Structural Engineering and Mechanics

  • 제19권4호
  • /
  • Pages.425-440
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  • 2005
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

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Investigation of the behavior of a crack between two half-planes of functionally graded materials by using the Schmidt method

  • Zhou, Zhen-Gong (Center for Composite Materials, Harbin Institute of Technology) ;
  • Wang, Biao (Center for Composite Materials, Harbin Institute of Technology) ;
  • Wu, Lin-Zhi (Center for Composite Materials, Harbin Institute of Technology)
  • 투고 : 2004.04.08
  • 심사 : 2004.11.24
  • 발행 : 2005.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the behavior of a crack between two half-planes of functionally graded materials subjected to arbitrary tractions is resolved using a somewhat different approach, named the Schmidt method. To make the analysis tractable, it is assumed that the Poisson's ratios of the mediums are constants and the shear modulus vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite different from those adopted in previous works. Numerical examples are provided to show the effect of the crack length and the parameters describing the functionally graded materials upon the stress intensity factor of the crack. It can be shown that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation method. As a special case, when the material properties are not continuous through the crack line, an approximate solution of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near the crack tips is negligible. It is found that the stress singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials.

키워드

참고문헌

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피인용 문헌

  1. Fracture analysis of a weak-discontinuous interface in a symmetrical functionally gradient composite strip loaded by anti-plane impact vol.78, pp.11, 2008, https://doi.org/10.1007/s00419-007-0194-1
  2. Two collinear Mode-I cracks in piezoelectric/piezomagnetic materials vol.29, pp.1, 2008, https://doi.org/10.12989/sem.2008.29.1.055
  3. An anti-plane crack perpendicular to the weak/micro-discontinuous interface in a bi-FGM structure with exponential and linear non-homogeneities vol.146, pp.4, 2007, https://doi.org/10.1007/s10704-007-9161-7
  4. Stress intensity factors for an interface crack between an epoxy and aluminium composite plate vol.26, pp.1, 2007, https://doi.org/10.12989/sem.2007.26.1.099