In previous papers, the authors discussed the path integral expression of the J-integral range, ΔJ, for short fatigue cracks emanating from notches under uniaxial stresses and showed that ΔJ evaluated based on the crack-opening level was an appropriate parameter for characterizing the near-tip stress and strain fields. In this paper, finite element simulations of fatigue crack growth at notches under biaxial stresses are conducted. It is found that ΔJ values evaluated by the path integral are almost path independent when the minimum-load level or the crack-opening level was selected as a reference level for the evaluation. The examination of the relationship between ΔJ and the crack-tip-opening displacement leads to the conclusion that ΔJ evaluated by the path integral based on the crack-opening level is the most appropriate parameter for representing the mechanical state near the tip of a crack emanating from notches under biaxial stress conditions. Furthermore, it is shown that ΔJ evaluated by Dowling's simple estimation formula based on the crack-opening level agrees well with ΔJ evaluated by the path integral.
