Formulas for the critical length of mode II and III cracks emanating from circumferential U-notches

The crack emanating from the notch reaches its critical length when the notch ceases to have effect on the crack tip stress field. In this paper a semi-empirical approach to the critical length previously proposed for mode I cracks is extended to shear-mode cracks using finite element calculations. The existing formula for the critical crack length aIc of mode I cracks emanating from circumferential U-notches in round specimens is verified also for its invariance to the specimen thickness variation and its uncertainty is quantified to be less than 1 %. This uncertainty level is then employed to obtain statistically compatible formulae for critical crack lengths aIIc and aIIIc as functions of the notch depth, the notch-root radius and the notch depth normalized to specimen thickness. These formulae are useful for a correct determination of the pre -crack length free of the notch effect in fracture toughness experiments and for a proper evaluation of stress intensity factors in experimental investigations of fatigue crack propagation.