Functionally graded wedge weakened by a semi-infinite crack


In the paper, the problem of a semi-infinite antiplane interface crack located between two functionally graded wedge-shaped regions has been considered. The shear modules of the materials’ regions are quadratic functions of the polar angle. This kind of functional inhomogeneity made it possible to express all the components of the elastic field through a single harmonic function. Using the Mellin integral transform, the problem was reduced to the Wiener – Hopf scalar equation, for which an exact solution was obtained. The influence of gradients of elastic properties of materials on the stress intensity coefficient at the crack tip and the singularity value at the angular point of the structure was studied.