The effect of the lattice parameter of functionally graded materials on the dynamic stress field near crack tips

  • Jun Liang
  • Zhen Gong Zhou
Original Paper


In this paper, the effect of the lattice parameter of functionally graded materials on the dynamic stress fields near crack tips subjected to the harmonic anti-plane shear waves is investigated by means of non-local theory. By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present near crack tips. The non-local elastic solution yields a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials.


Crack Non-local theory Functionally graded materials Lattice parameter 


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The authors are grateful for the financial support by the National Natural Science Foundation of China (90405016, 10572043), the Natural Science Foundation of Hei Long Jiang Province (A0301) and the Natural Science Foundation with Excellent Young Investigators of Hei Long Jiang Province (JC04-08).


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© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Center for Composite MaterialsHarbin Institute of TechnologyHarbinP. R. China

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