UTC 2012
`General Electric v. United Technologies
`IPR2016-01289
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`1.2.1. Generalities .................................................................................. ..511
`
`1.2.2. Specific mechanisms ..................................................................... ..513
`1.2.3. Related observations .................................................................... ..514
`
`1.3. Overarching principles ........................................................................... ..5l6
`
`2. Thermally grown oxides ................................................................................. ..517
`2.1. Growth phenomena ................................................................................ ..517
`2.1.1. Thermodynamics .......................................................................... ..518
`2.2. Stresses .................................................................................................... ..52l
`
`2.2.1. Thermal expansion misfit stresses around imperfections ............. ..522
`2.2.2. Redistribution of misfit stresses by bond coat Visco-plasticity ..... ..523
`2.2.3. Growth stresses .......................... ..‘ ................................................ ..524
`
`2.2.4. Creep relaxation ........................................................................... ..527
`2.3. Adhesion ................................................................................................. ..528
`
`2.3.1. Metal/oxide interfaces .................................................................. ..528
`2.3.2. Mechanics .................................................................................... ..529
`
`2.3.3. Test protocols ............................................................................... ..530
`2.3.4. Measurements .............................................................................. ..531
`
`2.4. Failure ..................................................................................................... ..531
`
`3. TBC failure mechanisms ................................................................................. ..532
`
`3.1. TBC properties ....................................................................................... ..532
`3.1.1. Stress/strain relationships ............................................................. ..532
`3.1.2. Fracture resistance ....................................................................... ..533
`
`3.2. The role of imperfections ........................................................................ ..535
`3.3. Stresses, cracking and failure ................................................................. ..538
`
`4. Closure ............................................................................................................ ..542
`
`Appendix A. Small scale buckling ....................................................................... ..543
`A1. Buckling maps ......................................................................................... ..543
`A2. Role of imperfections .............................................................................. ..544
`
`Appendix B. Stresses ........................................................................................... ..545
`B1. Thermal expansion misfit ........................................................................ ..545
`B2. Oxide growth .......................................................................................... ..546
`
`Appendix C. Stress intensity factors .................................................................... ..547
`
`Appendix D. TGO creep/growth dynamics ......................................................... ..548
`
`Appendix E. Ratcheting ...................................................................................... ..549
`
`References ........................................................................................................... .. 549
`
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`1. Background
`
`1.1. The system
`
`Thermal barrier coatings (TBCS) are widely used in turbines for propulsion and
`power generation [l—9]. They comprise thermally insulating materials having suificient
`thickness and durability that they can sustain an appreciable temperature difference
`between the load bearing alloy and the coating surface. The benefit of these coatings
`results from their ability to sustain high thermal gradients in the presence of adequate
`back-side cooling. Lowering the temperature of the metal substrate prolongs the life
`of the component: whether from environmental attack, creep rupture, or fatigue. In
`addition, by reducing the thermal gradients in the metal, the coating diminishes the
`driving force for thermal fatigue. Both of these benefits can be traded off in design for
`greater component durability, or for reduced cooling air or for higher gas temperature/
`improved system efliciency. As a result, TBCS have been increasingly used in turbine
`engines. Successful implementation has required comprehensive testing protocols,
`facilitated by engineering models [9—l2]. Expanded application to more demanding
`scenarios (Fig. 1) requires that their basic thermo-mechanical characteristics be
`understood and quantified. This need provides the opportunities and challenges
`discussed in this article.
`
`There are four primary constituents in a thermal protection system (Fig. 2). They
`comprise (i) the TBC itself, (ii) the superalloy substrate, (iii) an aluminum containing
`bond coat (BC) between the substrate and the TBC, and (iv) a thermally grown
`oxide (TGO), predominantly alumina, that forms between the TBC and the BC. The
`TBC is the insulator, the TGO on the BC provides the oxidation protection and the
`alloy sustains the structural loads. The TGO is a reaction product. Each of these
`elements is dynamic and all interact to control the performance and durability.
`
`
`
`Gas
`
`Temperature
`
`New Materials
` Super Alloys
`
`*
`
`T
`
`
`
`
`
`Fig. 1. Schematic indicating the operating domain for TBCs and the challenge for a new generation of
`materials.
`
`Log (Cyclic Life)
`
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`The thermal barrier coating is a thermally insulating, “strain tolerant” oxide. Zirconia
`has emerged as the preferred material, stabilized into its cubic/tetragonal forms by
`the addition of yttria in solid solution. This material has low thermal conductivity
`(~l W/m2 K) with minimal temperature sensitivity (Fig. 3) [13,83]. The thermal
`resistance at lower temperatures corresponds to a phonon mean free path governed by
`structural vacancy scattering. Complex oxides having even lower conduction are being
`investigated, but there is no aflirmation of their viability as TBCS. Strain tolerance is
`designed into the material to avoid instantaneous delamination from the thermal
`expansion misfit. Two methods are used to deposit strain-tolerant TBCS. Electron
`beam physical Vapor deposition (EB-PVD) evaporates the oxide from an ingot and
`directs the vapor onto the preheated component [2,5, 14]. The deposition conditions are
`designed to create a columnar grain structure with multiscale porosity (Fig. 2) that pro-
`vides the strain tolerance and also reduces the thermal conductivity (to about 0.5 W/m K,
`Fig. 3). Air plasma spray (APS) deposition is a lower cost alternative [l5—l7]. The
`deposition is designed to incorporate intersplat porosity and a network of crack—like
`voids that again provides some strain tolerance, while lowering the thermal conductivity.
`The thermally grown oxide has a major influence on TBC durability [8—l2,l8—20].
`The bond coat alloy is designed as a local Al reservoir (Fig. 2), enabling cc-alumina
`to form in preference to other oxides, as oxygen ingresses through the TBC (which is
`
`REQUIREMENTS is
`
`Low Thermal Conductivity.
`Strain Tolerance.
`OXIDE THERMAL
`
`
`BARRIER (TBC)
` Chemical Compatibility.‘
`
`
`
`
`
`Ot-Ail2O3
`Lowest Thickness.
`THERMAL” GROWN
`war» if’ ”§;‘,312l.Z“§L”§.°J&§Y‘
`
`
`Adherent with BC.
`
`
`
`
`
`
` DESIGNATION
`
`
`
`ill
`
`
`
`
`-
`
` Chemically Homogeneous.
`
`
`
`
`Forms on — N2 03.
`
`Intermetallic (B, Y’, Y)
`
`Bond Coat (BC) -’
`Devoid Of Segteganis.
`
`Creep/Yield Resistant.
`
`
`
`Fig. 2. The four major elements of a thermal barrier system: each element changes with exposure/cycling.
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`1 transparent to oxygen). Alumina is the preferred oxide because of its low oxygen
`diffusivity and superior adherence. This layer develops extremely large residual
`compressions (3-6 GPa, Fig. 4), as the system cools to ambient, primarily because of
`its thermal expansion misfit with the substrate (Fig. 5, Table 1) [2l—27]. Stresses also
`arise during TGO growth [19,21]. They are much smaller (generally less than l GPa),
`
`Fiuorite-Type
`Oxides
`
`(W/mK)
`ThermalConductivity
`
`
`Solid Solution Thu, U030
`
`0
`
`500 i
`
`1000
`
`1500
`
`2000
`
`Temperature,
`
`(C)
`
`Fig. 3. The thermal conductivity of several insulating oxides illustrating the major role of solid solutions
`in aifecting phonon transport.
`
`Tex = 1100°c
`
`[GPa]
`CompressiveStress
`
`
`@ Ni-based
`
`Superalloys
`
`0.1
`
`1.0
`
`10
`
`100
`
`1000
`
`OxidationTime [h]
`
`Fig. 4. Ambient residual compressions measured in the TGO developed on several alloy systems (after
`[21]).
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`
`ENGINE
`ALLOYS
`
`(‘.0O
`
`NO
`
`
`
`
`
`
`
` .4. C ThermalExpansionCoefficient(ppmC'l)
`
`1
`
`100
`10
`Thermal Conductivity (W/mK)
`
`A
`
`0
`
`1000
`
`Fig. 5. Cross plot of the thermal expansion coefficient and thermal conductivity of the major material
`constituents in the TBC system.
`
`Table 1
`
`Summary of material properties
`
`TGO (O!-A1103)
`Young’s modulus, E0 (GPa)
`Growth stress, afix (GPa)
`Misfit compression, 0'0 (GPa)
`Mode I fracture toughness, F0 (J m”-)
`Thermal expansion coefficient, ozo (C"‘ ppm)
`
`Bond coat
`Young’s modulus, ES (GPa)
`Yield strength (ambient temperature) ay (MPa)
`Thermal expansion coefficient, as (C“ ppm)
`
`Interface (oz-A1203/bond coat)
`Mode l adhesion energy, F? (J m"2)
`Segregated
`Clean
`
`TBC (ZrO2/YZO3)
`Thermal expansion coefl"1cient, oztbc (C‘1 ppm)
`Young’s modulus, Etbc (GPa)
`Delamination toughness PM (I m‘2)
`
`350-400
`0-1
`3-4
`20
`8-9
`
`200
`300-900
`l3-16
`
`5-20
`> 100
`
`ll-13
`0-100
`l-100
`
`
`
`\
`
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`x
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`511
`
`but still important. Though thin (3—l0 pm), the high energy density in the TGO
`motivates the failure mechanisms discussed in Section 3.
`
`The bond coat is arguably the most crucial component of the TBC system. Its
`chemistry and microstructure influence durability through the structure and mor-
`phology of the TGO created as it oxidizes [19]. Moreover, system performance is
`linked to its creep and yield characteristics. Bond coats are in two categories. One is
`based on the NiCo CrAl Y system, typically deposited by low-pressure plasma spraying
`(LPPS). It is usually two-phase [[3-NiAl and either y-Ni solid solution or y’-Ni3Al].
`The y/y’ phases have various other elements in solution. The Y is added at low
`concentrations to improve the adhesion of the TGO, primarily by acting as a solid
`state gettering site for S [28—31], which diffuses up from the substrate. In some cases,
`small amounts of a Ni—Y intermetallic may also be present. The second category
`consists of a’Pt-modified diflusion alaminide, fabricated by electroplating a thin layer
`of Pt onto the superalloy and then aluminizing by either pack cementation or chemical
`vapor deposition. These coatings are typically single-phase-[3, with Pt in solid solution
`[19]. Their composition evolves during manufacture and in-service. Diffusion of Al into
`the substrate results in the formation of y’ at [3 grain boundaries [19].
`The interface between the TG0 and bond coat is another critical element. It can be
`embrittled by segregation, particularly of S [28—3 1]. During thermal exposure, S from the
`alloy migrates to the interface. Dopant elements present in the BC getter much of this S
`and suppress (but not eliminate) the embrittlement. As already noted, bond coats based
`on NiCoCrA1 contain Y for this purpose. The Pt—aluminide BCs do not contain elements
`which getter S. Nevertheless, they are durable and can have longer lives in cyclic oxida-
`tion than NiCoCrAlY systems [30]. While it has been proposed that the Pt mitigates the
`eifects of S [31], there is no fundamental reason to expect this. A number of etfects of
`Pt on the behavior of Pt-modified aluminides have been documented [32] but a
`complete understanding of the “Pt effect” is an important goal for future research.
`A systems approach to TBC design and performance requires that several basic bifur-
`cations be recognized and characterized. Three of the most important are addressed.
`i. The NiCoCrAlY and Pt—aluminide bond coats result in distinct TGO char-
`
`acteristics as well as differing tendencies for plastic deformation. Accordingly, the
`failure mechanisms are often different.
`
`ii. TBCS made by APS and EB-PVD are so disparate in their microstructure, mor-
`phology and thermo-physical properties that different failure mechanisms apply.
`iii. The failure mechanisms may differ for the two predominant areas of application
`(propulsion and power generation), because of vastly different thermal histories.
`Systems used for propulsion and for power peaking experience multiple thermal
`cycles, whereas most power systems operate largely in an isothermal mode with few
`cycles. The frequency aifects coating durability.
`
`1.2. Failure phenomena
`
`1.2.]. Generalities
`
`Thermal barrier systems exhibit multiple failure mechanisms. Some of the most
`prevalent are indicated in Fig. 6. (i) In some cases, spinels form either between the
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`
`
`Chemical
`
`Thermomechanical
`
`
`
`® All Depletion
`
`© "Planar“ Interface with imperfection
`
`Faiture
`Plane
`
`
`
`Plane
`
` Failure
`
`
`
`Fig. 6. Five of the major failure categories documented for TBC systems.
`
`TGO and the bond coat or between the TGO and TBC [19]. When this happens, it
`is surmized (but not substantiated) that the “brittleness” of the spinel results in
`delamination. (ii) In other instances, regions of the component are subject to particle
`impact and foreign object damage (FOD) that locally compresses the TBC, resulting
`in hot spots in the underlying bond coat that contribute to failure [33]. Neither of
`these failure modes is addressed in this article. Instead, the emphasis is on the third
`category, (iii) wherein the energy density in the TGO and imperfections in its vicinity
`(Fig. 7) govern durability. This failure process occurs through a sequence of crack
`nucleation, propagation and coalescence events
`[8,24—27,34—38]. Prototypical
`sequences sketched in Fig. 8 will be elaborated in Section 3. These three elements,
`while analogous to the stages of cyclic failure in structural alloys [39], have the fol-
`lowing special features: (a) Small cracks and separations nucleate at imperfections in
`(or near) the TGO. The tensile stresses that arise around these imperfections and the
`associated energy release rates govern the details. (b) Once nucleated, the small
`
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`513
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`cracks extend and coalesce, but the TBC may remain attached at remnant ligaments.
`(C) Failure happens when the ligaments are detached over a sufficient area that a
`separation becomes large enough to create either a large-scale buckle (designated
`LSB) or an edge delamination that eventually spalls from the substrate (see Fig. 20)
`[40].
`
`1.2.2. Specific mechanisms
`The specific ways in which the cracks nucleate and grow relate to the increase in
`the severity of the imperfections as the system is exposed and cycled. While this
`occurs in many ways, all are ultimately linked to the magnitude and scale of tensile
`azz stresses that amplify as either the TGO thickens or the imperfections increase in
`size, or both. In turn, the stresses translate into stress intensity factors acting on
`
`<a>
`
`
`
`lmperfelcltii”
`
`TGO
`
`Thicknessfleierogeneites
`
`
`
`Undulations 1:
`
` rem.
`
`at
`
`
`
`Fig. 7. (a) A schematic of two major categories of TGO imperfection that govern the TBC failure
`sequence; (b) a thickness imperfection in a TGO grown on a NiCoCrAlY bond coat; (c) an undulation
`imperfection that develops in a Pt—aluminide system upon thermal cycling.
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`g
`
`
`
`
`
`~
`
`Fig. 7 (continued).
`
`cracks that nucleate and propagate around the imperfections [41]. The examples
`presented in Fig. 8 illustrate the effects of increasing the TGO thickness and of
`enlarging the imperfection, respectively. Detailed analyses of these mechanisms are
`summarized in Section 3.
`
`1.2.3. Related observations
`
`After spalling of the TBC from the substrate, the exposed surfaces exhibit two
`broad morphological categories [19,42]. These observations must be consistent with the
`failure mechanisms.
`
`i. One predominates for NiCoCrAlY bond coats with EB—PVD TBCS. In such
`systems, the exposed surface on the substrate side comprises predominantly bond
`coat with an imprinted TGO grain morphology [42] (Fig. 9a). The exposed surface
`on the TBC side consists of the TGO with a granular appearance that mirrors the
`imprint in the bond coat (Fig. 9b). Morphological imperfections in the TGO are
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`515
`
`also in evidence. Most prominent are small (about 10 um) polycrystalline oxide
`domains embedded in the bond coat [42]. They contain cleavage facets, indicating
`that they were mechanically detached from the TGO. There are corresponding features
`on the underside of the TGO.
`
`ii. In other systems, especially those where the TBCS were deposited by the air
`plasma spray process, a substantial proportion of the delamination traverses the
`
`Fig. 8. Two examples of early and late stages of failure from imperfections: (a) schematic of a mode
`exhibited for scenarios subject to minimal thermal cycling showing how cracks can initiate in the TBC
`isothermally, due to the growth stresses, and then coalesce with an interface. Separation occurs upon
`cooling because of the thermal expansion misfit; (b) schematic of the growth of imperfections by ratchet-
`ing upon thermal cycling; (c) micrograph of an actual cross section of an APS TBC system highlighting
`the imperfections [44]. Cracks are in evidence near these imperfections; (d) cross-sections of an EB—PVD
`TBC on a Pt~aluminide bond coat showing the imperfections that enlarge by ratcheting and the cracks
`induced in the TBC [82].
`
`
`
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`.
`
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`12
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`517
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`TBC itself, with local segments entering the TGO as well as the interface with the
`bond coat [44]. This mixed appearance diminishes the utility of such observations
`for interpreting failure mechanisms.
`
`1.3. Overarching principles
`
`Based on the above considerations and on detailed analyses to be elaborated
`below, the following three overarching principles govern the failure of TBC systems,
`as sketched in Fig. 10.
`i. The TGO experiences large in-plane compressions, especially upon cooling. As with
`any compressed thin film, it attempts to alleviate the stress (and associated strain energy
`density) by lengthening itself, through out-of-plane displacements. This can happen by
`buckling as well as by visco-plastic deformation of the bond coat. These displacements
`induce tensile ozz stresses normal to the interface that motivate delamination mechanisms.
`
`ii. When imperfections exist (or are developed) around the TGO, tensions are
`induced normal
`to the TGO/bond coat interface, as well as in the TBC, that
`nucleate and grow cracks in this vicinity. The coalescence of these cracks leads to
`failure.
`
`iii. The TBC, despite its compliance, has sufficient stiffness to suppress small scale
`buckling (SSB) of the TGO. Accordingly, eventual failure often occurs by large scale
`buckling (LSB) [40], but only after a sufficiently large separation has developed near
`the interface, typically several mm in diameter. The durability of the TBC is governed
`by the time/cycles needed to develop such separations:
`through a nucleation,
`propagation and coalescence sequence, involving the energy density in the TGO, as
`well as the size and spacing of the prominent imperfections.
`
`2. Thermally grown oxides
`
`2.] . Growth phenomena
`
`While the mechanisms of alumina formation prior to Al depletion are not quan-
`titatively comprehended, especially in the presence of a TBC, the following four
`findings are pertinent.
`i. The growth is essentially parabolic until spalling occurs:
`
`/12 = zkpz
`
`(1)
`
`t time and kp the parabolic rate constant (Table 1).
`where h is the thickness,
`Accordingly, growth is diffusion (rather than interface) controlled. The alumina
`grows predominantly by inward diffusion of anions along the TGO grain bound-
`aries but there is a contribution to kp by outward ditfusion of cations. This outward
`growth appears to be sensitive to cations dissolved in the alumina.
`ii. In some cases, 6~alumina forms first, particularly on B-NiAl, and transforms to
`oc-A1203 [45,46]. The 9-phase has an acicular morphology, indicative of growth by
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`
`outward diffusion of Al [47]. This morphology is retained upon transformation. The
`subsequent growth of oc—Al2O3 appears to be unaffected by the prior transformation.
`iii. In some case, the TGO formed on NiCoCrAlY bond coats entrains yttria [42].
`The yttria in the TGO is related to the distribution of the Y in the bond coat. When
`yttria domains of suflicient size are incorporated into the TGO, it thickens more
`rapidly in these regions and produces thickness imperfections (see Fig. 7). Si1nul—
`taneously, the yttria reacts with the surrounding alumina to form YAG.
`iv. Present the TBC, the TGO may exhibit two distinct microstructural domains: a
`columnar zone (CZ) next to the BC and an equi—axed zone (EZ) next to the TBC
`[19]. The EZ found on MCrAlY coatings (which contain Fe), incorporates small (nm)
`oxide precipitates containing Fe and Cr cations [48], while that on Pt-aluminides
`comprises a mixture of zirconia and alumina [19].
`
`2.1.1. Thermodynamics
`The stability of oxide product phases that form on bond coat materials may be
`rationalized by constructing thermodynamic stability diagrams. Such a diagram for
`the Ni—Al—O system is presented in Fig. lla [19]. This diagram describes the equili-
`bria between the phases in this system (A1203, NiAl2O4, NiO and Ni—Al alloys),
`with the oxygen activity, ao, as the ordinate and the aluminum activity, am (inter-
`changeable with aN,), asthe abscissa. Fig. lla can be constructed by formulating
`
`
`
` a
`
`Bond Coat Surface
`
`Bond Coat
`
`Fig. 9. SEM images of separated interface between a NiCoCrAlY bond coat and a TGO: (a) exposed
`bond coat; (b) matching surface of the TGO [42].
`
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`
`equilibrium reactions, provided that the standard free energies of formation are
`available and the activities are understood. The activity of A1 in the alloy is related
`to XA1 through the activity coeflficient 3/A1:
`
`J/A1 = aA1/XA1
`
`The activity of Ni is related to that for Al by the Gibbs—Duhem equation:
`
`log VNi = —j
`
`XNi
`
`XNi=1
`
`X
`
`(XA?)d1og m
`
`N1
`
`(2)
`
`(3)
`
`-
`
`Accordingly, in order to relate aA1 to compositions of the Ni—Al alloys, additional
`
`_ THREE OVERARCHJNG PRINCIPLES
`
`a Separations iklucteate And Propagate 5
`Around Imperfections Induced 5
`V [,|l11heTGO e
`it
`
`e
`
`Compressed TGO AtteimptsTo Lengthen (Strain Energy)
`L Large Enough To Satisfy Large Scale Buckling
`
`E
`
`*
`
`Separations coalesce And iBeico‘mie_ 5
`
`*
`
`TBC
`
`Fig. 10. Sketch illustrating the overarching principles governing TBC failure.
`
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`AG. Evans et al. /Progress in Materials Science 46 (2001) 505-553
`
`thermodynamic data are required [49] (Fig. llb). Note that the activity of Al in the
`alloy is always much less than XA1.
`The important equilibria described in Fig. lla are as follows:
`
`0 Line (1) represents A1203 in equilibrium with Ni—Al alloys through the reaction;
`
`2Al(al1oy) + 30 = A1203
`
`0 Line (2) refers to NiAl2O4 in equilibrium with the alloy Via the reaction;
`
`Ni(alloY) + 2Al(all0y) + 40 = NiA12O4
`
`(4a)
`
`(413)
`
`logao
`
`AILActivity,am <3;3
`
`
`
`0.2‘
`‘Q3
`0.4
`0.5
`
`Mole Fraction An, XAQ
`
`Fig. 11. (a) The thermodynamic stability diagram; (b) the activity coefficient for Al as a function of
`concentration for the Ni/Al binary [19].
`
`i
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`
`0 Line (3) involves Ni0 in equilibrium with the alloy;
`
`Ni(alloy) + 0 = NiO
`
`(4c)
`
`The junction of lines (1) and (2) defines a three—phase equilibrium through the reaction;
`
`3Ni(al10y) + 4A12O3 = 3NiA12O4 + 2Al(alloy)
`
`and the junction of lines (2) and (3), the three phase equilibrium;
`
`3Ni(all0y) + NiA12O4 = 4NiO + 2Al(alloy)
`
`(4d)
`
`(4c)
`
`The lines (4) and (5) involve two-phase equilibria that can be described through
`reactions (4d) and (4e), respectively, except that the activities of Al and Ni must be
`those in the oxide phases.
`The stability diagram (Fig. lla) indicates that at Al activities in the bond coat satis—
`fying aA1 > l0“7, reaction (4a) dominates, resulting in A1203 formation [l9]: the ther-
`modynamic situation most favorable for a durable TBC. Whenever A1203 is stable, the
`oxygen activity at the interface is too low to form alternative oxides. Upon alumina
`growth, as the aluminum activity decreases, the oxygen activity at the interface increases
`along line (1) i11 Fig. lla. When ao reaches the intersection of lines (1) and (2), the
`A1203 converts to NiAl204 through reaction (4d). When this happens, the durability of
`the TBC may be compromised. [For practical bond coats, reaction (4c) never occurs].
`Kinetic processes also play a significant role in phase evolution. The effects of kinetics
`could be included on the stability diagrams by indicating reaction paths, but these
`kinetics are currently incompletely understood. Two salient findings are as follows [l9]:
`i. Before am in the bond coat decreases to a level that would cause spinel to form,
`the oxygen flux into the bond coat may exceed the Al flux toward the TGO, where-
`upon Al203 precipitates form beneath the TGO in the bond coat.
`ii. In some circumstances, as ao at the interface increases, the solubilities of nickel
`and chromium (as well as Fe when present) in the A1203 also increase. This con-
`dition can result in outward difiusion of cations, through the TGO. Upon encoun-
`tering higher oxygen activities,
`these cations can form new oxide phases. For
`example, in regions between the TGO and the TBC,
`the thermodynamics and
`kinetics are such that spinel formation is allowed (Fig. lla).
`
`2.2. Stresses
`
`The stresses in the TGO exert a central influence on TBC failure. Understanding
`these stresses is crucial to any model of the durability. There are two main sources of
`stress: one from the thermal expansion misfit upon cooling and the other from TGO
`growth [l9,2l—27,4l,50,5l]. Both stresses may be alleviated by TGO creep [52—54]
`and redistributed in the vicinity of imperfections [38,41]. Moreover, the stresses can
`be substantially modified by thermal cycling conditions that cause cyclic plasticity in
`the bond coat [37]. Sources of stress development, redistribution and relaxation are
`
`17
`
`17
`
`

`
`522
`
`A.G. Evans er al. / Progress in Materials Science 46 (2001) 505—553
`
`addressed with emphases on the sign and magnitude in the vicinity of imperfections
`and on the consequences of thermal cycling. Ambient temperature measurements by
`X-ray diffraction [27] and laser piezo—spectroscopic techniques [2l] indicate that
`thermal expansion misfit results in compressions that, on the average, range between
`3 and 6 GPa (see Fig. 4). Direct measurement of the growth stresses by high tem-
`perature X—ray peak shift measurements [27,55] indicate that these stresses are also
`compressive and much smaller than the thermal stresses. They range from near zero
`for Ni-base alloys to about 1 GPa for FeCrAl(Y) alloys. Nevertheless, they may
`have an important role in TBC failure. In the vicinity of imperfections the stresses
`deviate from these average values. Upon thermal cycling, they can even change sign
`[37]. The specifics are assessed next.
`
`2.2.]. Thermal expansion misfit stresses around imperfections
`Imperfections cause the thermal expansion misfit stresses to redistribute. Normal
`tensions exist where the TGO is concave and vice versa (Fig. 12) [34]. Shear stresses
`exist at inclined sections. These stresses depend on the elastic mismatch and the ratio
`of the amplitude A, to the wavelength, L, of the oscillations. When the TGO is thin
`(I1/L <<1), the stresses are given by [34]:
`
`017/C70 = Hzj(0lD)A/L
`
`(53)
`
`......s
`
`(II
`
`1
`
`
`
`STTGSS,H51‘?(O';J'/O'o)(L/A)
`
`' o
`
`0.1
`
`0.2
`
`0.3
`
`0.4
`
`0.5
`
`Distance, x/L
`
`Fig. 12. Distribution of stresses at an undulating TGO interface [34].
`
`18
`
`18
`
`

`
`A.G. Evans et al. /Progress in Materials Science 46 (2001) 505-553
`
`523
`
`where the misfit stress (the stress that would exist in a planar thin film) is [34]:
`
`O‘() = EQAOZQAT/(l — U),
`
`~
`
`and egg is the Dundurs’ parameter, defined as [56]:
`_E1 -1532
`E1-I-E2
`
`05D
`
`(5b)
`
`(50)
`
`with E the plane strain Young’s modulus and the subscripts 1 and 2 referring to the
`two adjoining materials. The functions I1,-7 are plotted in Fig. 12. As the TGO
`thickens, there are additional effects of I1/L (Fig. 13).
`
`2.2.2. Redz'sz‘ributz'on of misfit stresses by bond coat visco—pIas2‘icity
`The misfit stresses are redistributed by creep or yielding of the bond coat during
`thermal cycling. Measurements and models characterizing the important eifects are
`developmental [37]. Local misfit stresses around imperfections in the bond coat may
`become large enough to exceed its yield strength and, thereafter, to induce cyclic
`yielding. The response may be characterized through a Bree diagram [37,57,58] that
`identifies domains of elasticity, shakedown and cyclic plasticity (Fig. 14). The specifics
`are addressed in Section 3. Some elaboration is also given in Appendix E. The
`coordinates of this diagram are the undulation amplitude-to-wavelength ratio, A0/L
`and the misfit stress, 0'0, relative to the bond coat yield strength (TY. When these
`coordinates reside in the elastic domain, yielding is prohibited and the stresses in the
`
`3
`
`2.5
`
`(G22/Go)
`
`(L/A)
`
`-1
`
`-0.8
`
`-0.6
`
`-0.4
`
`0.2
`
`0
`
`0.2
`
`0.4
`
`0.6
`
`0.3
`
`1
`
`Dundur's Parameter, cap
`
`Fig. 13. The effect of elastic mismatch on the stress normal to the interface [34].
`
`19
`
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`
`19
`
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`
`524
`
`A.G. Evans et al. / Progress in Materials Science 46 (2001) 505~553
`
`TGO are given by the above elasticity solutions. When the bond coat yield strength
`is exceeded, the stresses are redistributed such that the ambient compressive stress in
`the TGO is reduced (Fig. 15). Moreover, upon re—heating, regions of tensile stress
`may develop. These stresses tend to relax by creep (discussed below) but, in some
`cases, may cause the TGO to crack. In subsequent cycles, the stresses are “reset” by
`the plasticity that occurred in the first cycle [37]. The response thereafter depends on
`whether the system is within the “shakedown” or “cyclic plasticity” domain
`(Fig. 14). In the former, the system becomes elastic after a few cycles and, thereafter,
`the stresses vary linearly with temperature between the new limits established in the
`first cycle. Outside this range, the stresses are non-linear and exhibit hysteresis, with
`consequences for fatigue of the bond coat.
`While further changes in the TGO stress may arise when growth strains are added
`to the thermal expansion misfit, the effect is relatively small, because of the equili-
`brating influence of bond coat yielding [37]. However, as discussed later, when
`ratcheting conditions are satisfied, the displacements of the TGO into the bond coat
`have a major efiect on TBC failure.
`
`2.2.3. Growth stresses
`
`Oxidation is accompanied by growth strains and associated stresses [37,59,60].
`The strain represents the overall Volume increase upon converting the alloy to
`A1203. It comprises normal, mzz, and in—plane, 111“, components that depend on the
`growth mechanism and the induced stresses. In general it can be expressed in the