Sharp evaluation of the Oore–Burns integral for cracks subjected to arbitrary normal stress field

This paper presents a new approximation formula for the Oore–Burns integral related to three‐dimensional weight functions. The approach drastically reduces the computational time of the Oore–Burns integral with respect to previous formulations because the mesh over the integration domain can be very coarse without loss of accuracy. This is made possible by analytic evaluation of the coefficient of δ^1/2 of the deviation between the integral and its Riemann sum (δ is the size of the mesh over the crack). In the case of a penny‐shaped crack, the new equation can be considered as an explicit formulation of the exact weight function of Galin. In order to confirm the accuracy of our new formulation, we consider the case of penny‐shaped cracks under different types of mode I loading. Predictions of the stress intensity factor are compared with analytical predictions along the crack, and the new equation appears to be stable with respect to the refinement of the mesh. Furthermore, it is accurate even when the stress field is represented with high‐order polynomial terms. Finally, we apply our approximation of the Oore–Burns integral to an elliptical crack with small eccentricity under uniform pressure. Agreement with the Irwin solution is excellent.