Stress intensity factor for cracks problems in an elastic half plane using singular integral equations

Single and multiple cracks in two dimensional half plane isotropic elastic solid are considered. The cracks are subjected to uniaxial tension s¥ x = p with free traction on the boundary. These problems are formulated into a system of singular integral equations (SIEs) with the distribution dislocation functions as unknown by using the modified complex potential. In solving the obtained SIEs, the cracks configurations are mapped into a straight line on a real axis by using the curved length coordinate method. By applying the appropriate quadrature formulas with the appropriate collocation points the SIEs are reduced to the system of algebraic linear equations with M unknown coefficients. These M unknowns coefficients are solved using the Gauss-Jordan elimination method. The obtained unknown coefficients will later be used in evaluating the stress intensity factor. The stress intensity factor at the tips of single and multiple cracks are obtained for various crack configurations and positions. Numerical results showed that the stress intensity factor influenced by the distance between the cracks, the crack configuration, and the distance between the cracks and the boundary of the half plane. For the test problems, our results are in good agreements with the existence results.

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