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

Abstract

In this paper, the problem of a crack along an interface between inhomogeneous orthotropic 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.

Two Collinear Interface Cracks between Two Dissimilar Functionally Graded Piezoelectric/Piezomagnetic Material Layers under Anti-Plane Shear Loading

“…As discussed in the works (21), (22), (30) and the above discussion, it can be seen that the Schmidt method performs satisfactorily if the first ten terms of the infinite series in Eq. (43) are retained.…”

Fracture analysis of a weak-discontinuous interface in a symmetrical functionally gradient composite strip loaded by anti-plane impact

“…Hu et al [11] studied the singular nature of the crack-tip stress and electric displacement fields in two bonded functionally gradient piezoelectric half spaces, and also found that the square-root singularity of the crack-tip stress field and electric displacement field is unaffected by the discontinuity in the derivative of the material coefficients. Zhou et al [12] investigated the behavior of an interface crack between two half-planes of orthotropic functionally graded materials by using the Schmidt method, and found that the stress singularities of the present interface crack solution are similar with ones for the ordinary crack in homogenous Orthotropic materials. Zhou et al [13] also used the Schmidt method to investigate the behavior of a crack between two half-planes of functionally graded materials subjected to arbitrary tractions, and showed the effect of the crack length and the parameters describing the functionally graded materials on the stress intensity factor.…”