Weibull stress solutions and applications under mixed mode I-II loading for 2-D cracks in elastic and elastic–plastic materials

Abstract

Since the fracture toughness of materials in the ductile and brittle transition region presents obvious scatter, Weibull stress based on the local approach to fracture is widely used to clarify the randomness. A large number of detailed finite element analyses are necessary to be carried out for the calculation of Weibull stress, especially for the complex structures and loads. In order to simplify the calculation of Weibull stress, this paper derives Weibull stress solutions as functions of stress intensity factor or J integral for elastic and elastic–plastic materials under mode I-II loading. These solutions are verified by using modified boundary layer model and applied in the analysis of fracture toughness test results by four-point bending specimens. The relationship between failure probability Pf and SIF or J integral under mode I-II loading is derived and verified with experimental data. The result shows that the failure probability can predict the experimental data well.