Estimation procedure for the Weibull parameters used in the local approach

The local approach was recently proposed by Beremin and Mudry for evaluating the statistical behaviour of toughness results of materials. This approach introduces a stress parameter _w , termed the Weibull stress, as a measure of the fracture resistance of materials instead of the conventional toughness parameters such as K _c, _c and J _cl (critical stress intensity factor, CTOD and J-integral, respectively). The Weibull stress _w obeys the Weibull distribution with the two parameters m and _u (the shape and the scale parameter, respectively). The first parameter m is normally estimated to be 22 irrespective of the kind of material. In this paper a procedure for the determination of the Weibull parameters m and _u is developed. This procedure consists of the determination of the plastic zone ahead of the crack tip, from which cleavage fracture originates, and of the maximum likelihood estimation of the parameters m and _u based on the stress distribution in the plastic zone. Calculations using this procedure confirm that the distribution of the Weibull stress _w is a material property independent of specimen thickness, and in particular that the shape parameter m depends on the material, e.g. m12 for a German reactor pressure vessel steel (20 Mn Mo Ni 5 5). Using these parameters for the distribution of the Weibull stress the size effect in fracture toughness values is predicted and an improved agreement between theory and experiments is obtained compared to the Weakest Link model.