Effects of Negative Biaxial Loadings and Notch on Failure Assessment Diagrams

The failure assessment diagram (FAD) is a simplified and robust flaw assessment methodology, which simultaneously connects two dominant failure criteria: linear elastic fracture mechanics on one end and plastic collapse on the other end. This interaction is in the realm of elastic-plastic fracture mechanics. It is popularly known as the R6 approach, which graphically characterizes the impact of plasticity on crack driving force. In recent years, there has been continuous interest in using FADs to assess the failure of cracked structures subjected to biaxial loadings. Biaxiality is defined as the ratio of stress applied parallel and normal to the crack. Some pressure loaded aircraft components operate under negative biaxial ratios up to −0.5. In this paper, a detailed study on FAD was conducted using finite element analysis computed $J$-integral methods to investigate the effect of biaxial loading using different FAD approaches for geometries with notches. Geometries with a crack that emanates at a fillet region were simulated with various biaxial loading ratios from −0.5 to $+0.5$ using 2014-T6 material. FAD curves were numerically generated for cracks at notched regions subjected to various biaxial loadings using $J$-integral values from finite element analyses. These results were compared with standard FAD approaches. All comparison studies were made between uniaxial and biaxial loading cases with FAD curves created using four different crack sizes. Under small scale yielding, this study clearly shows that FAD curves are not influenced by negative biaxial loading at low load (up to 40% of yield strength). It was clearly confirmed that the majority of previously developed analytical FAD curves do not effectively account for notch and plasticity effects due to negative biaxiality. Based on this study, tension normal to the crack and compression parallel to the crack is the worst combination, and it has a very pronounced effect on FAD curve shapes. The standard analytical FAD curves are nonconservative compared with the approach recommended here, particularly under the worst case condition. FAD curves developed are shown to predict lower failure loads as compared with the currently accepted analytical FAD approaches defined in existing standards, e.g., R6 and API 579. The impact of negative biaxial loading can be investigated directly using a $J$-integral FAD approach but can be compared with ease by plotting both approaches in a FAD format.