Bimodal Beremin-type model for brittle fracture of inhomogeneous ferritic steels: Theory and applications

In the present paper two kinds of Beremin-type models are developed to incorporate, in the statistical analysis of brittle fracture, the effect of both microscopic and macroscopic inhomogeneities. The macroscopic inhomogeneities are represented as thin platelets of segregated zones intersecting the crack front. These zones have a strength and fracture properties different from those of the matrix. In the first approach (semi-probabilistic model), an extension of the original Beremin model (1983) is proposed. The distribution of a type of inhomogeneities is deterministic but the fracture behaviour of each component (matrix & inhomogeneities) is described by a Weibull law. Finite element simulations show that for low linear fraction of inhomogeneities and relatively low strength mismatch between the matrix and the inhomogeneities, the crack tip opening displacement of the inhomogeneities and that of the matrix are the same. This produces an elevation of the local stress intensity factor and increases the probability of failure.In the second approach (fully-probabilistic model), inhomogeneities are statistically distributed along the crack front. The probability of failure is calculated by coupling the results of the semi-probabilistic model with those of either Monte-Carlo type simulations or mathematical expressions for the distribution of inhomogeneities. A closed-form solution for the probability of failure is obtained using Poisson’s law. These theoretical calculations predict that the usual size effect (KIC4B=constant, where KIC is the fracture toughness and B is the thickness) is no longer observed. Moreover these calculations reveal that the scatter in the predicted KIC values is largely increased, in particular when the specimen thickness is comparable to the mean distance between inhomogeneities.These theoretical results are compared to two experimental studies. The first one is devoted to the influence of segregated zones on the fracture toughness of a pressure vessel steel (16MND5). In this material the macroscopic inhomogeneities are associated with a bimodal fracture process, which is intergranular in these zones and transgranular cleavage in the matrix. It is shown that the fully-probabilistic model describes reasonably well the scatter in fracture toughness measurements on CT25 specimens, unlike the original Beremin model. The second study is that of the Euro fracture toughness data set. It is confirmed that the original Beremin model is able to describe the variation of the fracture toughness and its scatter with temperature. However this model does not account for some of the observed size effects “anomalies”.