Anti-plane Shear Cracks Approaching a Bi-material Interface

A novel procedure is proposed for evaluation of stress intensity factors of planar Mode III shear cracks perpendicular to a nearby interface between two isotropic elastic solids. Shear cracks traversing a flat layer bonded to two different elastic solids are also analyzed. The method is based on superposition of singular near tip stress and displacement fields generated by both the main crack and certain image cracks. Both the main and the image cracks are loaded by self-equilibrating shear tractions of different magnitude, such that matching parts of the said fields are made to satisfy traction and displacement continuity conditions at the interface. Selected comparisons with results obtained by different methods show good agreement. Applications of the method to other crack problems are discussed.