High-order asymptotics and perturbation problems for 3D interfacial cracks

We present an asymptotic algorithm for analysis of a singularly perturbed problem in a domain containing an interfacial crack. The crack is assumed to be flat and its front, initially straight, is perturbed in the plane containing the crack. The aim of the work is to determine the asymptotic representation of the stress-intensity factors near the edge of the crack. Mathematically, the limit problem is reduced to the analysis of a matrix, 3×3, Wiener-Hopf problem, and its solution generates the “weight matrix-function” characterised by a special singular solution near the crack edge. The two-term asymptotic representation for the weight function components is required by the asymptotic algorithm, together with two-term asymptotics for stress components associated with the physical fields near the edge of the crack. The particular feature of the solution is the coupling between the normal opening mode (Mode-I), and the shear modes (Mode-II and Mode-III), and the oscillatory behaviour of certain stress components near the crack edge. Explicit asymptotic formulae for the stress-intensity factors are obtained at the edge of a “wavy crack” at an interface.