Improved weight functions for infinitely long axial and circumferential cracks in a cylinder

The goal of this paper is to derive an accurate analytical representation of the weight functions for infinitely long axial and circumferential cracks in a cylinder based on available numerical data for the case of a crack face loading by a pair of concentrated forces (finite-element solution of Bryson and Dickson). The analysis is restricted to inner surface cracks in a cylinder having the ratio of wall thickness to inner radius of 0.1. Although the results are believed to be rather accurate, they are found to deviate from the well-known asymptotic behaviour of the weight function if approaching the crack tip. This inaccuracy of the original numerical solution is eliminated by applying the weight function technique. The resulting weight functions are represented in an analytical form that enables their efficient integration for an arbitrary crack face loading.