Measurement of the strains induced upon thermal oxidation of an alumina-forming alloy

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1 Acta Materialia 51 (2003) Measureent of the strains induced upon theral oxidation of an aluina-foring alloy K.-J. Kang a,, J.W. Hutchinson b, A.G. Evans c a Departent of Mechanical Engineering, Chonna National University, Kwangju, , South Korea b Division of Engineering and Applied Sciences, Harvard University, Cabridge, MA 02138, USA c Materials Departent, University of California, Santa Barbara, CA , USA Received 24 Septeber 2002; accepted 31 October 2002 Abstract The echaniss that govern the foration of a therally grown aluina on Al-containing super-alloys has been the subject of uch recent speculation, because of the key influence of this oxide on the durability of theral barrier systes for gas turbines. Aong the iportant issues to be resolved are the location of the new oxide growth (interface, surface or internal grain boundary), the strains induced by the growth on non-planar surfaces and the associated stresses. To address soe of the uncertainties, an experiental probe is designed. The experients are based on the curvature changes,, that occur on curved thin foils, caused by differences in strain accoodation on convex and concave surfaces. Experients perfored on thin FeCrAlY foils provide a vivid illustration of the strains induced upon growth, deonstrating a large increase in the radius of curvature upon oxidation. The sign and agnitude of the changes affir that ost of the new oxide fors at the interface Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Theral barrier coatings; Oxidation; Therally grown oxides; Growth stresses 1. Introduction Multi-layer theral barrier systes are now coonly used in gas turbines [1 3]. They coprise a single crystal Ni alloy substrate, an interediate Ni(Al) alloy layer (the bond coat) that acts as a barrier to oxidation and an outer layer, typically yttria-stabilized zirconia, that provides the theral insulation. A therally grown oxide Corresponding author. Tel.: ; fax: E-ail address: kjkang@chonna.ac.kr (K.-J. Kang). (TGO), generally α Al 2 O 3, fors between these two layers upon exposure to oxygen at high teperature [1 11]. The presence of the TGO often doinates the perforance and durability of the syste. That is, as the TGO layer thickens, the stresses induced in this layer, as the syste therally cycles, interact with the surrounding aterial to instigate failure echaniss. Several such echaniss have been described [1 4,7 10]. There are two sources of stress in the TGO: both noinally copressive [1,4,6,11]. One is governed by the theral expansion isfit with the substrate. It has been coprehensively characterized by piezo-spectroscopy and X-ray easureents [ /03/$ Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. doi: /s (02)

2 1284 K.-J. Kang et al. / Acta Materialia 51 (2003) ]. The other, associated with strains induced upon growth of the TGO, has only recently been subject to a fundaental assessent [15]. This strain is the source of growth related displaceents and stresses. When the oxide fors, it occupies a larger volue than the original alloy. The ratio of the volue of the oxide to the alloy consued,, is a basic paraeter [1,16 19]. It is related to (but not the sae as) the Pilling Bedworth ratio [19]. It will be estiated experientally in this study. For typical bond coats, ost of the new oxide has been surised to for at the interface, as oxygen anion ingress along the TGO grain boundaries encounters the Al in the alloy, resulting in thickening of the TGO [1 3,15,20] (Fig. 1). Soe of the oxide also fors on grain boundaries internal to the TGO, presuably due to a counter flux of Al cations and O anions [15,20,22]. New easureent protocols are needed to guide further understanding. The present article describes a ethod capable of deterining where the new TGO fors. The ethod originates with two prior explorations: (a) an analysis of the displaceent of curved, thin foils upon oxidation [16] and (b) a series of easureents involving α Al 2 O 3 foration on thin, flat foils of FeCrAlY [20]. On curved surfaces, the sign of the stresses induced as the TGO grows depends on the predoinant foration site for the new oxide, as well as whether the surface is concave or convex. The consequence is that a thin ribbon of curved bond coat aterial develops a bending oent as it oxidizes, causing the curvature to change [16,21]. The sign of the curvature change (positive or negative), and its agnitude, are sensitive to the growth site. Based on these concepts, an experiental approach is devised, based priarily on the U-configuration depicted on Fig. 2. Measureents are perfored on ribbons of FeCrAlY, which oxidizes to for α Al 2 O 3, with the new oxide believed to for predoinantly at the interface [1,15,20,22]. 2. Basic concepts For anion-controlled oxide growth, on a convex surface, the alloy beneath the interface is replaced by an oxide with a larger radial diension Fig. 1. Scheatic of the growth of oxide layers under: (a) cation-diffusion controlled and (b) anion-diffusion controlled conditions, showing the ion fluxes and diffusion paths. In both cases, oxide growth occurs noral to the etal/oxide interface. (c) Mixed internal and interface foration of new oxide. The diensions used in Appendix A are also shown. [1,15,21]. For displaceent copatibility, the oxide ust expand radially by placing it in tangential tension, cobined with a sall radial copression [16]. For a concave surface, the corresponding growth requires that the oxide contract

3 K.-J. Kang et al. / Acta Materialia 51 (2003) radially, causing it to be in tangential copression. The converse effects occur for cation-controlled growth [16]. Accordingly, the TGO experiences growth stresses of opposite sign on concave and convex surfaces and, oreover, the signs are inverted for the anion and cation controlled cases. These signs reain unchanged when the configuration becoes a curved thin ribbon (Fig. 2), although the agnitudes are altered. Because the stresses in the TGO have opposite signs on the opposing surfaces, they ipose a bending oent that causes the curvature to change. For anion-control, since the concave surface is in copression and vice versa, the oent acts outward and the radius of curvature, R, increases. Conversely, for cation-control, the inward acting oent causes R to decrease. The experients are perfored on FeCrAlY foils. To facilitate interpretation, the foil thickness and test teperature have been chosen to assure that the stresses in the FeCrAlY are relaxed by creep, while the TGO reains essentially elastic. Based on the extensive assessent by Tolpygo and Clarke [11,22], this criterion appears to be satisfied for foils having thickness, H 160 µ, and a test teperature about 1200 C. 3. Experiental protocol 3.1. Experiental procedures Fig. 2. Scheatic of the test ethodology based on a U- shaped specien. The as-received alloy foils, which were in the as-rolled state, were cut into ribbons and the edges polished. They were annealed at 800 C for 10 in to equilibrate the icrostructure, then echanically polished to optical flatness using 3 µ diaond paste and cleaned in acetone. Subsequently, they were defored around a 4 diaeter andrel to create a U by tensile loading to 250 N in a servo-hydraulic achine, through a friction grip, at a displaceent rate of 1 µ/s. They were degreased in acetone and annealed at 420 C for 12 h to reove the residual stress. The U-shaped foils were claped into a ceraic fixture within a resistance furnace (Fig. 2). Tests were conducted at 1200 C. The axiu width, d ax, was easured as a function of the exposure tie, by using an optical telescope. The ass of the speciens was deterined before and after each test. Once the tests had been copleted, the oxidized ribbons were sectioned using a focused ion bea (FIB) syste to avert the edge rounding that occurs upon echanical grinding and polishing. The thickness of the TGO was easured and recorded. 4. Measureents and observations 4.1. Voluetric strain The experients were conducted on 90 µ thick FeCrAlY foils in the U-configuration. The TGO thickness, h, was easured on speciens subjected to a range of exposure ties by creating FIB sections and iaging. The results revealed a thickening (Fig. 3) that deviates slightly fro parabolic. The thickness is found to be the sae on both the concave and convex sides. A plot of the ass change against the easured TGO thickness

4 1286 K.-J. Kang et al. / Acta Materialia 51 (2003) Fig. 3. Plot of TGO thickness as a function of exposure tie: The square root of tie ( h) is used as the abscissa to assess the suitability of the parabolic rate approxiation. Fig. 5. Change in the ribbon thickness as a function of total TGO thickness. obtained on the sae speciens (Fig. 4) indicates the expected linearity. The sae sections were used to easure the change in the overall thickness of the foils, H H 0, plotted against the total TGO thickness, 2h, on Fig. 5. Fro geoetry, the slope of this plot, l (H H 0 )/2h, is related to the noral coponent of the stress-free strain upon oxidation (Appendix A). Moreover, since the fraction of the new oxide created at the interface appreciably exceeds that fored on the internal grain boundaries [15], this easureent provides an estiate of the voluetric strain: [1 λ] (1) Fig. 4. Correlation between change in ass per unit area and the TGO thickness. This strain is larger than the Pilling Bedworth ratio for conversion of Al α Al 2 O 3 [19], presuably because of the sall reduction in the β FeCrAlY lattice constant as Al is reoved U-configuration In situ optical iages taken of the FeCrAlY foils at the beginning and the end of an isotheral exposure are shown in Fig. 6. The outward deflections caused by TGO growth are illustrated. The sign of the change iediately indicates that the new oxide fors priarily at the alloy/oxide interface. Such iages were used to easure the displaceent at the location of the axiu, d ax. Results for five of the tests are suarized in Fig. 7(a). While there is evident variability between speciens, the trend appears to be systeatic. After subjecting such speciens to various exposures, FIB sections were used to easure the TGO thickness. This procedure allows deterination of the relationship between d ax and h, as plotted on Fig. 7(b). This result provides the basis for a coparison with theory, upon superposing predicted curves onto the figure.

5 K.-J. Kang et al. / Acta Materialia 51 (2003) Fig. 6. Iages obtained before and after isotheral oxidation, showing the change in the shape of the U-geoetry. 5. Deflection analysis 5.1. Constant curvature segent The U-specien is analyzed by first iagining that the curved segent is detached fro the straight sides and its curvature change deterined as a function of the growing oxide. This segent drives the deforation of the entire U-specien (Fig. 8). The re-attachent is addressed in the subsequent section. A detached segent of constant Fig. 7. (a) Changes in the axiu deflection of the U with tie easured on five different speciens (designated A E) using h the abscissa (see Fig. 3). (b) Variation in the axiu deflection with the TGO thickness easured on eight separate speciens. Theoretical results are superposed for two choices of the volue expansion paraeter,.

6 1288 K.-J. Kang et al. / Acta Materialia 51 (2003) following stress changes in the TGO layers (Fig. 8): ṡ + 1 Ē tgo ḣ Ē tgo ė g ṡ 1 Ē tgo ḣ Ē tgo ė g (2) where Ē tgo E tgo /(1 v 2 tgo) is the plane strain tensile odulus. Since the lateral growth strain is sall [15], it has not been subtracted fro the contribution to the TGO thickness increent. For cation-controlled growth, the corresponding stress changes in the TGO layers would be: ṡ + 1 Ē tgo ḣ Ē tgo ė g ṡ 1 Ē tgo ḣ Ē tgo ė g (3) The stresses (2) and (3) arise when the U-segent is otherwise constrained against deforation. The associated bending oent and lateral force increents are, for anion-control: Fig. 8. Sketches of the geoetry and the ethod used to deterine the displaceents and stresses that develop upon oxidation of a thin ribbon in a U-configuration. Ṁ (ṡ + ṡ )hhb 1 Ē tgo hhbḣ Ḟ 0 (ṡ + ṡ )bh 2Ē tgo hbė g. (4) radius of curvature, R, and curvature, 1/R, is considered (Fig. 8). The width of the strip is b, s bc Y is the flow strength of the alloy at the oxidation teperature and h 0 is a reference (initial) thickness of the TGO. Attention will be directed to the condition, h / H 1, such that the change in curvature,, reains sall copared to. For anion-controlled growth, pertinent to TGO foration on FeCrAlY, an increent ḣ of new TGO fors at the TGO/bond coat interface by consuption of bond coat, thickness ḣ/. During the sae increent, an unconstrained lateral growth strain, ė g, occurs uniforly through the TGO. If the curvature change,, as well as the id-surface strain change, ė 0, is constrained to be zero (subsequently, they will be deterined by superposition), the growth increent induces the Increents of curvature,, and id-surface strain, ė 0, of the coposite segent are obtained by superiposing equal and opposite oent and force increents to those in (4). The TGO is taken to be elastic. The bond coat is elastic/perfectly plastic in accordance with its low creep resistance at the TGO growth teperature [19]. The additional strain increents in the segent are ė z ė 0 where z is the distance fro the id-surface. The additional stresses in the TGO are given by ṡ Ē tgo ė and those in the bond coat by ṡ Ē bc ė for s s bc Y and ṡ 0 for s s bc Y. For anion-control, consistent with the outward deflection of the U observed experientally (Fig. 6), the equations for and ė 0 obtained fro iposing Ṁ Ṁ 0 and Ḟ Ḟ 0 are (h/h 1):

7 K.-J. Kang et al. / Acta Materialia 51 (2003) H ė 0 1 /2 2hĒ tgo ṡdz ė H/2 (5) H 2 /2 Ē tgo hh ṡzdz ḣ H. H/2 The integrals in (5) are the contributions fro the bond coat. Two liits are of interest. If the bond coat is elastic, (5) gives: ė 0 ė g 1 H 1 Ē bc 2hE tgo 2 1 H 1 ḣ H (6) Ē bc 6hE tgo If the bond coat is fully plastic (at yield though the thickness), the solution is: ė 0 ė g 2 1 ḣ H. (7) It is evident fro both liits that the integrated initial TGO thickness h h 0. The resulting curvature change as a function of h is plotted in Fig. 9 for five values of e Y s bc Y /Ē bc, including the fully plastic liit, e bc Y 0. The paraeter values chosen for this plot are appropriate for the speciens used in the experients: i 1/R i 1/2, H 90 µ, 2.2, and Ē tgo /Ē bc 2. The lateral growth strain increent is taken ė g 0.4ḣ/H which results in e g 0.02 when h /H The TGO thickness at the start of the growth calculation was taken to be h 0 /H The curves in Fig. 9 show that the transition fro elastic to fully plastic behavior is abrupt. Moreover, the transition occurs when the TGO thickness is sufficiently large that the growth strain fully yields the bond coat core. Should this transition be explored experientally it would be possible to extract inforation about the lateral growth strain. This has not been accoplished in the present experients The full U-specien The second step of the analysis neglects the creep resistance of the bond coat. This is tanta- change in curvature,, is sall copared to the initial curvature whenever h /H 1. Note that the lateral growth strain has no influence on the change in curvature, but it does play an iportant role in deterining the transition between the two liits, as evident fro the following nuerical exaple. Accordingly, the present easureent protocol has liited potential for exploring lateral strains that lead to the TGO growth stress. Its priary utility is in understanding the preference for the new TGO growth to occur at the interface relative to the free surface. The increental Eq. (5) have been solved nuerically for the transition fro elastic to fullyplastic behavior by explicitly accounting for the expanding regions of plastic yielding in the bond coat as TGO growth progresses. The increental solution was integrated with respect to increasing h, starting fro an initial stress-free state at an Fig. 9. The role of the yield strength of the bond coat in deterining the transition fro elastic to fully plastic behavior of the core, anifest in a plot of the ratio of the change in curvature to initial curvature, /, as a function of TGO to bond coat thickness, h /H, for an unconstrained curved segent undergoing anion controlled growth. The paraeters for the syste are specified in the text.

8 1290 K.-J. Kang et al. / Acta Materialia 51 (2003) ount to assuing the increental bending resistance of the bea derives solely fro the outer elastic TGO layers: B Ē tgo hh 2 b/2. The justification is apparent fro Fig. 9. Note that, for this situation, the strains resulting fro lateral growth are uncoupled fro the bending and have essentially no influence on the deflection. The increental proble for the full U is shown in Fig. 8. A oent equal but opposite in sense to that produced by the constrained growth increent, is applied at the intersections of the curved and straight segents of the U. That is, the U is notionally held at the intersection of curved segent with the straight sides and then released by applying Ṁ 0, as depicted in Fig. 8, resulting in adeflection. The proble in Fig. 8 can be solved by standard ethods in structural echanics. Each segent is statically deterinant and subject to unknown oent and transverse force at its ends. Continuity of displaceent and rotation ust be enforced at the intersections. (The sides are claped at the top.) The solution for the increent in the deflection of the straight 3 sides, ḋ(x), is found to be: ḋ(x) Ṁ 0 R 2 /B c 1 L x L 3 c x 2 L 2. x (8) Here, L/R, and the coefficients c 1 and c 2 satisfy c 1 [p/4 3 /3] c 2 [1 2 /2] 1 c 1 [1 2 /2] c 2 [p/2 ] p/2. Accordingly, fro (4): 10 for three values of L/R. For the specien to be used in the experients, 15. For l 1, the axiu displaceent, d ax, occurs at x /L 2/3 and is given by: d ax 8p L 27 1 h H. (11) This asyptotic expression neglects ters of relative order 1/. For 15, (11) overestiates the axiu deflection by 17%. The coparisons between (11) and the easureents are presented in Fig. 7(b). As already noted, the sign affirs that the new TGO fors priarily at the TGO/alloy interface. The prediction soewhat underestiates the easureents when the volue expansion paraeter, 2.2, (derived above) is used. Moreover, the largest realizable displaceent (that arises when ) exceeds the easureents. The iplication is that a close correlation between experient and theory requires, 3. This coparison shows that, subject to independent inforation about the volue expansion paraeter, the U-test identifies the preferred location for new TGO foration in a consistent anner. Moreover, by expanding the scope of the test to different teperatures in order to exaine responses around the transition fro elastic to fully plastic behavior in the alloy (Fig. 9), it ight be possible to assess the lateral growth strain and the associated growth stress. Ṁ 0 R 2 B 2 1 R ḣ (9) H Note that the deflection increents are proportional to ḣ and independent of h. It follows that the total deflection of one side can be integrated trivially (h /H 1) to give: d(x) R H c h 1 L x L 2 x 3 c 2 L x 2. (10) Plots of noralized deflection are presented in Fig. Fig. 10. Noralized deflection of the sides of the U-specien.

9 K.-J. Kang et al. / Acta Materialia 51 (2003) Conclusion An experiental probe has been designed to explore the location of the new oxide foration upon oxidation. The experients are based on the curvature changes,, that occur on curved thin foils, caused by differences in strain accoodation on convex and concave surfaces. Experients perfored on thin FeCrAlY foils deonstrate a substantial increase in the radius of curvature upon oxidation, affiring that the new oxide fors priarily at the TGO/alloy interface. The situation has been analyzed by accounting for the stress relaxation that occurs in the alloy during the oxidation process. The agnitudes of the changes are found to be consistent with the experiental easureents for reasonable choices of the volue expansion paraeter governing conversion of the alloy to oxide. This consis tency suggests the possibility that the scope of the tests ight be expanded to explore the lateral growth strain. The odel reveals that this ight be achieved upon testing over a sufficient range of teperature to cause the alloy to respond to the TGO strain in a anner that changes fro fully plastic (as in the present tests) to elastic/plastic or elastic. Appendix A Growth strain Consider the proble where the volue rate of etal to be oxidized per unit area of interface is, V. Let this volue partition between the interface, V I, and the internal grain boundaries, V GB, (Fig. 1) such that V V I V GB. (A1) Since 1 is the net stress-free strain noral to the interface as the etal is converted into oxide, the thickening rate for the TGO is related to V I by: ḣ ( 1)V I. (A2) If grains in the TGO are taken to be colunar and have diension D, the volue of new oxide created on the grain boundaries causes the grains to increase in width, resulting in a growth strain. Since the etal is drawn into the boundaries and then oxidizes, fro geoetry (Fig. 1): 2hDḊ D 2 V GB. (A3) The growth strain-rate is related to the grain size change as: ė g Ḋ/D (A4) whereupon, with (A3): ė g V GB /2h. (A5) With the assuption that a fixed fraction R of the new TGO fors internally, regardless of the TGO thickness, then fro (A2) and (A5): ḣ ( 1)(1 R)V ė g RV /2h. (A6) Eliinating V fro (A6) gives: ė g kḣ/hk R/2( 1)(1 R). (A7) References [1] Evans AG, Mu DR, Hutchinson JW, Meier GH, Pettit FS. Prog. Mater. Sci. 2001;46: [2] Stiger MJ, Yanar NM, Topping MG, Pettit FS, Meier GH. Z. Metallkd 1999;90: [3] Padture N. Jordan. Science 2002;296: [4] Tolpygo VK, Clarke DR. Acta Mater. 2000;48: [5] Shillington EAG, Clarke DR. Acta Mater. 1999;47: [6] Evans AG, He MY, Hutchinson JW. Prog. Mater. Sci. 2001;46: [7] He MY, Evans AG, Hutchinson JW. Acta Mater. 2000;48: [8] Karlsson AM, Evans AG. Acta Mater. 2001;49: [9] Mu DR, Evans AG, Spitsberg IT. Acta Mater. 2001;49: [10] Gell M, Jordan E, Vaidyanathan K, McCarron K. Surf. Coat Technol. 1999; : [11] Tolpygo VK, Dryden JR, Clarke DR. Acta Mater. 2001;46: [12] He J, Clarke DR. J. A. Cera. Soc. 1995;78: [13] Lipkin DM, Clarke DR. Oxid. Met. 1996;45: [14] Christensen RJ, Lipkin DM, Clarke DR. Appl. Phys. Lett. 1996;69: [15] Clarke DR, Acta Mater., in press. [16] Dove DB, Baldwin DH. Metall. Trans. 1974;5: [17] Cannon RM, Hou PY. In: Hou PY, McNallan MJ, Oltra R, Opila EJ, Shores DA, editors. Proceedings of the Syposiu on High Teperature Corrosion and Materials Cheistry. Pennington, NJ: Electrocheistry Society; p [18] Evans AG, Cannon RM. Mater. Sci. Foru 1989;43: [19] Pilling NB, Bedworth RE. J. Inst. Met. 1923;29: [20] Tolpygo VK, Clarke DR. Oxid. Met. 1998;49: [21] Rhines FN, Wolf JS. Metall. Trans. 1970;1: [22] Tolpygo VK, Clarke DR. Acta Mater. 1999;47: