On the dependence of the Weibull exponent on geometry and loading conditions and its implications on the fracture toughness probability curve using a local approach criterion

In a previous paper the authors assessed the probability of failure of a three point bend specimen, SE(B), using a local approach criterion. In that paper the Weibull exponent, m, was derived from tests performed on round notch bars in traction, RNB(T), following the procedure suggested by Mudry. In the present study, it is addressed the issue of the dependence of the Weibull exponent m on geometry and loading conditions. It is shown that the amplitude and shape of the notch tip stress field and, in particular, the triaxiality characterising the stress state determines the value of the exponent m. Tests performed on RNB(T) specimens of carbon steel 22NiMoCr37, type A 508 Cl 3, at temperatures ranging from –18 °C to –196 °C actually indicate that m varies from 6 to 40, depending on the notch depth and root radius while for specimens carrying sharp cracks its value drops down to 4. This last result seems to be consistent with the Wallin hypothesis of a theoretical value equal to 4 for fracture mechanics specimens with high constraint, such as C(T) or SE(B), with positive values of the Q-stress or T-stress and triaxiality factor, TF, approaching 2.5. Temperature, in as long as it does not modify the stress state from plane strain to plane stress and the TF, has no effect on the value of m which is independent of the material as well.