Asymptotic behaviour of the Oore-Burns integral for cracks with a corner and correction formulae for embedded convex defects

In this paper, the asymptotic behaviour of the stress intensity factor (SIF) near a corner of a crack is discussed. The weight function of Oore-Burns and FE analysis are used in order to explain the trend of the SIF. The analytical analysis shows that the SIF at the corner has a cusp behaviour as a function of the distance from the corner. This is a crucial mathematical property obtained from the Oore-Burns integral. Explicit formulae for the estimation of the SIF are obtained for square and equilateral triangular cracks. Then, the value of the SIF along the crack border is corrected (quantitative intervention) by means of a new simple formulation that is able to considerably increase the accuracy of the Oore-Burns integral. Finally, in the case of a crack with a rounded corner, a new simple correction formula is given and, in order to check the accuracy of the proposed equations, a comparison is carefully made with an FE analysis as well as with numerical results taken from the literature.