Non-destructive Detection of a Circular Cavity in a Finite Functionally Graded Material Layer Using Anti-plane Shear Waves

The multiple scattering of shear waves and dynamic stress in a semi-infinite functionally graded material with a circular cavity is investigated, and the analytical solution of this problem is derived. The analytical solutions of wave fields are expressed by employing the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the cavity. The image method is used to satisfy the traction-free boundary condition of the material structure. As an example, the numerical solution of the dynamic stress concentration factors around the cavity is also presented. The effects of the buried depth of the cavity, the incident wave number, and the nonhomogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the nonhomogeneity parameter of materials is <0, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the nonhomogeneity parameter of materials is >0, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.

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Scattering of anti-plane shear waves in a functionally graded material strip with an off-center vertical crack

Applied Mathematics and Mechanics ◽

10.1007/s10483-006-0603-1 ◽

2006 ◽

Vol 27 (6) ◽

pp. 731-739 ◽

Cited By ~ 2

Author(s):

Lin Li ◽

Zhen-gong Zhou ◽

Biao Wang

Keyword(s):

Functionally Graded Material ◽

Shear Waves ◽

Functionally Graded ◽

Vertical Crack ◽

Plane Shear ◽

Graded Material

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Dynamic Response of a Crack in a Functionally Graded Material under an Anti-Plane Shear Impact Load

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.251-252.123 ◽

2003 ◽

Vol 251-252 ◽

pp. 123-136 ◽

Cited By ~ 8

Author(s):

Jan Sladek ◽

Vladimir Sladek ◽

Chuan Zeng Zhang

Keyword(s):

Dynamic Response ◽

Functionally Graded Material ◽

Impact Load ◽

Functionally Graded ◽

Plane Shear ◽

Graded Material

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Behaviour of three parallel non-symmetric mode III cracks in a functionally graded material plane

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1010 ◽

2008 ◽

Vol 222 (12) ◽

pp. 2311-2330 ◽

Cited By ~ 4

Author(s):

P-W Zhang ◽

Z-G Zhou ◽

L-Z Wu

Keyword(s):

Integral Equations ◽

Functionally Graded Material ◽

Jacobi Polynomials ◽

Functionally Graded ◽

Shielding Effect ◽

Mode Iii ◽

Dual Integral Equations ◽

Plane Shear ◽

Graded Material ◽

Material Plane

In this article, the behaviour of three parallel non-symmetric finite-length cracks in an infinite functionally graded material plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier transform into three pairs of dual integral equations, in which unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress intensity factors depend on the crack lengths, spacing of cracks, and the material parameters. It was also revealed that the crack shielding effect is present in functionally graded materials.

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