A thin-film-covered mode III crack with dislocation-free zones

We use complex variable methods and the theory of singular integral equations to study a thin-film-covered mode III crack with dislocation-free zones (DFZs) under uniform remote anti-plane shear stress. The equilibrium condition is formulated in terms of a single singular integral equation constructed in the image plane via the solution of the problem of a single screw dislocation interacting with a completely coated crack and the method of continuously distributed dislocations. The singular integral equation is solved numerically using the Gauss-Chebyshev integration formula to arrive at the dislocation distribution function, the DFZ condition, the total number of dislocations in the plastic zone and the local mode III stress intensity factor at the crack tip.

Automated summary

This paper uses complex variable methods and the theory of singular integral equations to study a thin-film-covered mode III crack with dislocation-free zones (DFZs) under uniform remote anti-plane shear stress. The equilibrium condition is formulated using a singular integral equation constructed in the image plane. The numerical solution of the integral equation provides the dislocation distribution function, the DFZ condition, the total number of dislocations in the plastic zone, and the local mode III stress intensity factor at the crack tip.