New weight functions and second order approximation of the Oore–Burns integral for elliptical cracks subject to arbitrary normal stress field

In this paper, by means of a specific coordinate transformation, the singularity of the weight function is overcome. A strong advantage is obtained for a penny-shaped crack. In this case, a new exact formulation is given and a new alternative non-singular integral is proposed in terms of trigonometric functions. The new approach gives a remarkable streamlining of the Galin’s function with the advantage of reducing the complexity of the double integral. Furthermore, we give a second order analytical approximation of Oore–Burns integral for elliptical cracks with respect to deviation from the disk. This approach drastically simplifies the computational procedure without loss of accuracy.