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Research Papers

Higher-Order Terms for the Mode-III Stationary Crack-Tip Fields in a Functionally Graded Material

[+] Author and Article Information
Linhui Zhang

Department of Civil and Environmental Engineering, University of Connecticut, 261 Glenbrook Road, Unit 2037, Storrs, CT 06269

Jeong-Ho Kim1

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

1

Corresponding author.

J. Appl. Mech 78(1), 011005 (Oct 12, 2010) (10 pages) doi:10.1115/1.4002289 History: Received June 11, 2009; Revised July 28, 2010; Posted August 02, 2010; Published October 12, 2010; Online October 12, 2010

This paper provides full asymptotic crack-tip field solutions for an antiplane (mode-III) stationary crack in a functionally graded material. We use the complex variable approach and an asymptotic scaling factor to provide an efficient procedure for solving standard and perturbed Laplace equations associated with antiplane fracture in a graded material. We present the out-of-plane displacement and the shear stress solutions for a crack in exponentially and linearly graded materials by considering the gradation of the shear modulus either parallel or perpendicular to the crack. We discuss the characteristics of the asymptotic solutions for a graded material in comparison with the homogeneous solutions. We address the effects of the mode-III stress intensity factor and the antiplane T-stress onto crack-tip field solutions. Finally, engineering significance of the present work is discussed.

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Figures

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Figure 1

Antiplane mode-III fracture in Cartesian (x1,x2) and polar (r,θ) coordinates originating from the crack-tip in a nonhomogeneous isotropic material

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Figure 2

Out-of-plane displacement (u3) in exponentially graded (β=1, x1 gradation) material considering: (a) leading term, (b) leading and third-order terms, and (c) leading, third-order, and fifth-order terms (see Eq. 27)

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Figure 3

Out-of-plane displacement (u3) in exponentially graded material: (a) β=−1 (x1 gradation), (b) homogeneous (β=0), (c) β=1 (x1 gradation), (d) β=−1 (x2 gradation), and (e) β=1 (x2 gradation). The nonzero constant considered for all asymptotic terms is a1 only. Note that positive values are toward the positive x3 axis.

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Figure 4

The out-of-plane shear stress (σ23) in exponentially graded material: (a) β=−1 (x1 gradation), (b) homogeneous (β=0), (c) β=1 (x1 gradation), (d) β=−1 (x2 gradation), and (e) β=1 (x2 gradation)

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Figure 5

The out-of-plane shear stress (σ13) in exponentially graded material: (a) β=−1 (x1 gradation), (b) homogeneous (β=0), (c) β=1 (x1 gradation), (d) β=−1 (x2 gradation), and (e) β=1 (x2 gradation)

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Figure 6

The effective shear stress (σe=σ132+σ232) in exponentially graded material: (a) β=−1 (x1 gradation), (b) homogeneous (β=0), (c) β=1 (x1 gradation), (d) β=−1 (x2 gradation), and (e) β=1 (x2 gradation)

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Figure 7

The effect of T13 in a homogeneous material: (a) u3, (b) σ13, and (c) σe

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Figure 8

The effect of T13 in a FGM (β=1, x1 gradation): (a) u3, (b) σ13, and (c) σe

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Figure 9

Out-of-plane displacement (u3) of the crack faces in homogeneous (β=0) and exponentially graded (β=−1 and β=1, x1 gradation) isotropic YSZ materials

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