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Triple circular arc cracks problems subjected to shear stress in half-plane elasticity is investigated. Modified complex potentials (MCP) with the free traction boundary condition are applied to formulate the hypersingular integral equation (HSIE) for the problems. The unknown crack opening displacements (COD) of the HSIE are solved numerically by using the appropriate quadrature formulas. Mode I and Mode II of nondimensional stress intensity factor (SIF) at all cracks tips are presented for the problems of three adjacent circular arc cracks, three circular arc cracks with dissimilar radius and three circular arc cracks in series in a half-plane. The results exhibit that as the crack opening angle increases and the distance of cracks closer to the boundary of half-plane, the nondimensional SIF increases. This indicates that the strength of material becomes weaker and the tendency of material to fail is higher. [ABSTRACT FROM AUTHOR]

The problems of multiple inclined or curved cracks in circular positions is treated by using the hypersingular integral equation method. The cracks center are placed at the edge of a virtual circle with radius R. The first crack is fixed on the x-axis while the second crack is located on the boundary of a circle with the varying angle, θ. A system of hypersingular integral equations is formulated and solved numerically for the stress intensity factor (SIF). Numerical examples demonstrate the effect of interaction between two cracks in circular positions are given. It is found that, the severity at the second crack tips are significant when the ratio length of the second to the first crack is small and it is placed at a small angle of θ. [ABSTRACT FROM AUTHOR]

The formulation for the curved crack in a finite plate is established. The technique is the curved crack in a finite plate is divided into two subproblems i.e. the curved crack problem in an infinite plate and the finite plate without crack. For the first problem, the curved problem is formulated into Fredholm integral equation, where as for the second problem the complex boundary integral equations based on complex variables are considered. The solution of the coupled boundary integral equations gives the solution on the domain of the boundary. [ABSTRACT FROM AUTHOR]