Kokini,
K., DeJonge,
J., Rangaraj,
S., and Beardesly,
B., 2002, “Thermal Fracture in Functionally Graded Thermal Barrier Coatings with Similar Thermal Resistance,” Surf. Coat. Technol., 154, pp. 223–231.

Rangaraj,
S., and Kokini,
K., 2003, “Multiple Surface Cracking and Its Effects on Interface Cracks in Functionally Graded Thermal Barrier Coatings,” ASME J. Appl. Mech., 70, pp. 234–245.

Kokini,
K., Takeuchi,
Y. R., and Choules,
B. D., 1996, “Surface Thermal Cracking Owing to Stress Relaxation: Zirconia vs. Mullite,” Surf. Coat. Technol., 82, pp. 77–82.

Choules, B. D., Kokini, K., and Taylor, T. A., 2001, “Thermal Fracture of Ceramic Thermal Barrier Coatings under High Heat Flux with Time-Dependent Behavior-Part I: Experimental Results,” *Materials Science and Engineering A299*, pp. 296–304.

Rangaraj,
S., and Kokini,
K., 2003, “Estimating The Fracture Resistance of Functionally Graded Thermal Barrier Coatings From Thermal Shock Tests,” Surf. Coat. Technol., in press.

Liebowitz, H., 1969, *Fracture: An Advanced Treatise, Volume V-Fracture Design of Structures*, Academic Press, New York.

Budiansky,
B., Amazigo,
J. C., and Evans,
A. G., 1988, “Small-Scale Crack Bridging and the Fracture Toughness of Particulate Reinforced Ceramics,” J. Mech. Phys. Solids, 36(2), pp. 167–187.

Mataga,
P. A., 1989, “Deformation of Crack-Bridging Ductile Reinforcements in Toughened Brittle Materials,” Acta Metall., 37(12), pp. 3349–3359.

Bao,
G., and Zok,
F., 1993, “On the Strength of Ductile Particle Reinforced Brittle Matrix Composites,” Acta Metall. Mater., 41(12), pp. 3515–3524.

Jin,
Z.-H., and Batra,
R. C., 1996, “Some Basic Fracture Mechanics Concepts in Functionally Graded Materials,” J. Mech. Phys. Solids, 44(8), pp. 1221–1235.

Jin,
Z.-H., and Batra,
R. C., 1998, “R-Curve and Strength Behavior of a Functionally Graded Material,” Mater. Sci. Eng., A242, pp. 70–76.

Jin,
Z.-H., Paulino,
G. H., and Dodds,
R. H., 2002, “Finite Element Investigation of Quasi-Static Crack Growth in Functionally Graded Materials Using a Novel Cohesive Zone Fracture Model,” ASME J. Appl. Mech., 69, pp. 370–379.

Tvergaard,
V., 2002, “Theoretical Investigation of The Effect of Plasticity On Crack Growth Along a Functionally Graded Region Between Dissimilar Elastic-Plastic Solids,” Eng. Fract. Mech., 69, pp. 1635–1645.

Tvergaard,
V., 2001, “Crack Growth Predictions By a Cohesive Zone Model for Ductile Fracture,” J. Mech. Phys. Solids, 49, pp. 2191–2207.

Arun Roy,
Y., and Dodds,
R. H., 2001, “Simulation of Ductile Crack Growth in Thin Aluminum Panels Using 3-D Surface Cohesive Elements,” Int. J. Fract., 110, pp. 21–45.

Guinea,
G. V., Elices,
M., and Planas,
J., 1997, “On The Initial Shape of The Softening Function of Cohesive Materials,” Int. J. Fract., 87, pp. 139–149.

Elices,
M., Guinea,
G. V., Gomez,
J., and Planas,
J., 2002, “The Cohesive Zone Model: Advantages, Limitations and Challenges,” Eng. Fract. Mech., 69, pp. 137–163.

Planas, G., Guinea, G. V., and Elices, M., 1993, “Softening Curves for Concrete and Structural Response,” *Fracture and Damage in Concrete and Rock-FDCR2*, H. P. Rossmanith, ed., pp. 66–75.

Elfgren, L., 1989, “Fracture Mechanics of Concrete Structures-From Theory to Application,” Rilem Report, Chapman and Hall, New York.

Needleman,
A., 1987, “A Continuum Model for Void Nucleation By Inclusion Debonding,” ASME J. Appl. Mech., 54, pp. 525–531.

Finot,
M., Shen,
Y.-L., Needleman,
A., and Suresh,
S., 1994, “Micromechanical Modeling of Reinforcement Fracture in Particle-Reinforced Metal Matrix Composite,” Metall. Trans. A, A25, pp. 2403–2420.

Shet,
C., and Chandra,
N., 2002, “Analysis of Energy Balance when Using Cohesive Zone Models to Simulate Fracture Processes,” ASME J. Eng. Mater. Technol., 124, pp. 440–450.

Tvergaard,
V., and Hutchinson,
J. W., 1992, “The Relation Between Crack Growth Resistance and Fracture Process Parameters in Elastic-Plastic Solids,” J. Mech. Phys. Solids, 40(6), pp. 1377–1397.

Tvergaard,
V., and Hutchinson,
J. W., 1993, “The Influence of Plasticity on Mixed Mode Interface Toughness,” J. Mech. Phys. Solids, 41(6), pp. 1119–1135.

Xu,
X. P., and Needleman,
A., 1994, “Numerical Simulations of Fast Crack Growth in Brittle Solids,” J. Mech. Phys. Solids, 42(9), pp. 1397–1434.

Rose,
J. H., Ferrante,
J., and Smith,
J. R., 1981, “Universal Binding Energy Curves for Metals and Bimetallic Interfaces,” Phys. Rev. Lett., 47, pp. 675–678.

Siegmund,
T., and Needleman,
A., 1997, “A Numerical Study of Dynamic Crack Growth in Elastic Viscoplastic Solids,” Int. J. Solids Struct., 34, pp. 769–788.

Ortiz,
M., and Pandolfi,
A., 1999, “Finite-Deformation Irreversible Cohesive Elements for Three-Dimensional Crack-Propagation Analysis,” Int. J. Numer. Methods Eng., 44, pp. 1267–1282.

Munz, D., and Fett, T., 1999, *Ceramics: Mechanical Properties, Failure Behavior, Materials Selection*, Springer-Verlag, New York.

Qian,
G., Nakamura,
T., Berndt,
C. C., and Leigh,
S. H., 1997, “Tensile Toughness Test and High Temperature Fracture Analysis of Thermal Barrier Coatings,” Acta Mater., 45(4), pp. 1767–1784.

Choi, S. R., Zhu, D., and Miller, R. A., 2003, “Mode-I, Mode-II and Mixed-Mode Fracture of Plasma-Sprayed Thermal Barrier Coatings at Ambient and Elevated Temperatures,” NASA/TM-2003-212185.

Giannakopoulos,
A. E., Suresh,
S., Finot,
M., and Olsson,
M., 1995, “Elastoplastic Analysis of Thermal Cycling: Layered Materials With Compositional Gradients,” Acta Metall. Mater., 43(4), pp. 1335–1354.

Williamson,
R. L., Rabin,
B. H., and Drake,
J. T., 1993, “Finite Element Analysis of Thermal Residual Stresses at Graded Ceramic-Metal Interfaces. Part I: Model Description and Geometrical Effects,” J. Appl. Phys., 74(2), pp. 1310–1320.

Hershey,
A. V., 1954, “The Elasticity of an Isotropic Aggregate of Anisotropic Cubic Crystals,” ASME J. Appl. Mech., 21, p. 236.

Hill,
R., 1965, “Continuum Micromechanics of Elastoplastic Polycrystals,” J. Mech. Phys. Solids, 13, pp. 89.

Chen,
I. W., and Argon,
A. S., 1979, “Steady State Power Law Creep in Heterogeneous Alloys With Coarse Microstructures,” Acta Metall., 27, pp. 785–791.

Rangaraj,
S., and Kokini,
K., 2002, “Time-Dependent Behavior of Ceramic (Zirconia)-Metal (NiCoCrAlY) Particulate Composites,” Mech. Time-Depend. Mater., 6, pp. 171–191.

Bazant, Z. P., and Planas, J., 1998, *Fracture and Size Effects in Concrete and Other Quasi-Brittle Structures*, CRC Press, Boca Raton, FL.

Choules, B. D., 1998, “Thermal Fracture of Ceramic Coatings under High Heat Flux with Time Dependent Behavior,” Ph.D. thesis, Purdue University, West Lafayette, IN.

Sia Nemat-Nasser, and Hori, M., 1999, *Micromechanics: Overall Properties of Heterogeneous Materials*, Elsevier, Amsterdam, New York.

Benveniste,
Y., 1987, “A New Approach To The Application of Mori-Tanaka’s Theory In Composite Materials,” Mech. Mater., 6, pp. 147–157.

Rangaraj,
S., and Kokini,
K., 2003, “Interface Thermal Fracture In Functionally Graded Zirconia-Mullite-Bond Coat Alloy Functionally Graded Thermal Barrier Coatings,” Acta Mater., 61, pp. 251–267.

McDonald,
K. R., Dryden,
J. R., Majumdar,
A., and Zok,
F. W., 2000, “Thermal Conductance of Delamination Cracks in a Fiber Reinforced Ceramic Composite,” J. Am. Ceram. Soc., 83(3), pp. 553–562.

Sampath,
S., Smith,
W. C., Jewett,
T. J., Kim,
H., 1999, “Synthesis and Characterization of Grading Profiles in Plasma Sprayed NiCrAlY-Zirconia FGMs,” Mater. Sci. Forum, 308–311, pp. 383–388.

Rangaraj, S., and Kokini, K., 2003, “Fracture in Single-Layer YSZ-BC Alloy Composite Coatings Under Thermal Shock,” in press.

ABAQUS®/Standard User’s Manual, 2001, Hibbitt, Karlsson and Sorenson, Inc.