Stress intensity factor for multiple cracks in bonded dissimilar materials using hypersingular integral equations

Abstract

• The multiple cracks problem in bonded dissimilar materials is formulated into hypersingular integral equations. • This hypersingular integral equations is solved numerically using the appropriate quadrature formula. • The stress intensity factors at the crack tips decreases as the elastic constants ratio increases. This paper deals with the multiple inclined or circular arc cracks in the upper half of bonded dissimilar materials subjected to shear stress. Using the complex variable function method, and with the help of the continuity conditions of the traction and displacement, the problem is formulated into the hypersingular integral equation (HSIE) with the crack opening displacement function as the unknown and the tractions along the crack as the right term. The obtained HSIE are solved numerically by utilising the appropriate quadrature formulas . Numerical results for multiple inclined or circular arc cracks problems in the upper half of bonded dissimilar materials are presented. It is found that the nondimensional stress intensity factors at the crack tips strongly depends on the elastic constants ratio, crack geometries , the distance between each crack and the distance between the crack and boundary.