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Research Papers

Mixed-Mode Crack-Tip Fields in an Anisotropic Functionally Graded Material

[+] Author and Article Information
Linhui Zhang

Department of Civil and Environmental Engineering,  University of Connecticut, 261 Glenbrook Rd. U-2037, Storrs, CT, 06269

Jeong-Ho Kim1

Department of Civil and Environmental Engineering,  University of Connecticut, 261 Glenbrook Rd. U-2037, Storrs, CT, 06269jhkim@engr.uconn.edu

1

Corresponding author.

J. Appl. Mech 79(5), 051011 (Jun 29, 2012) (10 pages) doi:10.1115/1.4006378 History: Received May 10, 2010; Revised January 06, 2012; Posted March 15, 2012; Published June 28, 2012; Online June 29, 2012

This paper provides asymptotic full crack-tip stress field solutions for an in-plane mixed-mode stationary crack in an anisotropic functionally graded material. A monoclinic graded material that has a material symmetry plane is considered. The complex variable approach and the asymptotic scaling factor are used to solve the governing fourth-order partial differential equation for exponentially graded anisotropic materials with gradation either parallel or perpendicular to the crack. Full crack-tip stress fields under mode-I and mode-II loading are visualized and discussed for homogeneous and exponentially graded anisotropic materials. We observe that higher-order terms are affected by material gradation and play an important role on crack-tip stress fields in functionally graded materials.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The mode-I crack-tip stress fields for orthotropic homogeneous (β = 0) and exponentially graded (β = 1, x1 gradation) materials

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Figure 3

The effect of material nonhomogeneity (β) on σ22 for an anisotropic material under mode-I loading condition: (a) β = −1 (x1 gradation), (b) homogeneous (β = 0), (c) β = 1 (x1 gradation), (d) β = −1 (x2 gradation), (e) β = 1 (x2 gradation)

Grahic Jump Location
Figure 4

The effect of material nonhomogeneity (β) on σ12 for an anisotropic material under mode-I loading condition: (a) β = −1 (x1 gradation), (b) homogeneous (β = 0), (c) β = 1 (x1 gradation), (d) β = −1 (x2 gradation), (e) β = 1 (x2 gradation)

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Figure 5

The mixed-mode (KI  = 1 and KII  = 1) stress fields for exponentially graded material (x1 gradation, β = 1) anisotropic material: (a) σ11 , (b) σ22 , (c) σ12 , (d) maximum shear stress

Grahic Jump Location
Figure 2

The mode-II crack-tip stress fields for orthotropic homogeneous (β = 0) and exponentially graded (β = 1, x1 gradation) materials

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