Treating mixed-mode problems with path-independent integrals

Plane cracks under mixed-mode loading conditions are mostly assessed by fracture criteria based on the stress-intensity factors KI and KII. The well known connection to the J-integral of fracture mechanics is given by J = K I 2 + K II 2 / E ∗ (E* equals Young’s modulus E for plane stress and E/(1 − ν2) for plane strain, Poisson’s ratio ν). In this paper, a new path-independent integral (say N) is proposed which is equal to N = K I 2 - K II 2 / E ∗ when evaluated along a path surrounding a crack tip. It is as easy to handle (analytically and numerically) as the J-integral. From the knowledge of both J and N, the calculation of KI and KII is very convenient. An example is given to illustrate the applicability of the new integral.