness, the interfacial toughness increases as the cooling rate increases. This is because the slow cooling provides more time for impurity segregation. In contrast, for the same cooling rate, the mode I toughness does not vary with the change of substrate thickness. Additional evidence for the increasing interfacial toughness with an increase of cooling rate can be obtained from the compression test. As shown in Fig. 9, at the same compressive strain, a large amount of spallation was produced for 1 °C/min cooled specimen. Conversely, for air-cooled specimen, the scale is adherent. This confirms that the interface becomes weaker after slow cooling.

Fig. 9
figure 9

Surface morphology of the alumina oxide formed on specimens with different cooling rates under the same compressive strain after 25 h oxidation at 1200 °C, a 1 °C/min; b air-cooling. The substrate thickness is 1.4 mm

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Glow discharged optical emission spectroscopy was employed to measure the chemistry across the oxide of the FeCrAlY substrate (0.14 mm) after oxidation for 25 h at 1200 °C with cooling rate of 30 °C/min. In Fig. 10, no sulfur segregation can be identified at the oxide–metal interface, possibly due to the fact that Y in the alloy can inhibit the sulfur segregation. This result consists with that reported by Tolpygo and Viefhaus [8]. Instead, a strong carbon peak was found at the interface. Figure 11a shows etched cross-section of the same FeCrAlY substrate. The segregation was observed at grain boundaries. Figure 11b–d show EDX mapping of Cr, Al and Fe, respectively. The bright area in Fig. 11b suggested that Cr element is segregated at grain boundaries. Other researchers also reported such enrichment at the alumina–metal interface [22–24]. It was proposed that chromium carbide forms at the interface. In addition, Hou’s study on a FeCrAl alloy clearly demonstrated that the amount of chromium carbide depends on the cooling rate. The quantity increases with decreasing cooling rate.

Fig. 10
figure 10

The profiles of carbon and sulfur across the oxide–metal interface measured by GDOES at room temperature. The segregation of carbon at the interface is evident. The substrate thickness is 1.4 mm and cooling rate is 30 °C/min. Specimens were oxidized at 1200 °C for 25 h

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Fig. 11
figure 11

a Cross-sectional SEM image of the etched substrate after oxidation for 25 h in air at 1200 °C with cooling rate of 30 °C/min; and corresponding EDX mapping of b Cr, c Al and d Fe

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Since the formation of chromium carbide degrades the interface [22, 25], the spallation behaviour of alumina scales formed on FeCrAlY substrate can be explained as follows: at high cooling rate, the carbide segregation at the interface is less, thus the bonding between the oxide scale and the substrate is stronger. Although the residual stress is large, there is no buckling. At very low cooling rate, the bonding is weaker, but the residual stress is too low to drive the spallation. In contrast, at a fixed cooling rate, the bonding strength is the same. The scale formed on a thicker substrate has a higher stress, and thus the scale is more prone to spall. In summary, the carbide segregation acts in conjunction with residual stress in the oxide to control the spallation of alumina scales grown on FeCrAlY substrate.

The effects of MIDS and DTS are not considered in this study due to two reasons: i) All specimens are thermal oxidized without cyclic thermal treatment; ii) The FeCrAlY contains Y which may lead to a larger impact than the moisture.

Crack Nucleation by Local Tensile Stress

When undulations are present in the interface, the compressive stresses redistributes at these sites, leading to a normal tensile stress at the peaks [21]. It provides the driving force for local debonding at the interface. For a rough estimation, the undulation was approximated as a thin film attached to a hemisphere. In this case, the wrinkle has a height of 2A and a size of 2L (Fig. 6b). The radius of the hemisphere (R) can be calculated by:

$$R = \frac{{(2A)^{2} + L^{2} }}{4A}$$
(4)

Assuming the stress in the oxide is only caused by the thermal mismatch, the normal stress at the interface is [26]:

$$\sigma_{r} (r = R) = - \frac{{E_{ox} (\alpha_{s} - \alpha_{ox} )\Delta T\left[ {\left( {\frac{{R + h_{ox} }}{R}} \right)^{3} - 1} \right]}}{{1 - 2v_{ox} + \frac{{1 + v_{ox} }}{2}\left( {\frac{{R + h_{ox} }}{R}} \right)^{3} + (1 - 2v_{s} )\frac{{E_{ox} }}{{E_{s} }}\left[ {\left( {\frac{{R + h_{ox} }}{R}} \right)^{3} - 1} \right]}}$$
(5)

where E is the Young’s modulus, α is the coefficient of the thermal expansion, ∆T is the temperature drop from oxidation temperature, ν is Poisson ratio, h is the thickness. The superscripts ‘ox’ and ‘s’ refer to the oxide and the substrate, respectively.

The thermal misfit stress in the alumina oxide on a flat substrate is given by the following approximate expression which is generally used for uniaxial stress [27]:

$$\sigma = \frac{{E_{ox} (\alpha_{s} - \alpha_{ox} )\Delta T}}{{1 - v_{ox} }}$$
(6)

Combining Eq. (5) and (6), the ratio between the normal tensile stress at the interface and the thermal misfit stress (σ p ) in a planar area can be written as:

$$\frac{{\sigma_{r} }}{{\sigma_{p} }}(r = R) = - \frac{{(1 - v_{ox} )\left[ {\left( {\frac{{R + h_{ox} }}{R}} \right)^{3} - 1} \right]}}{{1 - 2v_{ox} + \frac{{1 + v_{ox} }}{2}\left( {\frac{{R + h_{ox} }}{R}} \right)^{3} + (1 - 2v_{s} )\frac{{E_{ox} }}{{E_{s} }}\left[ {\left( {\frac{{R + h_{ox} }}{R}} \right)^{3} - 1} \right]}}$$
(7)

As can be seen, the thermal misfit stress (σ p ) is cancelled at the right side of this equation. Therefore, it can be applied for general conditions without considering the origin of the residual stress. Since the residual stress in the scale contains thermal mismatch stress and growth stress, the values measured by PLPS was substituted for σ p to calculate the normal tensile stress σ r at room temperature.

Figure 12a, b plot the normal tensile stresses estimated for different cooling rates (1, 5, 10, 30 °C/min and air cooling; for thickness of 1.4 mm) and substrate thicknesses (0.48, 1.4, 3.4 and 7.6 mm; under 30 °C/min), respectively. With an increase in the substrate thickness, the tensile stress increases from 0.4 GPa to 1.5 GPa. For a fixed substrate thickness, the tensile stress at intermediate cooling rates, e.g., 5–30 °C/min, is slightly higher than that for slow and fast cooling, indicating a larger driving force for crack nucleation. The values of tensile stress are well beyond the adhesion strength of alumina-iron interface (<0.2 GPa [28]), suggesting the crack could be generated at the peak position. However, this does not necessary lead to buckling. Because the initial separation is usually trapped in the vicinity of wrinkle peak [29], the size is much smaller than the critical value predicted in Fig. 4. Therefore, for buckling to occur, the separation needs to expand by the crack coalescence. This process could be achieved by local plastic deformation of the interface, as will be describe in next part.

Fig. 12
figure 12

The normal tensile stress at the undulation peak for specimens with a different cooling rate; and b different substrate thickness. Specimens were oxidized at 1200 °C for 25 h. The parameters used in this calculation are: E ox  = 400 GPa, E s  = 200 GPa, v ox  = 0.25, and v s  = 0.3

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Crack Coalesce by Local Plastic Deformation

Around the undulated interface, the local stress in the substrate may become large enough to exceed its yield strength and, thereafter, to introduce plastic deformation [30, 31]. If the oxide does not deform, the metal deformation will induce cracks at the interface. Therefore, it is of interest to know if the plastic deformation occurs at room temperature. This requires the effective von Mise stress in the substrate to exceed the yielding strength of the substrate. The effective von Mise stress in the substrate just below the interface can be approximated as [31]:

$$\sigma_{e} = \left| \sigma \right|\frac{A}{L}Q(\alpha_{D} )$$

with

$$Q(\alpha_{D} ) = 3(1 - \alpha_{D} ) - \frac{1}{2}(1 - \alpha_{D} )^{2}$$
(8)

where σ is the residual stress of the oxide in a planar position, A and L are the amplitude and the half wavelength of the wrinkle, respectively. α D is the Dundur’s parameter which dependent on the elastic modulus of the oxide and the substrate (α D  = 0.31 in this work).

Figure 13 gives the effective von Mise stress in the substrate just below the wrinkles. In general, the von Mise stress is higher for a higher cooling rate, or a thicker substrate. All values, except the 0.48 mm thick substrate, are higher than the yielding stress of FeCrAlY at room temperature. This indicates that, even after cooling to the room temperature, plastic deformation still occurs under the wrinkled interface. Since the amplitude to wavelength (A/L) ratio is rather small (0.07–0.2), the plastic deformation is almost parallel to the interface. Because the oxide at room temperature is much stiffer, the plastic deformation in the substrate cannot match the oxide, leading to crack at the interface. By this way, the local debonding presented at the peak of a wrinkle could coalesce and expand with time. Once it reaches the critical size, spontaneous buckling occurs. This might explain the time-dependent buckling behaviour for alumina scales.

Fig. 13
figure 13

The effective von Mise stress just below the undulation peak for specimens with a different cooling rate; and b different substrate thickness. Specimens were oxidized at 1200 °C for 25 h. The yielding strength (σ Y ) of FeCrAlY substrate at room temperature is also indicated by the dash-dot line

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One implication from the above discussion is that, the microscopic roughness at the interface is crucial to the crack nucleation and coalescence. The microscopic roughness is induced by the creep of the oxide, either during oxidation or during cooling. It is expected that reducing the growth stress, or increasing the creep strength of the oxide, should minimize the wrinkling of the oxide. The latter is of importance for practical reasons. For example, doping the grain boundary by yttrium can improve the creep resistance of alumina [32, 33]. Thus the addition of yttrium to alumina forming alloy usually results in a flat scale. In this case, the tensile stress and von Mise stress are smaller, which in turn, suppressing the crack nucleation and coalescence. This partially explains the beneficial effect of yttrium.

It should be emphasized that, as seen from Figs. 12a and 13a, for a given substrate thickness, both the tensile stress and von Mise stress favor the crack nucleation and coalescence. However, the experimental observations do not support this argument. Figure 12a indicates that values of tensile stresses are all larger than the adhesion strength of alumina-iron interface (0.2 GPa). Figure 13a indicates that the effective von Mise stresses in the substrates are all beyond the yielding stress of FeCrAlY at room temperature. Therefore, spallation should be observed on all specimens. However, in the experiment, only at intermediate cooling rate, the spallation can be seen. There should be another mechanism that affects the crack nucleation and propagation. Further works need to be carried out to investigate this phenomenon.

Conclusions

The spallation behaviour of an alumina scale formed on FeCrAlY alloy was investigated. Two interesting phenomena were observed: (i) the extent of spallation is not only dependent on the residual stress in the oxide, but also dependent on the cooling rate; (ii) The spallation does not occur immediately after cooling, but requires a period of incubation. Analysis into those phenomena leads to the following conclusions:

  1. (1)

    The carbide segregation acts with residual stress in the oxide to control the spallation of alumina scale. After cooling, the chromium carbide forms at the interface and weaken the interface. Its quantity decreases with increasing cooling rate. After very slow cooling, the interface is weakened but the stress is too low to motivate spalling. After fast cooling, the stress is high but the interface is strong (no buckling). At a fixed cooling rate, the segregation is the same while the stresses are larger in a thicker substrate, and thus the scale is more prone to buckle.

  2. (2)

    The microscopic winkling at the interface is crucial to the crack nucleation and coalescence. The residual stresses redistribute at the undulation sites and generate a normal tensile stress at the ridges, resulting in local debonding at the interface. Meanwhile, the effective von Mise stress under the wrinkle exceeds the yielding strength of the substrate, resulting in a local plastic deformation. As a result, the cracks coalesce. Once the separation reaches the critical size, buckling spontaneously occurs.