Solving crack problems in bonded dissimilar materials using hypersingular integral equations

Inclined or circular arc cracks problems and thermally insulated inclined or circular arc cracks problems subjected to remote stress in bonded dissimilar materials are formulated. The modified complex variable function method with the continuity conditions of the resultant force and displacement function are used to formulate the hypersingular integral equations (HSIEs) for these problems. Whereas, the continuity condition of heat conduction function is utilized to formulate the HSIEs for the thermally insulated cracks problems. The unknown crack opening displacement (COD) function is mapped into the square root singularity function using the curved length coordinate method. Then the appropriate quadrature formulas are used to solve the obtained equations numerically, with the traction along the crack as the right hand term. The obtained COD function is then used to compute the stress intensity factors (SIF) in order to determine the stability behavior of bodies or materials containing cracks or flaws. Numerical results of the nondimensional SIF at all the cracks tips are presented. Our results are totally in good agreements with those of the previous works. It is observed that the nondimensional SIF at the cracks tips depend on the remote stress, the elastic constants ratio, the crack geometries, the distance between each cracks and the distance between the crack and the boundary. Whereas for thermally insulated cracks, the nondimensional SIF at the cracks tips depend on the heat conductivity ratio and the thermal expansion coefficients ratio.

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