A general expression for an area integral of a point-wise J for a curved crack front

The expression for the J-integral at a point on a three-dimensional crack f ront, obtained from a surface independent integral, is in general a sum of a contour integral and an area integral. In this work a general expression of an area integral for a crack with a curved front is derived in curviline ar coordinates. In certain situations the area integral vanishes and previo usly known cases are a straight crack front in plane stress or plane strain . The general conditions for a vanishing area integral are studied. It is s hown that the area integral is non-zero for cracks with a curved front in t he direction of crack extension. Some examples of curved cracks are given, for which the area integral vanishes and that are of interest in practice.