The well-known J integral of elastic fracture mechanics has been related to potential energy-release rate associated with crack extension and has proved to be of great value in fracture testing. In particular, the path-independence of the J integral has been used to an advantage in performing acoustoelastic measurements along a closed contour surrounding a crack tip. In Mode I (opening mode) for example, the J integral depends essentially only on the corresponding stress intensity factor K_Iwhich can thus be determined.

Actually, J is the component of a vector in the plane of the crack and there exists a component of this vector normal to the crack plane, which, however, has not been interpreted properly in the past. It is one aim of this paper to supply a valid interpretation of this path-independent integral and to relate it to still another integral, also path-independent, which has been termed the L integral. It will be further shown explicitly that for a crack under mixed-mode loading this latter integral represents the energy release rate for rotation which can be used to determine both K_I and K_II .