Hyper-singular Integral Equation Method On Smooth Curve Crack In Plane Bi-Material

In practical engineering, the structure is often constituted of a variety of materials, and cracks are often connected in the body of the two materials appeared. With the extensive use of composite materials, influence to the structural safety caused by materials defects, such as cracks and inclusions, aroused extensive attention.Based on the elasticity fundamental solutions of plane bi-material, Betti's exchange law, generalized Hooke's law, and coordinate transformation etc., the displacement expressions and stress intensity factor of smooth curve crack in the bi-material plane can be achieved. By use of the stress boundary conditions of crack, a super singular integral equations to displacement discontinuity of the crack coast as basic unknown parameters for generally smooth curve crack derived, and thus hyper-singular integral equations of two different cases, i.e. linear and circular-shaped cracks could be obtained.In addition, the dimensionless stress intensity factor for small-scale circular crack problem by use of substitution of variables and functions were established. The calculation of typical crack showed that this method could calculate non-dimensional stress intensity factor for straight-line cracks and small-scale circular arc crack, making the application of hyper-singular integral equation method for crack problems in plane bi-material generalized one step further.