Numerical implementation of the Bordet model for the brittle fracture behavior of high strength steels

Abstract

Modelling brittle fracture is a difficult task due to large scatter of the fracture toughness. The fracture toughness depends on the position of the individual particle relative to the crack tip. Therefore, the critical stress level incurring the failure is impossible to determine exactly. The statistical fracture mechanics is a means to treat statistical phenomenon such as cleavage.

Beremin introduced a local approach method to model brittle fracture. The Beremin model is based on the probability of finding micro cracks which cause the cleavage initiation and failure. Bordet et al. developed a more advanced local approach method that takes account of the probability of the initiation and the propagation. Both of these models contain material parameters that need calibration.

The goal of this work is to implement the Bordet statistical model for cleavage in Matlab. The parameters of the model are calibrated in the temperature of -155 °C using the Master Curve. The Master Curve is also used to verify the implementation. The implementation is compared to the Beremin model as well. Specimen shape and size are constant in these comparisons. The results indicate that the Bordet model produces failure probabilities similar to the Master Curve while being more stable than the Beremin model.