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The Interface Crack Problem in Nonhomogeneous Bonded Materials of Finite Thickness

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Final project rept.

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In a recently developed material forming method called Functionally Gradient Materials as well as applications of material deposition processes such as ion plating, composite materials are being created where the interface possesses a gradually varying material composition and properties. This study was directed at the mechanics of such materials when there is a crack on the interface, and sought to find parameters that govern the crack growth such as the crack tip stress intensity factors, strain energy release rate and probable direction of crack extension. The mixed boundary value problem involved two bonded materials having finite thicknesses with an interface crack under plane strain or generalized plane stress conditions. One material is homogeneous and the other nonhomogeneous with an exponential property variation in the y- direction. Fourier transforms was applied to Naviers equations to derive a system of singular integral equations with a simple Cauchy kernel and Fredholm kernels. The x-derivatives of the two crack opening displacements are assumed to be the unknowns. Extensive asymptotic expansions of the kernels, which were the algebraic sum of rational functions of 7 by 7 and 8 by 8 determinants as the numerator and denominator were carried out in order to separate the Cauchy kernel and to facilitate the integral equations numerical computation. The problem was solved numerically by converting to a system of linear algebraic equations and by using a collocation technique. The stress field near the crack tip is mixed mode and is shown to have a standard square root singularity.

Subject Categories:

  • Laminates and Composite Materials
  • Fabrication Metallurgy
  • Numerical Mathematics
  • Theoretical Mathematics

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