Development of New Formulation and Likelihood Function on Probabilistic Fracture Initiation Model

Abstract

The authors propose a new model on cleavage fracture toughness of steels. Fracture toughness of steels is controlled by the weakest link mechanism, so it has intrinsic scatter. Beremin proposed Weibull stress through probabilistic fracture initiation model based on the weakest link theory, and it has been widely used for describing fracture toughness scatter. In his model, only propagation of micro crack is considered. However, micro crack nucleation should also be incorporated in order to estimate fracture toughness distribution more accurately. Bordet introduced micro crack initiation to the Beremin model, in which probability of micro crack nucleation is assumed proportional to plastic strain. Some previous studies have shown, however, that micro crack nucleation probability increases non-linearly with plastic strain. Then, we developed a new probabilistic model by introducing micro crack nucleation probability as a non-linear function of plastic strain.Furthermore, the authors developed a new method for obtaining Weibull parameters, in which not only distribution of fracture toughness values but also location of fracture initiation sites are considered through a newly developed likelihood function. We conducted fracture toughness tests with different specimen configurations and carried out convergence calculation for determining Weibull parameters by applying the likelihood function mentioned above. As a result of the calculation, the authors confirmed that the present model can obtain the Weibull parameters less sensitive to the specimen configurations and simulate distribution of fracture toughness more accurately than the previous models.