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Mode I crack problem in an inhomogeneous orthotropic medium

International Journal of Engineering Science
Publication Date
DOI: 10.1016/s0020-7225(97)80005-5
  • Engineering


Abstract In the symmetric crack problem considered the material is both oriented and graded. The properties of the medium is assumed to vary monotonously in the x 1-direction, x 1 and x 2 are the principal axes of orthotropy, and the crack is located along the x 1-axis. The loading is such that x 2=0 is a plane of symmetry. The mode I crack problem for the inhomogeneous orthotropic plane is formulated and the solution is obtained for various loading conditions and material parameters. In the formulation four independent engineering constants, E 11, E 22, G 12 and ν 12, are replaced by a stiffness parameter E = √ E 11 E 22, a stiffness ratio c = ( E 11/ E 22) 1/4, a Poisson's ratio ν = √ ν 12 ν 21 and a shear parameter κ = E/2 G 12 − ν. The results show that the stress intensity factors are independent of E and c and generally the effect of κ and ν on the stress intensity factors is not very significant. The exception is the values of κ approaching − 1, where the physical range of κ is − 1 κ < ∞. In the isotropic case the kernel of the related integral equation is evaluated in closed form, which simplifies the numerical solution and improves the accuracy of the results.

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