Modelling cracks in arbitrarily shaped finite bodies by distribution of dislocation

This paper presents an analytical method based on the principle of continuous distribution of dislocation to model curved cracks in solids of arbitrarily shaped finite geometries. Both the boundary of the finite body and the curved crack are modelled by distributed dislocation. In this method the influence function of the dislocation along the finite body boundary is reduced to a product of the Hilbert kernel with a normal function. Similarly the influence function for the curved cracks is reduced to the product of Cauchy kernel and a normal function. This approach results in a system of singular integral equations. Using the order decreasing method, the system is reduced to normal integral equations, which are solved numerically. Stress intensity factors are evaluated for a well-known crack problem and two railhead crack problems with a view to assessing the capability of the developed method to solve complex engineering problems.