Extrapolation methods for calculating the contour J ₂ ‐integral at the mixed mode of fracture

Abstract In order to improve the accuracy of the invariant contour J 2 ‐integral computation in the context of mixed‐mode fracture, various approaches to its calculation have been proposed. In contrast to J 1 ‐integral, to ensure the invariance of the J 2 ‐integral, it is necessary to take into account the contributions from the crack faces, whose calculation near the crack tip leads to significant errors. To eliminate them, various extrapolation methods based on the asymptotic solution for the stresses near the crack tip are proposed. Validation of the considered methods and evaluation of their accuracy are carried out on the basis of comparison with the analytical solution for uniaxial tension of a plane with an inclined crack at different crack angles.