1. Mechanical Characterization of Coating-Interconnect Interfaces and Anode-
Electrolyte Interfaces for Solid Oxide Fuel Cells
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
By
Sajedur Rahman Akanda, M.Sc
Graduate Program in Mechanical Engineering
The Ohio State University
2012
Dissertation Committee:
Professor Mark E. Walter, Advisor
Professor Noriko Katsube
Professor Brian Harper
Professor Daniel Mendelsohn

2. Copyright by
Sajedur Rahman Akanda
2012

3. ii
Abstract
A planar solid oxide fuel cell (SOFC) consists of multiple layers of dissimilar materials
with distinct physical, mechanical, and thermal properties. High operating temperatures
and mechanical loadings during service can significantly weaken the interfaces of
different components in an SOFC. The strength and integrity of various interfaces, for
example, coating-interconnect interfaces and electrode-electrolyte interfaces play an
important role in increased power density of an SOFC.
In the first part of the present investigation, the interfaces between oxide coatings and
interconnects are characterized. The repeating anode-electrolyte-cathode units in a planar
SOFC stack are physically separated by electrically conductive interconnects. With the
reduction of operating temperature to 800o
C, it is possible to replace lanthanum based
ceramics with less expensive, more readily available chromium alloyed iron metals as
interconnects. However, when incorporating chromium-alloyed interconnects, steps must
be taken to inhibit chromium poisoning of cathodes. To prevent the chromium poisoning,
a dense manganese cobalt spinel oxide (MCO) coating is applied on the cathode side
surface of interconnect prior to its installation in the fuel cell. But highly ceramic brittle
nature of MCO coatings makes them susceptible to damage under mechanical loads and
thermal stresses developed during cooling down the fuel cell from operating temperature
to room temperature. A room temperature four-point bend experiment is designed to

4. iii
assess the quality of coatings and coating adhesion. Resulting tensile cracking patterns on
the coatings on the convex side of the bend specimen are used to quantify the interfacial
shear strength from a shear lag model. In addition, the onset strain of coating spallation is
incorporated in an energy based fracture mechanics model to obtain the interfacial
fracture energy. Images from scanning electron microscopy (SEM) of the tested coating
surfaces are processed to analyze the interface failure mechanisms, the crack spacing, and
the spalled areas at higher strains. The analysis obtained from the present investigation is
able show distinct differences between coatings processed with different parameters. In
addition, based on the results obtained from the bend experiments, coating lifetime is
predicted. Lifetime prediction of coatings will greatly assist in optimizing the coating
process parameters and assessing the reliability of coated interconnects.
In the second part of this dissertation, anode-electrolyte interfaces at which the important
electro-chemical hydrocarbon fuel reactions take place are investigated. Frequent
anticipated and unanticipated shut down and startup of fuel cells can cause delamination
and failure of the anode-electrolyte interfaces. Room temperature four-point bend
experiments are performed to obtain the interfacial fracture energy of the anode-
electrolyte interfaces. The notched bend test specimens consist of NiO-YSZ anode and
ScSZ electrolyte bi-layers are sandwiched between two steel stiffeners. A stable crack is
forced to propagate along the interfaces and is monitored with a long distance camera
lens. The constant load at which the stable crack propagates is recorded and utilized to
obtain the critical strain energy release rate of the interfaces. The cracked surfaces are
studied with SEM and energy dispersive spectroscopy (EDS).

5. iv
Dedication
To my parents
Abdur Razzak Akanda
Sabiha Sultana

6. v
Acknowledgments
The author would like to express his sincere and deepest gratitude to Professor Mark E.
Walter for his constant encouragements and guidance to conduct this research. The
author’s thanks are also extended to Matthew M. Seabaugh, Director, Nexceris for his
valuable advices time to time. The author would also like to mention the name of Neil J.
Kidner of NexTech Materials with thankfulness for his constant technical supports and
advices. The author also thanks all the employees and staffs of NexTech Materials Ltd.
The author appreciates the technical supports from Sean O Fallon of TestResources,
Cameroon Begg of CEOF and Chad Bivens of Machine Lab. The author acknowledges
herewith the moral supports received from Ryan Berke, Angel Suresh, Bodhayan Dev,
Andrew Davis and Eric Belknap of Experimental Mechanics of Materials laboratory
(EMML).
This project was financially supported by National Science Foundation (NSF) CMMI
GOALI Grant No. 082558. NSF’s contribution to this project is greatly acknowledged.
Special gratitude is expressed to author’s parents for their unconditional love and support.
Author also likes to mention the name of Nusrat Sharmin for her love. Finally author
acknowledges that it is the God’s blessings only which shone light upon the deepest dark
throughout the years.

7. vi
Vita
1999................................................................Notre Dame College, Dhaka, Bangladesh
2005................................................................B.Sc. Mechanical Engineering, Bangladesh
University of Engineering and Technology
(BUET), Dhaka, Bangladesh
2007................................................................M.Sc. Mechanical Engineering, Tuskegee
University, Tuskegee, AL, USA
2008 to 2012 .................................................Graduate Research Associate, Department
of Mechanical and Aerospace Engineering,
The Ohio State University, Columbus, OH,
USA
Publications
Akanda S.R., Walter M.E., Kidner N.J., Seabaug M.M, Mechanical characterization of
oxide coating–interconnect interfaces for solid oxide fuel cells, Journal of Power Sources
210 (2012) 254-262.
Zhou Y., Akanda S.R., Jeelani S., Lacy T.E., Nonlinear constitutive equation for vapor-
grown carbon nanofiber-reinforced SC-15 epoxy at different strain rate, Material Science
and Engineering A465 (2007) 238-246.

8. vii
Rahman M.A., Akanda S.R., Hossain M.A., Effect of Cross-section Geometry on the
Response of SAM Column, Journal of Intelligent Material Systems and Structures 19
(2008) 243-252.
Fields of Study
Major Field: Mechanical Engineering

9. viii
Table of Contents
Abstract…………………………………………………………………………………....ii
Dedication………………………………………………………………………………...iv
Acknowledgments…………………………………………………………………………v
Vita………………………………………………………………………………………..vi
List of Tables…………………………………………………………………………….xii
List of Figures…………………………………………………………………………...xiii
Chapter 1: Introduction……………………………………………………………………1
1.1 Background…............................................................................................................1
1.1.1 Basic Principles of an SOFC…………………………………………………...1
1.1.2 SOFC Materials ………………………………………………………………..2
1.1.3. Applications of SOFCs……………………………………………...................3
1.2 Problem Statement………………………………………………………………….4
1.3 Dissertation Structure ………………………………………………………………5
References………………………………………………………………………………9
Figures…………………………………………………………………………………10
Chapter 2: Adhesion of Reduced and Oxidized Spinel Coatings on Metallic Interconnects
……………………………………………………………………………………………12
Abstract………………………………………………………………………………..12

10. ix
2.1 Introduction………………………………………………………………………..13
2.1.1 Requirements of Interconnects………………………………………………..13
2.1.2 Drawback of Metallic Interconnects…………………………………………..15
2.1.3 Protective Coatings on Interconnects…………………………………………15
2.1.4 Experimental Techniques for Measuring Coating Adhesion…………………18
2.2 Experimental………………………………………………………………………20
2.2.1 Materials………………………………………………………………………20
2.2.2 Bend Experiments……………………………………………………………..21
2.3 Theory……………………………………………………………………………..22
2.3.1 Interfacial Shear Strength……………………………………………………..22
2.3.2 Interfacial Fracture Energy……………………………………………………25
2.4 Results……………………………………………………………………………..27
2.4.1 Cumulative AE………………………………………………………………..27
2.4.2 Interfacial Shear Strength……………………………………………………..29
2.4.3 Interfacial Fracture Energy……………………………………………………30
2.5 Discussions………………………………………………………………………...32
2.5.1 Effects of Reduction and Oxidation Heat Treatment…………………………32
2.5.2 Effects of Interconnect Compositions………………………………………...34
2.6 Conclusions………………………………………………………………………..34
References……………………………………………………………………………..36
Tables………………………………………………………………………………….38
Figures…………………………………………………………………………………39

11. x
Chapter 3: Lifetime of MCO Coatings on Metallic Interconnects………………………50
Abstract………………………………………………………………………………..50
3.1 Introduction………………………………………………………………………..51
3.2 Materials…………………………………………………………………………...54
3.3 Analytical Model for Residual Stress Distributions……………………………….55
3.3.1 Background……………………………………………………………………55
3.3.2 Interface Displacements……………………………………………………….56
3.3.3 Equilibrium Relations and Governing Equations……………………………..58
3.3.4 Boundary Conditions………………………………………………………….59
3.3.5 Analytical Interfacial Fracture Energy………………………………………..61
3.4 Results and Discussions…………………………………………………………...62
3.4.1 Experimental Results………………………………………………………….62
3.4.2 Analytical Results……………………………………………………………..64
3.4.3 Lifetime of MCO……………………………………………………………...65
3.5 Conclusions………………………………………………………………………..67
References……………………………………………………………………………..69
Tables………………………………………………………………………………….71
Figures…………………………………………………………………………………72
Chapter 4: Effects of reduction Heat Treatments on Coating Performances………….....86
Abstract………………………………………………………………………………..86
4.1 Introduction………………………………………………………………………..87
4.2 Experimental………………………………………………………………………88

12. xi
4.3 Results……………………………………………………………………………..88
4.4 Conclusions………………………………………………………………………..90
References……………………………………………………………………………..92
Tables………………………………………………………………………………….93
Figures…………………………………………………………………………………94
Chapter 5: Investigating Anode-Electrolyte Interface by a Steady-State Crack
Propagation………………………………………………………………………………99
Abstract………………………………………………………………………………..99
5.1 Introduction………………………………………………………………………100
5.2 Experimental……………………………………………………………………..101
5.2.1 Test Specimen………………………………………………………………..101
5.2.2. Strain Energy Release Rate…………………………………………………102
5.3 Results……………………………………………………………………………104
5.4 Conclusions………………………………………………………………………106
References……………………………………………………………………………108
Tables………………………………………………………………………………...109
Figures………………………………………………………………………………..110
Chapter 6: Conclusions and Future Works……………………………………………..118
6.1 Conclusions………………………………………………………………………118
6.2 Future Works……………………………………………………………………..121
Bibliography……………………………………………………………………………122
Appendix A: List of Symbols…………………………………………………………..128

13. xii
List of Tables
Table 2.1. Mechanical and thermal properties of MCO coating, native scale and
interconnect………………………………………………………………………………38
Table 2.2. Average values of critical tensile stress ( ), interfacial shear strength ( ),
experimental interfacial fracture energy ( ), and % spall area for each type of test
specimen…………………………………………………………………………………38
Table 3.1. Average critical tensile stress of coating (σc
ct
), Average saturated crack spacing
(l), interfacial shear strength (τst
i1
), interfacial fracture energy (Gexp
i1
), and % spall area
for each type of test specimen……………………………………………………………71
Table 4.1. Process conditions for standard and modified heat treatment………………..93
Table 4.2. Interfacial fracture energy of standard and modified fired test specimen……93
Table 5.1. Mechanical and thermal properties of anode and electrolyte………….........109

14. xiii
List of Figures
Figure 1.1. A schematic diagram of an SOFC with its components and basic principles….
……………………………………………………………………………………………10
Figure 1.2. (a) FlexCellTM
. (b) An SEM micrograph of an anode-electrolyte bi-layer…..11
Figure 2.1. Steps of chromium poisoning of a cathode………………………………….39
Figure 2.2. Steps of processing MCO coatings on interconnects……………………….40
Figure 2.3. SEM images of (a) Reduced MCO on Crofer (tested). (b) Oxidized MCO on
Crofer (tested)……………………………………………………………………………41
Figure 2.4. Experimental setup to characterize coating-interconnect interfaces………...42
Figure 2.5. (a) Schematic of failure mechanisms of a brittle coating during bend
experiments. (b) Shear stress distributions at interface and tensile stress distributions in a
coating segment………………………………………………………………………….43
Figure 2.6. (a) Experimental stress-strain curve synchronized with AE data. (b) An
enlarged view of region 1 of cumulative AE data……………………………………….44
Figure 2.7. Saturate parallel in-plane transverse cracks in (a) Reduced MCO on SS441.
(b) Oxidized MCO on Crofer……………………………………………………………45
Figure 2.8. Calculated values of interfacial shear strength for each type of test
specimen…………………………………………………………………………………46

15. xiv
Figure 2.9. (a) Interfacial fracture due to buckling of coating. (b) SEM image of MCO
buckling before spallation (reduced MCO -SS441)……………………………………..47
Figure 2.10. Representative SEM and processed images of MCO coating surfaces at 3%
strain (a) Reduced MCO-SS441. (b) Oxidized MCO-SS441. (c) Reduced MCO-Crofer.
(d) Oxidized MCO-Crofer……………………………………………….........................48
Figure 2.11. SEM and EDS analysis of spalled sections of (a) Reduced MCO on SS441.
(b) Oxidized MCO on Crofer…………………………………………………………….49
Figure 3.1. Integrated experimental-analytical methodology to predict lifetime of MCO
coatings on metallic interconnects……………………………………………………….72
Figure 3.2. SEM images of MCO coatings oxidized at 900o
C for (a) 100 hours. (b) 600
hours. (c) 1000 hours…………………………………………………………………….73
Figure 3.3. Native scale growth kinetics at 900o
C……………………………………….74
Figure 3.4. Normal forces, shear forces and bending moments generated in each layer due
to experiencing temperature differences.………………………………………………...75
Figure 3.5. Differential element of each layer subjected to normal force, shear force and
bending moment………………………………………………………………………….76
Figure 3.6. Steps to obtain analytical interfacial fracture energy………………………..77
Figure 3.7. Cumulative AE data synchronized with strain………………………………78
Figure 3.8. Saturated parallel in-plane transverse cracks in 900o
C-1000 hour oxidized
MCO……………………………………………………………………………………..79
Figure 3.9. MCO coatings with native oxide scale in spalled area………………………80

16. xv
Figure 3.10. Representative SEM and processed images of MCO coating surfaces at 3%
strain (a) 900o
C-100 hour. (b) 900o
C-600 hour. (c) 900o
C-1000 hour…………………..81
Figure 3.11. (a) Variation of normal compressive stress of MCO and curvature of
composite along x-direction. (b) Resultant stress distribution in MCO thru MCO
thickness. (hn = 6.14 μm)………………………………………………………………...82
Figure 3.12. (a) Residual shear stress distribution at MCO-native scale interface τr
i1
(hn =
6.14 μm). (b) Shear strength from experiments τst
i1
and maximum shear stress from
analytical model τr,max
i1
as a function of native scale thickness………………………….83
Figure 3.13. (a) Determination of critical native scale thickness to initiate MCO spallation
during cooling from 750o
C to room temperature. (b) Native scale growth kinetics at
750o
C…………………………………………………………………………………….84
Figure 3.14. Projected lifetime of MCO coatings as a function of operating temperature
of a fuel cell……………………………………………………………………………...85
Figure 4.1. A schematic diagram of an ASR setup………………………………………94
Figure 4.2. SEM observation of microstructure of (a) Standard MCO. (b) Modicfied
MCO. ………………...………………………………………………………………….95
Figure 4.3. (a) Cumulative AE data synchronized with strain. (b) Post-test SEM image of
modified MCO.…………………………………………………………………………..96
Figure 4.4. Long-term ASR behavior of standard vs. non reduction firing MCO coated
interconnect………………………………………………………………………………97
Figure 4.5. Post-ASR SEM observations of cross section of (a) Standard MCO (6500
hours). (b) Modified MCO (2000 hours)………………………………………………...98

17. xvi
Figure 5.1. Notched four-point bend test specimen to propagate a steady-state crack along
the interface……………………………………………………………………………..110
Figure 5.2. High magnification camera image of an anode-electrolyte test
specimen………………………………………………………………………………..111
Figure 5.3. SEM micrograph of porous anode and dense electrolyte…………………..112
Figure 5.4. Steps to Steps to strengthen anode by inserting glue………………………113
Figure 5.5. Steady-state crack propagation along anode-electrolyte interface…………114
Figure 5.6. SEM and EDS analysis of (a) Electrolyte (b) Anode………………………115
Figure 5.7. Experimental load-displacement curve…………………………………….116
Figure 5.8. Steady-state energy release rate as a function of applied load……………..117

18. 1
Chapter 1
Introduction
This dissertation is divided into 5 chapters from Chapter 2 to Chapter 6 that make up two
separate topics. The first topic, focusses on adhesion of coatings on metallic interconnects
of a solid oxide fuel cell (SOFC) stack. The coats are assessed in terms of interfacial
shear strength and interfacial fracture energy. In addition, lifetime of coated interconnects
is estimated. The second topic investigates the anode-electrolyte interface of an SOFC by
characterizing the propagation of a steady-state crack along the interface.
In Chapter 1, the general background and the organization of this dissertation are
discussed.
1.1 Background
1.1.1 Basic Principles of an SOFC
Solid oxide fuel cells (SOFCs) convert chemical energy of hydrocarbon fuels to electrical
energy at high temperatures generally ranging from 600 – 800o
C. Figure 1.1 presents a
schematic diagram of an SOFC with its components and basic chemical reactions. The
main constituent of an SOFC is the gas-tight, dense ceramic electrolyte which is a good
oxygen ion conductor at high temperatures. The solid ceramic electrolyte is sandwiched
between two porous fuel and air electrodes known as the anode and cathode, respectively.

19. 2
In the basic principle, the air or oxygen at the cathode combines with an electron and
forms an oxygen ion. The oxygen ion diffuses through the electrolyte to the anode. At the
anode, an electron is liberated by oxidation of hydrocarbon fuels, thus producing water.
The emitted electron is routed through an external circuit to the cathode and completes an
electrical, power-producing circuit [1, 2]. In practical applications, unit fuel cells are
connected in series to form a fuel cell stack. Interconnects are the devise that physically
separate but electrically connect the adjacent cells.
1.1.2 SOFC Materials
NexTech Materials Ltd. (NTM) has developed a family of electrolyte-supported planar
cells that have sufficient mechanical robustness and excellent electro-chemical
performance. As shown in Fig. 1.2(a), the FlexCellTM
is formed from a thin electrolyte
membrane (40 μm) sintered with a support layer consisting of thicker electrolyte material
(150 μm) that has hexagonal cut-outs. The thin regions within each hexagon are called
“active areas” where ion transport is most active. The electrolyte is typically composed of
either yttria (Y) stabilized or scandia (Sc) stabilized zirconia (Zr). The thin electrolytes
and 30 μm screen-printed electrodes minimize the component thickness and results in
mechanically flexible components that are compliant during stack assembly and
operation. Electrochemical performances of the FlexCellTM
are comparable to the best
anode supported cell designs and enable a wider window of material selection for the
electrodes [3]. This electrode material flexibility can enable lower operating temperatures
and is more tolerant of the use of sulfur contaminated fuels.

20. 3
Over the years NTM has found that an LSM (lanthanum strontium manganese) based
cathode and Ni-GDC/Ni-YSZ anode, where GDC refers to gadolinium doped cerium,
provide the best performance and stability. The anode material is produced by controlled
mixing of NiO, GDC and YSZ (yttria stabilized zirconia) powders with well-defined
powder size and tape-casting the powder slurry into sheets. The sheets are subsequently
stacked and co-sintered with adjoining materials. Finally exposure to an H2 environment
converts NiO to Ni [2].
In Fig. 1.2(b) an SEM image of an anode-electrolyte bi-layer is shown. As can be seen in
the figure, the anode is separated into two distinct layers: the active anode layer and the
current collector layer. The active anode layer is 10 μm in thickness and current collector
layer is 25 μm in thickness.
Within an operating temperature of 600-800o
C, it is preferable to use iron based metals as
interconnects because of their low cost and availability [4, 5]. To protect the metallic
interconnects from oxidation at high temperature, the cathode side interconnect surfaces
are coated by ceramic oxides [6].
1.1.3 Applications of SOFCs
Due to their high efficiencies and low emissions, SOFCs have the potential to radically
alter the distributions and productions of electrical energy. Although SOFCs operate at
high temperatures, they have several advantages over other fuel cell types. The principal
advantage is fuel flexibility. Because the ceramic membrane is an oxygen ion conductor,
oxygen partial pressure gradients create voltage that allows cell operation. Thus both H2
and CO can be consumed as fuel, allowing a range of reformed hydrocarbon fuels to be

21. 4
considered. The high operating temperatures create advantages both by enabling catalysis
of the fuels without special, expensive materials and by paving the way to enhanced
efficiency within combined cycle systems. Another important advantage is the enhanced
tolerance of SOFCs to fuel impurities. CO, which poisons proton exchange membrane
(PEM) fuel cells, is a fuel for SOFCs. H2, another common contaminant in hydrocarbon
and some biomass-derived hydrogen fuels, is tolerated in SOFCs currently being
developed; competing fuel cells require large desulfurizers which reduces overall system
efficiency. In addition, as the SOFCs do not require combustion to generate energy, they
produce cleaner energy with lower emissions compared to the conventional power
systems [7].
With increasing demands of global power consumptions in the next decades, SOFCs may
be a promising source of power generation in stationary, mobile and military
applications. Capability of producing cleaner energy has made SOFCs an attractive
option from an environmental point of view. Because of high operating temperatures,
SOFCs are integrated with combined heat and power systems ranging from 1 KW to
several MW. The potential applications of SOFCs include individual households, large
residential units, industries and business perimeters, and hospital backup power.
1.2 Problems Statement
Degradation and failure of SOFC components while operating and after anticipated and
un-anticipated shutdowns and subsequent start-ups are largely a consequence of high
operating temperatures. With such a range of materials within stack monolith, challenges
with spatially and temporally non-homogenous high temperature environment are

22. 5
tremendous and a direct result of (a) widely varying of thermal coefficient of expansion
(TCE) (b) non-equilibrium and low temperature phases (especially at interfaces) and (c)
ceramic components with low toughness and low thermal conductivity. In SOFCs,
thermal gradients associated with improper thermal balance between low temperature
inlet gas streams and the exothermic oxidation reactions can result in catastrophic stack
failure. The current approach to solving problems associated with thermal gradients and
TCE mismatches is to increase the mechanical strength of various components. To some
extent, this has been done; however, strengthening of different components has exposed
weakness at interfaces. Clear evidences from NTM and literature show that during
thermal cycling coating-interconnect interfaces and electrode-electrolyte interfaces
degrade and delamination occurs [8-15].
1.3 Dissertation Structure
In Chapter 2, a room temperature four-point bend experimental technique is applied in
close collaboration with NexTech Materials (NTM) for the mechanical characterization
of coating-interconnect interfaces in an SOFC stack. The experimental set up is designed
in such a way as to placing the brittle coatings under tensile stresses. The spacing
between the resulted saturated tensile cracks on the coating surface is incorporated in a
shear lag model to quantify the interfacial shear strength. At higher strains, coating
spallation occurs. Interfacial fracture energy is calculated from an energy based fracture
mechanics utilizing the strain at onset of spallation. Thus the coating adhesion is assessed
by both the interfacial shear strength and the interfacial fracture energy. The coatings are
subjected to two different heat treatments by NTM: (a) reduction heat treatment and (b)

23. 6
oxidation heat treatment. In this chapter, the evolution of the coating adhesion from the
reduction heat treatment to the oxidation heat treatment is described. Scanning electron
microscopy (SEM) along with the energy dispersive spectroscopy (EDS) are performed
on the cracked and spalled coating to analyze the failure mechanisms of coatings. Two
types of interconnect materials are considered: SS441 (441-HP) and Crofer 22 APU and
their effects on the coating adhesion are also discussed.
In Chapter 3, the lifetime of coating at a particular stack operating temperature is
estimated by implementing an integrated experimental-analytical methodology. Although
coating is intended to act as a barrier to oxidation of interconnects, the formation of
native oxide scales (Cr2O3) between coatings and interconnects is still inevitable during
stack operations. With operating time, the native scales grow in thickness experiencing
growth stresses and as a consequence the thicker native scales alter the adhesion of the
coatings. In addition, when cooling down the fuel cell stack from operating temperature
to room temperature, thermal coefficient mismatch between the native scales and the
coatings causes coating spallation. Therefore, effective interconnect lifetime is mainly
limited by the cooling induced coating spallation. The following steps are considered in
Chapter 3 to predict the coating lifetime at a particular stack operating temperature:
 Four-point bend experiments are performed on heat treated, coated interconnects
oxidized at 900o
C for 100, 600 and 1000 hours. The reason for oxidizing the
coated interconnects at higher temperature than the operating temperature (600-
800o
C) is to accelerate the oxidation driven failure mechanisms of the interface.

24. 7
 The experimental results describe the evolution of interfacial shear strength and
interfacial fracture energy with oxidation time, i.e. native scale thickness. The
oxidation time is related to the native scale thickness by native scale growth
kinetics.
 An analytical model for a tri-layer coating-native scale-interconnect assembly is
implemented to obtain the cooling induced residual stress distributions in the
coating and shear stress distribution at the interface as a function of native scale
thickness. From the residual stress distributions in the coating, the analytical
interfacial fracture energy as a function of native scale thickness is also assessed.
 Equating the experimental fracture energy with the analytical fracture energy, the
critical native scale thickness at which cooling induced coating spallation occurs
is obtained.
 The critical native scale thickness is converted to the equivalent coating lifetime
by incorporating the critical native scale thickness to native scale growth kinetics
chart at a particular operating temperature.
In Chapter 4, whether reduction heat treatment has beneficial impacts on coating
performances is evaluated. In coating process, it is the reduction heat treatment that
contributes to a significant portion of coating coasts. From an economical point of view,
it would be preferable for NTM if the reduction heat treatment is removed from the
process flow. But it is anticipated that the absence of reduction heat treatment may
degrade the coating performances by producing a less dense and poorly adherent coating.
In addition to the four-point bend tests, in Chapter 4 electrical resistance tests are

25. 8
performed on coated interconnects. Based on the results obtained in Chapter 4,
recommendation whether the reduction heat treatment is necessary is made.
In Chapter 5, the anode-electrolyte interfaces are characterized. Four-point bend tests are
conducted in controlled environment in the laboratory. The brittle bi-layer test specimens
are sandwiched between two steel stiffeners. A notch is created in the relatively thicker
electrolyte which acts as a crack initiator at higher load. The crack initiated from the
notch tip is forced to stop at the interface and then to propagate along the interface in a
stable manner upon further loading. Critical strain energy release rate of the interface is
calculated by applying the beam bending theory. SEM and EDS analysis are performed to
study each separate layer.
Finally in Chapter 6, overall conclusions are drawn and some recommendations for future
works are made.
Experimental results and analysis obtained from this research will be helpful for NTM to
modify the manufacturing processes in order to develop the interfacial strength of
coating-interconnect interfaces and anode-electrolyte interfaces of an SOFC stack. Also
the scientific knowledge gained through the present research will be useful to other
researchers seeking to enhance understanding and control of thermo-physical stresses in
similar interface systems.

26. 9
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10. Li W., Hasinska K., Seabaugh M., Swartz S., Lannutti J.J., Curvature in Solid Oxide
Fuel Cells. Journal of Power Sources 138 (2005) 145-155.
11. Walter M., GOALI: Electrode Interfaces Stresses, Degradation and Failure, NSF
Proposal 2008.
12. Recknagle K.P., Williford R.E., Chick L.A., Rector D.R., Khaleel M.A., Three-
dimensional thermofluid electrochemical modeling of planar SOFC stacks. Journal of
Power Sources 113 (2003) 109-114.
13. Malzbender J., Wessel E., Steinbrech R.W., Reduction and re-oxidation of anodes for
solid oxide fuel cells. Solid State Ionics 176 (2005) 2201-2203.
14. Zhang Y., Liu B., Tu B.F., Dong Y.L., Cheng M.J., Redox cycling of Ni-YSZ anode
investigated by TPR technique. Solid State Ionics 176 (2005) 2193-2199.
15. Fouquet D., Muller A.C., Weber A., Ivers-Tiffee E., Kinetics of oxidation and
reduction of Ni/YSZ cermets. Ionics 9 (2003) 103-108.

27. 10
Figures
Figure 1.1. A schematic diagram of an SOFC with its components and basic principles.

28. 11
(a)
(b)
Figure 1.2. (a) FlexCellTM
. (b) An SEM micrograph of an anode-electrolyte bi-layer.

29. 12
Chapter 2
Adhesion of Reduced and Oxidized Spinel Coatings on Metallic
Interconnects
Abstract
This chapter reports on the mechanical characterization of coating-interconnect interfaces
for coating processed in two different conditions: reduction heat treatment and reduction
heat treatment followed by an oxidation heat treatment. The interconnect materials
considered are ferritic AL 441-HP (SS441) and Crofer 22 APU to explore the effects of
the alloying elements in interconnects on the coating adhesion. An acoustic emission
(AE) sensor is coupled with a four-point bend fixture to monitor the coating cracking and
spallation. A long-distance camera lens is also incorporated in the experimental setup to
accurately identify the acoustic signals correlated with the coating and interface fracture.
Resulting tensile cracking patterns on the coatings on the convex side of the bend
specimen are used to quantify the interfacial shear strength with a shear-lag model. Using
energy based fracture mechanics; interfacial fracture energy is calculated from the strain
at the onset of coating spallation. Post-test SEM is performed to analyze the cracked and
spalled surfaces and to gain the insight of coating failure mechanisms. The experimental

30. 13
results presented in this chapter are able to distinguish between two different coating-
substrate systems and reduction heat treatment versus reduction-oxidation heat treatment.
2.1 Introduction
2.1.1 Requirements of Interconnects
It is well known that, to reach practical power levels, individual cells are repeated to form
a fuel cell stack. Interconnects are the components that physically separate individual
cells and provide the means to complete the electrical circuit. Thus interconnects
maintain the uniform fuel and air flow as well as play a critical role in increased
efficiency and power density of a fuel cell stack. Since opposite sides of interconnects are
exposed to reducing (fuel) and oxidizing (air) environments, the resulting chemical
potential gradients place severe constraints on selecting the most appropriate materials
for interconnects. The additional design requirements that an interconnect should possess
are excellent electrical conductivity, chemical and physical inertness in high temperature
corrosive environments, good thermal conductivity, high strength and creep resistance,
and low material and fabrication cost [1].
As the main purpose of an interconnect is to maintain an electrical connection between
anode and cathode of the adjacent cells, the most important property of interconnect is to
exhibit excellent electrical conductivity, preferably with 100% electron conduction.
Electrical conductivity of 1 S-cm-1
is the minimum acceptable conductivity for use in a
fuel cell stack [1]. The next important property of interconnect is the stability of
geometry and microstructure in high temperature, corrosive environments. The anode
side of the interconnect is exposed to a high temperature, reducing environment whereas

31. 14
the cathode side is exposed to an oxidizing atmosphere. The different oxygen partial
pressures on the anode and the cathode sides builds up significant oxygen partial pressure
gradients in the interconnects. The resulting geometrical changes can yield considerable
amount of mechanical stresses in interconnects and can cause breakage of interconnects
as well as cracking of seals [1]. Phase or microstructural changes in interconnects due to
chemical potential gradients can significantly alter the electrical conductivity. Sufficient
lack of chemical inertness of interconnects can result in formation of an electrically
insulating oxide scales in high temperature oxidizing atmospheres. Thus instability of
geometry and phase of interconnects can deteriorate the performance of an SOFC stack.
Finally, closely matched thermal coefficients of expansion (TCE) of interconnects with
electrodes is desirable to minimize the generation of thermal stresses due to start up and
shut down cycles [1].
With the use of thin electrolytes or thin electrolyte regions, the maximum operating
temperature of an SOFC can be kept below 800o
C. This allows replacing conventional
but expensive LaCrO3 ceramic interconnects with metal-based interconnects. There are
many advantages of using metallic interconnects over the ceramic ones such as high
electrical and thermal conductivity, low cost, availability, and workability. However the
main difficulties associated with metallic interconnect are low resistance to oxidizing and
corrosive environments, low strength at high temperatures and thermal and mechanical
mismatch with electrode materials. In light of the necessary requirements on
interconnects, chromium alloyed iron (Fe) based (stainless-steel) interconnects such as
Crofer 22 APU or Allegheny Ludlum (AL) 441-HP are the most promising interconnect

32. 15
materials for intermediate temperature (600 – 800o
C) SOFCs. The formation of chromia
scale (Cr2O3) gives the property of fairly moderate oxidation and corrosion resistance at
high temperatures. The most attractive feature of stainless steel interconnects is the
closely matched TCE with the electrodes. High ductility, high compliance, high strength
and creep resistance at high temperature are other advantageous features when
considering chromium alloyed ferritic metals as interconnects [1].
2.1.2 Drawback of Metallic Interconnects
An important drawback of chromium alloyed metallic interconnects is chromium
poisoning of cathodes. Figure 2.1 demonstrates the sequential steps of chromium
poisoning. Depending on the atmosphere at the cathode, chromium rich alloy forms CrO3
chromium trioxides or CrO2(OH)2 chromium hydroxides. Upon combining with oxygen
ions in the cathode active area, the chromium compounds reduce to Cr2O3 chromia
scales. Thus the chromia scale formation results in decreased cathode active area. In
addition, the electrically insulating nature of chromia scales increases the contact area
specific resistance (ASR) between the interconnect and cathode. As a consequence, the
performance and efficiency of a fuel cell stack is significantly degraded [2, 3, 4].
2.1.3 Protective Coatings on Interconnects
It is therefore critical to inhibit chromium migration to cathodes and oxygen inward
diffusion to interconnects. One way to achieve the necessary chemical inertness of
interconnects is to protect the surfaces with application of a thin, dense coating. The
protective coating layer acts as a diffusion barrier to chemical reactions between the
interconnects and the corrosive environment, thus inhibiting chromium volatility in the

33. 16
cathode active area and slowing the rates of chromia scale formation. Either bulk alloy
modification or bulk surface modification can be performed to form coatings on
interconnects. In bulk alloy modification, manganese is added in interconnects to form a
unique scale comprised of (Mn,Cr)3O4 spinel at the top with a chromia or chromia-rich
sub-layer beneath the top layer. But research conducted at Pacific Northwest National
Laboratory (PNNL) indicates that the (Mn,Cr)3O4 spinel coatings from bulk alloy
modification reduce Cr poisoning by only a factor of 3 over unmodified alloy [5]. This
may still result in an unacceptable amount of chromium poisoning in stack operation.
In bulk surface modification, a dense, protective coating on the surface of the cathode-
side interconnect is applied externally. Generally pervoskite compositions with a
chemical structure of (AB)2O3, where A and B are metallic cations are used as protective
coatings. The most commonly used pervoskite coatings are lanthanum manganese oxide
and lanthanum cobalt/chromium oxide. One potential challenge associated with this type
of coatings is to manufacture a dense protective layer. In general, insufficient density of
pervoskite coatings makes them unable to prevent inward oxygen diffusion. As a result,
pervoskite coatings possess poor thermo-mechanical stability due to extensive oxide scale
growth between the coatings and interconnects. A promising alternative to pervoskite-
type coatings is the spinel structure materials of (AB)3O4 where A and B are again
metallic cations [6].
Several researchers have recently applied manganese cobalt spinel oxide (MCO) as a
protective layer on interconnects in an SOFC stack. Larring et al. observed increased
capability of (Mn,Co)3O4 to prevent chromium evaporation compared to that of

34. 17
pervoskite composites [6]. In addition, with iron (Fe) doping of the spinel MCO, it is
possible to achieve excellent electrical conductivity and thermal compatibility with
interconnects. Yang et al. studied thermally grown (Mn,Co)3O4 with a nominal
composition of Mn1.5 Co1.5 O4 on Crofer22 APU substrate [2, 5]. The substrate was slurry
coated and then heat treated in reducing and oxidizing environments. Their experimental
results indicate decreased ASR between LSF cathodes and interconnects due to
significant inhibition of subscale growth. The spinel coating acted as an effective barrier
to both chromium migration and oxygen inward diffusion.
The ceramic MCO coating is extremely brittle. In practice, the mechanical integrity of
this protective coating layer can be severely affected by the mechanical stresses from
mechanical loading and the residual stresses originating from oxide scale growth and
thermal cycling. The complex thermo-chemical stresses in addition to mechanical
stresses can result in coating fracture and spallation. The coating-substrate interfaces play
an important role in the mechanisms of coating fracture and spallation. For weaker
coating-substrate interfaces, coatings first buckle under high compressive stresses and
then spall if through-thickness cracks develop. For relatively stronger interfaces, shear
cracks can form in the coatings, which cause shear sliding in the cracked segments and
finally spallation in the protective coatings [7]. For SOFCs, when the protective coating
layer spalls, uncoated interconnect metal is exposed to the corrosive environments more
severely. The resulting damage to interconnects can cause significant degradation of the
electrochemical performances of the SOFCs. Therefore it is important to characterize

35. 18
coating interfaces/measuring coating adhesion, for reliability assessments of
interconnects in SOFC applications.
2.1.4 Experimental Techniques for Measuring Coating Adhesion
Several researchers have incorporated different experimental methods to measure the
adhesion of coatings to substrate. Some of the experimental techniques include tensile
pulling test, scratch test, laser induced or shock wave induced spallation, micro-
indentation test, bend test etc. Although some of them have simple experimental setups,
each of them has their own drawbacks. For example, in a tensile pull test a stud-pull is
attached to the specimen by means of applying an adhesive. Failure can occur between
the stud-pull and the organic adhesive if the interfacial strength between them is less than
that of coating-substrate interface. Moreover, if the coating is porous, adhesive can
penetrate through the porosities of the coating to the interface and can affect the test
results by producing scattered data [8].
In a scratch test, a stylus or indenter is traversed along the film with either step wise or
continuously applied load. The critical load at which some well-defined film failure
occurs is a measure of film adhesion. Depending on the load, depth of penetration and
mechanical properties of the coating and substrate, various failure modes may exist.
Indenter wear and tip radius, loading rate and scratch speed can scatter the experimental
results significantly [8, 9].
In a laser test, a compressive wave pulse which is generated from a high energy laser
source propagates through substrate normal to the coating-substrate interface. After
reflecting back from the free surface of the coating, the compressive wave converts to a

36. 19
tensile wave and can break the bond at the interface. Although attractive, this is a
complicated and expensive method. Extensive calibration is required to obtain reliable
results. The mechanical and thermal properties of coating and substrate also limit the use
of this technique [8, 10].
Indentation tests involve creating micro-indents on the surfaces of coatings. Indentation
creates a plastically deformed zone beneath the surface. Residual stress provides the
driving force for lateral and radial cracking. If the interfacial toughness is less than that of
the coating and substrate, a crack will propagate through interface. Together with finite
element simulations, Sun et al. performed stair stepping indentation tests to quantify the
interfacial shear strength of coating-oxide-crofer tri-layer systems in SOFCs [11]. The
critical load at which the scale spallation occurred was used to quantify the interfacial
shear strength. However, the formation of a plastically deformed zone beneath the surface
limits the depth of indentation to be less than the coating thickness [12].
In the present research, a room temperature four-point bend experimental technique is
applied in close collaboration with NexTech Materials (NTM) for the mechanical
characterization of coating-interconnect interfaces in an SOFC stack. The coatings are
subjected to two different heat treatments by NTM: (a) reduction heat treatment (b)
reduction and oxidation heat treatment. The experimental set up is designed in such a
way as to placing the brittle coatings under tensile stresses. The spacing between the
resulted saturated tensile cracks in the coating surface is incorporated in a shear lag
model to quantify the interfacial shear strength. At higher strains, coating spallation
occurs. Interfacial fracture energy is calculated from an energy based fracture mechanics

37. 20
utilizing the strain at onset of spallation. Thus the coating adhesion is assessed by both
the interfacial shear strength and the interfacial fracture energy. The evolution of the
coating adhesion from the reduction heat treatment to the oxidation heat treatment is
described. Scanning electron microscopy (SEM) along with the energy dispersive
spectroscopy (EDS) are performed on the cracked and spalled coating to analyze the
failure mechanisms of coatings. Two types of interconnect materials are considered:
SS441 (441-HP) and Crofer 22 APU and their effects on the coating adhesion are also
discussed.
2.2 Experimental
2.2.1 Materials
Interconnects coated with manganese cobalt spinel oxide (MCO) are provided by NTM.
The ferritic interconnect substrates are: AL 441-HP (SS441) and Crofer 22 APU. SS441
is mainly composed of 17.6% chromium (Cr), 0.33% manganese (Mn), 0.47% silicon
(Si), 0.46% niobium (Nb), 0.18% titanium (Ti), 0.2% nickel (Ni) by weight with minor
amount of alloying elements such as carbon (C), aluminum (Al), phosphorus (P), sulpher
(S) and with the balance being iron (Fe) [13]. Crofer 22 APU is an Fe–Cr–Mn steel
specifically developed for SOFC interconnect applications [14, 15]. It has 22.3% Cr with
0.45% Mn, other alloying elements such as Ti, C, P, S in minor amounts and a balance of
Fe. In addition to having higher amounts of Cr and Mn, Crofer has also trace amounts of
rare earth elements, for example, 0.06% of lanthanum (La).
NTM’s coating processing steps are shown in Fig. 2.2. In the first step of coating process,
an MCO suspension is applied through a cost-effective, commercially viable aerosol

38. 21
spray deposition (ASD) on the metallic interconnects at room temperature [16]. The
spray suspension is prepared by mixing an appropriate binder, solvent and dispersants
with MCO powder having a nominal composition of Mn1.5Co1.5O4. The thickness of the
MCO ranges from 10 - 15 μm. The MCO coated interconnect is then heat treated in two
different stages to develop a dense, adherent MCO coating: a controlled reduction heat
treatment at high temperature followed by an oxidation heat treatment at elevated
temperature. The reduction heat treatment reduces the spinel into two distinct
components: metallic Co and lower valence MnO. The organic binder is burned out
during the reduction firing. During subsequent oxidation in air, the Co and MnO react
with oxygen to reform the spinel with enhanced densification via reaction-sintering [17]:
6Co + 6MnO + 5O2 = 4 Mn1.5Co1.5O4
Figure 2.3 (a) and 2.3 (b) shows two SEM images of a reduced and a dense oxidized
MCO coating respectively.
2.2.2 Bend Experiments
The four-point bend experiment is set up such that the coatings will experience tensile
stresses during bending. The loading configuration and dimensions of the test specimen
are shown in Fig. 2.4. The inner and outer loading spans are 20 and 60 mm, respectively.
The stresses at the outer surfaces of coating-interconnect test specimen are calculated
from the applied loads by the method of Timoshenko [18]. Surface strains are obtained
from a conventional resistant strain gage attached to the uncoated side of the test
specimen and the specimens were loaded in displacement control up to 3% strain. An
acoustic emission (AE) sensor that is coupled to a Vallen System AMSY-4 is placed on

39. 22
the coated side of the specimen to monitor coating failure. The AE sensor detects the
transient surface waves generated from cracking and other failure and deformation
phenomena of coatings that release strain energy. After the AE signal is pre-amplified by
34 dB, the signal threshold is set to 40 dB to eliminate unwanted noises from the load
frame and the test environment. To accurately identify the acoustic emission events
associated with coating spallation, the coating is observed in situ with a high
magnification camera lens. The stress-strain data and the AE data are synchronized for
subsequent analysis of failure mechanisms.
2.3 Theory
2.3.1 Interfacial Shear Strength
The tensile loading failure mechanisms of a brittle coating on a ductile substrate are
schematically illustrated in Fig. 2.5(a). When the tensile stresses exceed the critical
tensile stress of the coating, initial thru-thickness tensile cracks are produced in the
coating. The initial cracks, also called primary cracks, are created by stresses generated
from the applied bending moment. After formation of the primary cracks, tensile stresses
are no longer transferred to the coating segment directly from the applied bending
moment. Instead, as a result of continuous loading, the tensile stresses are transferred
from the ductile substrate to the coating segment through interfacial shear stresses or
what is also called “shear-lag.” As a consequence of stress transfer through shear at the
interface, tensile stresses continue to develop in the coating segment, creating further
thru-thickness tensile crack and as a consequence new coating segments. The crack from
shear-lag is known as secondary crack as this is not generated from the applied bending

40. 23
moment directly. Secondary crack density increases as the applied strain increases until at
one point, the formation of the tensile thru-thickness cracks saturates [19, 20].
The formation of thru-thickness tensile cracks is described as elastic stress relaxation and
can be modeled by a shear-lag theory [21]. For a coating segment, Fig. 2.5(b) shows
shear stress distributions at the interface and the resulting tensile stress distributions in
the coating segment along x-direction. Although bending creates a thru-thickness stress
gradient, the coating is 0.5% of the substrate thickness and the effects of the stress
gradient thru the coating thickness are therefore negligible. At both ends (free surfaces)
of the segment where the tensile stress in the coating segment is minimum, all the stresses
are supported by the substrate resulting in maximum interfacial shear stress at both ends
of the segment. The tensile stress is highest at the middle of the coating segment and the
shear stress is lowest at the midpoint of the interface. When the maximum tensile stress
exceeds the critical tensile stress of the coating, a new cracked segment is formed. For a
coating segment of length l in Fig. 2.5(b), the segment is infinitely long in z-direction
comparing the length, l, and hence the variation of stresses in z-direction is neglected.
The equilibrium equation along x-direction can be written as [22]
Here is the normal stress distribution in the coating segment along x-direction and
is the shear stress.
Integrating Eq. (2.1) over the coating thickness, hc and then dividing by the thickness
yields

41. 24
( ∫ ) ∫
Considering the thru-thickness stress gradient in the coating segment is negligible and at
x = hc, (free surface) and after doing some mathematical manipulations, equation
(2.2) finally yields
∫
Here is the interfacial shear stress distribution. Tien and Davidson [13] considered
purely elastic behavior of the interface with a linear shear stress distribution along the
interface and for this case the maximum shear stress at the interface, can be related
to the critical tensile stress of the coating, from Eq. (2.3) by the following relation:
For an ideal plastic interface where the shear stress distribution is assumed to be constant,
the Eq. (2.4) takes the form as [24]:
In general, the maximum interfacial shear stress is related to the critical tensile stress of
coating thru coating thickness and crack spacing by:
Here K is an integration constant which depends on assumed shear stress distribution and
its value is bound between 2 and 4 as shown in Fig. 2.5(b). In the present case, a

42. 25
sinusoidal shear stress distribution is considered along the interface to allow the interface
to have limited plastic stress relaxation next to the thru-thickness cracks. In this case, K is
π which is between an ideal elastic and plastic behavior [25].
Once the shear strength of the interface has been exceeded, the shear stresses are relaxed
by non-elastic mechanisms such as interface slip next to the tensile cracks or by substrate
yielding at the base of the thru-thickness cracks. This phase is described as plastic stress
relaxation, and the secondary crack formation saturates during this phase [25]. Interface
slip is followed by an interface delamination. By replacing l with the saturated crack
spacing, it is possible to calculate the interfacial shear strength, from Eq. (2.6).
2.3.2 Interfacial Fracture Energy
At higher strains, coating spallation is observed. If it is assumed that the coating is
perfectly adhered to interconnect and only elastically strained during the experiment,
elastic strain energy will be stored in the coating. At some point, it is energetically
favorable to release the stored elastic energy as interfacial fracture, resulting in coating
spallation. The interfacial fracture energy, can be calculated from the relation [26]
where W is the stored elastic energy density in the coating and hc is the coating thickness.
The subscript ‘exp’ refers to the experimentally determined interfacial fracture energy. W
is a function of in-plane stress-strain evolution in the coating along both the longitudinal
(x-axis) and in-plane transverse (z-axis) axes. Despite the bend loading, stress
perpendicular to the interface would be very small and are thus assumed to be neglected
[25]. During the experiment, the coating deforms elastically whereas the metal

43. 26
interconnect undergoes elastic and plastic deformation. For a continuous, un-cracked
coating, the tensile stresses developed in the coating during elastic interconnect
deformation; can be expressed as a function of applied tensile strain on the coating by the
following equation [26]:
where E is Young’s Modulus, v is Poisson ratio, ε is strain and σ is stress. The subscript
‘c’ stands for coating and the subscript ‘s’ stands for substrate. The superscript ‘x’
corresponds to the longitudinal axis. If the interconnect undergoes plastic deformation,
the tensile stress-strain relation in the coating takes the following form [26]:
[ ( )]
During elastic deformation of the interconnect, the compressive stresses generated in the
coating along the in-plane transverse axis can be calculated by [26]
here the superscript ‘z’ corresponds to the in-plane transverse axis. During plastic
deformation of the interconnect, compressive stresses can be described by the following
relation [26]:
[ ( )]
As mentioned in Section 2.2.2, the longitudinal compressive strains of the interconnect
surface on the uncoated side of the test specimen are obtained from a strain gage. From
the four-point bend theory and for a very thin coating (hc << hs), the tensile strains in the
un-cracked coating are equal in value to the compressive strains from the strain gage and

44. 27
the compressive strains in the coating along the in-plane transverse axis are equal to the
in-plane transverse compressive strains of the surface of coated side interconnect [27].
Considering the area under the stress-strain curve of the MCO coating, the stored elastic
energy in the coating at the onset strain of spallation (εsp) can be calculated from the
following relation [26]
∫
If the first thru-thickness transverse crack and the onset of spallation occur at nearly the
same strain, both the tensile and compressive stress evolution would need to be
considered. However, if the coating spallation occurs at a comparatively higher strain, the
tensile stresses are relaxed by the formation of the cracked segments in coating, and only
the z-axis compressive stresses in coatings are involved in computing the fracture energy
[26].
2.4 Results
2.4.1 Cumulative AE
The flexural stress–strain curve of a MCO coating–interconnect specimen together with
cumulative AE data is presented in Fig. 2.6. Two types of interconnects, SS441 and
CroferTM
, are considered. For each type of interconnect, the effects of both the reduction
and oxidation heat treatment are investigated. Both SS441 and Crofer are ferritic stainless
steels, and the young’s modulus (∼250 GPa) and yield stress (∼350 MPa) were found to
be same for both the substrates. Since the MCO coating is extremely thin comparing to

45. 28
the interconnect, it has no effect on the stress–strain curve. The stress–strain curve shown
in Fig. 2.6 is representative of all coating–substrate systems.
The AE data provides information on cracking events. The cumulative AE curve for each
type of test specimen is plotted by adding the individual AE hits cumulatively. In Fig.
2.6(a) each type of cumulative AE curve is representative for the respective specimen
type and reveals three distinct regions of AE activity. In the figure, the regions are
labeled for oxidized MCO-Crofer only. In the initial region of each curve which is shown
in an enlarged view in Fig. 2.6(b), the cumulative AE hits are observed to increase with
the applied strain. Each individual AE hit in each curve in this region represents the
formation of thru-thickness tensile cracks in the MCO during the elastic stress relaxation.
The first AE hit is considered to take place at the critical strain for the tensile crack
formation in the MCO. Assuming elastic deformation of the MCO, the critical tensile
stress of the MCO is calculated from the critical strain and the mechanical properties of
the MCO. The mechanical properties of MCO are tabulated in Table 2.1.
For each type of specimen, at least ten experiments were conducted. The critical tensile
stresses obtained were consistent for each type of test specimen. The average value of the
critical tensile stresses of MCO for each type of test specimen is tabulated in Table 2.2.
As is observed in Fig. 2.6(b) and Table 2.2, the oxidation heat treatment decreases the
critical tensile stress of MCO significantly. The more dense structure of oxidized MCO is
favorable for thru-thickness crack propagation generated from a pre-existing defects or
voids in the coatings. In Fig. 2.6(b), the higher slopes of the cumulative AE curves for the

46. 29
oxidized test specimen indicate that the oxidized MCO has higher crack density than that
of the reduced MCO.
After the elastic stress relaxation, the saturation of tensile cracks during the plastic stress
relaxation is illustrated by a relatively flat Region 2 in the cumulative AE curves as
shown in Fig. 2.6(a). Presumably because of the 40 dB threshold setting, the plastic stress
relaxation was not detected by the AE sensor. Due to the statistically variable nature of
the interface strength, there may still be some thru-thickness crack formation in Region 2.
In other words, one section of the interface may still have sufficient strength to transfer
tensile stresses to the MCO whereas the shear stresses of the interface in other sections
are no longer sufficient to cause damage in the MCO.
Finally in the third region, a sharp increase in the slope of the cumulative AE curves is
observed at higher strains for each type of test specimen except the reduced MCO-Crofer.
The strain at which the slope begins to increase sharply is the onset strain of MCO
spallation. The onset strain of spallation was also identified with in-situ coating
observations by imaging with a long-distance camera lens. Post-experiment SEM
observations found no spallation for the reduced coated Crofer interconnects, which is
consistent with the lack of AE events in Region 3 for this specimen.
2.4.2 Interfacial Shear Strength
SEM images of the coating were taken after the bend experiments. Figure 2.7 shows
representative images of saturated in-plane transverse cracks in reduced and oxidized
MCO coating on SS441 and Crofer interconnect. The tensile stresses were applied
perpendicular to the in-plane transverse cracks. Crack spacing was measured with Matlab

47. 30
image processing tools. Coating thickness was measured from back scattered SEM
images of the specimen cross-sections. After incorporating the values of saturated crack
spacing and thickness into Eq. (2.6), interfacial shear strength was calculated for each
type of test specimen. The calculated values of interfacial shear strength are plotted in
Fig. 2.8. As a result of interface defects as well as variability in bulk microstructure,
interfacial shear strength is going to be statistical in nature. There are a number of
stochastic variables in Eq. (2.6) that would provide statistical variability. For example,
the coating strength varies from point to point, the thickness is not constant, and crack
spacing varies throughout. Since crack spacing incorporates other physical phenomena, it
was decided to plot the interfacial shear strength of each specimen by measuring
saturated crack spacing in different locations in each specimen. The mean shear
strength was calculated from at least 50 measurements in each specimen type and is
provided in Table 2.2. It is observed in Fig. 2.8 that the interfacial shear strength has
higher statistical variability for reduced test specimen. Comparing Fig. 2.7(a) and Fig.
2.7(b), it is found that the oxidized MCO has more continuous in-plane transverse cracks
with more uniform crack spacing than the reduced MCO. Furthermore, in Fig. 2.8, the
interface is clearly weaker after oxidation heat treatment for both types of interconnects.
2.4.3 Interfacial Fracture Energy
The interfacial fracture is preceded by buckling of coating due to Poisson induced
compressive stresses developed in the coating [28, 29]. The bucking is assumed to initiate
from a pre-existing separation or crack at the interface. The pre-existing separation may
originate from the interface slip induced delamination during the plastic stress relaxation.

48. 31
As shown in Fig. 2.9(a), the buckling of coating results in tensile stress generation near
the crack tip at the perimeter of the buckled area. The tensile stress across the interface
induces crack propagation along the interface. With increase of the applied strain, thru-
thickness cracks may develop at the location of the buckled coating where the
combination of stresses and defects in the coating exceed the fracture toughness of the
coating and finally spallation occurs. Figure 2.9(b) shows an example of the early coating
buckling before the spallation with thru-thickness cracks developed in the coating. Thus
the spallation indicates interface fracture. The interfacial fracture energy for each type of
test specimen was calculated from the onset strain of spallation obtained from the
acoustic emission data and the in situ observations with high magnification camera lens.
Table 2.2 provides the computed values of interfacial fracture energy for each specimen
type.
The SEM images of the cracked and spalled surfaces obtained at the end of the
experiment (3% strain) were processed in Matlab image processing tools to measure the
percentage spallation area (%SA). In Fig. 2.10, the SEM images and their corresponding
processed images are presented for each type of test specimen. In the processed images,
the white portions denote the spalled areas whereas the black portions indicate the un-
spalled coatings. The values of %SA are also tabulated in Table 2.2. As illustrated in Fig.
2.10, reduced MCO-Crofer specimens have almost no spallation. The little-to-no
spallation in reduced MCO-Crofer is also consistent with the AE results in Fig. 2.6(a)
where there is no increase of slope in Region 3 of reduced MCO-Crofer. The tensile yield
stress of the Crofer substrate is approximately 350 MPa [31]. The shear yield stress is

49. 32
therefore 200 MPa and 175 MPa from the Von Mises criteria and the Tresca criteria,
respectively. In Table 2.2, the average interfacial shear strength for reduced MCO-Crofer
has been found to be 230 MPa. Since the interfacial shear strength exceeds the shear yield
stress for the reduced MCO-Crofer specimen, it is likely that yielding of the substrate
relaxes the interfacial shear stresses during the phase of plastic stress relaxation. The
absence of interface slip induced delamination inhibits the buckling of the coating. This
results in almost no spallation of the reduced MCO on Crofer within 3% strain. Since the
onset strain of spallation in the reduced MCO-Crofer specimens was not measureable
during the experiment, the interfacial fracture energy was not calculated for this specimen
type. Although it has higher interfacial fracture energy than the oxidized and reduced
MCO-SS44, the oxidized MCO-Crofer has the maximum %SA at 3% strain. The sizes of
the spalled sections are also comparatively larger. Therefore, the fracture energy
distribution of the oxidized MCO-Crofer interface is such uniform that, after attaining the
critical energy for fracture at approximately 2% strain, extensive coating spallation takes
place with a small increase of the applied strain. Oxidized coating has the lowest
adhesion with Crofer interconnect at 3% strain.
2.5 Discussions
2.5.1 Effects of Reduction and Oxidation Heat Treatment
As is listed in Table 2.2, the oxidation heat treatment decreases the tensile strength of
MCO and both the interfacial shear strength and the interfacial fracture energy. The
oxidation heat treatment yields a denser but more brittle MCO decreasing the critical
tensile stress of the coating. Energy dispersive spectroscopy (EDS) was performed on the

50. 33
spalled areas. The EDS results are presented in Fig. 2.11. In case of the reduction heat
treatment, Fe element was detected in spalled sections as shown in Fig 2.11(a).
Therefore, the interface fracture occurs between the interconnect and the MCO in case of
reduced specimen. It is the metallic bond between the cobalt in reduced MCO and the
interconnect that strengthens the interfaces in case of reduced specimen.
Conversely, in case of oxidized specimens porous, chromium oxide scale is found in the
spalled sections as shown in Fig. 2.11(b). During the oxidation heat treatment, selective
oxidation of the alloying elements in the substrate forms a very thin layer (3 - 5 um) of
native oxide scales of interconnects between MCO coatings and interconnects. The dual
phase native scales are mainly composed of (Mn,Cr)3O4 on top of a chromia (Cr2O3) rich
sub-layer at the bottom. The top layer is relatively thin ( 1μm) and for this reason, the
term ‘native scales’ in the present dissertation refers to Cr2O3 only. As indicating by Fig.
2.11(b), for the oxidized specimens the fracture is observed to occur along the brittle
native scale-MCO interface instead of the native scale-interconnect interface. The
interfacial shear strength and the interfacial fracture energy in Table 2.2 for oxidized
specimen refer to the interface between the native scale and the MCO. And it is the
formation of the native scales by oxidation heat treatment that degrades the oxidized
MCO adhesion significantly. The native scale-MCO interface is a much weaker interface
than the ductile-brittle interconnect-native scale interface. In their research using nano-
indentation on a coating-oxide-Crofer tri-layer system, Liu et al. also report that
interfacial fracture occurs along the native scale-coating interface [32].

51. 34
2.5.2 Effects of Interconnect Compositions
When only the reduction heat treatment is considered, CroferTM
has a better bonding with
MCO than SS441. The rare earth (RE) element, lanthanum (La) present in the Crofer
substrate improves the adhesion between the MCO and the interconnects [2].
Conversely, after oxidation heat treatments, the tensile strength of the coating and the
shear strength of the interface become lower for Crofer interconnects than for SS441. It is
interesting to observe in Table 2.2 that although the interfacial shear strength is lower for
oxidized MCO-Crofer than that of oxidized MCO-SS441, the interfacial fracture energy
is higher for oxidized MCO-Crofer. Therefore, it can be concluded that the interfacial
shear strength does not correlate directly with the coating spallation; rather shear strength
indicates the capability of stress transfer from the substrate to the coating. Shear stresses
exceeding the shear strength of the interface do not necessarily cause instant coating
spallation. This can be seen in Fig. 2.5(a) where the Region 2 in a cumulative AE curve
separates the crack saturation due to shear strength in Region 1 from spallation due to
interface fracture in Region 3. At 3% strain, the significant amount of spallation for
oxidized MCO-Crofer specimen reveals that the adhesion quality between oxidized MCO
and Crofer interconnects degrades at high strain.
2.6 Conclusions
Four-point bend experiments are performed to characterize the interfaces between MCO
coatings and SS441 or Crofer interconnects. The shear strength and the fracture energy at
the interfaces are determined. Effects of both the reduction and oxidation heat treatments
are investigated. Interfacial shear strength calculated by a shear-lag model, measures the

52. 35
capability of the interfaces to transfer stresses from interconnects to the coatings.
Interfacial fracture energy is more related to the assessment of coating adhesion.
Oxidation heat treatment is a necessary step to perform in coating process in order to
inhibit chromium poisoning by producing denser protective coatings on interconnects.
However, the denser structure of the oxidized MCO coating decreases the tensile strength
by increasing the brittleness of the MCO. In addition, the chromium rich native oxide
scales formed by the oxidation degrade the interfaces and lower the adhesion of MCO
coatings. The weakest interface is found to be between the MCO coatings and the native
scales rather than the interface between the interconnects and the native oxide scales.
Furthermore, in case of oxidation heat treatment, the interfacial fracture energy is higher
for Crofer interconnects than that of SS441 but at 3% strain Crofer has the maximum
amount of oxidized coating spallation.

53. 36
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Cells. Materials Science and Engineering A348 (2003) 227-243.
2. Yang Z., Xia G., Simner S.P., Stevenson, J.W., Thermal Growth and Performance of
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Interconnects. Journal of Electrochemical Society 152 (2005) 1896-1901.
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Vuoristo P., The Structure and Properties of Plasma Sprayed Iron Oxide Doped
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MnO3 Cathode Materials for Solid Oxide Fuel Cells. Journal of Electrochemical
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Scales. Materials at High Temperatures 12 (1994) 119 199-209.
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Adhesion Test. Surface and Coating Technology 141 (2001) 15-25.
10. Youtsos A.G., Kiriakopoulos M. Tinke T. Experimental and Theoretical/Numerical
Investigation of Thin Film Bonding Strength, Theoretical and Applied Fracture
Mechanics 31 (1999) 47-59.
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Strength Between Oxide Scale and Substrate for Metallic Interconnects. Journal of
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12. Akanda S.R., Walter M.E., Kidner N.J., Seabaugh M.M. Mechanical
Characterization of Oxide Coating-Interconnect Interfaces for Solid Oxide Fuel
Cells. Journal of Power Sources, 210 (2012) 254-262.
13. Yang Z., Xia G., Nie Z., Templeton J., Stevenson J.W., Ce-Modified (Mn,Co)3O4
Spinel Coatings on Ferritic Stainless Steels for SOFC Interconnect Applications.
Electrochemical and Solid-State Letters 11 (2008) B140-B143.
14. Simner S.P., Anderson M.D., Xia G.G., Yang Z., Pederson L.R., Stevenson J.W.,
SOFC Performacne with Fe-Cr-Mn Alloy. Journal of the Electrochemical Society 152
(2005) A740-A745.
15. Yang Z., Singh P., Stevenson J.W., Xia G. Investigation of Modified Ni-Cr-Mn Base
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153 (2006) A1873-A1879.

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16. Kidner N., Seabaugh M., Ibanez S., Chenault K., Day M., Thrun L., Lifetime
Predictions of Oxide Protective Coatings for Solid Oxide Fuel Cell Interconnects.
Nextech Materials Ltd 2011.
17. Yang Z., Xia G., Simner S. P., Stevenson, J. W., Thermal Growth and Performance
of Manganese Cobaltite Spinel Protection Layers on Ferritic Stainless Steel SOFC
Interconnects. Journal of the Electrochemical Society 152 (2005) A1896-A1901.
18. Timoshenko S., Strength of Materials, part 1, D. Van Nostran Company, NewYork,
1930.
19. Yanaka M., TsukaharaY., Nakaso N., Takeda N. Cracking Phenomena of Brittle
Films in Nanostructure Composites Analysed by a Modified Shear Lag Model with
Residual Strain. Journal of Materials Science 33 (1998) 2111-2119.
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San diego, 1992.
21. Nagl M. M., Saunders S. R. J., Evans W.T., Hall D.J., The Tensile Failure of Nickel
Oxide Scales at Ambient and At Growth Temperatures. Corrosion Science 35 (1993)
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22. Hsueh C.H., Yanaka M., Mutiple Film Cracking in Film/Substrate Systems with
Residual Stresses and Unidirectional Loading. Journal of Material Science 38 (2003)
1809-1817.
23. Tien, J.K., Davidson, J.M. Stress Effects and the Oxidation of Metals. J.V. Cathcard
ed. AIME, 1974.
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Engineering Failure Analysis 2 (1995) 85-103.
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the Tensile Failure of Oxide Scales. Oxidation of Metals 42 (1994) 431-449.
26. Chandra-Ambhorn S., Dherbey R.F., Toscan F., WoutersY., Galerie A., Dupeux M.
Determination of Mechanical Adhesion Energy of Thermal Oxide Scales on AISI
430Ti Alloy Using Tensile Test. Materials Science and Technology, 23 (2007) 497-
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27. Schutze M., Mechanical Properties of Oxide Scales. Oxidation of Metals 44 (1995)
29-61.
28. Evans A.G., Hutchinson J.W., On the Mechanics of Delamination and Spalling in
Compressed Films. Int. J. Solids Structures 20 (1984) 455-466.
29. Evans H.E., Cracking and Spalling of Protective Oxide Layers Materials Science and
Engineering A120 (1989) 139-146.
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Power Sources 189 (2009) 1044-1050.

55. 38
Tables
Table 2.1. Mechanical and thermal properties of MCO coating, native scale and
interconnect [20].
Table 2.2. Average values of critical tensile stress ( ), interfacial shear strength ( ),
experimental interfacial fracture energy ( ), and % spall area for each type of test
specimen.
Component Elasticity, E
(GPa)
Poisson ratio, ν Thermal
coefficient of
expansion, α
(C-1
)
MCO 124.7 0.36 9 -6
Native Scale 260 0.27 6.5 -6
Interconnect 250 0.3 12 -6
Interconnect Average
σc
ct
(MPa)
Average
τst
i
(MPa)
Average
Gexp
i
(J.m-2
)
% Spall Area
at 3% strain
Reduced Oxidized Reduced Oxidized Reduced Oxidized Reduced Oxidized
SS441 131.76 3.70 130.32 3.70 4.94 2.76 3.23 9.43
CroferTM
225.50 1.38 229.95 2.0 _ 10.02 No Spall 18.80

56. 39
Figures
Figure 2.1. Steps of chromium poisoning of a cathode.

57. 40
Figure 2.2. Steps of processing MCO coatings on interconnects.

58. 41
(a)
(b)
Figure 2.3. SEM images of (a) Reduced MCO on Crofer (tested). (b) Oxidized MCO on
Crofer (tested).

59. 42
Figure 2.4. Experimental setup to characterize coating-interconnect interfaces.

60. 43
(a)
(b)
Figure 2.5. (a) Schematic of failure mechanisms of a brittle coating during bend
experiments. (b) Shear stress distributions at interface and tensile stress distributions in a
coating segment.

61. 44
(a)
(b)
Figure 2.6. (a) Experimental stress-strain curve synchronized with AE data. (b) An
enlarged view of Region 1 of cumulative AE data.

62. 45
(a)
(b)
Figure 2.7. Saturate parallel in-plane transverse cracks in (a) Reduced MCO on SS441.
(b) Oxidized MCO on Crofer.

63. 46
Figure 2.8. Calculated values of interfacial shear strength for each type of test specimen.

64. 47
(a)
(b)
Figure 2.9. (a) Interfacial fracture due to buckling of coating. (b) SEM image of MCO
buckling before spallation (reduced MCO-SS441).

65. 48
(a)
(b)
(c)
(d)
Figure 2.10. Representative SEM and processed images of MCO coating surfaces at 3%
strain (a) Reduced MCO-SS441. (b) Oxidized MCO-SS441. (c) Reduced MCO-Crofer.
(d) Oxidized MCO-Crofer.

66. 49
(a)
(b)
Figure 2.11. SEM and EDS analysis of spalled sections of (a) Reduced MCO on SS441.
(b) Oxidized MCO on Crofer.

67. 50
Chapter 3
Lifetime of MCO Coatings on Metallic Interconnects
Abstract
Although MCO coatings are intended to act as a barrier to oxidation of interconnects;
formation of native oxide scales of interconnects (Cr2O3) is still inevitable during fuel
cell stack operations. With native scale growth during the operations, the strength of the
MCO-native scale interfaces will degrade. Besides, because of the temperature
coefficient of expansion (TCE) mismatch between the native scales and the MCO, for
thicker native scales, MCO spallation will most likely to occur when cooling down the
fuel cell from an operating temperature to room temperature. Therefore, it is the
spallation tendency of MCO that plays a critical role in lowering the service lifetime of
interconnects from an expected lifetime of 40,000 hours. In this chapter, the effects of the
native scale thickness on the coating adhesion are explored. Previously described room
temperature, four-point bend experiments are performed on coating-interconnect test
specimens oxidized at 900o
C for 100 hours, 600 hours, and 1000 hours. Utilizing the
native scale growth kinetics at 900o
C, the experimental results characterize the
degradation of the MCO-native scale interfaces as a function of native scale thickness.
Comparing the evolving interface properties with the cooling-induced interfacial fracture

68. 51
energy obtained from an analytical model, the lifetime of MCO is estimated. The
estimated lifetime of MCO at 750o
C operating temperature is approximately 34,700
hours.
3.1 Introduction
In Chapter 2, it is concluded that, the native scales (Cr2O3) of interconnects are formed by
oxidation heat treatment and the formation of native scales decrease the coating adhesion
significantly. Therefore, it is anticipated that, although interconnects are protected by
MCO coatings, the native scales will grow in thickness during the stack operations. As a
result of experiencing growth stresses, the native scales may degrade the interfaces
between the native scales and the coatings. Because of the degraded interfaces, TCE
mismatch between the native scales and MCO coatings can cause early coating spallation
when shut-down the fuel cell stack from high operating temperature to room temperature.
As a consequence, in addition to losing the protective properties of the coatings, it is also
expected that the damaged interfaces will result in lower electrical conductivity, thus
decreasing the power density of the SOFC stack.
An important source of growth stresses is epitaxial constraint. Differences between lattice
parameters of the oxide and substrate cause stresses to become maximum in oxide-metal
phase boundaries. The stresses fall off toward the oxide surface. Borie et al. employed X-
ray techniques to reveal that thin oxide films on copper are strained because of the
epitaxial relationship between the oxides and underlying material [1]. Epitaxial stresses
are only important for thin oxide scales as they are inversely related to the oxide scale
thickness.

69. 52
Appleby et al. studied the effect of microstructural composition of oxide scales on growth
stresses. Their study revealed that the transition of an initially formed scale on the surface
of (Cr,Fe)2O3 to a scale with increasing Cr and decreasing Fe content caused tensile
stresses to develop. A decrease in atomic volume associated with the transition is the
apparent explanation for the tensile stress development [2].
The formation of fresh oxides inside the scales themselves can be an important source of
compressive stresses in oxide scales. Jaenicke et al. found that in the oxidation of copper,
micro-cracking induced by the growth stresses provide pathways for gas migration [3].
The availability of copper molecules results in the formation of fresh oxides in the scale.
Since the new oxides have higher volume than the cracked volume, significant
compressive stresses are developed and there is a further development of compressive
stresses.
Mismatch of the thermal coefficients of expansion (TCE) between oxide coatings and
substrates is arguably the most significant reason for residual stress generation in the
oxide coatings during cooling or heating [4]. Thermal stress is a function of TCEs and
temperature differences. In most cases, oxides have lower TCE values than that of metal
substrates. In that case, cooling to room temperature from elevated temperature generates
compressive stresses in the oxide coatings. Conversely, heating to high temperature
develops tensile stresses in the oxide coatings. Thus both the tensile and compressive
stresses are developed in the oxide coatings due to frequent thermal cycling during
services. Moreover with temperature changes, phase transformation in both oxide
coatings and substrates can result in a high stress development.

70. 53
Different researchers have studied thermal cycling induced stresses in oxide coatings. For
example, Christl et al. incorporated acoustic emission techniques to detect thermal
cycling-induced oxide scale cracking on low alloy steel [5]. In a different work, Zhang et
al. monitored the scale cracking and spalling on Ni-30Cr alloys oxidized at 1000o
C and
then cooled to room temperature either by furnace cooling or constant rate cooling [6].
In the present chapter, an integrated experimental-analytical methodology is implemented
to estimate the effective lifetime of MCO coatings. The key steps of the methodology are
shown in Fig. 3.1. The experimental part consists of conducting room temperature four-
point bend tests on specimens having native scales of various thicknesses. The
experimental results describe the evolution of the fracture energy of the MCO-native
scale interfaces with the growth of the native scale thickness. In the analytical part, the
residual stress distributions developed in MCO of an MCO-native scale-interconnect tri-
layer assembly due to cooling from an high operating temperature to room temperature
are obtained. From the residual stress distributions in MCO, the analytical fracture energy
of MCO-native scale interfaces as a function of native scale thickness is assessed.
Comparing the experimental fracture energy with the analytical fracture energy, the
critical native scale thickness at which the cooling induced MCO spallation occurs is
obtained. Therefore, the MCO lifetime at a particular operating temperature is equivalent
to the time the native scales require to grow at critical thickness at that operating
temperature. Thus the MCO lifetime is estimated by incorporating the critical native scale
thickness to the native scale growth kinetics chart at a particular operating temperature.

71. 54
3.2 Materials
After performing the heat treatment on MCO coated interconnects as described in
Chapter 2, the coated specimens were run under isothermal oxidations at 900o
C for 100
hours, 600 hours, and 1000 hours. Oxidation at higher temperature than the fuel cell
operating temperature generally ranging from 600-800o
C was performed in order to
accelerate the oxidation driven failure mechanisms of the interfaces. Figure 3.2 presents
the evolution of the microstructure of MCO coatings with increasing oxidation time. The
microstructure of MCO oxidized for 600 hours are coarser than that oxidized for 100
hours but the microstructural differences are not as prominent as between 600-hour and
1000-hour oxidized MCO. The native scale thickness in each type of test specimen was
obtained from the native scale growth kinetics at 900o
C. Figure 3.3 shows the native scale
growth kinetics of an MCO coated specimen at 900o
C. To obtain the native scale growth
kinetics, NTM performs isothermal cyclic oxidation on coated interconnects up to 1000
hours at 900o
C. Samples were removed periodically from the furnace and the weight gain
was measured. The weight gain was converted to the native scale thickness by using the
density of the native scales. The growth of the native scales follows a parabolic law,
, where is the native scale thickness, is the time in hours, is the parabolic
rate constant [7]. The native scale growth rate, at 900o
C is 0.0189 μm2
/hr. From the
native scale growth chart in Fig. 3.3, the native scale thickness after 100, 600 and 1000
hours oxidation at 900o
C are calculated as 1.95 μm, 4.77 μm and 6.14 μm respectively.

72. 55
3.3 Analytical Model for Residual Stress Distributions
3.3.1 Background
The analytical model considered in the present analysis to obtain the cooling induced
residual stresses or thermal stresses in a tri-layer assembly is based on a ‘strength-of-
materials’ or ‘structural’ approach. The main advantage of the ‘strength-of-materials’
approach is the ability to obtain a closed form solutions with sufficient accuracy. The
easy-to-use practical formula can clearly differentiate the roles of different geometrical
and mechanical properties on resulting thermal stresses. Simple numerical methods such
as finite difference scheme can also be applied instead of an analytical technique in order
to solve the governing differential equations.
The ‘strength-of-materials’ approach was first proposed by S. Timoshenko. In his
pioneering paper at 1925, Timoshenko applied the ‘strength-of-materials’ method on a bi-
material thermostat to estimate the temperature difference induced residual stresses in
each layer of the thermostat [8]. Although he was able to predict the existence of shear
stresses at the interface developed near the edge due to the so called ‘edge effect’, he was
not able to mathematically calculate the shear stresses. Based on S. Timoshenko’s
method, later E. Suhir invented an innovative approach to this problem. Considering the
displacement compatibility at the interface, Suhir’s method is able to calculate the
stresses at the interface and in each layer with sufficient accuracy comparable to the
experimental and FEM results [9-15]. In general, the basic assumptions used in the
present model to obtain the residual stress distributions are as following [13, 16-19]:

73. 56
1. The aspect ratio (thickness/length) of the layered structure is very small. Each
layer is considered as a thin elongated beam experiencing small deformations.
2. The classical Euler-Bernoulli beam theory is applicable in each layer such that the
vertical displacement is governed by the bending moment only.
3. The interfaces between components are not perfect rather they are weak
interfaces. The weak interfaces are characterized by interface compliances that
allow interfaces to slip. Normal stresses across the interfaces are considered to be
negligible.
4. The radius of curvature is constant through the thickness of the layered structure
but varies along the lateral direction.
3.3.2 Interface Displacements
In Fig. 3.4, the free body diagrams of each layer of a coating-native scale-substrate tri-
layer specimen are shown with the normal forces, shear forces and bending moments
generated due to experiencing temperature differences. In the figure, N denotes the
normal force per width, V denotes the shear force per width and M denotes the bending
moment per width. The temperature difference induced residual shear stress at the MCO-
native scale interface (i1) is denoted by and the native scale-interconnect interface
(i2) by .The displacement function in x-direction at i1 of coating can be written as
[13]:
∫

74. 57
where is the thermal coefficient of expansion (TCE) of the coating, is the
temperature change, and is the axial compliance of the coating,
is the interface compliance and w(x) is the y-direction displacement of each layer and is
constant thru y-direction but varies along x-direction. The first term in the right hand side
of the equation represents the unrestricted thermal displacement. The displacement in the
second term originates from the thermal induced normal force at the cross section and
this displacement is assumed to be same at all points of the cross section. Correction of
the second term for the interface is done by the third term where the interface
displacement is assumed to be higher than the inner points of the cross section and is
proportional to the interfacial shear stresses. Finally in the fourth term, the interface
displacement due to moment induced curvature is presented.
Similarly, the x-direction displacement function of i1 of native scale and i2 of native
scale and interconnect can be written respectively as,
∫
∫
∫

75. 58
3.3.3 Equilibrium Relations and Governing Equations
To obtain equilibrium relations, differential elements are considered from each layer and
are shown in Fig. 3.5 [19]. The sum of the x-direction forces of each layer yields the
following relations:
Similarly from the moment equilibrium of each layer, the following relations are found:
( )
… … … (3.2)
The total bending moment applied at the tri-layer assembly is the summation of the
bending moment at each layer,
From Eq. (3.3) and Eq. (3.2), it is found that
∫
Where D is the flexural rigidity of the composite beam and D = Dc + Dn+ Ds, where Dc
can be written as and so on. From the equilibrium of forces in y
direction , the Eq. (3.4) reduces to
Considering the displacement compatibility at the i1 and i2, and
utilizing Eq. (3.1), (3.2) and (3.5), the following differential equations are found [7]:

76. 59
where, and
Finallly separating Nc and Ns from Eq. (3.6) and (3.7), the governing differential
equations are obtained as [13]:
where
√ , √ ,
3.3.4 Boundary Conditions
Considering the condition of a free surface at the edge of each layer (x = -L, L), the
following boundary conditions (BC) of the governing Eq. (3.8) and (3.9) can be written:

77. 60
… … … (3.10)
For the second boundary conditions, the beam bending theory is used such that:
From Eq. (3.11) it is found that
and finally
Now Eq. (3.12) yields,
Eq. (3.13) implies that
Incorporation of Eq. (3.14) in to Eq. (3.2) with the condition of free surface at each layer
where Vc(BC) = Vn(BC) = Vs(BC) = 0, implies that,
, … … … (3.15)
Finally Eq. (3.15) with Eq. (3.1) gives the required second boundary conditions of the
governing differential equations (Eq. (3.8) and (3.9)) as