Investigation of the Behavior of an Interface Crack between Two Half-Planes of Orthotropic Functionally Graded Materials by Using a New Method

摘要

In this paper, the problem of a crack along an interface between inhomogeneous or-thotropic media is solved by using a new method, named the Schmidt method. To make the analysis tractable, it is assumed that the Poisson's ratios of the mediums are constant and the material modulus varies 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. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the length of the crack and the parameter describing the functionally graded materials upon the stress intensity factor of the cracks. When the material properties are continuous across the crack line, the numerical results are the same as those obtained so far. When the material properties are not continuous across the crack line, an approximate solution of the interface crack problem is given under the assumptions that the effect of the crack surface overlapping very near the crack tips is negligible. Contrary to the previous solution of the interface crack, it is found that the stress singularities of the present interface crack solution are similar with ones for the ordinary crack in homogenous Orthotropic materials.