Abstract
A periodic array of cracks in a functionally graded coating bonded to a homogeneous substrate is considered. The medium is subjected to transient or static mechanical loads. The problem is formulated in terms of a singular integral equation with the crack face displacement as the unknown variable. In addition to the time-varied stresses and stress intensity factors for various parameters of the problem, the effect of periodic cracking on the relaxation of the transient stress on the coating surface is discussed. Also included is the influence of the material gradient (material nonhomogeneity) on the crack tip intensity factors and stresses. Solutions for a single graded layer and a graded coating bonded to an infinite substrate are given.
1.
Miyamoto
, Y.
, Kaysser
, W. A.
, Rabin
, B. H.
, Kawasaki
, A.
, and Ford
, A. G.
, 1999, Functionally Graded Materials: Design, Processing and Applications
, Kluwer
, Boston.2.
Hasselman
, D. P. H.
, and Youngblood
, G. E.
, 1978, “Enhanced Thermal Resistance of Structural Ceramics With Thermal Conductivity Gradients
,” J. Am. Ceram. Soc.
0002-7820, 61
, pp. 49
–52
.3.
Lee
, Y.-D.
, and Erdogan
, F.
, 1995, “Residual/Thermal Stresses in FGM and Laminated Thermal Barrier Coatings
,” Int. J. Fract.
0376-9429, 69
, pp. 145
–165
.4.
Ravichandran
, K. S.
, 1995, “Thermal Residual Stresses in a Functionally Graded Material System
,” Mater. Sci. Eng., A
0921-5093, 201
, pp. 269
–276
.5.
Noda
, N.
, 1999, “Thermal Stresses in Functionally Graded Materials
,” J. Therm. Stresses
0149-5739, 22
(1
), pp. 477
–512
.6.
Nomura
, N.
, Gasik
, M.
, Kawasaki
, A.
, and Watanabe
, R.
, 2001, “Thermomechanical Modelling of Functionally Graded Thermal Barrier Coatings
,” Ceram. Trans.
1042-1122, 114
, pp. 223
–229
.7.
Delale
, F.
, and Erdogan
, F.
, 1988, “Interface Crack in a Nonhomogeneous Elastic Medium
,” Int. J. Eng. Sci.
0020-7225, 26
, pp. 559
–568
.8.
Ozturk
, M.
, and Erdogan
, F.
, 1993, “The Axisymmetric Crack Problem in a Nonhomogeneous Medium
,” ASME J. Appl. Mech.
0021-8936, 60
, pp. 406
–413
.9.
Konda
, N.
, and Erdogan
, F.
, 1994, “The Mixed Mode Crack Problem in a Nonhomogeneous Elastic Medium
,” Eng. Fract. Mech.
0013-7944, 47
, pp. 533
–545
.10.
Erdogan
, F.
, and Wu
, B. H.
, 1997, “The Surface Crack Problem for a Plate With Functionally Graded Properties
,” ASME J. Appl. Mech.
0021-8936, 64
, pp. 449
–456
.11.
Dhaliwal
, R. S.
, and Singh
, B. M.
, 1978, “On the Theory of Elasticity of a Nonhomogeneous Medium
,” J. Elast.
0374-3535, 8
, pp. 211
–219
.12.
Gerasoulis
, A.
, and Srivastav
, R. P.
, 1980, “A Griffith Crack Problem for a Nonhomogeneous Medium
,” Int. J. Eng. Sci.
0020-7225, 18
, pp. 239
–247
.13.
Schovanec
, L.
, and Walton
, J. R.
, 1988, “On the Order of the Stress Singularity for an Antiplane Shear Crack at the Interface of Two Bonded Inhomogeneous Elastic Materials
,” ASME J. Appl. Mech.
0021-8936, 55
, pp. 234
–236
.14.
Ang
, W. T.
, and Clements
, D. L.
, 1987, “On Some Crack Problems for Inhomogeneous Elastic Materials
,” Int. J. Solids Struct.
0020-7683, 23
, pp. 1089
–1104
.15.
Eischen
, J. W.
, 1987, “Fracture of Nonhomogeneous Materials
,” Int. J. Fract.
0376-9429, 34
, pp. 3
–22
.16.
Craster
, R. V.
, and Atkinson
, C.
, 1994, “Mixed Boundary-Value Problems in Nonhomogeneous Elastic Materials
,” Q. J. Mech. Appl. Math.
0033-5614, 47
, pp. 183
–206
.17.
Vrbik
, J.
, Singh
, B. M.
, Rokne
, J.
, and Dhaliwal
, R. S.
, 2002, “The Problem of a Penny-Shaped Crack in a Non-Homogeneous Medium Under Shear
,” Eur. J. Mech. A/Solids
0997-7538, 21
, pp. 773
–777
.18.
Jin
, Z. H.
, and Noda
, N.
, 1994, “Crack Tip Singular Fields in Nonhomogeneous Materials
,” ASME J. Appl. Mech.
0021-8936, 61
(3
), pp. 738
–740
.19.
Bao
, G.
, and Cai
, H.
, 1997, “Delamination Cracking in Functionally Graded Coating/Metal Substrate Systems
,” Acta Mater.
1359-6454, 45
(3
), pp. 1055
–1066
.20.
Quian
, G.
, Nakamura
, T.
, and Berndt
, C. C.
, 1998, “Effects of Thermal Gradient and Residual Stresses on Thermal Barrier Coating Fracture
,” Mech. Mater.
0167-6636, 27
, pp. 91
–110
.21.
Gaudette
, F. G.
, Giannakopoulos
, A. E.
, and Suresh
, S.
, 2001, “Interface Cracks in Layered Materials Subjected to a Uniform Temperature Change
,” Int. J. Fract.
0376-9429, 110
(4
), pp. 325
–349
.22.
Kim
, J. H.
, and Paulino
, G. H.
, 2002, “Mixed-Mode Fracture of Orthotropic Functionally Graded Materials Using Finite Elements and the Modified Crack Closure Method
,” Eng. Fract. Mech.
0013-7944, 69
, pp. 1557
–1586
.23.
Wang
, Y. S.
, Huang
, G. Y.
, and Gross
, D.
, 2004, “On the Mechanical Modeling of Functionally Graded Interfacial Zone With a Griffith Crack: Plane Deformation
,” Int. J. Fract.
0376-9429, 125
, pp. 189
–205
.24.
Li
, C. Y.
, Weng
, G. J.
, and Duan
, Z. P.
, 2001, “Dynamic Behavior of a Cylindrical Crack in a Functionally Graded Interlayer Under Torsional Loading
,” Int. J. Solids Struct.
0020-7683, 38
, pp. 7473
–7485
.25.
Zhang
, C.
, Sladek
, J.
, and Sladek
, V.
, 2003, “Effects of Material Gradients on Transient Dynamic Mode-III Stress Intensity Factors in a FGM
,” Int. J. Solids Struct.
0020-7683, 40
, pp. 5251
–5270
.26.
Guo
, L. C.
, Wu
, L. Z.
, Zeng
, T.
, and Ma
, L.
, 2004, “Fracture Analysis of a Functionally Graded Coating-Substrate Structure With a Crack Perpendicular to the Interface, Part II: Transient Problem
,” Int. J. Fract.
0376-9429, 127
, pp. 39
–59
.27.
Ma
, L.
, Wu
, L. Z.
, Zhou
, Z. G.
, and Zeng
, T.
, 2004, “Crack Propagating in a Functionally Graded Strip Under the Plane Loading
,” Int. J. Solids Struct.
0020-7683, 126
(1
), pp. 39
–55
.28.
Lee
, K. H.
, 2004, “Characteristics of a Crack Propagating Along the Gradient in Functionally Gradient Materials
,” Int. J. Solids Struct.
0020-7683, 41
(11–12)
, pp. 2879
–2898
.29.
Chalivendra
, V. B.
, Shukla
, A.
, and Parameswaran
, V.
, 2002, “Dynamic Out of Plane Displacement Fields for an Inclined Crack in Graded Materials
,” J. Elast.
0374-3535, 69
(1–3
), pp. 99
–119
.30.
El-Hadek
, M. A.
, and Tippur
, H. V.
, 2003, “Dynamic Fracture Parameters and Constraint Effects in Functionally Graded Syntactic Epoxy Foams
,” Int. J. Solids Struct.
0020-7683, 40
(8
), pp. 1885
–1906
.31.
Meguid
, S. A.
, Wang
, X. D.
, and Jiang
, L. Y.
, 2002, “On the Dynamic Propagation of a Finite Crack in Functionally Graded Materials
,” Eng. Fract. Mech.
0013-7944, 69
(14–16
), pp. 1753
–1768
.32.
Shukla
, A.
, and Jain
, N.
, 2004, “Dynamic Damage Growth in Particle Reinforced Graded Materials
,” Int. J. Impact Eng.
0734-743X, 30
(7
), pp. 777
–803
.33.
Rousseau
, C. E.
, and Tippur
, H. V.
, 2002, “Influence of Elastic Variations on Crack Initiation in Functionally Graded Glass-Filled Epoxy
,” Eng. Fract. Mech.
0013-7944, 69
(14–16
), pp. 1679
–1693
.34.
Grot
, A. S.
, and Martyn
, J. K.
, 1981, “Behavior Plasma-Sprayed Ceramic Thermal Barrier Coating for Gas Turbine Engines
,” Bull. Am. Ceram. Soc.
0002-7812, 60
(8
), pp. 807
–811
.35.
Nied
, H. F.
, 1987, “Periodic Array of Cracks in a Half Plane Subjected to Arbitrary Loading
,” ASME J. Appl. Mech.
0021-8936, 54
, pp. 642
–648
.36.
Rizk
, Abd El-Fattah
, 2004, “Periodic Array of Cracks in a Strip Subjected to Surface Heating
,” Int. J. Solids Struct.
0020-7683, 41
(16–17
), pp. 4685
–4696
.37.
Schulze
, G. W.
, and Erdogan
, F.
, 1998, “Periodic Cracking of Elastic Coatings
,” Int. J. Solids Struct.
0020-7683, 35
, pp. 3615
–3634
.38.
Timm
, D. H.
, Guzina
, B. B.
, and Voller
, V. R.
, 2003, “Prediction of Thermal Crack Spacing
,” Int. J. Solids Struct.
0020-7683, 40
, pp. 125
–142
.39.
Erdogan
, F.
, and Ozturk
, M.
, 1995, “Periodic Cracking of Functionally Graded Coatings
,” Int. J. Eng. Sci.
0020-7225, 33
(15
), pp. 2179
–2195
.40.
Choi
, H. J.
, 1997, “A Periodic Array of Cracks in a Functionally Graded Nonhomogeneous Medium Loaded Under In-Plane Normal and Shear
,” Int. J. Fract.
0376-9429, 88
, pp. 107
–128
.41.
Bao
, G.
, and Wang
, L.
, 1995, “Multiple Cracking in Functionally Graded Ceramic-Metal Coatings
,” Int. J. Solids Struct.
0020-7683, 32
, pp. 2853
–2871
.42.
Guler
, M. A.
, and Erdogan
, F.
, 2004, “Contact Mechanics of Graded Coatings
,” Int. J. Solids Struct.
0020-7683, 41
, pp. 3865
–3889
.43.
Giannakopoulos
, A.
, and Suresh
, S.
, 1997, “Indentation of Solids With Gradients in Elastic Properties: Part I. Point Force Solution
,” Int. J. Solids Struct.
0020-7683, 34
(19
), pp. 2357
–2392
.44.
Giannakopoulos
, A.
, and Suresh
, S.
, 1997, “Indentation of Solids With Gradients in Elastic Properties: Part II. Axisymetric Indenters
,” Int. J. Solids Struct.
0020-7683, 34
(19
), pp. 2393
–2428
.45.
Wang
, B. L.
, Mai
, Y.-W.
, and Noda
, N.
, 2002, “Fracture Mechanics Analysis Model for Functionally Graded Materials With Arbitrarily Distributed Properties
,” Int. J. Fract.
0376-9429, 116
, pp. 161
–177
.46.
Miller
, M. K.
, and Guy
, W. T.
, 1966, “Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials
,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
0036-1429, 3
, pp. 624
–635
.47.
Murakami
, Y.
, 1987, Stress Intensity Factors Handbook
, Pergamon
, New York.48.
Sih
, G. C.
, 1977, “Elastodynamics Crack Problems
,” Mechanics of Fracture Mechanics
, Noordhoff
, Leyden, Vol. 4
.Copyright © 2006
by American Society of Mechanical Engineers
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