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Special Issue Honoring Professor Fazil Erdogan’s Contributions to Mixed Boundary Value Problems of Inhomogeneous and Functionally Graded Materials

Mixed-Mode Fracture Analysis of Orthotropic Functionally Graded Material Coatings Using Analytical and Computational Methods

[+] Author and Article Information
Serkan Dag1

Department of Mechanical Engineering, Middle East Technical University, Ankara 06531, Turkeysdag@metu.edu.tr

K. Ayse Ilhan

Department of Mechanical Engineering, Middle East Technical University, Ankara 06531, Turkey

1

Corresponding author.

J. Appl. Mech 75(5), 051104 (Jul 10, 2008) (9 pages) doi:10.1115/1.2932098 History: Received May 28, 2007; Revised December 27, 2007; Published July 10, 2008

This article presents analytical and computational methods for mixed-mode fracture analysis of an orthotropic functionally graded material (FGM) coating-bond coat-substrate structure. The analytical solution is developed by considering an embedded crack in the orthotropic FGM coating. The embedded crack is assumed to be loaded through arbitrary self-equilibrating mixed-mode tractions that are applied to its surfaces. Governing partial differential equations for each of the layers in the trilayer structure are derived in terms of the effective parameters of plane orthotropic elasticity. The problem is then reduced to a system of two singular integral equations, which is solved numerically to evaluate the mixed-mode crack tip parameters. The computational approach is based on the finite element method and is developed by applying the displacement correlation technique. The use of two separate methods in the analyses allowed direct comparisons of the results obtained for an embedded crack in the orthotropic FGM coating, leading to a highly accurate numerical predictive capability. The finite element based approach is used to generate further numerical results by considering periodic cracking in the orthotropic FGM coating. Parametric analyses presented in this article illustrate the influences of the material nonhomogeneity and orthotropy constants, the bond coat thickness, and the crack periodicity on the mixed-mode stress intensity factors and the energy release rate.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

The trilayer structure and an embedded crack in the orthotropic FGM coating

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Figure 2

(a) A quarter-point element in global and local coordinate systems; (b) quarter-point elements around a crack tip located in a graded orthotropic medium

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Figure 3

Normalized mixed-mode SIFs versus δ14 and βc for the crack problem depicted in Fig. 1: (a) Mode I SIFs; (b) Mode II SIFs. S2∕S1=exp(−βhc), S3∕S2=1.5, κ1=κ2=2, κ3=1, δ1=δ2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.5, h2∕c=0.5, and h3∕c=2.

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Figure 4

Deformed shape of the finite element mesh and close-up view of the crack surfaces. S2∕S1=exp(−βhc), βc=1, S3∕S2=1.5, κ1=κ2=2, κ3=1, δ14=δ24=2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.5, h2∕c=0.5, and h3∕c=2.

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Figure 5

Normalized energy release rate versus δ14 and βc for the crack problem depicted in Fig. 1. S2∕S1=exp(−βhc), S3∕S2=1.5, κ1=κ2=2, κ3=1, δ1=δ2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.5, h2∕c=0.5, and h3∕c=2.

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Figure 6

Normalized mixed-mode SIFs versus h2∕c and βc for the crack problem depicted in Fig. 1: (a) Mode I SIFs; (b) Mode II SIFs. S2∕S1=exp(−βhc), S3∕S2=3, κ1=κ2=2, κ3=1, δ14=δ24=2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.05, and h3∕c=2.

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Figure 7

Normalized energy release rate versus h2∕c and βc for the crack problem depicted in Fig. 1. S2∕S1=exp(−βhc), S3∕S2=3, κ1=κ2=2, κ3=1, δ14=δ24=2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.05, and h3∕c=2.

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Figure 8

Periodic cracks in an orthotropic FGM coating

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Figure 9

Unit cell in the trilayer structure and the symmetry and periodicity conditions

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Figure 10

Normalized mixed-mode SIFs versus c∕W and βc for the crack problem depicted in Fig. 8: (a) Mode I SIFs; (b) Mode II SIFs. S2∕S1=exp(−βhc), S3∕S2=1.5, κ1=κ2=2, κ3=1, δ14=δ24=2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.5, h2∕c=0.5, and h3∕c=2.

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Figure 11

Deformed shape of the unit cell. S2∕S1=exp(−βhc), βc=1, S3∕S2=1.5, κ1=κ2=2, κ3=1, δ14=δ24=2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.5, h2∕c=0.5, h3∕c=2, and c∕W=0.3.

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Figure 12

Normalized energy release rate versus c∕W and βc for the crack problem depicted in Fig. 8: (a) Mode I SIFs; (b) Mode II SIFs. S2∕S1=exp(−βhc), S3∕S2=1.5, κ1=κ2=2, κ3=1, δ14=δ24=2, δ3=1, ν1=ν2=0.25, ν3=0.3, h1∕c=1, hc∕c=0.5, h2∕c=0.5, and h3∕c=2.

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