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TECHNICAL PAPERS

Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials—Part I: Crack Perpendicular to the Material Gradation

[+] Author and Article Information
G. H. Paulino

Department of Civil and Environmental Engineering, University of Illinois, Newmark Laboratory, 205 North Mathews Avenue, Urbana, IL 61801

A. C. Fannjiang

Department of Mathematics, University of California, Davis, CA 95616

Y.-S. Chan

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

J. Appl. Mech 70(4), 531-542 (Aug 25, 2003) (12 pages) doi:10.1115/1.1532321 History: Received October 18, 2000; Revised September 06, 2001; Online August 25, 2003
Copyright © 2003 by ASME
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Figures

Grahic Jump Location
Functionally graded material (FGM) with continuously graded microstructure
Grahic Jump Location
Mode III crack in a functionally graded material
Grahic Jump Location
Plot of the integrand in Eq. (62) for l=0.05,l=0.005,γ=0.1,r=(√3)/7, and s=(√2)/3. (a) ξ∊[0,5000]; (b) Zoom for the range ξ∊[0,500]. Moreover, as ξ→0, the limit of N(ξ)sin[ξ(s−r)] is about 22.4×10−3.
Grahic Jump Location
Full crack displacement profile in an infinite medium of homogeneous material (γ̃=0) under uniform crack surface shear loading σyz(x,0)=−p0 with choice of (normalized) l̃=0.2 and l̃=0
Grahic Jump Location
Crack surface displacement under uniform crack surface shear loading σyz(x,0)=−p0 and shear modulus G(y)=G0eγy with choice of (normalized) l̃=0.05,l̃=0, and various γ̃. The dashed line stands for the homogeneous material case (γ̃=0).
Grahic Jump Location
Crack surface displacement under uniform crack surface shear loading σyz(x,0)=−p0 and shear modulus G(y)=G0eγy with choice of (normalized) l̃=0.2,l̃=0.04, and various γ̃. The dashed line stands for the homogeneous material (γ̃=0) in a gradient elastic medium.
Grahic Jump Location
Crack surface displacement profiles under uniform crack surface shear loading σyz(x,0)=−p0 and shear modulus G(y)=G0eγy with choice of (normalized) l̃=0.05,γ̃=0.1, and various l̃. The values of l̃ are listed in the same order as the solid-line curves.
Grahic Jump Location
Crack surface displacement profiles under uniform crack surface shear loading σyz(x,0)=−p0 and shear modulus G(y)=G0eγy with choice of (normalized) l̃=0.05,γ̃=0.1, and various l̃. The values of l̃ (and ρ=l/l) are listed in the same order as the solid-line and dashed-line (ρ=0) curves representing the strain gradient results.
Grahic Jump Location
Crack surface displacement profiles under discontinuous loading p(x/a)=−1+0.5 sgn(x/a) and shear modulus G(y)=G0eγy with choice of (normalized) l̃=0.05,γ̃=0.2, and various ρ=l/l. The values of ρ are listed in the same order as the solid-line and dashed-line (ρ=0) curves representing the strain gradient results.

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