Abstract
The mechanical behavior near crack tip for periodic parallel cracks in an orthotropic composite plate subjected to the uniformly distributed load within the cracks surface is studied. The mechanical problem is turned into the boundary value problem of partial differential equation. By using the periodicity of the hyperbolic function in the complex domain and constructing proper Westergaard stress function, the periodicity of parallel cracks can be removed. Using the complex variable function method and the undetermined coefficients method, the boundary value problem of partial differential equation can be solved with the help of boundary conditions. The analytic expressions for stress intensity factor, stress, and displacement near the crack tip of periodical parallel cracks are obtained. When the vertical distance of cracks tends to infinity, the stress intensity factor degenerates into a single central crack situation. The stress intensity factor around the crack tip of periodic parallel cracks in an orthotropic composite plate depends on the shape factor. The interaction happens between the cracks. Finally, a numerical analysis of the stress and displacement changed with the polar angle is done.
Highlights
Defects in the materials will cause singular stress and cracks
It is difficult to deal with a body containing agminate cracks
One simple way to model a body containing agminate cracks is to assume that the cracks are arranged in a regular pattern
Summary
Defects in the materials will cause singular stress and cracks. Cracks in the interface, in particular, are the main reason that lessens the structural strength. Pak and Goloubeva [14] studied the anti-plane problem of periodic parallel cracks in piezoelectric materials by using distributed dislocation method. Mathematical Problems in Engineering anti-plane problem for a functionally graded piezoelectric strip containing a periodic array of parallel cracks, which were perpendicular to the boundary. By using Laplace transform and Fourier transform, Wang and Mai [20] analyzed the dynamic anti-plane problem in an infinite functionally graded material containing a periodic array of parallel cracks. Xiao and Jiang [25, 26] used the mapping technique to obtain a closed form solution of stress intensity factor to the problem of periodic open type parallel cracks in an infinite orthotropic elastic body. The analytic expressions for stress intensity factor, stress, and displacement near the crack tip of periodical parallel cracks are obtained
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