Effects of Negative Biaxial Loadings and Notch on Failure Assessment Diagrams

Abstract

The Failure Assessment Diagram (FAD) is a simplified and robust flaw assessment methodology which simultaneously connects two dominant failure criteria: Linear Elastic Fracture mechanics (LEFM) on one end and Plastic collapse on other end. This interaction is the realm of Elastic Plastic Fracture Mechanics (EPFM.) It is popularly known as the R6 approach which graphically characterizes the impact of plasticity on crack driving force. In the recent years, there has been continuous interest in using Failure Assessment Diagrams (FAD) 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 aircraft components operate under negative biaxial ratios up to −0.5. In this paper, a detailed study on FAD was conducted using FEA 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 and validated its practical application. Comparison studies were made between uniaxial and biaxial loading cases with FAD curves created using standard approaches for 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 biaxilaity. 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 non-conservative compared to the approach recommended here, particularly under the worst case condition. The proposed method is expected to predict lower failure loads relative to currently accepted analytical methods.