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PHASE TRANSFORMATION STRESS FIELD DUE TO HOT CORROSION IN THE TOP COAT OF TBC

Abba Abdulhamid Abubakar Mechanical Engr. Dept.

King Fahad University of Petroleum & Minerals Dhahran, Dammam, Saudi Arabia

Syed Sohail Akhtar Mechanical Engr. Dept.

King Fahad University of Petroleum & Minerals Dhahran, Dammam, Saudi Arabia

Abul Fazal M. Arif Mechanical Engr. Dept.

King Fahad University of Petroleum & Minerals Dhahran, Dammam, Saudi Arabia

E-mails: g201201760@kfupm.edu.sa, ssakhtar@kfupm.edu.sa, afmarif@kfupm.edu.sa

ABSTRACT Due to the use of low quality fuels in Saudi Arabia,

hot corrosion occurs at the top coat of Thermal Barrier Coatings (TBCs) as a result of the formation of a molten salt, V2O5, which penetrates it through either diffusion mechanism or the open porosities in the YSZ. The interaction between this molten salt and the Zirconia stablizer is a dissolution-precipitation type reaction which occurs throughout the Planar Reaction Zone (PRZ) and the Melt-Infiltrated Reaction Zone (MIRZ) leaching a new phase, YVO4, and also causing tetragonal to monoclinic phase transformation of Zirconia. Swelling due to transformation-mismatch plasticity causes the development of localized stresses in the topcoat which subsequently contributes to the premature failure of the coating. In the current work, a 1D-Phase field model was developed that could estimate the kinetics and micro-structural evolution during the isothermal (diffusional) tetragonal-to-monoclinic phase transformation at 9000C in the top coat. The result obtained from the Phase Field Model was sequentially coupled with Finite Element Method, and the resulting stress field in the top coat was predicted.

Keywords: Phase Field Model(PFM), Finite Element Analysis(FEA), monoclinic phase(m-phase), tetragonal phase(t-phase), Yttria Stabilized Zirconia(YSZ), Thermal Barrier Coatings (TBC)

INTRODUCTION Thermal Barrier Coatings (TBCs) are highly advanced

coating materials that are usually applied to turbine blades operating at very high temperatures in order to improve the

thermal and corrosion resistance of such blades. The use of this coating, along with internal cooling, enables the base metal to safely operate at temperatures that even exceed its melting point. This results in tremendous improvement in the efficiency and performance of heat engines [1].

Thermal Barrier Coating consists of four layers: the single-crystal base metal for structural support, metallic bond coat for corrosion/oxidation resistance, thermally grown oxide for oxidation resistance, and ceramic topcoat for thermal insulation. The ceramic topcoat is composed of porous Yttria-Stabilized Zirconia (YSZ) which has a very low thermal conductivity and adequate stability at the operating temperatures (of up to 23700C) typically seen in thermal systems. Thus, it enables the blade to withstand very hot gas, erosion, corrosion, and foreign objective damage [2,3].

Yttria-Stabilized Zirconia (YSZ, 7% to 8% by weight) is the material most widely studied and used for TBCs, because it provides the best performance at temperatures below 1,200°C. It mostly contains the tetragonal phase of Zirconia which remains even on cooling to room temperature due to stabilization by Yttrium Oxide [1, 4].

Different types of hot corrosion mechanisms that occur in TBCs were reviewed by Jones [6, 10]. Previous experiments showed that the hot corrosion of the Top Coat occurs as a result of the reaction between the impurities in fuel (such as Vanadium, Phosphorous, Sodium and Sulfur) and ceramic top coat at high temperatures (range, 7470C<T<12000C) [12, 13, 14, 15, 16]. This reactions result in the formation of molten salts which further reacts with the Yttrium ions in the top coat to leach a new phase, YVO4 and cause the destabilization transformation of Zirconia. Overall effect of the evolution of these two new phases is the volumetric

Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition IMECE2013

November 15-21, 2013, San Diego, California, USA

IMECE2013-63138

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expansion of the top coat by 4-5%, the development of localized stresses, formation of horizontal cracks and subsequent failure of the TBC [4, 5, 6, 7, 8, 15]. In fact, failure of the top coat caused by molten salt can precede failures due to sintering or the development of a thermally grown oxide [9].

Some experiments (Shown in Figure1) also show that as V2O5 reacts with the top coat, a fine-grained section, the PRZ, appears initially at the surface of the top coat and thickens/grows with increase in reaction time and temperature. The second section, the MIRZ, is a dense infiltrated region with lamella structure and results from the reaction between the V2O5 that infiltrate through the pores and micro-cracks in the coating and the Yttrium oxide [14]. Active research is going on in developing a suitable corrosion inhibitor to be added to the low quality fuels for improving the life time of the TBC.

Figure 1: PRZ and MIRZ in a YSZ Top Coat at 9000C [8]

Figure 2: PRZ and MIRZ(Zoomed) in a typical YSZ Top Coat

In the current work, a 1-Dimensional phase field model (Shown in Figure 2) is used to simulate the rate of destabilization-transformation of the Zirconia in the top coat due to the V2O5 hot corrosion. The data for this phase transformation from the PFM is then used to predict the resulting localized stress field using Finite Element Method.

The phase field model (PFM) is a mathematical tool for solving interfacial problems. It treats interface as a surface of finite thickness using a variable called the phase field variable (or an order parameter) [18] which describes the evolution of various phases in terms of space and time. Phase Field Model is also very powerful because it treats topology changes such as coalescence of two solid regions that come into close proximity [18]. Although that the Phase Field Model was used in modeling the diffusionless tetragonal-to-monoclinic phase transformation of zirconia [27], It has never been applied to the diffusion-activated phase transformation of Zirconia. However, many PFM have been reported for a variety of solid-state transformation problems such as corrosion kinetics of metals

under dual oxidants[19], phase transformation of Low Carbon Steel[20], precipitation of Al-Cu and Ti-Ni alloys [21] in the literatures. In the following section, a Phase Field Model formulation for diffusional tetragonal-to-monoclinic phase transformation of zirconia is described in detail. The solid state phase transformation is caused by the diffusion of chemical specie (V2O5) into TBC top coat due to hot corrosion. The result of the Phase Field Model is sequentially coupled with the FEM in order to predict the resulting stress field generated due to the hot corrosion attack. METHOD

PHASE FIELD MODEL

For the description of the model, the reactions for the corrosion process needs to be considered as follows.

V2 O5 + Na2SO4 → 2푁푎푉푂3 + 푆푂3

ZrO2(Y2O3) + 2푁푎푉푂3 → 푍푟푂2 (푀표푛표푐푙푖푛푖푐) + 2푌푉푂4 + 푁푎푂2

As reported in [22, 15], the Sulphur impurities present in the fuel reacts with air-borne NaCl to form the mixed salt Na2SO4.So initially the Vanadium(VI)Oxide reacts with Na2SO4 to form NaVO3 which transforms the YSZ to monoclinic crystalline form, YVO4 and NaO2. It should be noted that previous EDS analysis of the top coat showed that NaO2 was not detected due to its sublimation at high temperatures [15].The molten NaVO3 is also reported to increase the atomic mobility, and hence further promote the resulting phase transformations [23].

So, when V2O5 deposits on a conventional YSZ thermal barrier, it leads to the following general reaction.

YSZ (tetragonal) + V2O5 (in melt) 2YVO4+ ZrO2(monoclinic) MODEL ASSUMPTIONS

Some major assumptions are made in formulating the Phase Field Model as follows:

1. The solid-state phase transformation in the PRZ is unidirectional.

2. The phase transformation is Isothermal at 9000C. 3. Only two phase system is assumed in the current work. 4. Parabolic approximation is assumed for the double well

potential/chemical driving force as normally used in the literature [19].

5. Direct coupling of the phase field variables is assumed based on popular KKS model [26].

MATHEMATICAL FORMULATIONS The kinetic equations that describe the evolution of the

phase field variables are derived according to non-equilibrium (irreversible) thermodynamic principles.

Considering the phase evolution of the monoclinic phase, three phase-field variables, i.e. XVO, η1(r, t) and η2(r, t), are needed to represent the micro-structural distribution at a given time, t. Where, η1(r, t) = order parameter for the m-phase = 1

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η2(r, t) = order parameter for the t-phase = 0 XVO = concentration of the melt=0 to 1

An isothermal treatment forms the total free energy functional (F), which must decrease during any process [19], given in (1): 퐹(휂1 ,푋푉푂) = ∫ 푓(휂1,푋푉푂) + 훼1

2

2(∇휂1)2 + 훾1

2

2(∇푋1)2 푑푉 (1)

[Ginzburg-Laudau energy form]

According to the summation rule, we have 휂2(푟, 푡) = 1 − 휂1(푟, 푡) (2)

Where α and γ are the so-called gradient energy coefficients In the absence of elastic energy, the variational

derivative of total free energy (F) must satisfy the equation[19]: 훿퐹훿휂1

=휕푓휕휂1

− 훼1∇2휂1 (3)

훿퐹훿푋푉푂

=휕푓휕푋푉푂

(4)

Using the Allen-Cahn Equation for the non-conserved parameters [24] and the Cahn-Hillard equation for conserved parameters [25], we have:

휕휂1 (푟,⃗ 푡)휕푡 = −퐿1

훿퐹(휂1 ,푋푉푂)훿휂1

= −퐿1휕푓휕휂1

− 훼1∇2휂1 (5)

휕푋푉푂(푟,⃗ 푡)

휕푡 = 푀푉푂∇.∇훿퐹(휂1,푋푉푂 )

훿푋푉푂= 푀푉푂∇.∇

휕푓휕푋푉푂

(6)

Where r and t represent spatial coordinates and time, respectively, L1 is the kinetic mobility that describes the transformation rate and MVO is the structure-dependent diffusion/atomic mobility of V2O5.

Initial Conditions for model are:

휂1(푟,⃗ 0) = 0 , only t-phase exist (7)

푋푉푂(푟 ,⃗ 0) = 0, diffusion of V2O5 has not started (8)

Boundary Conditions are:

휂1(0, 푡) = 1 & 푋푉푂(0, 푡) = 1 (9)

휂1(푥, 푡) = 0 & 푋푉푂(푥, 푡) = 0 (10)

The boundary conditions signifies that at all times, the top x=0 is exposed to 100% of the diffusing specie (XVO=1) and

also the m-phase nucleates form there (η1=1). However at the bottom x=50, at all times 0% of the diffusing specie exists and the t-phase exists/finishes diminishing there.

Using Kim-Kim Suzuki model [26], the local free energy function/density of the two phase zone can be expressed as:

푓(휂1,푋푉푂) = ℎ(휂1 )푓푚(푋푚−푧푣표 ,푇) + [1 − ℎ(휂1 )]푓푡(푋푡−푧푣표 , 푇)

+ 푤1푔(휂1) (11)

Where, w1 = constant determining the height of the imposed double-well free energy hump that describes the energy barrier with minima at 0 and 1.

푓푚(푋푚−푧푣표 ,푇) = 푓푟푒푒 푒푛푒푟푔푦 표푓 푚− 푍푟푂2

푓푡(푋푡−푧푣표 , 푇) = 푓푟푒푒 푒푛푒푟푔푦 표푓 푡 − 푍푟푂2

ℎ(휂1) = 푇푌푃퐸 퐼퐼 푖푛푡푒푟푝표푙푎푡푖표푛 푓푢푛푐푡푖표푛 = −2휂13 + 3휂1

2

푔(휂1 ) = 퐷표푢푏푙푒 − 푤푒푙푙 푝표푡푒푛푡푖푎푙 = 휂12(1 − 휂1)2

The local/chemical free energy of m-ZrO2 and t-ZrO2 is

given by the following simple parabolic approximations [19]:

푓푡(푋푡−푧푣표 , 푇) = 퐴(푇)(푋푉푂 − 푋푡−푧푣표)2 (12)

푓푚(푋푚−푧푣표 ,푇) = 퐵(푇)(푋푉푂 − 푋푚−푧

푣표)2 (13)

Where Xt-zvo & Xm-z

vo are the equilibrium mole compositions of the molten salt in the different phases which can be obtained from a thermodynamic database.

Analytical solution to the free energy density exists as [21]:

푓(휂1 ,푋푉푂 ,푇) = 퐴(푇)퐵(푇)[푋푉푂 − 푋푡−푧푣표 − (푋푚−푧

푣표 − 푋푡−푧푣표 )ℎ(휂1)]2

퐵(푇) + [퐴(푇)− 퐵(푇)]ℎ(휂1)+ 푤1푔(휂1) (14)

Approximated to the following bulk free energy with similar

curvatures [21]:

푓(휂1 ,푋푉푂 ,푇) = 퐴(푇)[푋푉푂 − 푋푡−푧푣표 − (푋푚−푧푣표 − 푋푡−푧푣표 )ℎ(휂1)]2

+ 푤1푔(휂1) (15)

Based on common tangent construction between the Gibb’s free energy of the two phases, the Gibb’s free energy translate into the parabolic fitting[21]:

퐴(푇) =퐺(푋푉푂 , 푇)

(푋푉푂 − 푋푡−푧푣표)2 (16)

The diffusion mobility coefficient is related to the diffusion

coefficient by [21]:

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푀푉푂 =퐷(푇)

2퐴(푇) (17)

퐷(푇) = 퐷0 exp −푄푅푇

(18)

The value of the interface mobility coefficient (L1) can

be interface-controlled, diffusion-controlled or mixed type [25]. It greatly affects the evolution behavior and is normally obtained experimentally.

The interface energy and thickness can be obtained from the following relation [21]:

휎 ≈ 훼1 ∗ ∆푓푚푎푥 (19)

푙 ≈훼1

∆푓푚푎푥 (20)

Where, Δfmax=height of the imposed double well potential NORMALIZATION

Due to the fact that the dimensional parameters are at microscale, it is necessary to normalize the Governing Equations for the Phase Field Model with the following characteristic constants.

푥̅ =푥푙0

,푓̅ =푓

∆푓푚푎푥 , 푡̅ =

푀푉푂∆푓푚푎푥 푡(푙0)2 , (21)

푀푉푂 = 1 , L1 =L1(푙0)2

푀푉푂 , 훼1 =

훼1

(푙0)2 ∗ ∆푓푚푎푥 (22)

FINITE ELEMENT FORMULATION MODEL ASSUMPTIONS

For the Finite Element Analysis, the assumption that the materials of the existing phases are homogenous and Isotropic is made. CONSTITUTIVE FORMULATION

A constitutive model is developed, based on a micromechanics approach and a swelling model is developed that takes care of the effect of the 4-5% volume expansion of the monoclinic phase in terms of swelling strain.

The increment in Cauchy stress tensor is given by, 푑휎 = 퐶푒 : 푑휀푒 (23)

Where, Ce is the elastic stiffness tensor and =elastic strain tensor By additive decomposition the incremental strain at any given time,

푑휀푒 = 푑휀 − 푑휀푆푊 (24) Where, = total strain tensor, swelling strain tensor

The inelastic part is assumed to be dominated by the swelling strain and proceed according to the kinetics for the phase transformation as follows:

휀푆푊푡+1 = 휀푆푊푡 + 휀̇푆푊 × ∆푡 (25) Note that the swelling (volumetric) strain rate changes according to the transformation kinetics as will be shown later.

RESULTS AND DISCUSSION SOLUTION METHODOLOGY & SIMULATION PARAMETERS

The model is formulated to simulate the tetragonal to monoclinic phase transformation of zirconia due to V2O5 hot corrosion. The Phase Field Model and the Finite Element Model are simulated in COMSOL MULTIPHYSICS 4.3. Parameters used for the simulation as well as the solution methodology are outlined in Tables1 & 2 and figure 3.

Table 1: PFM Simulation Parameters Dimensionalized Parameters Value

Spatial Coordinate/ Depth (x) 50µm

Time of Diffusion 14.05 hrs

Temperature (T) 9000C

Equil. Conc. of V2O5 in YSZ(푋푡−푧푣표 ) 0.001

Equil. Conc. of V2O5 in m-ZrO2(푋푚−푧

푣표) 0.55

Diffusion Coefficient(퐷(푇)) 1.0701 × 10−9푐푚2/푠

Gibb’s Free Energy of YSZ 129.74KJ/mol at 9000C

Mobility Coefficient(푀푉푂) 4.1181 × 10−19푚2푚표푙/ (퐽 푆)

Height of Double Well Potential(∆푓푚푎푥 ) 0.12 푘퐽 푚표푙⁄

Thickness of Interface(푙) 0.5푙휇푚

Gradient Energy Coefficient(훼1) 3 × 10−7 퐽 푚⁄

Non-Dimensionalized parameters

Characteristic Length (푙표) 1휇푚

Depth(푥̅) 50

Time(푡̅) 25

Gradient Energy Coefficient(훼) 0.25

Atomic Mobility(푀푉푂 ) 1

Kinetic Mobility(퐿1) 0.6

Time Step Size(∆푡) 0.01

Grid Step Size(∆푥) 0.1

Elements 500

Degree of Freedoms 2002

Error Tolerance/Convergence criteria 0.001, MUMP Direct Solver

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Table 2: FEA Simulation Parameters

Geometry 50휇푚 푋 50휇푚 푅푉퐸 Modulus of Elasticity of m-phase

11.23GPa

Modulus of Elasticicty of t-phase

40GPa

Poisson Ratio of m-phase 0.20 Poisson Ratio of t-phase 0.22 Total Swelling Strain 0.05 Swelling Strain rate Varying, non-linear Boundary Conditions Roller Support, Left and Bottom Mesh Type Mapped, ALE-Moving Interface Number of Elements 875 Quadrilateral Elements Degree of Freedoms 37035 Number of time steps 510 Error Tolerance 0.001, GMRES Iterative Solver

CORROSION KINETICS

The evolution of the monoclinic phase in Zirconia destabilization transformation was simulated using the one dimensional PFM. The transformation occurs due to the diffusion of molten salt V2O5 at 9000C and constant composition/concentration of the salt was assumed at the surface of the top coat. The transformation was assumed to proceed in one direction (in the PRZ), from the surface to a distance of 50 µm as confirmed from experimental work [18].

(a)

(b)

Figure 4: (a) order parameter (b) Concentration gradient for melt (all rep. in terms of space and time)

(a)

(b)

Figure 5:

(a) Growth of m-phase with time (Non-Dimensionalized) (b) Growth of m-phase with time ( Dimensionalized)

Figure 3: Solution Methodology

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(a)

(b) CORROSION KINETICS

Figure 4 (a) describes the growth of the monoclinic phase with time. It can be seen that at the TBC surface (represented by x=0), the order parameter was initially 0-representing the tetragonal phase. It then changes to 1-representing the monoclinic phase when the transformation starts. It can be seen that the L-SHAPED curve, representing the interface between the two phases, moves as the transformation is in progress. A total duration of 14.05 hours was taken for the transformation to reach depth of 32.5μm where it stops.

Experimental result obtained earlier [16] showed that at 9000C, 10µm thickness of the monoclinic phase in the planar reaction zone was achieved after duration of 90 minutes. Thus, the result obtained in the current work is close to reality as 8µm transformation depth was achieved after the same duration (as shown in Figure 5). It can also be seen that the monoclinic phase (evolving phase) grows up during the simulation while the tetragonal phase (diminishing phase) reduces in volume.

Figure 4 (b) shows the concentration gradient for the dissolution-precipitation process, where the concentration varies from a non-dimensional value of 1 from the surface to a value of 0 at the other extreme end. It can be seen that the concentration gradient, which is the driving force for the transformation is non-steady as well as non-linear. It also

becomes stiffer with time causing a continuous decrease in the rate of diffusion/transformation.

STRESS ANALYSIS

For the stress analysis, the results for the dissolution-precipitation reaction obtained using the PFM was sequentially coupled the Structural Analysis Module of COMSOL Multiphysics for the prediction of the resulting stress field. A plain strain RVE model based on the total depth for the transformation considered is developed. The geometry was drawn and different material properties for m-ZrO2 and t-ZrO2 were specified as obtained from the literature. Symmetric boundary condition was applied at the left edge while the bottom was constraint to move in the vertical direction using roller supports (as Shown in Figure 6(a)). A mapped mesh was created with 875 quadilateral elements and the volumetric swelling of 5% was applied according to the transformation. ‘’Creep and Viscoplasticity node’’ of structural mechanics module of COMSOL was used for the stress analysis.

In order to confirm the accuracy of the FEA, a convergence test was carried out (Shown in Figure 7) at three points in the domain which falls into either of the phases. The test shows that the mapped mesh having 875 quadilateral elements can accurately give the desired results. Figures 8(a), (b) and (c) shows that the von Mises stress field developed when the transformation has reached 10μm, 20µm and 32.5μm m-ZrO2 thickness. It can be seen that the maximum stress, which was developed at the interface increases with the growth/ continuous swelling of the m-phase. A highest value of about 850MPa was obtained towards (as

Figure 7: Mesh Convergence Test shown in figure 9). This residual stresses which are developed near the interface will greatly contributes to the formation of horizontal cracks which were observed after the hot corrosion attack [7,8].

Also, it was observed that the average magnitude of stress developed in the existing phases increases continuously during the transformation. After the transformation completes, an average von Mises stress magnitude of about 150MPa was obtained in the monoclinic phase, and a higher average von Mises stress magnitude of 270MPa in the t-phase results. This clearly shows that the stresses developed in the t-phase which is closer to the TGO and the Bond Coat increases more in magnitude during the transformation than the stresses developed in the m-phase.

Figure 6: (a) F.E. Mesh in COMSOL, (b) 5% volumetric swelling attained after transformation (Spatial Dimensions in m and time in seconds)

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(a)

(b)

(c )

Figure 8: Von-Mises Stress field developed in the Top Coat at (a) 10µm m-phase thickness, (b) 20μm m-phase thickness, (c) 32.5µm m-phase thickness

Thus, the hot corrosion process of zirconia which is considered to occur at 9000C results in severe transformation-mismatch stresses which contribute to the formation of experimentally observed horizontal cracks and the spallation failure of the Top Coat. Moreover, additional stresses developed when the TBC is loaded will further aid the failure of the system. VALIDATION

The results obtained from the Phase Field Model shows that closer prediction of the experimental results was obtained, where in 90 minutes 8µm depth of transformation was attained in the current model as against the experimental value, 10µm.

Also, Convergence test carried out (shown in figure7) confirms the accuracy of the Finite Element Results presented

(a)

(b)

(c )

Figure 9: Max. stress developed in the top coat, average stress developed in the m-phase and t-phase during the transformation in the current work. Experimental set-up for predicting the developed stress field due to the V2O5-hot corrosion attack on the TBC system is in progress.

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CONCLUSION Experimental observation shows that Vanadium

impurities present in Low-Quality Fuels react with the Zirconia stabilizer, Y2O5, in the top coat to form a new phase, YVO4, and cause the tetragonal-to-monoclinic phase transformation of Zirconia. This results in the overall volumetric change of 4-5% in the top coat due to the difference in the thermodynamic and crystallographic properties of the resulting phases. Overall, this results in the development of severe internal stresses in the TBC system, thus aiding in the failure of the system.

A 1-D phase field model was developed to simulate the hot corrosion kinetics in the top coat. The result obtained shows that the PRZ grow to a thickness of 32.5µm in approximately 14.05 hours of transformation.

The result obtained from the PFM was sequentially coupled with structural analysis in order to analyse the effect of this transformation on mechanical behavior of the system. It was found out that severe stresses were being developed during this transformation in the Zirconia matrix and especially near the TGO/Bond Coat which has a strong contribution on the premature failure of the TBC system.

ACKNOWLEDGMENTS The authors will like to thank the King Fahd University of

Petroleum and Minerals in Dhahran, Suadi Arabia, for funding the research reported in the paper through the Center for Clean Water and Clean Energy at KFUPM and MIT under project number R9-CE (DSR # MIT 11101)

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