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Mathematical Problems in Engineering
Volume 2013, Article ID 412172, 8 pages
Research Article

Analysis of Mode I Periodic Parallel Cracks-Tip Stress Field in an Infinite Orthotropic Plate

School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China

Received 17 July 2013; Revised 11 November 2013; Accepted 18 November 2013

Academic Editor: Sarp Adali

Copyright © 2013 Wenbin Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.